,,the ,,elements ,,of ,,qualitative ,,chemical ,,analysis ,,with ,,special ,,consideration ,,of ,,the ,,application ,,of ,,the ,,laws ,,of ,,equilibrium ,,and ,,of ,,the ,,modern ,,theories ,,of ,,solution ,,by ,,julius ,,stieglitz ,professor of ,chemistry in the ,university of ,chicago ,,volume ,i ,,parts ,i ,,and ,,ii ,,fundamental ,,principles ,,and ,,their ,,application ,illustration ,,new ,,york ,,the ,,century ,,co4 #aibj ,,copyright1 #aiaa1 ,,by ,,the ,,century ,,co4 ,printed1 ,october1 #aiaa ,reprinted1 ,august1 #aiab ,reprinted1 ,october1 #aiac ,reprinted1 ,october1 #aiae ,reprinted1 ,august1 #aiag ,reprinted1 ,january1 #aiai ,reprinted1 ,august1 #aiai ,reprinted1 ,november1 #aiai ,reprinted1 ,july1 #aibj ,,preface ,in venturing to add another book on ,qualitative ,chemical ,analysis to the long list of publications on this subject1 the author has been moved chiefly by the often expressed wish of students and friends to have his lectures on qualitative analysis rendered available for reference and for a wider circle of instruction4 ,parts ,i and ,,ii of the present book embody these lectures in the form to which they have developed in the course of the last sixteen years1 since1 in #ahid1 the teaching of analytical chemistry1 along the lines followed1 was first suggested by ,ostwald's pioneer ,wissenschaftliche ,grundlagen der ,analytischen ,chemie4 ,the author believes that instruction in qualitative analysis1 besides teaching analysis proper1 should demand of the student a very distinct advance in the study of general chemistry1 and should also1 consciously1 pave the way for work in quantitative analysis1 if it is not1 indeed1 accompanied by work in that subject4 ,the professional method of work1 whether routine or research work of the academic or the industrial laboratory is involved1 inevitably consists in first making an exhaustive study of the general chemical aspects of the subject under examination3 it includes a thorough study of books of reference and of the original literature on the subject2 and when the experimental work is finally undertaken1 it is carried out with a critical1 searching mind1 which questions every observation made1 every process used4 ,the method of instruction in this book aims at developing these habits of the professional1 productive chemist4 ,for the reasons given1 a rather thorough and somewhat critical study is first made 7in ,part ,i7 of the fundamental general chemical principles which are most widely involved in analytical work4 ,the applications of these principles to the subject matter of elementary qualitative analysis are then discussed 7in ,part ,,ii71 in closest connection with the laboratory work covering the study of analytical reactions 7in ,part ,,iii74 ,the material is presented1 not as a finished subject1 but as a growing one1 with which the present generation of chemists is still busy1 and which contains many important1 unsolved problems of a fundamental character4 ,numerous references to standard works and to the current literature are given1 of which those suitable for reading by the young student are specially designated4 ,the obvious demand is thereby made on the student to aim to remain in touch with the growth of the science1 after he has completed his studies under the guidance of an instructor4 ,finally1 to arouse and develop the critical1 questioning attitude of the professional chemist1 referred to above1 the subject matter of the laboratory work1 given in ,part ,,iii1 is put very largely in the form of questions1 which demand not only careful observation on the part of the student1 but also a thoughtful interpretation of the observations made4 ,in the experience of the author1 although the majority of students attending his lectures had already acquired some knowledge of chemical and physical equilibrium1 of the theories of solutions and of ionization and of their applications1 the more exhaustive treatment of parts of these subjects and of related topics1 to which a course in qualitative analysis lends itself1 has been of particular benefit to them1 bringing them into closer touch with the method of detailed study of a chemical topic1 than the broader1 more varied work of general chemistry courses usually does4 ,throughout the theoretical treatment of the subject1 the attempt is made to prepare the student for a more general quantitative expression of chemical relations4 ,for this reason1 chemical and physical equilibrium constants are given and used1 wherever it is possible4 ,the author is aware that these constants have1 in part1 only a temporary standing2 that more exact work will continually modify their numerical values and1 probably1 limit the field for their rigorous application4 ,the latter facts can be impressed on the student and still the invaluable principle be inculcated in his mind1 that chemistry is striving to express its relations1 as far as possible1 in mathematical terms1 exactly as its sister science1 physics1 has long been doing4 ,at the same time the treatment of physicochemical topics has been kept within the bounds set by the subject matter1 and by the chemical maturity of the students addressed3 it is elementary in form1 and quantitative relations are used1 in the main1 only to elucidate qualitative facts4 ,the rigorous development of the subjects presented and their elaboration from a purely physicochemical standpoint are left to advanced courses4 ,it has been found that this method interests the better class of students in seeking such advanced courses4 ,the relations of qualitative to quantitative analysis are touched upon in the theoretical treatment1 where it has been feasible to do so4 ,the laboratory methods aim also at beginning the training of students in the habit of accuracy demanded by quantitative analysis1 by laying special emphasis on the methods of detecting traces of a number of the common elements and by requiring a report on the relative quantities of components found4 ,the study of reactions is carried out1 almost wholly1 with solutions of known and uniform molar concentration4 ,however1 the actual development of quantitative accuracy is left to the instruction in the courses in quantitative analysis1 in which a successful training in this direction is far more readily attained4 ,simultaneous courses in the two branches of analysis seem to the author to be highly desirable1 whenever practicable4 ,the study of quantitative analysis adds neatness of manipulation and accuracy to the work in qualitative analysis2 and the latter supplies the opportunity for the further development of a student's knowledge of general chemistry1 for which there is a much smaller scope in quantitative analysis courses1 and thus relieves a condition where a serious pedagogical defect is likely to exist in the development of our students4 ,parts ,,iii and ,,iv of this book are published in a separate volume1 as a laboratory manual for qualitative analysis4 ,they comprise the instructions for laboratory work introductory to systematic analysis 7the study of reactions and of the analysis of groups1 in ,part ,,iii7 and an outline for elementary systematic analysis 7,part ,,iv74 ,the attempt has been made1 in particular1 to bring the laboratory work1 which otherwise follows the usual lines of instruction in systematic analysis1 also into closest relations to the development of the scientific foundations of analytical chemistry1 as represented in ,parts ,i and ,,ii4 ,it is believed that the subject matter lends itself especially well to such a close interweaving of the two sides of the study1 without any special loss of time to the student1 and with the result1 it is hoped1 of a greatly increased interest on his part and an increased stimulus of the habit of scientific thought4 ,the following plan of work is used by the author with his classes3 ,the first section 7lasting eleven weeks7 of the course in qualitative analysis is started with some seven to ten 7according to the ability of the class7 lectures or classroom exercises1 given daily1 and covering the first seven or the eight chapters of ,part ,i4 ,at the end of the second week the laboratory work is started4 ,during the remainder of this section of the course1 two hours of classroom work and eight hours of laboratory work per week are required1 and1 in this period1 ,part ,,iii1 comprising the first half of the laboratory manual1 is studied in the laboratory in closest connection with the classroom work on ,part ,,ii of the book4 ,as far as possible1 the laboratory work on a given topic precedes the classroom work4 ,this first course is followed by an eleven weeks' course in systematic analysis1 covering ,part ,,iv of the book4 ,a third 7graduate7 course1 optional for students specializing in chemistry1 is offered1 in which very complex commercial and natural products are analyzed and in which special attention is also given to rare elements4 ,during this course1 particular care is taken to familiarize students with other works on qualitative analysis1 such as the outlines of ,a4 ,a4 ,noyes and ,bray1 and the special parts of ,fresenius's manual4 ,students who have been prepared in general chemistry along physicochemical lines1 as represented1 for instance1 by ,smith's textbooks1 make more rapid and more easy progress in the first course than do students otherwise prepared4 ,but the treatment of the subject is intended to make it possible for students1 who have not paid particular attention to chemical equilibrium and to the modern theories of solution in their general chemistry course1 to complete the course within the time limit indicated4 ,perhaps one-third of the students in an average class1 in the past1 have taken the course under these conditions and no special difficulty was encountered by them4 ,in the theoretical treatment the author is particularly indebted to the original articles and to the larger works of ,arrhenius1 van 't ,hoff1 ,nernst1 ,a4 ,a4 ,noyes1 ,ostwald1 and ,walker4 ,for the systematic analytical material acknowledgment is due1 in particular1 to ,fresenius's ,qualitative ,chemical ,analysis1 and to the important publications by ,a4 ,a4 ,noyes and ,bray in the ,journal of the ,american ,chemical ,society4 ,some of the excellent methods of the latter authors have been adopted outright1 as indicated in the text4 ,for some special matters the author is indebted to the texts of ,w4 ,a4 ,noyes and of ,bttger4 ,constant references to his sources of information have been made by the author1 partly as a matter of acknowledgment1 and more particularly to give students and teachers the opportunity for more extended1 first-hand reading on any topic of interest4 ,references suitable for college students are indicated by the addition of 7,stud474 ,in two or three instances1 the original source of information has been forgotten and diligent search has failed to trace it4 ,for use in preparing any future edition of the book1 the author will be glad to have his attention called to the facts by authors4 ,the author wishes to express here his particular appreciation of the generous assistance given him by his former colleague1 ,prof4 ,alexander ,smith of ,columbia ,university1 whose suggestions and advice1 especially in the editing of the manuscript and proof1 have been invaluable4 ,he also wishes to make grateful acknowledgment to his colleagues1 ,profs4 ,h4 ,n4 ,mc,coy1 ,h4 ,schlesinger1 and ,dr4 ,edith ,barnard1 to ,prof4 ,l4 ,w4 ,jones of the ,university of ,cincinnati1 ,prof4 ,e4 ,p4 ,schoch of the ,university of ,texas1 ,prof4 ,b4 ,b4 ,freud of ,armour ,institute1 and ,prof4 ,w4 ,j4 ,hale of the ,university of ,michigan1 who have assisted him by reading the proofs or the manuscript1 or by carrying out experimental studies underlying part of the work1 or in other ways4 ,corrections of his mistakes of omission and commission1 and suggestions1 will be gratefully received by the author4 ,,julius ,,stieglitz4 ,,chicago1 ,september1 #aiaa4 ,,contents ,,part ,i ,,fundamental ,,principles ,,chapter ,,page ,i4 ,,introduction #c ,,ii4 ,,osmotic ,,pressure ,,and ,,the ,,theory ,,of ,,solution1 ,i #h ,,iii4 ,,osmotic ,,pressure ,,and ,,the ,,theory ,,of ,,solution1 ,,ii #ba ,,iv4 ,,the ,,theory ,,of ,,ionization3 ,,ionization ,,and ,,electrical ,,conductivity #cc ,v4 ,,the ,,theory ,,of ,,ionization1 ,,ii3 ,,ionization ,,and ,,osmotic ,,pressure2 ,,ionization ,,and ,,chemical ,,activity #fg ,,vi4 ,,chemical ,,equilibrium4 ,,the ,,law ,,of ,,mass ,,action #ij ,,vii4 ,,physical ,,or ,,heterogeneous ,,equilibrium4--,,the ,,colloidal ,,condition #aah ,,viii4 ,,simultaneous ,,chemical ,,and ,,physical ,,equilibrium4--,,the ,,solubility- ,,or ,,ion-,,product #aci ,,part ,,ii ,,systematic ,,analysis ,,and ,,the ,,application ,,of ,,fundamental ,,principles ,,ix4 ,,systematic ,,analysis ,,for ,,the ,,common ,,metal ,,ions4 ,,the ,,ions ,,of ,,the ,,alkalies ,,and ,,of ,,the ,,alkaline ,,earths4 ,,order ,,of ,,precipitation ,,of ,,difficultly ,,soluble ,,salts ,,with ,a ,,common ,,ion #aeg ,x4 ,,aluminium2 ,,amphoteric ,,hydroxides2 ,,hydrolysis ,,of ,,salts4 ,,the ,,aluminium ,,and ,,zinc ,,groups #aga ,,xi4 ,,the ,,copper ,,and ,,silver ,,groups4 ,,precipitation ,,with ,,hydrogen ,,sulphide #aii ,,xii4 ,,the ,,copper ,,and ,,silver ,,groups 7,continued74 ,,the ,,theory ,,of ,,complex ,,ions #baf ,,xiii4 ,,the ,,arsenic ,,group4 ,,sulpho-,,acids ,,and ,,sulpho-,,salts #bdb ,,xiv4 ,,oxidation ,,and ,,reduction ,,reactions1 ,i #bea ,,xv4 ,,oxidation ,,and ,,reduction1 ,,ii4 ,,oxidation ,,by ,,oxygen1 ,,permanganates1 ,,etc42 ,,oxidation ,,of ,,organic ,,compounds #bgg ,,xvi4 ,,systematic ,,analysis ,,for ,,acid ,,ions #bii ,,list ,,of ,,references ,,and ,,their ,,abbreviations ,,note4--7,stud47 affixed to a reference indicates that the original article is recommended as suitable reading for college students taking their second year of work in chemistry4 ,am4 ,chem4 ,j4--,american ,chemical ,journal4 ,ann4 de ,chim4 et de ,phys4--,annales de ,chimie et de ,physique4 ,ber4 d4 chem4 ,ges4--,berichte der deutschen chemischen ,gesellschaft4 ,,le ,,blanc',s ,lehrbuch der ,elektrochemie 7#aijc74 ,b,,ttger',s ,qualitative ,analyse 7#aijh74 ,compt4 rend4--,comptes rendus4 ,,fresenius',s ,manual of ,qualitative ,chemical ,analysis 7#aiji74 ,,fresenius',s ,quantitative ,chemical ,analysis 7#aijd74 ,,van ',t ,,hoff',s ,lectures on ,theoretical and ,physical ,chemistry 7#ahih74 ,h4 ,c4 ,,jones',s ,the ,elements of ,physical ,chemistry4 ,j4 ,am4 ,chem4 ,soc4--,journal of the ,american ,chemical ,society4 ,j4 ,chem4 ,soc4 7,london74--,journal of the ,chemical ,society 7,london74 ,j4 of ,physiology4--,journal of ,physiology4 ,j4 ,phys4 ,chem4--,journal of ,physical ,chemistry4 ,j4 prakt4 ,chem4--,journal fr praktische ,chemie4 ,,kohlrausch ,,und ,,holborn',s ,leitvermgen der ,elektrolyte 7#ahih74 ,,landolt-,b,,rnstein-,,meyerhoffer',s ,physikalisch-,chemische ,tabellen4 ,liebig's ,ann4--,liebig's ,annalen der ,chemie4 ,,nernst',s ,theoretical ,chemistry 7#aijd74 ,,nernst',s ,theoretische ,chemie 7#aiji74 ,,ostwald',s ,lehrbuch der allgemeinen ,chemie 7#ahic74 ,,ostwald',s ,scientific ,foundations of ,analytical ,chemistry 7#aijh74 ,,ostwald',s ,wissenschaftliche ,grundlagen der analytischen ,chemie 7#ahid74 ,phil4 ,mag4--,philosophical ,magazine4 ,phil4 ,trans4 ,royal ,soc4--,philosophical ,transactions of the ,royal ,society4 ,poggendorff's ,ann4--,poggendorff's ,annalen der ,physik und ,chemie4 ,proc4 ,am4 ,acad4--,proceedings of the ,american ,academy4 ,,remsen',s ,inorganic ,chemistry1 ,advanced ,course1 #aijd4 ,,smith',s ,general ,inorganic ,chemistry 7#aiji74 ,,smith',s ,general ,chemistry for ,colleges 7#aijh74 ,,treadwell',s ,qualitative ,analyse 7#aijb74 ,,walker',s ,introduction to ,physical ,chemistry 7#aiji74 ,wiedemann's ,ann4--,wiedemann's ,annalen der ,physik und ,chemie4 ,z4 analyt4 ,chem4--,zeitschrift fr analytische ,chemie4 ,z4 anorg4 ,chem4--,zeitschrift fr anorganische ,chemie4 ,z4 fr ,elektrochem4--,zeitschrift fr ,elektrochemie4 ,z4 phys4 ,chem4--,zeitschrift fr physikalische ,chemie4 ,,qualitative ,,chemical ,,analysis ,,part ,i ,,fundamental ,,principles ,,chapter ,i ,,introduction ,qualitative chemical analysis is concerned with the determination of the kinds of matter present in any given substance4 ,in its broadest sense it includes the determination of all kinds of matter1 the elements1 rare as well as common1 and all their combinations1 organic compounds as well as inorganic4 ,the recognition of the presence of rare elements1 such as radium1 uranium1 thorium1 tungsten1 cerium1 etc41 is becoming a matter of growing importance with the modern development of the subject of radioactivity and the technical exploitation of the rarer elements1 and it is a common experience for an analytical chemist to be called upon to determine the presence or absence of alcohol in beverages1 of formalin in milk or other foods1 and not a rare experience to be obliged to make tests for the presence of alkaloids like strychnine1 morphine1 cocaine1 or for the presence of numerous other organic compounds4 ,in this book1 however1 we shall limit our material to the more common elements and their most important inorganic combinations1 including only a few typical organic acids4 ,the limitation of our experimental material will make it possible to devote special attention to the scientific principles underlying analysis1 to secure a clear and definite grasp of them1 and to impart with simple material such experience in the technique and methods of analysis as will train the student to apply both his theoretical and practical knowledge to any field of analysis occasion may require4 ,accurate qualitative analysis1 p#jjd in any field1 will depend on the care taken in mastering the theoretical significance and the technique of the methods recommended for the specific problem before the analyst2 the details of the methods themselves1 in any problem involving more than elementary analysis1 are sought and found by him as a matter of practice in suitable larger works1 in monographs and in the original literature4 ,with the object of suggesting this broader application of the training acquired and of cultivating the invaluable habit of the professional chemist of consulting larger works and the literature1 frequent reference will be made to such larger works1 and to original papers in which more special subjects of analysis or theory are elaborately treated4 ,to recognize1 in a substance1 the presence of any element or compound1 one must know its characteristic reactions1 which will make it possible to distinguish it from all other elements or compounds4 ,further1 in order to reach conclusions with the greatest possible speed1 directness1 and conclusiveness1 it is usually best to carry out an examination in some systematic way1 rather than in a haphazard and irregular fashion4 ,we distinguish1 accordingly1 two parts in our laboratory work3 first1 the study of characteristic tests or reactions of the common elements and such of their compounds as are of importance in elementary analysis 7,part ,,iii71 and1 secondly1 practice in a systematic method of analysis 7,part ,,iv74 ,in the study of the reactions1 the way will be paved for systematic analysis1 by taking the elements in the groups1 which form the basis of the system of analysis employed1 and by analyses of mixtures of the elements of a group immediately after the group has been studied4 ,reliable and intelligent analysis is possible only with a clear knowledge of the chemistry of the reactions used1 and the chemistry of the most important typical reactions will therefore be considered 7in ,part ,,ii71 simultaneously with the laboratory study of the reactions and of systematic analysis4 ,the reactions for identifying an element or compound must bring physical evidence which can be recognized by our senses4 ,the sense of touch is scarcely ever appealed to2 perhaps the numbness or paralysis of the sense of touch imparted to the tongue or eyelid by the alkaloid cocaine and a few modern substitutes for it1 and the tingling sensation produced on the tongue p#jje by aconite and its preparations1 are the most important1 but rare1 instances of an appeal to this sense in analytical work4 ,the sense of taste is also rarely used1 and always with the greatest care to prevent poisonous effects4 ,acids and bases1 bitter alkaloids1 such as strychnine and brucine1 sweet substances1 such as cane sugar1 glucose1 glycerine1 are instances of compounds which affect our sense of taste4 ,in all these cases the taste is used rather as a confirmative test than as a conclusive proof of the identity of a suspected substance4 ,the sense of smell is rather more useful in qualitative analysis than that of taste or of touch4 ,hydrogen sulphide and ammonia1 unless present in traces only1 readily reveal themselves by their odor4 ,every chemist should be familiar with the faint but very characteristic odor of hydrocyanic acid1#a which should instantly and automatically warn him of the presence of this potent poison4 ,owing to partial decomposition by the moisture and carbonic acid absorbed from the atmosphere1 alkali cyanides also give this important warning signal4 ,tests based on the odors of compounds are particularly valuable in the field of organic chemistry1 where the sense of smell is extensively used for qualitative purposes2 for instance1 the pleasant smell of acetic ester1 and the nauseating odor of an organic arsenic derivative1 cacodyl oxide1 may be used with advantage in identifying acetic acid4 ,but the evidence of touch1 taste1 and smell is1 on the whole1 only occasionally available in chemical analysis--almost all the tests employed are visual ones4 ,a small proportion of these are color tests4 ,the color of iodine vapor or of the solution of iodine in chloroform1 the colors of metallic copper or gold1 of copper salts in ammoniacal solutions1 of sulphides1 such as the orange sulphide of antimony 7exps471 may be mentioned as instances1 in which a test of identity depends on the observation of some characteristic color4 ,but the great majority of analytical tests depend on observations of changes of state2 evidence consisting in the solution of solids1 the formation of precipitates1 the evolution of gases1 forms the most important part of the observations1 p#jjf on which our conclusions are based4 ,in organic chemistry1 determinations of melting-points and of boiling-points1 which are very commonly used for the qualitative identification of compounds1 form further instances of the application1 to qualitative purposes1 of observations based on changes of state4 ,in very many cases1 where the formation or nonformation of a precipitate is intended to be used as an indication of the presence or absence of a given substance1 the precipitating agent may throw down one or more of several different precipitates1 which1 seen without the aid of a microscope1 cannot be identified without further examination4 ,it is1 thus1 commonly necessary to use a sequence of such tests for the complete identification4 ,for instance1 the addition of hydrochloric acid to a solution of lead1 mercurous or silver nitrate will produce a white precipitate4 ,the precipitates may be distinguished by a further examination of their solubilities3 hot water will dissolve the lead chloride1 ammonia readily dissolves the chloride of silver and converts the mercurous chloride into a black insoluble mixture containing finely divided mercury 7exps474 ,by the same means the chlorides1 if present together1 may be separated from one another and subsequently identified4 ,systematic analysis consists very largely in the use of a proper1 logical sequence of such precipitation and solution reactions1 and in the drawing of definite conclusions from the results obtained4 ,by far the greatest part of the experimental work in qualitative analysis has to do1 then1 with solution and precipitation4 ,for intelligent and accurate analytical work a clear knowledge of the nature of solution and1 in particular1 of the simple laws governing chemical action in solution1 and of those governing the formation and the solution of precipitates1 is indispensable4 ,the discoveries of van 't ,hoff1 in #ahhe-h1 concerning the nature of solution1 and the subsequent discoveries of ,arrhenius1 ,nernst1 ,ostwald and others1 have advanced every branch of chemistry1 but perhaps no branch has profited quite so much as the theory of analytical chemistry1 which1 as a result of these discoveries1 for the first time1 received a clear1 precise and satisfying scientific formulation of its empirical processes4#b p#jjg ,on account of the fundamental importance of this modern scientific formulation of the principles of analytical chemistry for the proper understanding of our subject1 we shall consider first 7in ,part ,i7 the modern theories of solution1 with their experimental foundations1 and we shall then develop the simpler fundamental laws governing chemical action and physical changes in solution4 ,the analytical reactions themselves will be utilized as far as possible as the material for developing these general principles1 so that this study may lead to the desired grasp of the theory of analysis and yet1 at the same time1 advance the student's knowledge of the practice of analysis4 ,,footnotes3 #a ,on account of the poisonous character of this and other vapors1 the vessel containing a substance whose odor one wishes to test is not brought to the nose1 but a little of the vapor is carefully wafted towards one by a motion of the hand1 the vapor being thus greatly diluted with air4 #b ,we owe the first modern scientific treatment of the principles of ,analytical ,chemistry to ,ostwald's ,wissenschaftliche ,grundlagen der analytischen ,chemie1 #ahid4 p#jjh ,,chapter ,,ii ,,osmotic ,,pressure ,,and ,,the ,,theory ,,of ,,solution ,i ,if a concentrated solution of a substance like sugar or cupric nitrate is allowed to flow into a cylinder of water 7exp4 with cupric nitrate71 we find that the outside forces--gravity--tend to draw the solution1 whose specific gravity is greater than that of water1 to the bottom of the cylinder4 ,in this method of proceeding there is some inevitable mixing of the solution with the solvent1 as the result of friction1 but the main portion of the deep blue solution is drawn to the bottom of the vessel and forms a blue layer under the colorless water4 ,a much sharper line of separation may be obtained by allowing the cupric nitrate solution to enter a cylinder of water from under the water 7see ,fig4 #a71 the great density of the nitrate solution causing it to displace the water without perceptible mixing of the two liquids 7exp474 ,if these vessels are left at rest1 it may be noted1 from day to day1 that the copper nitrate diffuses further and further into the pure solvent1 and careful examination would show that the solvent1 in turn1 diffuses also into the copper nitrate solution4 ,the process is a very slow one1 but it will continue until a solution of uniform concentration is reached1 and this will be the case1 whatever the shape of the vessel may be4 ,if1 for the moment1 only the copper nitrate be considered--and what we are developing for the copper nitrate may be applied equally well1 mutatis mutandis1 to the diffusion of water into the copper nitrate solution--it is obvious then that copper nitrate in solution diffuses in all directions1 even against the force of gravity1 and it is plain also1 that any object1 resisting or arresting such a motion of material particles1 must have a force or pressure exerted upon it4 ,whatever the ultimate p#jji cause of the motion1 whether it is the result of inherent molecular velocities of the dissolved copper nitrate1 or of an attraction between the solute and the solvent1 or both1 it is inevitable that a pressure must result from the impact of the moving solute against the solvent4#c ,illustration3 ,,fig4 #a4 ,we have thus phenomena of diffusion of solutes through solvents1 exactly as we have the well-known diffusion of gases1 and the two phenomena are unquestionably very much alike1 the solute1 like the gas1 tending to diffuse from the place of higher1 to that of lower concentration4#d ,likewise1 if a solution of uniform concentration is heated in one part and not in another1 the solute1#d like a gas under similar conditions1 will move from the warmer to the colder part of the solution1 as was demonstrated by ,soret4#e ,without committing ourselves for the present to any given reason for the diffusion1 we note that the tendency to diffusion is a fact1 and we must accept the conclusion that every obstacle to such diffusion must have a pressure exerted upon it4 ,now1 if a solution is separated from the pure solvent by means of a so-called semipermeable membrane1 some of the results of this tendency to diffusion may be demonstrated4 ,,exp4 ,a concentrated solution of cane sugar in water1 colored with some aniline dye1 is enclosed in a thimble of parchment paper firmly fastened to a long narrow glass tube 7see ,fig4 #b7 and the cell is placed in a vessel of pure water4 ,the parchment is not absolutely semipermeable1 but it is approximately so1 allowing the solvent1 water1 to pass1 but being practically impervious to the solute sugar4 ,a ,schleicher and ,schll diffusion-thimble1 ,no4 #egi1 may be used1 with advantage1 as the thimble4 7,cf4 ,smith's ,introduction to ,inorganic ,chemistry1 p4 #bhd47 p#jaj ,we observe1 presently1 that the system is not in a condition of equilibrium2 water passes through the thimble into the sugar solution and the latter expands1 producing a decided difference of level1 and consequently a hydrostatic pressure1 between the liquid in the cell and the solvent outside of it4 ,we may note two facts3 first1 that the change includes an expansion of the solute1#f the sugar1 in the solution--that is1 the tendency of the solute to expand into larger volumes of the solvent is satisfied exactly as in the experiment 7,fig4 #a7 described above4 ,in the second place1 like all natural phenomena which proceed spontaneously1 the change is in the direction of equilibrium2 for when the hydrostatic pressure on the solution in the cell becomes sufficiently great1 or if it is made sufficiently great at once by the application of some outside pressure1 a point of equilibrium is reached1 at which water will pass neither into the cell nor out of it4 ,at that point1 the tendency to expansion1 both of the solute and of the solvent in the solution1 is just overcome by the pressure on the solution4 ,illustration3 ,,fig4 #b4 ,definition of ,osmotic ,pressure4--,the hydrostatic pressure which is necessary to bring the solution into equilibrium with the pure solvent1 when the two are separated by a semipermeable membrane1 may be defined1 according to van 't ,hoff1 as the measure of what is called the osmotic pressure of the solution4 ,we note that this definition still does not commit us to any theory as to the origin of the pressure1 but merely formulates an experimental relation4 ,measurement of ,osmotic ,pressure4--,more perfect semipermeable membranes can be produced4 ,these make possible quantitative measurements of the hydrostatic pressure on a solution1 when equilibrium between the solution and the pure solvent p#jaa has been reached4 ,such membranes were first used by ,pfeffer4 ,they consist of certain gelatinous precipitates1 notably copper ferrocyanide4 ,films of these precipitates may be formed1 under proper conditions1 which are permeable to water but not to certain solutes1 such as cane sugar1 glucose and galactose4 ,illustration3 ,,fig4 #c4 ,by precipitating these membranes in the pores of unglazed clay cells1 especially by the process devised by ,morse1#g we may make them sufficiently strong to resist enormous pressures--some used by the ,earl of ,berkeley were found to withstand a pressure of #acj atmospheres4 ,the hydrostatic pressure required to produce equilibrium may then be measured in either of two ways4 ,the first method1 used originally by ,pfeffer and more recently by ,morse and ,frazer#h and their collaborators in a wonderfully conscientious study of osmotic pressures1 consists in allowing the hydrostatic pressure to establish itself by the passage of very small quantities of the solvent1 through the membrane1 into the tightly closed cell containing the solution4 ,when the resulting pressure produces a condition of equilibrium1 it is measured#i by a manometer connected with the solution1 much as a gas pressure may be measured 7,fig4 #c74aj ,this process requires considerable time for exact measurements--weeks1 during which the cell must be kept at a constant temperature4 ,the second method1 which has been used by ,berkeley and ,hartley1#aa is very much more rapid and requires only a few hours for the measurement4 ,it consists in having the pure solvent within the cell1 instead of outside of it1 and in p#jab exerting an external pressure on the solution outside of the cell1 until a delicate manometer1 communicating with the pure solvent1 shows that water does not pass through the membrane in either direction--equilibrium having been reached4 ,osmotic ,pressure and the ,laws of ,gases4--,the work of van 't ,hoff1 which has proved of inestimable value to the development of chemistry1 succeeded in demonstrating that1 for dilute solutions1 the osmotic pressure1 as defined above1 obeys the common laws of gases1#ab--that1 in fact1 a substance in a dilute solution has an osmotic pressure equal to the gas pressure which it would exert if it were a gas of the same volume and at the same temperature4#ac ,space does not permit the presentation of all the details of the evidence confirming this conclusion1 but some of the most direct experimental proofs#ad will be considered4 p#jac ,boyle's ,law4--,boyle's law for gases states that1 at a constant temperature1 the pressure of a gas changes inversely as its volume1 or directly as its concentration4 ,mathematically we have ,p 3 ,p ,v 3 ,v or ,p ,v ,p ,v a constant1 and ,p 3 ,p ,c 3 ,c or ,p 3 ,c ,p 3 ,c a constant4 ,when van 't ,hoff published his first paper on the subject1 ,pfeffer's results from the direct measurement of the osmotic pressures of cane-sugar solutions were available1 and even these1 although experimentally not as exact as more recent determinations1 showed plainly that1 at a given temperature1 the osmotic pressure of a sugar solution varies directly as the concentration1 or inversely as the volume containing a given weight of the sugar4 ,at #ac-af we have3 ,concentration4 ,osmotic ,pressure4 ,pressure_/ mm4 ,mercury4 ,concentration4 #a4jj #ece #ece #b4jj #ajaf #ejh #b4gd #aeah #eed #d4jj #bjhb #eba #f4jj #cjge #eac ,the ratio of pressure to concentration varies irregularly round a mean value of #ebf1 and is approximately constant4 ,the more recent1 exceedingly careful measurements of ,morse and ,frazer confirm the conclusion1 that ,boyle's law holds for the osmotic p#jad pressures of dilute solutions2 they find that the osmotic pressures of glucose and of cane-sugar solutions vary directly as the concentrations of the solutions1 at a constant temperature4#ae ,gay-,lussac's ,law4--,gay-,lussac's law for gases states that1 if the volume of gas is kept constant1 its pressure increases by #a _/ #bgc of its value for every degree above #j ,c41 or ,pt ,p#j 7#a t _/ #bgc74 ,expressing the temperature in absolute degrees1 we have more simply3 ,pt ,p#j 7,t _/ #bgc7 or ,pt _/ ,t ,p#j _/ #bgc a constant4#af ,that is1 the pressure of a gas varies directly as its absolute temperature1 if the volume is kept constant4 ,pfeffer's results1 on the osmotic pressure of sugar solutions at different temperatures1 were not sufficiently accurate to enable van 't ,hoff to use them to confirm positively the rigorous thermodynamic proof 7footnote #c1 p4 #ab71 that the osmotic pressure must increase proportionally to the absolute temperature1 as required by ,gay-,lussac's law4 ,but the data did show1 uniformly1 a marked increase of the osmotic pressure with the temperature and1 frequently1 excellent agreement between theory and experiment4 ,more striking were the results obtained by van 't ,hoff in testing the correctness of this extension of ,gay-,lussac's law by means of ,soret's results on the diffusion of a solute from a warmer to a colder place4 ,it was found that the concentrations1 obtained by ,soret when equilibrium was reached1 agreed closely with the demand that the osmotic pressures in the colder and the warmer parts of the solution should be equal1 and that the osmotic pressure of a given weight of solute in a given volume should increase proportionally to the absolute temperature4 ,an elevation of temperature1 in a portion of a uniform solution1 will increase the osmotic pressure of this part4 ,diffusion will follow1 until the loss in concentration of the solute1 and therefore the loss of osmotic pressure 7,boyle's law71 of the warmer part1 and the increased concentration and increased pressure of the colder portion result in all parts of the solution having the same osmotic pressure4 p#jae ,as an example1 a concentration of #ag4cc copper sulphate at #bj was found to be in equilibrium with a concentration of #ad4jc at #hj4 ,now1 if the #ag4cc solution had an osmotic pressure of ,p mm4 at #bj1 a #ad4jc solution at the same temperature would have a pressure of 7#ad4jc _/ #ag4cc7 ,p mm4 7,boyle's law71 and this would increase to 7#ad4jc _/ #ag4cc7 ,p 7#cec _/ #bic7 mm4 at #hj ,c41 or #j4ige ,p mm4--a result showing that the osmotic pressure in the hot part was practically the same as that1 7,p71 in the cold part of the solution4#ag ,it is a source of great satisfaction1 that the recent very exact and painstaking work of ,morse and ,frazer1#ah in measuring osmotic pressures directly1 completely confirms this fundamentally important conclusion1 that the osmotic pressure of a solution does increase proportionally to its absolute temperature4 ,the ,avogadro-van 't ,hoff ,hypothesis4--,for chemists1 the most important part of van 't ,hoff's work lies in the extension of the ,avogadro ,hypothesis to solutions4 ,as van 't ,hoff expresses it1 equal volumes of the most different solutions1 having the same osmotic pressure and the same temperature1 contain the same number of dissolved molecules1--that number1 namely1 which would be found in the same volume of a gas at the same gas pressure and temperature4#ai p#jaf ,pfeffer's measurements1 with solutions of #a g4 of sugar in #ajj c4c4 of water 7the volume of the solution is #ajj4f c4c471 were shown to prove1 that the observed osmotic pressures agreed excellently with the gas pressures1 calculated for the equimolar weight of hydrogen1 in the same volume and at the same temperature3 ,osmotic ,pressure ,temperature4 ,found4 ,calculated4#bj ,atmosphere4 ,atmosphere4 #f4h #j4ffd #j4ffe #ac4g #j4fia #j4fha #ad4b #j4fga #j4fhb #ae4e #j4fhd #j4fhf #bb #j4gba #j4gja #cb #j4gaf #j4gbe #cf #j4gdf #j4gce ,morse's more recent and more exact results show1 that the osmotic pressure of solutions of cane sugar and of glucose 7corrected for the volume occupied by the sugar1 see footnote1 p4 #ae7 agrees within #f with the values demanded by van 't ,hoff's theory1 being about #f larger for concentrations ranging from #j4a to #a4j molar4 ,the difference of #f is noteworthy and is probably due to secondary causes1 but suggests extended investigation of its source4 ,indirect ,determinations of ,osmotic ,pressure4--,the experimental results given have been obtained by direct measurements of osmotic pressures with the aid of semipermeable membranes4 p#jag ,perfect membranes are very difficult to prepare1 and membranes of this kind can be used only with a few solutes4 ,nature offers us1 however1 forms of semipermeable walls between solutions and pure solvents1 which in many instances are perfect4 ,the atmosphere1 above a volatile pure solvent and a solution of a nonvolatile substance in that solvent1 when both liquids are placed side by side in a closed space1 would serve as a semipermeable wall3 the solvent vaporizes and may pass freely from solvent to solution and vice versa1 but the solute1 in the case under consideration1 is nonvolatile and therefore cannot pass through the atmosphere4 ,the vapor pressure of a pure solvent being always found to be higher than that of a solution in this solvent1 at the same temperature1 the solvent would pass in such a closed space as vapor from the pure solvent and would condense in the solution2 it thereby dilutes the solution and the solute1 and the solvent in the solution1 expand1 exactly as in the absorption of a solvent by a solution through a semipermeable membrane4 ,again1 the vapor pressure of a solution being lower than that of the pure solvent1 the solution 7of a nonvolatile solute7 must be heated higher than the pure solvent1 to bring both to the boiling-point2 that is1 there is an elevation of the boiling-point1 when a nonvolatile solute is dissolved in a solvent4 ,the solute being nonvolatile1 only the solvent passes off in the process of boiling1 the solute becomes more concentrated1 and1 according to van 't ,hoff's extension of ,boyle's law1 the osmotic pressure of the solution increases4 ,similarly1 when a solution is cooled until freezing occurs1 provided the solute does not crystallize out with the solvent1 the concentration of the solute is again increased1 and therefore the osmotic pressure of the solution is also increased4 ,van 't ,hoff recognized the relations existing between the freezing1 boiling and vaporization of solutions1 on the one hand1 and the changes of their osmotic pressures on the other4 ,by developing rigorously the relations between the lowering of the vapor tension1 the raising of the boiling-point1 the lowering of the freezing-point of a solvent by a solute and the osmotic pressure of the solution1 he made it possible#ba to use p#jah extensive experimental material1#bb on the elevation of boiling-points and the lowering of freezing-points and of vapor tensions1 to determine the osmotic pressures of solutions4 ,the theory of the relation of osmotic pressure to gas pressure is fully confirmed by these measurements1 for those cases to which it may properly be applied1 namely1 to sufficiently dilute solutions and such as have only negligible heats of dilution1 i4e4 in which dilution does not involve chemical changes4 ,apparent ,exceptions4--,instead of discussing the vast amount of material of this kind1 which agrees with van 't ,hoff's theory1 we may consider1 more profitably1 typical cases of apparent exceptions4 ,the most important instance of this kind1 the case of solutions of compounds which undergo electrolytic dissociation or ionization1 will be separately discussed in the next chapter1 and we shall find that van 't ,hoff's great generalization is a vital element in the evidence of this important form of dissociation4 ,of other apparent exceptions1 we may note the fact that some solutes seem to give abnormally low osmotic pressures#bc in certain solutions4 ,for instance1 benzoic acid1 in benzene solutions1 gives only a little more than half as great an osmotic pressure as it does in aqueous solutions of the same concentration and temperature1 and as would be calculated on the basis of the ,avogadro-van 't ,hoff ,hypothesis for a compound of the formula ,c#f;,h#e;,,cooh and the molecular weight #abb4 ,but a rigorous study#bd of the distribution of benzoic acid between water and benzene1 when solutions of the acid in the two solvents are shaken together until equilibrium is established 7,chapter ,,viii71 has proved that the distribution is strictly in accord with the assumption that benzoic acid1 in aqueous solution1 has the molecular weight #abb and the composition ,c#f;,h#e;,,cooh1 and that1 in benzene solution1 it has the molecular weight #bdd and the composition 7,c#f;,h#e;,,cooh7#b2 only a small part of the acid 7,c#f;,h#e;,,cooh7#b is decomposed in benzene solution into the simpler molecules1 of the composition ,c#f;,h#e;,,cooh4 ,in other words1 the simpler molecules ,c#f;,h#e;,,cooh are polymerized or associated to form larger molecules in benzene solution1 much as the gas nitrogen dioxide ,,no#b goes over more or less into the gas ,n#b,o#d1 especially at low temperatures1 and as hydrogen fluoride at low temperatures has the composition ,h#b;,f#b1 while at higher temperatures it is ,,hf4 ,the divergence of the benzene solutions of benzoic acid from the ,avogadro-van 't ,hoff principle is therefore only an apparent one1 not a real one1 inasmuch as the osmotic pressure of the solutions agrees perfectly with that calculated for solutions of a substance 7,c#f;,h#e;,,cooh7#b1 of molecular weight #bdd4 ,such associated molecules 7of organic acids1 alcohols1 phenols1 etc47 occur p#jai particularly readily in liquids of small dissociating power1 like benzene1 and such solutions show marked absorption of heat on dilution1#be the dilution being accompanied by a chemical change4 ,the associated molecules are dissociated more and more completely 7,c#f;,h#e;,,cooh7#b #b ,c#f;,h#e;,,cooh1 even in these solvents1 as the solutions are diluted4 ,since dilution results in a chemical increase in the number of molecules1 the osmotic pressure cannot decrease proportionally with the increase of volume in such a case as this4 ,nor does gas pressure1 it must be remembered1 decrease proportionally to the volume in the case of gases which show chemical changes with change of volume1 e4g4 in the case of nitrogen tetroxide1 for which we have ,n#b,o#d #b ,,no#b4 ,in still other instances1 apparently too high osmotic pressures1 or too low molecular weights1 have been found by the application of the ,avogadro-van 't ,hoff ,hypothesis to solutions3 for instance1 the molecular weight of sodium1 when dissolved in mercury1 was found by ,ramsay to vary from #ba4f1 in dilute1 to #ae4a in concentrated solutions4 ,but ,cady found that the heat of dilution of sodium in mercury solution is considerable1 and by taking this properly into account1 ,bancroft was able to show that the molecular weight1 correctly calculated in a given experiment1 is #bb4g 7agreeing well with the theoretical weight #bc71 in place of #af4e1 as calculated without making the required allowance for the heat of dilution4#bf ,these determinations are most instructive in showing that the sources of some of the most important deviations from the van 't ,hoff-,avogadro principle1 deviations which have been brought forward as arguments against its assumptions1 are due1 not to any untrustworthiness of the general principle1 but to the error of neglecting to observe the limiting conditions of the formulation1 or of neglecting to make corresponding corrections for the non-observance thereof4 ,summary4--,van 't ,hoff's theory of solution--that the osmotic pressure of substances in solution obeys the laws of gases1 and that equal volumes of the most varied dilute solutions1 having the same temperature and osmotic pressure1 contain the same number of dissolved molecules1 that number1 namely1 which would be found in the same volume of a gas at the same temperature and gas pressure1--accords thus1 not only with the demands of thermodynamics1#bg but is also1 within the limits demanded by the theory itself1 in agreement with the best experimental measurements of osmotic pressures that have been made in recent years4 ,the apparent exceptions1 as in the cases just described and1 as we shall find1 in the case of electrolytic dissociation1 are found to be no exceptions1 when the conclusions1 reached on the assumption that p#jbj the theory is correct1 are tested rigorously by independent methods of investigation4#bh ,the fundamental laws of gases and the ,avogadro ,hypothesis may be condensed into the following general equation1 expressing all of the laws1 viz43 ,p ,v n ,r ,t4 ,this equation applies equally to the osmotic pressures of dilute solutions1 the osmotic pressure being substituted for the gas pressure4 ,in the equation1 ,t is the absolute temperature of the gas or solution1 ,p the gaseous or osmotic pressure1 ,v the free space of the gas volume1 i4e4 the volume of the gas less the volume occupied by the gas molecules1 or the volume of the pure solvent in the solution used1 i4e4 the volume of the solution less the volume of the solute4 ,r is the so-called gas-constant1 and represents the work done against the external pressure when one gram molecule1 or mole1 of the gas is heated one degree and allowed to expand1 say at constant pressure ,p1 against an external pressure ,p2 n represents the number of gram molecules or moles of gas or solute used 7the total weight of solute or gas1 divided by the average weight of a mole in the gas or solute74 ,if a given weight of a gas or solute is taken1 and no dissociation or association occurs 7such as would involve appreciable heats of dilution71 then n is a given number2 and1 therefore1 at a given temperature ,t1 all the factors on the right side of the general equation being given numbers1 ,p ,v is a constant 7,boyle's law74 ,for a given quantity of gas or solute 7n is a given number71 kept at constant volume ,v1 the pressure must vary as the absolute temperature 7,gay-,lussac's law72 ,p _/ ,t n ,r _/ ,v a constant4 ,when the pressure1 volume and temperature of two gases1 or two dilute solutions1 are equal1 n1 the number of gas or solute molecules present1 must be the same 7,avogadro-van 't ,hoff ,hypothesis72 n ,p ,v _/ 7,r ,t71 and all the factors of the right side are the same for the gases and solutions which we are comparing4 ,finally1 if the pressure is expressed in atmospheres1 the volume in litres1 and the temperature in absolute degrees1 the gas-constant ,r ,p ,v _/ ,t #a #bb4d _/ #bgc #j4jhb4 ,,footnotes3 #c ,even after a solution of uniform concentration of the solute is formed1 the tendency toward diffusion1 and the diffusion itself1 and the resulting pressure must still persist4 ,but a state of dynamic 7or flowing7 equilibrium must be considered now to exist1 the loss caused by the moving away of the solute1 from a given part of the solution1 being balanced by the diffusion 7into that part7 of the solute from the neighboring parts4 ,whether one ascribes the diffusion to inherent molecular velocities of the solute1 or to an attraction between solvent and solute1 the discrete particles of the solute in a solution of uniform concentration will continue to have such inherent velocities 7,chap4 ,,iii71 and will also continue to be surrounded by pure solvent1 exactly as in solutions of unequal concentrations1 where the diffusion may be observed1 because the net result1 in such a case1 is a one-sided action4 #d ,this again holds equally for the solvent4 #e ,see below4 #f ,at the same time1 the change is also in the direction of an expansion of the solvent in the solution4 ,the two changes are not opposed to each other1 but supplementary4 #g ,am4 ,chem4 ,j41 #bh1 #a 7#aijb72 #dj1 #bff1 #cbe 7#aijh7 7,stud474 #h ,am4 ,chem4 ,j41 #cd1 #a 7#aije72 #cf1 #ci 7#aijf72 #cg1 #cbd1 #dbe1 #eeh 7#aijg72 #ch1 #age 7#aijg74 #i ,the exact concentration of the solution at the point of equilibrium is determined by subsequent analysis4 #aj ,cf4 ,smith's ,inorganic ,chemistry1 p4 #bhg4 #aa ,berkeley and ,hartley1 ,phil4 ,trans4 ,roy4 ,soc4 ,a1 #bjf1 #dha 7#aijf74 #ab ,when appreciable heat of dilution is shown by a solution1 some chemical change1 resulting from dilution1 is indicated 7such as1 dissociation of the solute1 hydration1 hydrolysis1 etc474 ,in such a case1 the ,avogadro-van 't ,hoff principle holds for each concentration for its actual composition1 and the principle may often be used to determine the extent of the chemical change produced by dilution4 ,but then the osmotic pressure will not obey ,boyle's and ,gay-,lussac's laws4 ,the same exception applies also to gases which undergo chemical changes1 as the result of dilution or change of temperature4 ,in the case1 for instance1 of nitrogen tetroxide1 which dissociates according to ,n#b,o#d #b ,,no#b1 the extent of the dissociation varies with changes of concentration 7pressure7 and of temperature1 and the gas does not obey the laws of ,gay-,lussac and of ,boyle4 ,in regard to the rle of heat of dilution in connection with osmotic pressure1 see ,bancroft1 ,j4 ,phys4 ,chem41 #aj1 #cai 7#aijf74 #ac ,see p4 #ae for a more rigorous statement concerning the volume4 ,cf4 ,morse and ,frazer1 ,am4 ,chem4 ,j41 #cd1 #a 7#aije74 #ad ,as a result of numerous vain endeavors1 as well as of much direct evidence of a positive character1 the scientific world has1 for many years1 held the opinion that any sort of perpetual motion machine is impossible4 ,every one now admits that a machine which would be able to work continuously1 without consuming energy1 is an impossibility--that is1 that a perpetuum mobile of the first class1 as it is called1 is impossible 7law of the conservation of energy or first law of thermodynamics74 ,from this law it does not of necessity follow1 however1 that it would be impossible to make a machine or device that would convert continuously into available energy or work1 say1 the enormous amounts of heat energy of the earth or of large bodies of water 7dissipated energy7 which would thereby be cooled below the temperatures of their surroundings4 ,such a hypothetical process has been termed a perpetuum mobile of the second class2 it has never been realized and is universally conceded to be an impossibility2 the so-called second law of thermodynamics gives expression to this fact4 ,now van 't ,hoff ,z4 phys4 ,chem41 #a1 #dha 7#ahhg7 showed1 first1 that a gas like oxygen1 nitrogen1 hydrogen1 etc41 which is soluble in proportion to its gas pressure 7,henry's law71 must exert1 in solution1 an osmotic pressure equal to the gas pressure1 which it would have1 if present in the same quantity as a gas in the same volume at the same temperature2 for1 if such were not the case1 the solution and gas could be used to produce a perpetuum mobile of the second class1 which1 according to the above law1 is an impossibility4 ,similar proofs were given by ,rayleigh ,nature1 #ee1 #bec 7#ahig7 and by ,larmor ,phil4 ,trans41 #aij1 #bff 7#ahig71 ,nature1 #ee1 #ede 7#ahig7 that the principle applies to solutions of other solutes4 ,provided1 then1 that we have 7#a7 perfect semipermeable membranes1 7#b7 sufficiently dilute solutions1 and 7#c7 none but negligible heats of dilution 7p4 #ab71 van 't ,hoff's generalization1 concerning the relation of osmotic pressure and the laws of gases1 must hold1 if the perpetuum mobile of the second class is impossible1 as is demanded by the second law of thermodynamics4 #ae ,see p4 #ae in regard to the relation for concentrated solutions4 #af ,the pressure ,p#j of a given quantity 7weight7 of a gas at #j ,c41 in a given constant volume1 is also a given number and consequently ,p#j_/bgc is a constant under these conditions4 #ag ,the slight differences in the ionization of copper sulphate solutions of #ad and #ag and at #bj and #hj are not included in the calculation1 ionization being unknown1 when van 't ,hoff made his calculations4 #ah ,am4 ,chem4 ,j41 #da1 #beh 7#aiji74 #ai ,in the light of recent work1 especially by ,morse and ,frazer1 the law would state1 more exactly1 that a substance in solution produces the osmotic pressure1 at a given temperature1 which it would exert1 if it were contained as a gas1 at the same temperature1 in the volume occupied by the pure solvent of the solution4 ,for sufficiently dilute solutions1 the volume of the solution and the volume of the solvent may be considered identical2 for more concentrated solutions1 there is a decided difference1 and the correct volume to use in calculation is the volume of the solvent alone1 i4e4 the volume of the solution reduced by the volume of the pure solute4 ,this corresponds to the correction of the volume in the more accurate expression for the behavior of gases1 developed by van der ,waals2 in place of v1 the total gas volume1 7v b71 the total volume of the gas less the volume of the spheres of action of the gas particles1 is used1 especially for strongly compressed or concentrated gases4 ,it may be added that van 't ,hoff's thermodynamic proof involves the same correct definition of the volume that ,morse and ,frazer subsequently developed experimentally4 ,cf4 ,bancroft1 ,j4 ,phys4 ,chem41 #aj1 #cai 7#aijf74 #bj ,one gram of cane sugar1 ,c#ab;,h#bb,o#aa 7the mol4 wt4 is #cdb7 corresponds to #a _/ #cdb gram molecule or mole and1 therefore1 to #b4jb _/ #cdb gram of hydrogen4 ,the volume containing this quantity of hydrogen is #ajj4f c4c42 a liter would contain #b4jb _/ #cdb #ajjj _/ #ajj4f gram of hydrogen4 ,the pressure of a mole or #b4jb grams of hydrogen1 contained in a liter at #j1 is #bb4d atmospheres1 and the pressure of the quantity of hydrogen given above1 in a liter1 would be 7#b4jb #ajjj7 _/ 7#cdb #ajj4f7 7#bb4d _/ #b4jb7 at #j4 ,at #cf ,c41 for instance1 the pressure would be #cji _/ #bgc times as great1 or ,pcalculated 7#b4jb #ajjj #bb4d #cji7 _/ 7#cdb #ajj4f #b4jb #bgc7 #j4gce atmosphere4 #ba ,the exact relations are discussed in van 't ,hoff's ,lectures on ,physical ,chemistry1 ,part ,,ii1 pp4 #db-ei1 ,nernst's ,theoretical ,chemistry 7#aijd71 pp4 #adb and #adh1 and ,h4 ,c4 ,jones's ,the ,elements of ,physical ,chemistry 7#aiji71 pp4 #beb1 #bga4 #bb ,vide ,raoult1 ,scientific ,memoir ,series1 #d1 #ga1 #abg4 #bc ,i4e4 abnormally small depressions of freezing-points or elevations of boiling-points4 #bd ,nernst1 ,theoretical ,chemistry1 p4 #dhf2 ,hendrixson1 ,z4 anorg4 ,chem41 #ac1 #gc 7#ahig74 #be ,cf4 ,bancroft1 ,j4 ,phys4 ,chem41 #aj1 #cai 7#aijf74 #bf ,for the discussion of other instances1 vide ,bancroft1 loc4 cit4 #bg ,footnote #c1 p4 #ab4 #bh ,for example1 determinations of distribution coefficients 7p4 #ah71 heats of dilution 7p4 #ai71 conductivities and chemical activity 7,chapters ,,iv-,,vi74 p#jba ,,chapter ,,iii ,,osmotic ,,pressure ,,and ,,the ,,theory ,,of ,,solution ,,ii ,accepting van 't ,hoff's theory of solutions1 then1 as based on experimental evidence as well as on sound thermodynamic reasoning1 we find a number of interesting questions still confronting us4 ,most insistent is the question as to the source of the remarkable agreement between the osmotic pressure of a solute and the gas pressure1 which it would exert in the same volume1 as a gas1 at the same temperature1 and as to the identity of the laws governing the two forms of pressure4 ,then1 we may also ask1 what is the mechanism of the process by which osmotic pressure reveals itself1 especially in the case of cells with semipermeable membranes4 ,and1 finally1 we may ask what is the cause of the semipermeability of the membranes4 ,semipermeability4--,taking up the last question first1 as the simplest one1 we find that it was long ago recognized that permeability depends on the power of membranes to dissolve certain substances1 or to form unstable combinations with them4 ,a membrane is semipermeable if it will dissolve one component only of a solution1 the solute or the solvent1 and not the other4#bi ,we find the simplest evidence of the cause of semipermeability in the case of gases4 ,palladium1 especially when heated1 dissolves hydrogen readily1 but not nitrogen or oxygen1 and a wall of palladium may be used as a semipermeable membrane to separate a mixture of hydrogen and nitrogen from pure hydrogen1 just as copper ferrocyanide membranes are used with aqueous sugar solutions and water4 ,the results with the gases duplicate in every particular the observations made on the solutions 7see below1 p4 #bd74 ,certain gases1 such as ammonia and hydrogen chloride1 are easily soluble in water1 while others1 like oxygen1 nitrogen and hydrogen1 are very difficultly soluble1 and a film of p#jbb water may be used as a semipermeable membrane for such gases4#cj ,,exp4 ,if the moist membrane of a cell 7,fig4 #d71 containing air1 is covered with an atmosphere of hydrogen1 there is no increase of pressure produced in the cell1 as indicated by the column of colored oil in the manometer in which the cell ends3 hydrogen1 being very little soluble in water1 cannot pass through the film of water in the few minutes it is allowed to act4 ,if now an atmosphere of ammonia is substituted for the hydrogen1 the gas passes through the film into the cell4 ,it turns the color of a piece of litmus paper placed in the cell and produces an increased pressure in the cell1 the air remaining in the latter1 because oxygen and nitrogen are very little soluble in water4 ,illustration3 ,,fig4 #d4 ,membranes will be1 similarly1 semipermeable to solvent or solute1 when only one of these is soluble in the membrane1 or is capable of forming an unstable compound with it4 ,for instance1 salts1 holding water of crystallization which is readily lost and recovered1 may easily be conceived of as assuming the rle of semipermeable membranes1 allowing the passage of water say from a wet atmosphere to a dry one1 or from pure water to a solution2 and ,tammann#ca has realized such membranes by the use of zeolites--silicates1 which hold water of crystallization but are insoluble in water4 ,kahlenberg#cb has recently used rubber membranes1 that are permeable for solvents like benzene1 pyridine1 etc41 which are soluble in rubber1 but not permeable for water1 which is insoluble in rubber4 ,illustration3 ,,fig4 #e4 ,osmosis4--,the recognition of this rle of the semipermeable membrane leads to the second question raised1 namely as to the mechanism of the process by means of which osmotic pressures are measured directly with the aid of such membranes 7p4 #aa74 p#jbc ,the answer hinges on the question of the mechanism of the diffusion of the solvent into the cell1 a diffusion which is called its osmosis4#cc ,if we consider the pure solvent1 say water1 on one side of a semipermeable membrane1 and a solution 7e4g4 of sugar in water7 on the other side1 it is obvious that the solvent itself has a higher concentration on the side where it is pure1 than on the side of the solution1 where it is diluted--distended by the solute in it4 ,the solvent is soluble in the membrane1 and its solubility will be proportional#cd to its own 7the solvent's7 concentration2 it will1 consequently1 be more soluble in the membrane on the side of the pure solvent than on the side of the solution4 ,if we bring such a membrane first into contact with the pure solvent 7,fig4 #e71 the membrane will take up the solvent 7from the side ,a7 until it is saturated with it4 ,let the solubility1 which represents the concentration of the solvent in the membrane at this stage1 be called c4 ,the membrane may then be considered to be taking up in unit time just as many molecules from the solvent as it gives up to it 7dynamic equilibrium71 exactly as1 when water is in equilibrium with water vapor1 we consider the water to be vaporizing just as fast as vapor is condensing to form water4 ,now1 if a solution of sugar is placed on the other side of the membrane1 the solvent will pass out of the membrane into the solution just as fast as it passes back into the pure solvent4 ,at first the concentration of the solvent on the surface ,b of the membrane is just as great 7c7 as on the surface ,a2 but the membrane will here receive the solvent more slowly from the solution1 which is less concentrated as to the solvent2 and consequently the membrane will lose water to the solution4 ,the solubility 7c7 of the solvent at this surface ,b of the membrane1 corresponding to the smaller concentration of the solvent in the solution1 will be less than the solubility 7c7 at ,a1 where the membrane is in contact with the pure solvent1 and water will pass into the solution at ,b1 until the concentration of the water in the membrane at ,b has fallen p#jbd from 7c7 to 7c74 ,in such a membrane1 as in every solution or gas1 there must be a tendency towards the establishing of uniform concentration by diffusion from points of higher concentration to those of lower1 and the solvent will1 therefore1 diffuse from points along the surface ,a of the membrane to points along the surface ,b2 the surface ,a will become unsaturated and will take up solvent from the pure liquid bathing it1 and the surface ,b will be kept continuously supersaturated and will lose solvent continually to the solution4 ,consequently1 the solvent will pass continuously through the membrane from the pure solvent to the solution4 ,equilibrium will be reached1 and the flow will cease1 only when the solution has become infinitely dilute1 equal hydrostatic pressure obtaining on solution and solvent1 or when the disturbing influence of the solute1 which dilutes the solvent in the solution1 is exactly counterbalanced by an external hydrostatic pressure1 exerted on the solution4 ,when such a pressure on the surface of the solution balances the force exerted against the solvent by the solute we shall have equilibrium4 ,it is clear1 then1 that the osmosis1 or passage of the solvent through the membrane1 is brought about by the unequal concentrations 7or1 more exactly1 the resulting unequal partial pressures7 of the solvent itself4 ,but this inequality is produced by the presence of the solute1 and it is a characteristic and significant fact1 that the effect of the latter1 in dilute solutions1 may be overcome by a hydrostatic pressure1 corresponding to the gas pressure which the same number of molecules of a gas in the same volume at the same temperature would exert against this hydrostatic pressure4 ,illustration3 ,,fig4 #f4 ,osmosis and ,gas ,pressure4--,the legitimacy of the interpretation given is most strikingly shown by experiments with a membrane1 semipermeable for gases1 which enables us to measure gas pressures1 that may be unknown1 by exactly the same process as is used to measure the unknown osmotic pressure of a solute in solution4 ,van 't ,hoff#ce and ,arrhenius#cf predicted such a result1 and ,ramsay#cg proved by experiment the correctness of their assumptions4 ,a mixture of nitrogen and hydrogen may be enclosed in a palladium vessel connected with a manometer 7see ,fig4 #f74ch ,the partial pressure ,p,n of the nitrogen may be p#jbe determined by surrounding the palladium vessel with pure hydrogen1 at a pressure which is known and is greater than the partial pressure of the hydrogen in the vessel1 and by observing the final total gas pressure which is obtained in the vessel4 ,the hydrogen diffuses from the point of higher concentration1 outside of the vessel1 through the palladium1 into the interior where the concentration of the hydrogen is lower4 ,the experiment may be carried out at #bhj1 a temperature at which palladium readily dissolves hydrogen and is permeable to it4 ,the metal does not dissolve nitrogen and is not permeable to it4 ,the volume of the enclosed gas is kept constant by raising the mercury level in the outside arm of the manometer1 and the total pressure of the enclosed gas is measured when equilibrium is reached4 ,if this total pressure is ,pfinal and the known pressure of the hydrogen outside of the vessel is ,p,h1 then1 if equilibrium is reached when the hydrogen on both sides of the semipermeable palladium membrane has the same concentration 7pressure71 ,p,h ,p,n ,pfinal and ,p,n ,pfinal ,p,h4 ,in other words1 the excess of the final combined pressure inside1 over the outside pressure of the hydrogen1 is equal to the pressure of the nitrogen in the vessel4 ,ramsay's results showed that the amount of hydrogen actually entering the vessel was #ij-ig of the amount predicted by the theory on the basis of the assumption that equilibrium will be reached1 when the hydrogen has the same concentration 7pressure7 on both sides of the palladium membrane4 ,the experiment is particularly instructive1 in the first place1 because it illustrates with a gas1 subject to the laws of gases1 why and how osmosis takes place through a semipermeable membrane--namely as a result of the solubility of the diffusing substance in the membrane1 and through the flow of the diffusing substance p#jbf from higher to lower concentrations4 ,in the second place1 while the increase in total pressure in the inner chamber undoubtedly is brought about by the osmosis of hydrogen into the chamber1 the excess pressure when equilibrium has been reached1 necessarily measures accurately the partial pressure of the nitrogen4 ,in other words1 the semipermeable membrane is merely a means or device for measuring the partial pressure of the nitrogen--the membrane is not the cause of the pressure2 the latter is a definite one1 whether we know what it is or not1 and the osmosis of the hydrogen through the palladium merely gives us a means of ascertaining it4 ,similarly1 it would be wrong to consider that the osmotic pressure of a solution is caused1 or brought about1 by the flow of the solvent through a semipermeable membrane 7osmosis72 the latter simply is a device which enables us to recognize and measure the pressure that exists in the solution1 both in the presence and the absence of such a membrane4 ,we may consider1 then1 that the osmosis1 or migration of the solvent through a semipermeable membrane into a solution1 is the result of the reduced concentration 7or partial pressure7 of the solvent in the solution1 resulting from the presence of the solute4 ,inasmuch as the effect of the solute on the solvent can be overcome by a pressure on the surface of the solution1 one is led to the conclusion that the solute acts by exerting1 in turn1 a force or pressure against the surfaces of the solvent1 in the directions opposite to the hydrostatic pressure required to overcome it4 ,the significant identity of the value of this pressure1 as thus measured1 with the gas pressure that would be exerted by a gas of the same number of molecules1 in the same volume and at the same temperature1 leads us to the last of the three questions which have been raised1 namely1 the question concerning the theory of the intimate relations between gas and osmotic pressures 7p4 #ba74 ,the ,kinetic ,theory and ,osmotic ,pressure4--,for an answer to this fundamentally interesting theoretical question one turns1 naturally1 to the kinetic theory1 which1 in the hands of ,clausius1 ,joule1 van der ,waals and others1 has given us a very satisfactory and essentially complete theoretical interpretation of the behavior of gases1 and of the liquids to which they may be compressed4 ,the laws of gases1 it is known1 are in accord with the two simple assumptions of the kinetic theory4 ,the first assumption is that p#jbg gases consist of ultimate discrete particles 7molecules71 which move in all directions through the space filled by the gas and1 at ordinary pressures1 are so far apart1 that the forces of molecular attraction between them are negligible2 the pressure of the gas is simply the net result of the impacts of these flying particles upon the walls of the containing vessel4 ,the second assumption of the kinetic theory is that temperature is a function of the mean kinetic energy of the moving molecules1 and that the molecules of gases of the same temperature have the same mean kinetic energy4 ,the kinetic energy of particles is a function of their mass m and their velocity u 7,k4,e4 m u#b74 ,when a gas is heated1 the kinetic energy of its molecules is increased1 and1 since their masses remain unchanged1 their velocity must increase4 ,as a result1 the number and the force of their impacts against the walls of a given space increase1 and thus the pressure is increased4 ,we may ask1 whether this theory cannot be used to explain the connection between osmotic and gaseous pressure4 ,if temperature is a function of the kinetic energy of the molecules of which a substance consists1--and the whole behavior of gases confirms such a conception1--then one must conclude1 that the mean kinetic energy of molecules1 at a given temperature1 must always be the same1 irrespective of whether they are present in gaseous1 or liquid1 or solid form1 or even in solution4#ci ,the tendency of the molecules to move1 resulting from the kinetic energy inherent at a given temperature1 may be largely balanced 7liquids71 or overcome 7solids71 by molecular attractions of surrounding particles1 but such conditions are altogether in harmony with the conception of a definite mean molecular kinetic energy1 persisting at a given temperature1 irrespective of the physical surroundings of the molecule4 ,according to the kinetic theory1 then1 when we have a dilute solution1 say of alcohol in water1 the molecules of alcohol1 at a given temperature1 would have a given mean kinetic energy1 p#jbh and would be tending to move in all directions with a mass#dj and velocity1 the same as if the alcohol were present as a gas or vapor at the same temperature4 ,if the solution is sufficiently dilute1 the dissolved alcohol molecules are sufficiently far apart1 for average time1 to make the molecular attractions between them negligible1 just as is assumed for gases4 ,as far as the alcohol 7solute7 molecules alone are concerned1 they may1 evidently1 be assumed to be present in the solution1 in the same condition1 as to number1 mean kinetic energy and mean velocity1 as they would be in alcohol vapor of the same concentration and temperature4 ,we may ask1 now1 whether the osmotic pressure of the solution may not result from the pressure on the solvent1 growing out of its bombardment by the solute molecules4 ,and we may ask1 further1 what numerical relation would subsist between such a pressure and the pressure of the solute1 if the latter were present as a gas1 under the same conditions of temperature and concentration4 ,in order to be prepared to answer these questions1 we must consider1 in what way the presence of the solvent must modify the motions and the forces of impact of solute molecules4 ,one great difference between the dissolved substance and the gas would be1 that1 in the solution1 the solute is in intimate contact with the solvent4 ,a decided attraction must exist between the solute molecules and the solvent molecules1 since we could not otherwise understand how a solvent1 like water1 in dissolving a nonvolatile substance like sugar1 could overcome those molecular attractions between the sugar molecules1 which make sugar a solid4 ,but we note1 that all the solute molecules in a solution1 except those at the surface1 are surrounded on all sides equally by the solvent4 ,the attractive forces1 exerted upon the single molecules of the solute by the solvent molecules1 thus sum up to zero1 and need not be considered further4 ,only the small number of solute molecules1 which are at the surface of the liquid1 would involve a minor correction in the application of the kinetic theory1 and this need not be considered here4 ,a second point of difference between a substance in solution1 and the same substance as a gas or vapor at the same temperature p#jbi in the same volume1 lies in the fact that a gas molecule will go a much greater distance without colliding with some second molecule and changing its path1 than would a solute molecule1 the latter molecule being closely surrounded by the molecules of the solvent4 ,the mean free path1 as it is called1 will be very much shorter for a solute molecule than for a gas molecule1 and we note1 as a matter of fact1 how slow is the diffusion through a solvent 7see exp4 p4 #h74 ,but the shortness of the previous path does not affect the force of a blow resulting from the impact of a moving mass1 the force of the impact being dependent only on the mass and the change in speed of the striking particle1 at the moment of impact4 ,thus the short free mean path of a dissolved molecule does not affect the mean force of the blow1 delivered when it strikes the resisting medium4 ,the slow diffusion of a dissolved substance represents a difference in degree1 not in kind1 between gases and dissolved substances4 ,even in gases1 we have such frequent collisions that the mean free path of an oxygen molecule at #j and atmospheric pressure is only #j4jjjja cm41 whereas the velocity1 the total path covered in one second1 is #db1ejj cm4 ,,exp4 ,if a bulb containing a few drops of bromine is broken at the bottom of a tall cylinder1 the bromine vapor is seen to diffuse rather slowly into the upper part of the cylinder1 the bromine molecules1 in their passage upward1 rebounding from the air molecules1 with which the cylinder is filled4 ,if a second cylinder is first evacuated1 and the bromine bulb is broken in vacuo1 the vapor is seen to fill the cylinder instantly1 the high velocity of the bromine molecules being thus revealed4 ,but a third question1 of fundamental importance in the comparison of the condition of a substance existing as a gas and its condition in a solution of the same concentration and temperature1 results from a consideration of the frequency of the impacts of the solute molecules against the solvent1 growing out of the reduction of the lengths of the mean free paths of the solute molecules4#da ,in order to be able to take this fact properly into account1 it will be necessary to consider somewhat more precisely the manner in which1 according to the kinetic theory1 gas pressure is produced4 ,we may consider that we have in a cube of unit volume 7#a c4c47 n molecules of a gas1 each of mass m and average velocity u cm4 per second4 ,we may assume that one-third of the total number p#jcj of molecules moves in each of the three dimensional directions4#db ,a single molecule of mass m1 striking the surface with a velocity u and rebounding with the same velocity in the opposite direction1 will exert on the surface a force of #b m u units4 ,but1 with a velocity of u cm4 per second1 it will reach the opposite wall and return to the surface we are considering1 u _/ #b times in one second4 ,a single molecule will consequently exert a force #b m u u _/ #b or m u#b on the surface1 and the n _/ #c molecules moving in the same direction will exert a force n _/ #c m u#b on the unit surface4 ,this represents1 therefore1 the pressure of such a gas1 as calculated on the basis of the assumptions of the kinetic theory4 ,now1 when a gas is so strongly compressed1 that the bulk of the molecules is not negligible in comparison with the total volume of the gas1 the number of impacts on unit surface in unit time becomes sensibly greater than n _/ #c u _/ #b1 since the distance to be covered between successive blows on the surface will be sensibly less than #b cm41 in a cube of unit volume4 ,if we imagine1 for the sake of a rough illustration1 that one-third of the molecules in #a c4c4 are united into one spherical mass 7indicated by ,a in ,fig4 #g71 moving upwards and downwards1 it is obvious that the distance covered between two successive blows on a surface is not #b cm41 but that distance diminished by twice the diameter of the sphere4 ,for strongly compressed gases1 the total number of impacts on unit surface is therefore sensibly greater than n _/ #c u _/ #b1 and the pressure is proportionately greater4 ,according to van der ,waal's correction for this effect1 ,p n _/ #c m u#b _/ 7#a b71 where b represents the volume actually occupied by the molecules in #a c4c4 of the gas4#dc ,illustration3 ,,fig4 #g4 ,now1 for solute molecules1 the free space of movement1 as we may call it1 is1 similarly1 very considerably reduced by the presence p#jca of the solvent1 and the reduction of this free space1 as ,nernst has shown1 will have the same effect on the pressure produced against unit surface of the solvent by the bombardment of the solvent by the solute1 as the reduction of the free space has on the gas pressure when a gas is strongly compressed4 ,the resulting pressure on unit surface of the solution must thus be increased1 from the pressure ,pgas1 which would be exerted by the solute against the walls of a vessel1 if it were present as a gas of the same concentration1 at the same temperature1 to ,pgas _/ 7#a v71 where v represents the real volume occupied by the solvent and 7#a v7 the free space for the solute molecules in unit volume of solution4#dd ,if osmotic pressure is the result of such a bombardment of the solvent by the molecules of the solute1 one might1 therefore1 expect to find the osmotic pressure very much greater than the gas pressure of the same substance in the same volume at the same temperature4 ,however1 in all the experimental determinations 7by means of semipermeable membrane1 vapor pressure1 boiling-point and freezing-point measurements7 of the osmotic pressure as defined on p4 #aj1 this corrective factor cancels out again4#de ,according to the kinetic theory1 the osmotic pressure of a substance in dilute solution should1 consequently1 be found by experiment to be equal to the gas pressure which a gas1 of the same molecular concentration1 would exert at the same temperature4#df ,we find thus that the significant coincidence between the osmotic pressure of a substance in dilute solution1 as defined and measured according to van 't ,hoff1 and the gas pressure which the substance would exert1 if it were present as a gas in the same volume and at the same temperature1 is in agreement with the fundamental assumptions of the kinetic theory4 ,this theory1 consequently1 gives us an adequate theoretical explanation of p#jcb osmotic pressure1 as it does of gas pressure4 ,as van 't ,hoff says1#dg if the osmotic pressure follows ,gay-,lussac's law and is proportional to the absolute temperature1 then1 like gas pressure1 it will become zero at #j absolute temperature and will vanish when molecular movements come to rest4 ,it is therefore natural to look for the cause of osmotic pressure in kinetic phenomena and not in attractions4#dh ,,footnotes3 #bi ,l',hermite1 ,compt4 rend41 #ci1 #aagg 7#ahed72 van 't ,hoff1 ,lectures on ,physical ,chemistry1 ,part ,,ii1 p4 #cg4 #cj ,nernst1 ,theoretical ,chemistry1 p4 #ajc4 #ca ,van 't ,hoff1 ,lectures on ,physical ,chemistry1 ,part ,,ii1 p4 #cg4 #cb ,j4 ,phys4 ,chem41 #aj1 #ada 7#aijf74 #cc ,this term must not be confounded with the term osmotic pressure1 which has been defined on p4 #aj4 #cd ,see ,chapter ,,vii on the law of physical or heterogeneous equilibrium1 where the relations are discussed in detail4 #ce ,z4 phys4 ,chem41 #e1 #age 7#ahij74 #cf ,ibid41 #c1 #aai 7#ahhi74 #cg ,phil4 ,mag41 #ch1 #bjf 7#ahid74 #ch ,cf4 van 't ,hoff's ,lectures on ,physical ,chemistry1 ,vol4 ,,ii1 #dj 7#ahii74 #ci ,the molecules may have different masses in the different conditions1 and the principle of the mean kinetic energy would always apply to them as they are1 in the condition under observation1 and not as they are in some other condition2 any change in mass1 in solution1 for instance1 would show itself in the osmotic pressure measurements 7see p4 #ah71 just as it is shown in the measurements of gases1 when the gas molecules show a change in composition1 as is the case with hydrogen fluoride 7,h#b;,f#b #b ,,hf71 nitrogen tetroxide 7,n#b,o#d #b ,,no#b71 phosphorus pentachloride 7,p,cl#e ,p,cl#c ,cl#b7 and other compounds4 #dj ,the molecular weight of alcohol in dilute aqueous solution is the same 7#df7 as in vapor form4 ,raoult1 ,z4 phys4 ,chem41 #bg1 #fef2 ,loomis1 ibid41 #cb1 #eib4 #da ,nernst1 ,theoretical ,chemistry1 p4 #bde4 #db ,this assumption is not made in the rigorous development of the above relations on the basis of the kinetic theory1 but it leads to the same net result4 #dc ,even for gases of ordinary concentration1 the introduction of the same correction gives an expression for the relation of pressure and volume1 which is more exact than ,boyle's law and is used in all exact calculations with gases4 #dd ,one may imagine1 first1 n molecules of the solute as a gas1 with the pressure ,pgas1 in #a c4c4 ,then1 one may imagine1 crudely1 the n molecules of solute1 in a free 7gas7 space of 7#a v7 c4c41 in the center of #a c4c4 of the solvent1 and exerting by their impacts a pressure ,posm41 against the solvent4 ,according to ,boyle's law1 we should then have1 ,pgas #a ,posm4 7#a v71 and therefore ,posm4 ,pgas _/ 7#a v74 #de ,vide ,nernst1 ,theoretical ,chemistry1 p4 #bde1 for the detailed discussion of this relation4 #df ,this conclusion is reached more rigorously and more simply by thermodynamic analysis4 #dg ,lectures on ,physical ,chemistry1 ,part ,,ii1 p4 #ce4 #dh ,rigorous developments of the relations between solute and solvent1 for dilute and concentrated solutions1 have been made by van der ,waals1 ,z4 phys4 ,chem41 #e1 #acc 7#ahij72 van ,laar1 ibid41 #ae1 #deg 7#ahid72 ,g4 ,n4 ,lewis1 ,j4 ,am4 ,chem4 ,soc41 #cj1 #fge 7#aijh71 and ,washburn1 ibid41 #cb1 #fec 7#aiaj74 ,an admirable review of the theories of osmotic pressure1 by ,lovelace1 will be found in the ,am4 ,chem4 ,j41 #ci1 #edf 7#aijh7 7,stud474 p#jcc ,,chapter ,,iv ,,the ,,theory ,,of ,,ionization2 ,,ionization ,,and ,,electrical ,,conductivity ,of the laws and hypotheses concerning gases1 the one that is perhaps of most importance to chemistry is ,avogadro's hypothesis4 ,with the aid of this hypothesis1 we are able to determine the relative molecular weights#di of such elements and compounds as are gases1 or are volatile at higher temperatures4 ,if equal volumes of gases1 under the same conditions of temperature and pressure1 contain the same number of molecules1 then the weights of such equal volumes also represent the relative weights of the molecules composing the gases4 ,as a standard1 for expressing the relative molecular weights in definite numbers1 the molecular weight of oxygen is taken by convention to be #cb1 and all other molecular weights are expressed in terms of this standard4 ,the density1 or weight of one liter of oxygen at #j and #gfj mm41 is #a4dbi grams1 and the molecular weight expressed in grams 7molar weight7 of oxygen1 #cb grams1 occupies1 therefore1 #cb _/ #a4dbi1 or #bb4d liters4 ,the weights of this same volume1 #bb4d liters1 of gases and vapors1 calculated for #j and #gfj mm4 pressure1#ej express then directly1 in terms of the oxygen standard1 the relative molecular weights of the elements or compounds forming the gases4 ,the weights themselves give us directly their gram-molecular or molar weights4 ,when molecular weights are determined in this way1 with the aid of ,avogadro's hypothesis1 results are obtained which agree p#jcd perfectly with the chemical behavior of the compounds or elements in question4 ,the molecular weights of hydrogen chloride1 water1 ammonia1 and marsh gas1 for instance1 are found to be #cf4e1 #ah1 #ag and #af1 respectively1 corresponding to the formul#ea ,h,cl1 ,h#b,o1 ,,nh#c and ,,ch#d1 and in confirmation of these results we find1 by methods used especially in organic chemistry1 that these compounds show a chemical behavior agreeing perfectly with the presence of one1 two1 three and four hydrogen atoms1 respectively1 in their molecules4 ,marsh gas1 for instance1 by treatment with chlorine1 yields a monochloride1 ,,ch#c;,cl1 a dichloride1 ,,ch#b;,cl#b1 a trichloride 7chloroform71 ,c,h,cl#c1 and a tetrachloride1 ,c,cl#d4 ,water1 by proper treatment1 may be converted in successive stages into alcohol1 7,c#b;,h#e7,,oh1 and then into ether1 7,c#b;,h#e7,o7,c#b;,h#e71 or into sodium hydroxide1 ,na,o,h1 and sodium oxide1 ,na#b,o4 ,it is this perfect agreement between the chemical behavior and the formul 7as based on these molecular weights and on the analysis of compounds71 which forms the strongest experimental evidence of the correctness of the fundamental assumption of ,avogadro's hypothesis4 ,the agreement has been shown to hold for innumerable compounds1 even for those of greatest complexity1 and it was such agreement which finally led to the general acceptance of the hypothesis4 ,the experimental evidence of this nature is so strong1 so extensive and so completely corroborative of the hypothesis1 that many chemists1 rather justly1 consider the hypothesis to have been established as a law1 although the evidence is circumstantial rather than direct4 ,while the application of ,avogadro's hypothesis thus gives results agreeing well with the observed chemical behavior of very many important compounds1 observations have been made which1 at first sight1 do not appear to agree with the requirements of the hypothesis and which seem to raise a doubt as to the universal truth of its fundamental assumption4 ,thus1 if equal volumes of hydrogen chloride and ammonia1 of the same temperature and pressure1 are brought together1 ammonium chloride is formed1 both gases being totally consumed4 ,since1 according to the hypothesis1 equal volumes1 under the conditions obtaining1 contain the same numbers of molecules1 the formation of ammonium chloride takes place according to the equation ,,nh#c ,h,cl ,,nh#d;,cl1 and we should anticipate that the molecular weight of p#jce ammonium chloride would be #ag #cf4e or #ec4e4 ,however1 when the molecular weight is determined by obtaining the weight of a measured volume of ammonium chloride vapor1 at a temperature sufficiently high to vaporize the salt1 and the observations are reduced to standard conditions of temperature and pressure1 #bf4ge grams is found as the calculated weight of #bb4d liters1 and this weight1 according to this hypothesis1 should be the molecular weight of the chloride4 ,this contradiction in two conclusions1 each reached by the application of ,avogadro's hypothesis to experimental observations1 would1 at the first glance1 make one hesitate to accept the hypothesis as representing a universal truth2 it might seem as if in some gases1 such as ammonium chloride vapor1 there might be only half as many molecules in a given volume as in the same volume of the majority of gases4 ,gaseous ,dissociation4--,the discrepancy between the two conclusions and any doubt as to the universal soundness of the great generalization expressed in ,avogadro's hypothesis disappear1 however1 in the light of a closer study of the composition of ammonium chloride vapor4 ,it was suggested simultaneously by ,cannizzaro1 by ,kopp and by ,kkul#eb that the abnormally low result1 obtained for the molecular weight of ammonium chloride from a study of its vapor density1 is due to the dissociation of the salt at high temperatures into its components1 ammonia and hydrogen chloride1 the average of whose molecular weights is1 in fact1 7#ag #cf4e7 _/ #b1 or #bf4ge1 the value found experimentally for the vapor of ammonium chloride4 ,proof of the correctness of this interpretation was furnished by ,pbal1#ec who showed that ammonium chloride vapor does consist of the two gases1 the lighter of which1 ammonia1 diffuses more rapidly through porous walls 7,pbal used an asbestos stopper7 than does the heavier1 hydrogen chloride4 ,the dissociation may be easily demonstrated by using an air cushion as a porous wall4#ed ,from the mixture produced by vaporizing ammonium chloride1#ee the ammonia will diffuse more rapidly through the layer of air than will the hydrogen p#jcf chloride1 and the gases may be recognized in succession by their action on litmus paper 7exp474 ,the gaseous dissociation of other ammonium salts1 of phosphorus pentachloride and pentabromide 7,,px#e ,,px#c ,x#b71 and of a number of less common compounds1 has been demonstrated in similar ways4 ,as a result of the study of each case1 the important conclusion has been reached that1 as far as our knowledge goes1 there are no exceptions to ,avogadro's hypothesis1 and this hypothesis seems therefore to represent a universal truth4#ef ,molecular ,weight ,determinations in ,solution4--,van 't ,hoff's extension of the ,avogadro ,hypothesis1 so that it shall apply to solutes in dilute solutions1 is the basis of another general method of greatest value for determining molecular weights4 ,equal volumes of dilute solutions of the same osmotic pressure and the same temperature contain1 according to van 't ,hoff1 the same numbers of dissolved molecules1 irrespective of the solvent used4 ,furthermore1 the number of dissolved molecules is identical with that which a gas of the same pressure and at the same temperature would contain in the same volume4 ,to determine the molecular weight of a solute1 therefore1 we may calculate1 from the osmotic pressure1 the temperature and the concentration of the solution1#eg that weight of the solute which1 in #bb4d liters of the solution1 at #j would give #gfj mm4 osmotic pressure2 the weight found represents1 in grams1 the molecular weight of the solute in the solution used4 p#jcg ,the fact that all solvents and all solutes are included in this hypothesis1 with the sole limiting condition that the solution must be dilute1 is one of great significance and of greatest practical importance1 as we may use any suitable solvent for determinations4 ,when molecular weights are determined in this way1 a very large number of compounds give the same molecular weight by the solution method as by the gas method4 ,for instance we have3 ,substance4 ,mol4 ,wt4 ,mol4 ,wt4 ,solvent4 ,gas ,method4 ,sol4 ,method4 ,chloroform1 ,c,h,cl#c #aai4e #aai4e ,benzene ,carbon bisulphide1 ,,cs#b #gf #gf ,benzene ,methyl 7wood7 alcohol1 ,,ch#d,o #cb #cb ,water ,ethyl 7ordinary7 alcohol1 ,c#b;,h#f,o #df #df ,water ,ether1 ,c#d;,h#aj,o #gd #gd ,acet4 ,acid ,further1 the molecular weight of glucose is found in aqueous solutions to be #ahj1 conforming to the formula ,c#f;,h#ab,o#f1 and agreeing with the molecular weight as obtained by a chemical study of compounds derived from glucose4 ,while there are1 then1 very many agreements in the molecular weights determined by the solution and by the older methods1 it was recognized1 at the outset1#eh that there is also a large number of apparently abnormal cases1 in which1 in particular1 much lower molecular weights are obtained by the solution methods than by the gas method1--lower even than the weights consistent with the accepted atomic weights of the elements in the compounds in question4#ei ,for instance1 we find #cf4e to be the molecular weight of hydrogen chloride in the gas form1 but in aqueous solution its apparent molecular weight1 as determined on the basis of van 't ,hoff's hypothesis1 is not even a constant2 it is found to be less than #cf4e and approaches the limit #ah4be1 the more dilute the solution1 p#jch the lower being the apparent molecular weight4#fj ,for sodium chloride1 the formula weight1 corresponding to the formula ,na,cl1 is #eh4e4 ,this would also represent its smallest molecular weight in gas form1 consistent with the accepted atomic weights for sodium and chlorine4 ,in aqueous solution1 again1 the apparent molecular weight of sodium chloride is found to be less than #eh4e1 and more than #bi4be1 the value found depending on the concentration of the solution used4 ,for zinc chloride we have1 likewise1 in aqueous solution values much less than #acf and tending toward the limit #de1 whereas the formula weight for ,zn,cl#b is #acf4 ,these are instances of a very large class of apparent gross discrepancies between the requirements of the ,avogadro-van 't ,hoff principle and the generally accepted molecular weights of common compounds4 ,there are three ways1 in particular1 in which one might be inclined to regard such results3 in the first place1 one might be tempted to consider that van 't ,hoff's extension of ,avogadro's hypothesis to solutions is justified in a considerable number of cases1 but not as a universal expression1 applicable to all dilute solutions4 ,this seems1 indeed1 to have been van 't ,hoff's own attitude originally4 ,such a view1 since it does not throw new light on the matter1 but simply shelves the question of the source of the discrepancy1 would be tenable only after all other explanations had been found unsatisfactory4 ,in the second place1 we might be inclined to consider whether a molecule like hydrogen chloride is not dissociated in aqueous solution into two smaller molecules1 hcl1 in which hydrogen and chlorine would appear as atoms with the weights h #j4e and cl #ag4ge1 which are half as large as the atomic weights determined from a study of volatile compounds of hydrogen and chlorine4 ,if we remember that our atomic weights are confessedly maximum weights1 and not minimum weights--although they are almost certainly also the true atomic weights--such a view would be1 at least1 worthy of some consideration4 ,but1 in the first place1 it would be extraordinary that we should never have found1 in the thousands of p#jci hydrogen derivatives that have been investigated1 any compound1 the molecule of which1 in the gaseous condition1 contained a single such atom of hydrogen1 with the weight #j4e1 or an uneven multiple of it3 that only even multiples or pairs h#b1 corresponding to the atom ,h1 should always have been found4 ,in the second place1 such an explanation of the results of the molecular weight determinations in aqueous solutions given above1 would soon lead to difficulties1 which make the view altogether untenable4 ,for instance1 the molecule of zinc chloride1 according to the data given1 would have to break down into three molecules and1 if these were of uniform composition1 we would have to assume chlorine atoms two-thirds or one-third as large as ,cl4 ,since a moment ago we had to assume chlorine atoms one-half as large as ,cl1 we would have to conclude that the atomic weight of chlorine could be1 at most1 ,cl _/ #f1 which is the largest common divisor of ,cl _/ #b and ,cl _/ #c4 ,no chemist would seriously consider an atomic weight for chlorine one-sixth as large as the accepted weight1 for that would mean that1 in all the chlorine compounds investigated in the condition of gases1 we have always at least six such atoms occurring together1 and otherwise always multiples of six4 ,consequently such an interpretation of the so-called abnormal behavior of solutions of hydrogen chloride1 sodium and zinc chlorides1 etc41 although at one time advanced by some chemists1 must be considered as altogether untenable4 ,a third explanation of the abnormally low molecular weights1 which certain substances in aqueous solutions possess1 is1 that the molecules of these compounds are capable of dissociation into smaller molecules of unlike composition1 somewhat like ammonium chloride when it is heated1 and that the substances in question are dissociated more or less considerably in this fashion in the solutions under consideration4 ,hydrogen chloride1 for instance1 besides existing as such 7as ,h,cl71 in aqueous solutions1 might be capable of dissociating1 and actually be dissociated1 to a considerable degree into molecules containing either only hydrogen or only chlorine 7,h,cl ,h ,cl72 the average of the weights of the molecules in a mixture of molecules1 ,h,cl1 ,h1 and ,cl1 would be less than #cf4e1 and1 according to the proportion of dissociated and undissociated molecules of hydrogen chloride1 the average would lie between the limits #cf4e and 7#a #ce4e7 _/ #b1 or #ah4be4 ,such an p#jdj explanation1#fa made with certain additions and restrictions1 was advanced in #ahhe by ,arrhenius1 a ,swedish chemist and physicist1 when he learned of the exceptional behavior of these solutions1 as noted by van 't ,hoff4 ,although at first this interpretation occasioned considerable criticism1 it has maintained itself successfully for twenty years1 on the basis of a wide range of accumulated facts1 and it has been of remarkable value and benefit in the development of all branches of chemistry and the allied sciences4 ,the ,theory of ,ionization4--,arrhenius#b made the simple observation that all those solutions1 in which the dissolved compounds seem to have abnormally low molecular weights1 are solutions through which an electric current may be readily passed1 they are electrolytes1 whereas the solutions which give normal results 7see1 for instance1 the table on p4 #cg7 do not allow the ready passage of a current1 they are nonelectrolytes4 ,,exp4 ,the fundamental difference between the two classes of solutions may readily be demonstrated4 ,to water contained in an electrolytic cell1 which is connected with a lighting circuit and with an electric lamp1 first some alcohol1 and later a small quantity of hydrochloric acid are added4 ,the lamp is seen to glow1 instantly1 when the acid is added4 ,this simple fact1 that the very solutions which give abnormally low molecular weights for the dissolved compounds are also good conductors of electricity1 was explained by a theory of electrolytic dissociation or of ionization1 which ,arrhenius had developed#fb from a study of the conductivity of electrolytes4 ,the same fact has aided in establishing this theory which has led to the elucidation of vital problems of electrical conductivity and to a successful p#jda explanation of the problem of the apparently abnormal osmotic pressures 7and molecular weights7 of electrolyte solutes4 ,it has thus removed the last difficulty in the way of accepting the van 't ,hoff-,avogadro ,hypothesis 7p4 #ae7 as true for all dilute solutions1 exactly as the discovery of gaseous dissociation made it possible to recognize in the original ,avogadro ,hypothesis a universal truth 7p4 #cf7 about gases4 ,and to these results was added1 chiefly as the fruit of the work of ,ostwald1 with the aid of the theory of ,arrhenius1 the most successful and accurate formulation of the problem of the chemical activity of electrolytes1 known in the history of chemistry4 ,main ,assumptions of ,arrhenius's ,theory of ,ionization4--,the main assumptions of the theory of electrolytic dissociation or ionization are the following3 7#a7 ,when an ionogen is dissolved in water1 its molecules are immediately1 more or less completely1 dissociated by the water into smaller fragments or molecules of unlike composition4 7#b7 ,these new molecules are charged with electricity2 the molecules of the one product are charged with positive1 the molecules of the other product#fc with negative electricity1 the unit positive charge being equal in quantity1 but opposite in kind1 to the unit negative charge2 the sum of all the positive charges in a solution is equal to the sum of all the negative charges1 and the whole solution is electrically neutral4 7#c7 ,the dissociation is a reversible reaction1 and all electrolytes must be considered to be completely ionized at infinite dilution4 7#d7 ,except for the dependence resulting from the electrical charges and the consequent attractions and repulsions between ions1 the ions must be considered independent molecules with their own specific chemical and physical properties4 ,when a current is passed through the solution of an ionogen1 the electrified particles carry their charges to the electrodes 7see p#jdb below74 ,they are called the ions#fd of the electrolyte2 the positively charged ions are distinguished as cations from the negatively charged anions1 and the electrode toward which the cations move is called the cathode 7negative electrode71 and the electrode to which the anions move is called the anode 7positive electrode74 ,the dissociation of hydrogen chloride may be expressed1 in the terms of the assumptions made1 in the following equation3 ,h,cl ,h ,cl2 that is1 hydrogen chloride is dissociated1 to a greater or smaller extent and in reversible fashion1 into positively charged hydrogen ions ,h1 and negatively charged chloride ions ,cl1 and the charge on each chloride ion is equal in quantity to the positive charge on each hydrogen ion4 ,zinc chloride is dissociated according to the equation ,zn,cl#b ,zn#b #b ,cl1 and1 according to 7#b71 the charge on each zinc ion is twice as great in quantity as the charge on each chloride ion1 and therefore twice as great also as the charge on each hydrogen ion 7see below1 p4 #eh74 ,it is practically certain1 according to more recent results1 that the ions are combined with water to form hydrates1 such as ,h7,h#b,o7x and ,cl7,h#b,o7y4#fe ,this does not modify1 essentially1 the fundamental assumptions of the theory1 but contributes rather to a satisfactory explanation of the rle of water as an ionizing agent1 a question to which we shall return later4 ,the ,theory of ,ionization and the ,electron ,theory of ,electricity and of ,matter4#ff--;,according to the views held by many leading physicists at the present time1 negative electricity consists of ultimate particles of matter called electrons or corpuscles4 ,the mass of an electron is about #a _/ #ajjj the mass of an atom of hydrogen1 and the electric charge of the electron is equal to that carried by a chloride ion in solution4#fg ,the atoms of the elements are considered to consist of aggregations of large numbers of electrons in a kind of shell or body of positive electricity4 ,this positive electricity1 in a given atom1 is equal in quantity to the total negative charge of the electrons in the atom1 the atoms as such p#jdc containing no excess of either positive or negative electricity4 ,the number of electrons in the atom of an element is considered to be definite and constant for that element1 but the number varies as we go from the atoms of one element to those of a second element1 the number increasing with the atomic weight of the element4 ,one of the most fundamental and most characteristic properties of elements is considered to be the affinity which their atoms show for electrons2 thus1 the atoms of metals like sodium and potassium1 which are generally called electropositive elements1#fh show an enormous tendency to lose one electron each and to form positively charged particles#fi ,na- 7 ,na7 and ,k- 7 ,k74#gj ,the atoms of strongly electronegative elements1 like chlorine1 have a tremendous tendency for gaining and holding electrons beyond the number originally in such atoms4 ,thus1 chlorine atoms tend to assume an electron each2 they thereby become negatively charged particles1 ,cl 7 ,cl74 ,on the basis of these views1 we have in sodium chloride ,na,cl a substance1 whose molecules contain an atom1 ,na1 with a tremendous tendency to lose an electron1 and an atom1 ,cl1 which has a tremendous affinity for an electron4 ,it is natural to suppose1 then1 that both tendencies will be satisfied by the passage of an electron from the sodium to the chlorine atom1 ,na,cl ,na-,cl4 ,or1 if we use the sign to designate the positive charge produced on an atom by the loss of an electron and the sign to indicate the charge gained through the assumption of an electron1 we have#ga3 ,na,cl is ,na,cl4 ,similarly we have in hydrogen chloride ,h-,cl or ,h,cl4 ,it is altogether likely1 therefore1 that the atoms in a molecule of sodium chloride or of hydrogen chloride already possess electric charges1#gb so that1 even while combined1 p#jdd their tendencies to lose or gain electrons are satisfied4 ,it is also possible that the atoms are held together in the molecule by the electrical attraction of the opposite charges4#gc ,the force with which opposite electrical charges attract each other depends1 as is well known1 on the nature of the surrounding medium4 ,now1 when molecular sodium chloride or hydrogen chloride is dissolved in water 7a favorable medium71 a decided decrease in the attraction 7see p4 #fb71 between the charged atoms within the molecules is brought about1 and a process of ionization results3 ,h,cl ,h ,cl4 ,the charged particles are called ions only after they have separated from one another and have become independent molecules1 capable1 for example1 of moving in opposite directions4 ,while the atoms of some metallic elements tend to lose a single electron and form ions ,me 7e4g4 ,na1 ,k71 the atoms of other elements tend to lose two or more electrons1 forming bivalent ions1 ,me#b 7e4g4 ,zn#b1 ,fe#b1 etc471 or trivalent ions1 ,me#c 7e4g4 ,bi#c1 ,fe#c71 and so forth4 ,similarly1 atoms of the so-called negative elements may assume two or more electrons1 forming bivalent ions1 ,x#b 7e4g4 ,s#b71 and so forth4 ,the ,validity of the ,theory of ,ionization4--,in determining the validity of the theory of ionization1 we may consider1 first1 the sufficiency of the explanations which it offers for observed facts and important phenomena4 ,we may then weigh1 more critically1 by any evidence offering itself1 the facts which will enable us to decide between this theory and the older theory of ionization1 that of ,clausius 7p4 #ea74 ,the latter1 although displaced1 is still often revived by opponents of the modern theory4 ,such facts as we will consider are found1 first1 in the domain of conductivity phenomena1 next1 in the osmotic pressure and related properties of solutions1 and1 finally1 in the study of the chemical activity of electrolytes 7see ,chapter ,v74 ,ionization and ,electrical ,conductivity4--,turning our attention first to the field of electrical phenomena1 and developing the theory for the present descriptively1 we find that the conductivity of a solution depends1 according to this theory1 on the fact that when two oppositely charged poles are placed in a solution1 the p#jde positive charge on the anode attracts all the negative particles within its field of action1 and repels all the positive particles1 exactly as a positive static charge of electricity would attract a negatively charged pith-ball and repel a positively charged one4 ,in the case of a solution of hydrochloric acid1 the negative charge on the cathode would attract the hydrogen ions and repel the chloride ions1 and the positive charge of the anode would attract the chloride ions and repel the hydrogen ions4 ,the net result would be a migration of all the chloride ions with their negative charges toward the anode1 and of the positively charged hydrogen ions toward the cathode1--a flow or current of electricity being thus produced4 ,the fact1 then1 that a current of electricity does readily pass through such a solution of an ionogen1 is easily understood on the basis of these views4 ,illustration3 ,,fig4 #h4 ,,exp4 ,the migration of the ions throughout the whole solution may be demonstrated by the passage of a current through a large ,u-tube containing a mixture of a cupric salt and a permanganate1#gd placed under some dilute sulphuric acid4 ,the cupric-ion is blue1 all ionized solutions of cupric salts1 with a colorless negative ion1 being blue1 while the permanganate-ion is of an intense purple color4 ,in the limb of the ,u-tube1 in which the cathode is placed1 a blue zone1 containing cupric ions1 is soon seen emerging from the purple liquid and rising toward the cathode 7see ,fig4 #h74 ,it will take some time for any cupric ions actually to reach the electrode and be deposited as metallic copper4 ,on the anode side1 purple permanganate ions are seen rising toward the positive electrode4 ,the movement of the electrically charged particles in opposite directions through the solution constitutes an electric current1 and such a current has the properties of a current through a p#jdf wire--producing1 for instance1 heat1 or being capable of deflecting a magnet placed in its field of action4#ge ,electrolysis4--,when ions touch an electrode1 they are discharged1 and with the discharge1 are changed chemically1 and1 according to the electron theory1 also materially4 ,cupric ions1 ,cu#b or ,cu#b 1 receiving two electrons at the cathode1 are precipitated as metallic copper4 ,when a current is passed through a solution of hydrochloric acid1 the hydrogen ions1 by the pairing of the discharged ions1 yield hydrogen gas consisting of molecules1 ,h#b2 the chloride ions are converted at the anode into chlorine ,cl#b4 ,the formation of these molecules1 ,x#b1 may be variously interpreted1 as resulting either from the union of two discharged or neutral atoms1 or as consisting1 for instance in the case of hydrogen1 in the discharge of a hydrogen ion ,h1 at the negative electrode1 followed by the assumption of a negative charge or electron by the neutral atom1 the new ion ,h combining at once with the positive ion ,h to form the molecule ,h,h4 ,at the positive pole1 by an analogous recharging of a discharged negative chloride-ion ,cl1 we should obtain a positive ion1#gf ,cl1 and immediately the formation of ,cl#b or ,cl,cl would follow4 ,helmholtz advocated the latter conception of the action at the electrodes1 and1 more recently1 ,j4 ,j4 ,thomson#gg brings forward1 as a very important argument in favor of it1 the fact that iodine1 which according to vapor density determinations dissociates into monatomic molecules at high temperatures 7,i#b #b ,i71 becomes1 simultaneously with this dissociation1 also an excellent gaseous conductor of electricity1 as would be anticipated from a dissociation1 ,i,i ,i ,i4 ,this fact is emphasized here1 because in it we seem to have a case of conductivity coinciding with gaseous dissociation1 the existence of which is recognized by the universally accepted laws of gases1 and differing in no important respect from the dissociation assumed for conductors in solution4 ,conductivity and ,dilution4--,the passage of a current through an electrolyte consists1 then1 in a transfer of electricity by material particles1 the ions4 ,according to the theory of ionization only p#jdg the ionized portion of an electrolyte can carry the current at any moment1 and1 consequently1 a given weight of an ionogen should1 under comparable conditions1 be the more efficient as a conductor1 the more completely it is dissociated into ions4 ,if the conductivity of a given weight of hydrogen chloride1 for instance1 is measured under comparable conditions1 it should be found to be greater1 the more completely the acid is ionized4 ,now1 in aqueous solutions1 hydrogen chloride ionizes under the influence of the solvent water 7pp4 #da1 #fa71 and the theory would lead us to anticipate that the greater the proportion of water used1 the more extensively will it ionize the acid4 ,consequently1 the addition of water to a given weight of acid should increase the latter's efficiency as a conductor4 ,this conclusion has been fully verified by exact methods of measurement and may be readily demonstrated by the following series of experiments3 ,,exp4#gh ,an electrolytic cell1 having the shape of a parallelopipedon and a capacity of about one liter1 is fitted with electrodes of copper1 which reach from the bottom to the top of the cell and are connected with a storage cell and an ammeter4 ,the cell is first filled with distilled water3 no perceptible current passes through the water and the latter is therefore practically a nonconductor4 ,the cell is then emptied by means of a siphon and #bj c4c4 of #d-molar hydrochloric acid is brought into it4 ,the ammeter shows that a definite current passes through the solution 7#j4ag ampere in an experiment#gi with a cell #d4f cm4 wide and #aa4e cm4 long1 with copper electrodes #d4f cm4 broad and #ba cm4 high74 7,see ,fig4 #i1 p4 #dh47 p#jdh ,illustration3 ,,fig4 #i4 ,the conductivity of a solution1 like that of a metal conductor1 is the reciprocal of its resistance4 ,since1 according to ,ohm's law1#hj the current for a given potential is inversely proportional to the resistance1 the current is also directly proportional to the conductivity4 ,the resistances of the metal connections and of the ammeter in the experiment are very small compared with the resistance of the solution1 and they may be considered negligible for our purpose4 ,thus1 the current indicated by the ammeter is a closely approximate measure of the conductivity of the solution4 ,now1 if a volume of water 7#bj c4c47 equal to the volume of acid1 were to be added to the latter1 the cross section through which the current flows from plate to plate would be doubled1 and1 since the conductivity of a liquid conductor1 like that of a metal1 increases proportionally to the cross section1 the current should be doubled by the change in this one factor4 ,on the other hand1 the concentration of the conducting acid is now one-half of the original concentration1 and this should in turn reduce the conductivity of the solution to one-half4 ,consequently1 if there were no further change in the electrolyte1 the original conductivity should be maintained when the acid is thus diluted4 ,but1 according to the theory of ionization1 as has just been shown1 the addition of p#jdi water to a given weight of hydrochloric acid should increase the proportion of ionized acid1 and since the ions are the carriers of the current1 the conductivity of the solution should be increased because of this change in the composition of the electrolyte4 ,experiment shows that such is the case4 ,,exp4 #bj c4c4 of water is added to the #bj c4c4 of #d-molar acid in the cell1 and the mixture is stirred4 ,the current is decidedly increased 7from #j4ag to #j4bb ampere in the experiment under discussion74 ,if #dj1 #hj1 #afj and #cbj c4c4 of water are added in succession to the contents of the cell1 the conductivity is increased by every addition of water4 ,but1 while each addition dilutes the acid to one-half the previous concentration1 the increase grows proportionally smaller and smaller with increasing dilution4 ,in the following table1 ,ratios ,i are the ratios of the observed conductivities to the original conductivity1 ,ratios ,,ii the ratio of each observed conductivity to the preceding one4 ,concentration ,observed ,ratios ,i4 ,ratios ,,ii4 of ,acid4 ,conductivity4,a #d-molar #j4ag #a #a4 #b-molar #j4bb #a4cj #a4cj #a-molar #j4bf #a4ec #a4ah #j4e-molar #j4cj #a4gf #a4ae #j4be-molar #j4ca #a4hc #a4jd #j4abe-molar #j4cb #a4hh;,b #a4jc ,,table ,,notes3 ,a4 ,this is an artificial scale 7see text7 of conductivities1 and does not represent reciprocal ohms1 the standard units of conductivity4 ,b4 ,in the exact data on the conductivities of #d-molar and #a_/h-molar ,h,cl 7,kohlrausch and ,holborn1 ,leitvermgen der ,elektrolyte 7#ahih7 p4 #afj71 the ratio #cdh _/ #aha4e1 or #a4ib1 is found1 in place of #a4hh as observed4 ,we should expect1 further1 that the increase in conductivity1 being dependent on the increased dissociation of a finite quantity of electrolyte1 should tend towards a limit1 a maximum conductivity being reached when 7practically7 all the acid is ionized4 ,as a matter of experience1 the conductivity of a given quantity of an acid or other ionogen does tend toward a limit4 ,in the experiment just made1 the conductivity of the acid increases very rapidly at first1 as the #d-molar acid is diluted by water2 but the increase in conductivity with the succeeding dilutions grows smaller and smaller and the conductivity is plainly approaching p#jej a limit 7see the ratios ,i and ,,ii in the table74 ,for hydrochloric acid at #ah1 the limit for one mole#ha 7#cf4e grams ,h,cl7 at infinite dilution1 as deduced from the curve of conductivities at finite dilutions1 is #chd reciprocal ohms4#hb ,degree of ,ionization of an ,electrolyte4--,the conductivity of a given weight of an electrolyte1 for instance of its gram-equivalent weight1 depends1 then1 at a given temperature on the extent to which it is ionized1 the ions being the only carriers of the current in a solution of an electrolyte4 ,the conductivity will also depend on the friction which the ions must overcome in moving through a solution1 but1 for sufficiently dilute solutions in a given solvent1 the friction may be assumed to be approximately constant for given ions4 ,for such solutions1 then1 the conductivity of a given weight of a given electrolyte at a given temperature may be said to depend wholly on the extent to which the electrolyte is ionized4 ,thus1 the proportion of ionized electrolyte in a solution may be determined by measuring the conductivity4 ,the extreme limit of its conductivity1 calculated for infinite dilution1 represents complete ionization of the electrolyte according to a fundamental postulate 7 #c1 p4 #da7 of the theory of ,arrhenius1 and the ratio of the conductivity in a given solution to the conductivity of the same weight of electrolyte at infinite dilution represents then the proportion of ionized electrolyte to the total electrolyte used4 ,this proportion is called its degree of ionization 7commonly designated by 74 ,if we call v the conductivity of a gram-equivalent weight of an electrolyte in a given solution1 and the limit of its conductivity for infinite dilution1 then the degree of ionization is found from v _/ 4 p#jea ,the method of calculation of in a specific case may be illustrated as follows3 the resistance of a cube of #a cm4 edge of a solution of hydrochloric acid1 which contains #a4hbe grams hydrogen chloride in a liter1 is found to be #ee4ee ohms at #ah4 ,its conductivity then is #a _/ #ee4ee reciprocal ohms4 ,now1 #a4hbe grams of hydrogen chloride is #a4hbe _/ #cf4e or #a _/ #bj gram-equivalent of the acid2 a whole gram-equivalent of the acid would be contained in #bj liters or #bj1jjj c4c4 ,then v 7#a _/ #ee4ee7 #bj1jjj1 or #cfj reciprocal ohms4 ,if we use the value at infinite dilution given above1 #cfj _/ #chd1 or #ic4ge4 ,that is1 #ic4ge of the hydrochloric acid is present in the ionized condition in such a solution1 and #f4be is not ionized4 ,by making the assumption that at infinite dilution electrolytes are completely ionized1 and by taking the ratio which the equivalent conductivity of a given solution of an electrolyte bears to the maximum limit-value 7calculated for the conductivity at infinite dilution7 to be the degree of ionization of the electrolyte1 as just explained1 the theory of ,arrhenius has thus made it appear possible to determine experimentally the proportion of ionized electrolyte present4 ,it is a significant fact that the equivalent conductivity of hydrochloric acid is close to its limit even at finite dilutions1 and that the same relation holds for the strong acids and the strong bases1 in general1 and for most salts4 ,but the equivalent conductivity of weak acids1 like acetic acid1 and of weak bases1 like ammonium hydroxide1 in finite dilutions is still far removed from the limits which may be calculated for infinite dilutions4 ,arrhenius was led then to the further important conclusion that1 in the case of the first electrolytes mentioned1 a very large proportion of the electrolyte must exist in the ionized form at finite concentrations1 their equivalent conductivities having almost reached the limit characteristic of infinite dilution4 ,clausius's ,theory of ,ionization and the ,modern ,theory4--,it is in these conclusions--in particular that the proportion of ionized electrolyte may be determined experimentally1 and that frequently a large proportion is found to be ionized at finite concentrations1--that the modern theory of ionization differs from the older theory of ,clausius4 ,the former is an elaboration of the latter1 and some opponents#hc of the modern theory still uphold the latter as offering an adequate explanation of the phenomena of conductivity4 ,all facts1 then1 in particular1 which confirm the validity of the conception of the degree of ionization1 as introduced by ,arrhenius1 p#jeb must be considered as criteria favoring his theory1 specifically4 ,the development of chemistry in the last twenty years is replete with such evidence and we shall meet it in many connections throughout our work4 ,clausius#hd also assumed dissociated molecules or ions to be the real carriers of electricity in the passage of a current through the solution of an electrolyte1 but he assumed only a minute quantity of these molecular fragments or ions to be free at any moment1 their existence being supposed to be transitory and dependent in particular on exchanges of atoms between molecules4 ,as a result of the oscillations of the atoms composing a molecule1 oscillations comparable with the motions of molecules assumed in the kinetic theory of gases1 molecules were considered by ,clausius occasionally to reach such a condition of instability1 that they dissociated into smaller particles2 since the atoms were supposed to be held in a molecule by attractions of electrical charges on the atoms 7theory of ,berzelius71 the fragments of the molecule would carry the charges1 positive and negative respectively1 which they possessed in the molecule4 ,such a breaking up or dissociation of molecules was1 further1 supposed to occur with particular ease during the collisions of molecules1 the electrical attractions and repulsions of the charged atoms favoring1 at such moments1 an exchange of atoms4 ,during the exchange1 the atoms were considered to be free molecules1 charged with electricity--essentially ions1--capable of moving under the influence of electrical forces and of thus carrying a current4 ,finally1 such ions were supposed1 in part1 to escape recombination1 and to remain free1 until each ion either collided and combined with an ion of opposite charge1 or collided with a molecule and displaced an atom of the same charge from that molecule1 a new ion being thus liberated4 ,the theory1 as usually interpreted1 assumed the existence of only a very small quantity of such free ions1 that being all that was supposed to be required to explain the facts known at the time it was advanced4 ,in what follows1 we shall confine the discussion strictly to such contrasts between the two theories as grow out of a consideration of the phenomena of conductivity1 and particularly consider some evidence which is directly concerned with the conductivity of solutions4 ,in the first place1 if the formation of ions occurs primarily during the exchange of atoms in collisions of molecules1 then1 as ,whetham#he has shown1 the specific conductivity 7of #a cm4#c7 of an electrolyte1 like hydrochloric acid1 must increase with the concentration and must increase1 approximately1 as a function of the third power of the concentration4 ,the more concentrated the solution1 the more frequent the collisions between the dissolved molecules must be4 ,as a matter of fact1 as shown in the following table1 the conductivity p#jec increases a little less than proportionally to the first power of the concentration--which is in conflict with the assumption made in the hypothesis of ,clausius1 but in perfect agreement with the hypothesis of ,arrhenius4 ,the small decrease with increasing concentration1 in the simple ratio between conductivity and concentration1 is due to the decreasing degree of ionization in the more concentrated solutions1 as demanded by the hypothesis of ,arrhenius4 ,the table gives1 in the first column1 the specific conductivities of hydrochloric acid at #ah1 and1 in the second column1 the concentrations2 these concentrations are expressed in moles or gram-equivalents per cubic centimeter2 the last column gives the ratio of conductivity to concentration4 ,conductivity ,conductivity of #a c4c4 ,concentration ,concentration4 #j4jjcgj #j4jjjja #cgj #j4jjgcd #j4jjjjb #cfg #j4jajib #j4jjjje #cfd #j4jahjj #j4jjjje #cfj #j4jceaj #j4jjjaj #cea ,furthermore1 facts admitted by ,clausius to be inexplicable by his own assumptions receive1 in the theory of ,arrhenius1 at least a quantitative formulation borne out by a mass of corroborative evidence4 ,the difference in conductivity between pure water and sulphuric acid is such a fact1 mentioned by ,clausius4 ,determinations of the ionization of sulphuric acid and of water1 by the conductivity methods which are based on the theory of ,arrhenius1 show that1 while sulphuric acid is very considerably ionized 7see p4 #ajd71 water is scarcely ionized at all4 ,the ionization of water 7see p4 #ajd7 has been determined quantitatively by at least four independent methods of examination1#hf and1 minimal as the ionization is1 the results agree so well with each other that van 't ,hoff#hg was led to write3 ,if one is not previously convinced of the correctness of the theory of electrolytic dissociation1 hardly any result won by means of it is so convincing1 as the agreement between the conclusions reached in completely different ways as to the degree of dissociation of water itself4 ,after such an agreement1 it is hardly conceivable that the basis on which all these results rest should further be altered4 ,mobilities or ,partial ,conductivities of ,ions3 ,principle of ,kohlrausch4--,if ions have a separate existence1 each kind of ion would be expected to move through a solution under a given electrical force at a given temperature with its own specific speed1 the speed being presumably dependent on the nature of the ion as well as on the weight of water combined with it and dragged with it through the solution 7p4 #db74 p#jed ,such relative speeds of ions may be demonstrated by means of an experiment3 the motion of the hydrogen ions1 formed by the ionization of hydrochloric and other acids1 may be observed by their action on a reddened 7alkaline7 solution of phenolphthalen1 which is decolorized by them2 and the motion of the hydroxide ions1 formed by the ionization of sodium hydroxide and other bases1 may be followed by their action on colorless phenolphthalen1 which turns red in their presence4 ,the hydrogen and the hydroxide ions are the fastest1 in aqueous solutions1 and their speeds are compared in the next experiment with that of blue cupric ions1 which have a speed roughly the same as that of many common ions4 ,in this experiment the hydrogen ions are readily seen to move about twice as fast as the hydroxide ions and five to six times as fast as the cupric ions4 ,illustration3 ,,fig4 #aj ,,exp4#hh ,five grams of agar-agar are dissolved in #bej c4c4 of boiling water4 ,to #ajj c4c4 of the hot solution1 #cb c4c4 of a saturated solution of potassium chloride and about #a c4c4 of phenolphthalen solution are added1 together with enough of a solution of potassium hydroxide1 added drop by drop1 to produce a deep red tint in the phenolphthalen4 ,of this mixture #ej c4c4 is treated with dilute hydrochloric acid1 added drop by drop1 until the red color is just discharged1 and then an excess of acid1 equal in amount to the quantity used to neutralize the #ej c4c41 is added to the mixture4 ,this colorless solution and #ej c4c4 of the red solution are poured1 while still warm1 into the two parts of a wide ,u-tube1 slowly and at equal rates1 so that the level on the two sides remains the same4 ,in this way it is possible without difficulty to have the solution on one side red 7alkaline7 and on the other side colorless 7acid74 ,the agar-agar is allowed to congeal1 and then a mixture of #j4e c4c4 of hydrochloric acid1 7sp4 g4 #a4ab71 #f c4c4 of saturated cupric chloride solution and #bj c4c4 of water is poured over the red half1 and a mixture of #bj c4c4 of saturated p#jee potassium chloride solution and #b c4c4 of #aj potassium hydroxide solution is poured over the colorless half4 ,the ,u-tube is surrounded by ice water during the passage of the current1 and the cathode is placed in the solution on the colorless side4 ,in ,fig4 #aj the ,u-tube is shown when first charged 7on the left71 and after the current has been running for a short time 7on the right74 ,the conductivity of a solution must be made up1 therefore1 of the sum of the shares which the positive ions and the negative ions1 respectively1 take in carrying the current4 ,this principle was first advanced by ,kohlrausch4 ,the share of each kind of ion in conducting a current may be determined1 for hydrochloric acid for instance1 in the following way3 ,a porous diaphragm may be used to divide the solution in an electrolytic cell into two halves1 the concentration of the acid being the same in both halves 7represented1 as indicated in ,fig4 #aa1 by #ae molecules#hi of ionized acid in each half74 ,a measured current is passed through the solution1 say1 sufficient to liberate #c molecules of hydrogen ,h#b1 and #c of chlorine ,cl#b1 corresponding to #f ions of each1 and the concentration of the acid in each half is then again determined by analysis4 ,say it is found to correspond to #ad molecules of hydrochloric acid in the half of the solution on the side of the cathode and #aj molecules in the half on the side of the anode 7see ,fig4 #ab74 ,then the anode half has lost #e ions of hydrogen1 which must have passed through the diaphragm toward the cathode and taken the place of five of the six hydrogen ions discharged at the cathode4 ,similarly1 the solution around the cathode has lost one chloride ion1 which must have passed through the diaphragm toward the anode1 and the hydrogen-ion corresponding to it1 remaining on the right side without a compensating negative ion1 must be the sixth hydrogen-ion discharged at the cathode4 ,in other words1 five hydrogen ions passed to the right1 while one chloride ion passed to the left4 ,the hydrogen ions then carried five-sixths of the current through the diaphragm1 and consequently through the solution1 and the chloride ions only one-sixth of the current4 ,since the solutions were of equal concentration to start with1 the hydrogen ions have moved five times as fast toward the cathode as the chloride ions have moved toward the anode4 ,illustration3 ,,fig4 #aa4 ,illustration3 ,,fig4 #ab4 ,the equivalent conductivity of #j4a-molar hydrochloric acid is #cea at #ah1 and experiment shows that the hydrogen-ion carries #hd of the current1 the chloride-ion only #af4 ,the conductivity may then be considered to be the p#jef sum of the share the hydrogen-ion has in carrying the current1 i4e4 #j4hd #cea1 or #bie1 and of the share of the chloride-ion1 #j4af #ceb4e1 or #ef4 ,these values may be called the equivalent partial conductivities or mobilities of the ions in this solution4 ,in a similar way1 the conductivity of every solution of an electrolyte may be shown to represent the sum of the mobilities of the ions carrying the current 7principle of ,kohlrausch74 ,the limit of the conductivity of one equivalent of an electrolyte is the sum of the mobilities of the ions composing the electrolyte4 ,the frictional forces being constant for infinitely dilute solutions1 at a given temperature1 an ion will always show the same mobility1 irrespective of the nature of the ion of opposite charge1 with which it forms the electrolyte4 ,we may then put 7l l71 if l and l are used to designate the limits of the mobilities of gram-equivalents of the positive and negative ions forming the electrolyte4 ,the following table#ij gives the limits of the mobilities for gram equivalents of some of the most important ions at #ah4 ,limits of ,mobilities of ,common ,ions at #ah4 ,k3 #fe4c ,ca3 #ec4j ,i3 #ff4g ,na3 #dd4d ,h3 #cah4j ,,no#c3 #fj4h 7,,nh#d73 #fd4b ,,oh3 #agd4j ,c#b;,h#c,o#b3 #cc4g ,ag3 #ee4g ,cl3 #fe4i ,,so#d3 #fi4g ,for quite dilute solutions1 in which the friction may be assumed to be approximately constant1 the conductivity will depend1 not only on the mobilities of the ions1 which may be taken to be the same as for solutions of extreme dilution1 but also on the proportion of electrolyte that is ionized1 i4e4 on the degree of ionization1 4 ,then v 7l l71 which is an elaboration of the original equation given on page #ej4 ,now1 ,kohlrausch discovered the principle of the summation of the mobilities of ions a number of years before the theory of ,arrhenius was advanced1 and the proportion in which the ion is present in a given solution being unknown1 the effect of what is here known as the degree of ionization was included empirically in the value of the mobility4 ,it is not surprising1 then1 that an ion was found to have approximately the same mobility only in solutions of the same concentration of strictly analogous and closely related salts1 which1 according to present methods of investigation1 are now found to have approximately the same degree of ionization4 ,for instance1 the mobility of the gram-equivalent of the chloride-ion was found to be approximately the same1 #dg4c and #ej4e respectively1 in molar solutions of sodium and potassium chloride at #ah1 no account being taken of the degrees of ionization4 ,however1 the degrees of ionization of the two salts are approximately the same1 #ff4i and #gd4i respectively1 and might be ignored in a comparison of the conductivities1 without affecting the result of the comparison in any marked way4 p#jeg ,when the conductivities of unlike electrolytes are compared1 the introduction of the conception of the degree of ionization 7by ,arrhenius17 into ,kohlrausch's principle of the independent conductivities of specific ions1 shows most striking results and demonstrates the value of the new conception4 ,for instance1 the equivalent conductivity of potassium chloride at #ah in #j4jge molar solution is #aac4h reciprocal ohms and the partial conductivity of the chloride-ion in the solution is #eg4d4 ,but the conductivity of an equivalent solution of mercuric chloride at #ah is only #a4ea1 which is very much less than the conductivity of the chloride-ion alone in the potassium chloride solution4 ,now1 mercuric chloride1 according to investigations of its conductivities and of its effect in depressing the freezing-point of water1#ia is one of a very few salts that are difficultly ionizable 7p4 #ajg72 according to the data mentioned1 it is ionized1 at most1 to the extent of #b4e per cent in the solution in question1 whereas #hg4e per cent of the potassium chloride is ionized in such a solution4 ,when the difference in the degree of ionization is taken into account1 the conductivity which mercuric chloride should show may be calculated1 on the assumption that the chloride-ion has the same mobility in the two solutions1 but that there is less of it in the mercuric solutions4 ,we put ,hg,cl#b 7l,hg l,cl7 #j4jbe 7#dh #fe4i7 #b4h4 ,we thus find that the conductivity of the mercuric chloride should be1 approximately1 only #b4h reciprocal ohms1 which is of the same order as that found 7#a4ea74ib ,in the same way1 when we compare the conductivity of a strong acid1 like hydrochloric acid1 with that of a weak acid1 like acetic acid--the conductivity of #j4a molar hydrochloric acid is #cea1 of #j4a molar acetic acid only #d4f--the principle of the specific1 characteristic mobility of the hydrogen-ion1 which is present in both solutions1 has significance only if we take into account the very different concentrations of the hydrogen-ion in the two solutions1 resulting from the different degrees of ionization of the two acids--#ia for the hydrochloric and only #a4g for the acetic acid4 ,the same relations hold in the comparison of the conductivity of a solution of a strong base like sodium hydroxide with that of an equivalent solution of a weak1 i4e4 much less ionized base like ammonium hydroxide1 or in comparing the conductivity of a weak acid or a weak base with the conductivities of their much more highly ionized salts4 ,in all these cases the use of the conception of the degree of ionization of the electrolytes makes possible a much broader and more general application of the principle of the independent migration or mobility of the ions than was possible before the theory of ,arrhenius was proposed1 and marks a distinct advance in the theory of conductivity1 over what was possible on the basis of the theory of ,clausius4 p#jeh ,faraday's ,law4--,if a definite quantity of electricity1 a faraday1#ic or #if1fjj coulombs1 is passed through a solution of hydrochloric acid1 a definite quantity 7#cf4e grams1 one mole7 of the hydrogen chloride is decomposed1 and one gram of hydrogen and #ce4e grams of chlorine are liberated by the discharge of one gram 7i4e4 one gram-ion7 of the hydrogen-ion and #ce4e grams or one gram-ion of the chloride-ion4 ,in a solution of cupric chloride1 the chloride-ion is identical in every respect with the chloride-ion found in a solution of hydrochloric acid4 ,in the solution of cupric chloride1 however1 a molecule of the salt1 when it is completely ionized1 produces two chloride ions for every cupric ion 7,cu,cl#b ,cu#b #b ,cl74 ,since the solution never shows the presence of an excess of either form of electricity1 and the negative charge on each chloride ion is the same as on a chloride ion formed by the dissociation of hydrogen chloride1 a cupric ion must hold exactly double the positive charge that a hydrogen ion does4 ,in modern terms1 each hydrogen atom1 present as an ion1 has lost one electron1 and each copper atom present in the form of a cupric ion has lost two electrons4 ,our unit quantity of electricity1 #if1fjj coulombs1 can discharge therefore only half as many of the cupric as of the hydrogen ions1 and since each cupric ion is #fc4f times as heavy as the hydrogen-ion 7,cu #fc4f1 ,h #a71 #fc4f _/ #b grams of copper1 the equivalent weight1 will be deposited in place of one gram of hydrogen4 ,similarly1 from a solution of ferrous chloride ,fe,cl#b1 #ee4i _/ #b grams of iron 7,fe #ee4i7 will be deposited1 the ferrous ion being ,fe#b2 while from a solution of ferric chloride ,fe,cl#c1 only #ee4i _/ #c grams of iron will be deposited by #if1fjj coulombs1 the ferric ion1 ,fe#c1 holding three times the charge that a hydrogen ion does4 ,in other words1 a given quantity of current will decompose equivalent quantities of electrolytes and deposit equivalent quantities of metals4 ,this is the well-known law of ,faraday4 ,the theory of ,arrhenius agrees with it1 as did the theory of ,clausius4 ,it cannot be considered as evidence bearing on the question of the preference to be given to either of the theories of ionization1 since the degree of ionization of electrolytes is not involved in the relations covered by the law4 ,but any other relation would have been incompatible with the theory of ,arrhenius4 ,the law is of particular importance in giving us p#jei the best clew that we have in regard to the ultimate nature of valence 7as shown for instance in the difference between the ferrous1 ,fe#b1 and the ferric ions1 ,fe#c74 ,on the basis of this law1 valence may be said to consist simply in the capacity of atoms to hold different multiples of the unit electrical charge 7positive or negative74 ,this conception will be of especial value to us when we come to consider the relation of the theory of ionization to oxidation and reduction 7,chapters ,,xiv and ,,xv74 ,diffusion of ,ions and ,concentration ,cells4--,when the1 apparently1 abnormally low molecular weight of ammonium chloride was explained as being due to the dissociation of each molecule of ammonium chloride into a molecule of ammonia and one of hydrogen chloride1 the evidence of the correctness of this interpretation was at once forthcoming--the vapor of ammonium chloride1 by the unequal rates of diffusion of its components1 was proved to be a mixture of the two gases 7p4 #ce74 ,now1 if an electrolyte like hydrochloric acid in aqueous solution is dissociated more or less into separate ions1 ,h and ,cl1 then one may well ask1 whether the dissociation cannot be demonstrated by the same kind of experiment1 as1 for instance1 by showing that hydrogen and chloride ions are molecules with unequal powers of diffusion and by separating them by virtue of such inequality4 ,ions being1 according to the theory under consideration1 independent molecules1 except for the attractive and repulsive forces of the electrical charges1 they should have1 like cane sugar1 copper nitrate and other solutes1 the capacity for diffusion from regions of higher to those of lower concentration4 ,further1 if ions show different degrees of mobility 7p4 #ec71 one would expect the more mobile or faster moving one to diffuse more rapidly than a less mobile ion4 ,such a relation should hold for the ions in a solution of hydrochloric acid1 the hydrogen-ion1 according to the calculations of ,kohlrausch#id and the observation of ,lodge1#ie moving at a rate about five times as great as that of the chloride-ion1 at #ah4 ,thus1 if a rather concentrated solution of hydrochloric acid were covered with a layer of water1 or with a very dilute solution of the acid1 one might expect the hydrogen ions to migrate faster than the chloride ions from the p#jfj point of higher to that of lower concentration1 i4e4 from the more concentrated to the dilute acid4 ,when the experiment is tried in this way1 no separation of the hydrogen from the chloride ions seems to occur4 ,the reason for the failure of the experiment is as follows3 ,if any such separation did occur1 even to the extent of say one milligram-equivalent of hydrogen and chloride ions1 we would have a separation of electrostatic charges of #if coulombs4 ,these charges1 on the small areas involved1 would inevitably produce enormous potentials1 that would operate against the separation4 ,the hydrogen ions1 which would tend to move from the concentrated to the dilute acid1 would therefore be held back by the powerful attraction between their positive charges and the negative charges left in the concentrated acid 7on the ,cl ions74 ,the separation of the electrical charges1 incidental to a faster diffusion of hydrogen ions1 if it occurred1 would result1 therefore1 in the development of electrical forces of attraction1 which would prevent a separation of the oppositely charged particles beyond any but distances too small to be measured4 ,it would follow1 however1 that no difficulty whatever should be experienced in observing such a separation1 as a result of unequal rates of migration of the ions in question1 if provision were made to preserve electrical neutrality in all zones of the two solutions1 i4e4 if provision is made for the immediate discharge of the ions1 as they separate by the unequal rates of diffusion4 ,for instance1 the part of the liquid into which the positive hydrogen ions move more rapidly1 charging it with positive electricity1 may be connected1 by means of a wire1 with the part of the liquid to which the chloride ions1 left behind by their slower movements1 are imparting a negative charge4 ,in such a circuit1 a current of electricity should be produced1 the positive current flowing through the wire from the dilute to the concentrated acid4 ,as a matter of fact1 we find that a current is produced1 when these conditions are observed4 ,,exp4 ,the lower plate in an ,arrhenius cell is covered with concentrated hydrochloric acid4 ,very dilute acid is allowed to flow slowly on to the surface of the concentrated acid1 from a pipette with a curved1 narrow point1 until the upper plate is submerged4 ,the two plates are connected with a sensitive galvanometer4 ,the current flows in the direction demanded by the observed mobilities of the ions1 the positive current entering the galvanometer from the plate covered by the dilute solution1 which is charged positively by the faster moving hydrogen ions coming from the concentrated solution4 ,if the cell is p#jfa connected with the electrodes of a very small cell containing copper sulphate1 in the course of twenty-four hours quite a deposit of metallic copper is formed on the electrode connected with the concentrated solution of hydrochloric acid4 ,the existence of the products of the electrolytic dissociation1 of hydrochloric acid may therefore be demonstrated1#if by the aid of the individual diffusion of the products of the dissociation1 in the same way as was the coxistence of the products of the gaseous dissociation of ammonium chloride1 when the conditions for the experiment are adapted to the nature of the dissociation products4 ,cells of this type1 depending for their current on unequal concentrations of given ions1 are called concentration cells4 ,if it can be shown that the flow of electricity1 resulting from such unequal diffusibility of ions1 is a function not only of the difference in the total concentration of the electrolyte in the two solutions brought into contact with each other1 but is also a function of the relative degrees of ionization of the electrolyte in the two solutions1 as defined by the theory of ,arrhenius1 then this method of experimentation may be used as a further test of the validity of this theory as against that of ,clausius4 ,it is obvious that if such currents are the results of the diffusion of ions from higher to lower concentrations1 then the essential concentrations do not embrace all of the electrolyte1 but only the ionized part4 ,w4 ,k4 ,lewis#ig has rather recently shown that the degrees of dissociation of electrolytes may be measured by the use of concentration cells1 and that the results agree well with the determinations of the degree of dissociation from conductivity measurements 7p4 #ej74 ,from calculations1 based on ,jahn's accurate measurements of the electromotive forces of concentration cells1 ,a4 ,a4 ,noyes#ih finds that when the conductivity ratio is assumed to represent the degree of ionization of the salt1 the calculated values of the electromotive force of concentration cells exceed the measured ones by only about one per cent1 in the case of potassium and sodium chloride between the concentrations of #a _/ #fjj and #a _/ #bj molar4 ,the ,rle of the ,solvent in ,ionization4--,a question that has profoundly interested chemists1 particularly during the last few years1 has been that of the rle which the solvent plays in the p#jfb dissociation of electrolytes into ions4 ,the most important ionizing solvent is water and1 of the common solvents which cause ionization1 it is the most powerful in this particular4 ,alcohols have also ionizing power2 methyl or wood alcohol1 which stands nearest to water1 has a higher ionizing power than ordinary ethyl alcohol4 ,the exact work#ii of ,franklin and ,kraus1 on the conductivity of solutions of salts in liquid ammonia1 showed that the same general relations obtain for such solutions as for solutions in water1 the differences being differences of degree rather than of kind4 ,salts are found to be less ionized in liquid ammonia than in equivalent aqueous solutions1 but their conductivities are higher1 the result of smaller friction in ammonia4 ,liquid hydrogen cyanide is also a very good ionizing medium4 ,solvents which cause ionization only to a minimal extent are benzene 7,c#f;,h#f71 carbon bisulphide1 ether1 chloroform1 petroleum ether 7gasoline7 and similar solvents4 ,hydrogen chloride dissolved in benzene has an extremely small conductivity1 indicating only a trace of ionization4#ajj ,the question may be raised1 why the first solvents mentioned should have the power to cause ionization1 while the second series of solvents named do not have this power1 or have it only to a very slight extent4 ,without attempting to enter into an elaborate discussion of this important question1 it may be said that ,j4 ,j4 ,thomson#aja and ,nernst#ajb suggested that the ionizing powers of solvents must be intimately connected with their dielectric behavior1 and this view has now been well established4 ,it may be said1 in simple terms1 that the so-called dielectric constant of a solvent determines the force with which electrical charges will attract and repel each other2 the higher the dielectric coefficient of a medium1 the smaller will be the attraction between opposite electrical charges1 other conditions being the same4 ,in solvents1 then1 of high dielectric powers1 the coxistence of oppositely charged particles must be more favored than in solvents of low dielectric powers4 ,the dielectric constants of a number of solvents are given in the following table3 p#jfc ,hydrogen cyanide1 ,,hnc #ie ,hydrogen peroxide1 ,h#b,o#b #ic ,water1 ,h#b,o #ha ,methyl 7wood7 alcohol1 ,,ch#d,o #cb ,ethyl 7ordinary7 alcohol1 ,c#b;,h#f,o #bb ,ammonia1 ,h#c,n #bb ,chloroform1 ,c,h,cl#c #e ,ether1 7,c#b;,h#e7b,o #d ,benzene1 ,c#f;,h#f #b ,it is quite apparent that the good ionizing media have1 as a matter of fact1 the highest constants2 those which cause ionization1 at most minimally 7e4g4 benzene71 the lowest4 ,recent extended and exact investigations by ,walden#ajc have succeeded in bringing the ionizing power of solvents into definite quantitative relations to their dielectric constants1 with the result that order has been brought out of a condition of chaos that1 for a number of years1 existed in this field1 as the result of conclusions based on incomplete data4 ,conductivity being a function both of the proportion of dissociated electrolyte and of the mobility of the ions in a given solution1 ,walden determined1 for a certain salt 7an organic derivative of ammonium iodide1 namely1 tetraethyl ammonium iodide ,n7,c#b;,h#e7d;,i71 for all solvents used1 not only the conductivities for finite dilutions but also1 by extrapolation1 the limiting values for infinite dilution4 ,he was thus able to determine the degree of ionization of the salt4 ,some of his results are particularly interesting2 for instance1 a poorly conducting solution1 such as that of the salt in glycol1 a solvent resembling glycerine in general character1 may contain the dissolved electrolyte in a highly ionized state1 while in a much better conducting solution the degree of ionization may be much smaller--the low conductivity of the first solution being the result of a very high friction and of the slow motion of the ions1 while the well-conducting solution might show a very high degree of mobility of the ions4 ,the mobility changes with the nature of the solvent1 and the limit1 1 of the equivalent conductivity of the salt1 as found by ,walden1 ranges from #h in glycol1 which is a thick1 viscous oil like glycerine1 to #bjj in acetonitrile1 a thin mobile solvent4 ,in the one solution1 an observed conductivity of #d represents #ej ionization of the salt1 in the other only #b4 ,now1 for solutions of a given electrolyte--tetraethyl ammonium iodide was used--,walden#ajd found the following exceedingly interesting relation between the ionizations in1 and the dielectric constants of1 various solvents3 e#a 3 c#a e#b 3 c#b a constant1 where e#a and e#b represent the dielectric constants of different solvents1 and c#a and c#b represent the concentrations of the salt in the solvents when the salt is ionized to the same degree#aje in the two solutions4 ,the bearing of the relation is apparent from the data in the following p#jfd table4#ajf ,the upper half of the table gives the dielectric constants 7column two7 of the solvents named in column one2 the concentrations which show identical degrees of ionization--#dg--;are given in the third column1 and the last column gives the value of the relation e 3 c4 ,the lower half of the table presents the same kind of data1 for the same salt1 when its degree of ionization is #ia1 in the different solutions examined4 ,it is clear that the numbers in the third column of each part represent approximately constants4 ,all solutions1 including aqueous solutions1 are thus brought into one general relation4 ,solvent4 e c e 3 c ,methyl alcohol #cb4e #j4abe #fe ,ethyl alcohol #ba4g #j4jbj #hj ,acetyl bromide #af4b #j4jaj #ge ,benzaldehyde #af4i #j4jaf #gh ,acetonitril #ce4h #j4ajj #gg ,water #hj #j4jjiaj #chc ,furfurol #ci4d #j4jjabe #cfe ,nitromethane #dj #j4jjabe #cga ,acetonitril #cf #j4jjajj #ceh ,methyl alcohol #cb4e #j4jjjej #cfe ,the ,ionizing ,power of ,solvents ,related to the ,unsaturated ,condition of their ,simple ,molecules and to their ,power of ,association4--,a careful scrutiny of the group of highly-ionizing solvents 7p4 #fb7 brings out another interesting relation1 to which attention is called because it is a chemical one1 and which should always be considered in connection with reactions in such solvents4 ,it is well known that ammonia is an unsaturated body1 combining readily with all acids1 and with many salts1 such as copper sulphate4 ,the fact may be recalled1 that this unsaturated condition is ascribed to the unsaturated nitrogen atom in the molecule of ammonia1 the nitrogen showing a valence of only #c in ammonia1 whereas in the derivatives it forms when it saturates itself with the compounds mentioned1 e4g4 in ,h#d,n,cl1 it has five saturated valences4 ,assuming that a valence consists in a unit charge1 positive or negative1 on the atom 7pp4 #db1 #ei71 a view which has almost become a certainty1 we should decide that the two free valences in ammonia must consist of a negative and a positive charge1 as expressed in ,h#c,n4 7,we may imagine such a double p#jfe charge to be produced by the movement of one electron of the nitrogen atom to a position in that atom which would make one point of the atom negative and the other positive47 ,as a matter of fact1 we find ammonia uniting with hydrogen chloride1 by absorbing a positive and a negative fragment of it--producing ,h#d,n,cl from ,h#c,n ,h ,cl4 ,it is also evident that1 through these charges1 ammonia could combine with itself to form larger complexes1 ,,nh#c-,,nh#c1 in which we would still have two opposite charges1 presumably removed further from each other than in the simple molecule4 ,the new molecule could1 in turn1 by virtue of its charges1 combine with a further molecule to form a still larger or more associated molecule1 ,,nh#c-,,nh#c-,,nh#c1 and such association could evidently go still further4 ,one can readily see that such molecules would be electrically polarized1 and their charges might easily have the power to cause#ajg electrolytic dissociation or ionization4 ,the larger the associated molecule1 the further apart might be the positive and negative charges upon it3 the further apart the charges1 the smaller would be their mutual attraction3 and the smaller the mutual attraction1 the stronger1 presumably1 would the dissociating power of such a molecule be4 ,the dissociation may be effected1 possibly1 by the action of these intensified charges upon charges already existing#ajh within the molecule of the dissolved ionogen4 ,in liquid ammonia we might well have1 for instance1 the action ,,nh#c-,,nh#c ,h,cl 7,,nh#c-,,nh#c7;,h ,cl1 or ,,nh#c-,,nh#c ,h,cl 7,,nh#c-,,nh#c7;,h ,cl4 ,now1 in liquid ammonia1 the salts ,,nh#d;,cl1 ,,nh#d,,no#c or1 more probably1 7,,nh#c7x,h,cl1 7,,nh#c7x1,,hno#c have the functions of the aqueous acids#aji2 that is1 the hydrogen-ion of the acids is found combined with the solvent ammonia4 ,the ion 7,,nh#c-,,nh#c7;,h1 and similar ions in liquid ammonia1 would correspond then to what is considered the hydrogen-ion in aqueous solutions#aaj 7formed according to ,h,cl ,h ,cl1 as ordinarily written71 and the polarized charges on molecules like ,,nh#c-,,nh#c appear thus as possible active agents in this dissociation of the hydrogen chloride molecules4 p#jff ,now1 it is a significant fact that all the best ionizing solvents are compounds whose simple molecules are unsaturated exactly like those of ammonia2 this is true for water ,h#b,o1 the unsaturated character of whose oxygen atom is now universally recognized4 ,it is now a familiar fact that liquid water is not represented by the formula ,h#b,o but consists of more complex molecules 7,h#b,o7n4 ,according to the most recent investigations1#aaa while steam is ,h#b,o1 or monohydrol1 ice is trihydrol 7,h#b,o7#c1 and liquid water1 at ordinary temperatures1 a mixture consisting chiefly of dihydrol 7,h#b,o7#b1 some trihydrol1 and very little monohydrol4 ,the proportion of the last appears to increase with a rise of temperature2 the proportion of trihydrol seems to increase with a fall in temperature4 ,one can easily see how such aggregates would result from the saturation of the free charges on oxygen1 by further molecules of water4 ,one can also see that such an association of water molecules could leave a positive and a negative charge on the associated molecules1 which would be polarized and more effective than the simple molecule would be4 ,that the molecule of hydrogen cyanide contains a similarly unsaturated atom was demonstrated by ,nef4#aab ,he proved that the behavior of hydrocyanic acid agrees with the structure expressed by the formula ,,hn,c1 which we may well write ,,hn,c4 ,in sulphur dioxide1 another good ionizing solvent1 we have1 similarly1 unsaturated sulphur1 the sulphur atom being here quadrivalent1 whereas its maximum valence is six4 ,now1 the ionizing power of solvents like water1 ammonia1 etc41 has been ascribed1 by various chemists1 not only to their dielectric properties1 but also to the unsaturated condition of their molecules1 and particularly to their powers of association into large molecules4 ,the relations developed suggest that all three properties are most intimately related1 the dielectric properties and the powers of association being consequences1 possibly1 of the fundamental condition of unsaturation1 and of the great tendency toward self-saturation1#aac of the simple molecules of the best ionizing solvents4 ,from ,walden's work it appears that the dielectric constant finally determines the quantitative ionizing effect of a solvent4 ,,footnotes3 #di ,from the molecular weights of elements and compounds1 the atomic weights of elements may be determined1 with the aid of analysis4 7,cf4 ,smith1 ,inorganic ,chemistry 7#aiji71 p4 #aif1 or ,general ,chemistry for ,colleges 7#aijh71 p4 #acj 7,stud471 or ,remsen1 ,inorganic ,chemistry1 ,advanced ,course 7#aijd71 pp4 #ga-hj 7,stud4747 #ej ,the weight of a small volume of a gas or vapor1 at any definite temperature and pressure1 is determined4 ,with the aid of ,boyle's and ,gay-,lussac's laws1 this observed volume is then reduced to standard conditions4 ,finally1 the weight of #bb4d liters1 under standard conditions1 is obtained by calculation4 #ea ,for the deduction of formul see ,smith1 ,inorganic ,chemistry1 #aif1 #bjc2 ,college ,chemistry1 #dj2 or ,remsen1 ibid41 p4 #gi 7,stud474 #eb ,kopp1 ,liebig's ,ann41 #aje1 #cij 7#aheh72 ,kkul1 ibid41 #ajf1 #adc 7#aheh7 7,stud474 #ec ,liebig's ,ann41 #abc1 #aii 7#ahfb7 7,stud474 #ed ,wanklyn and ,robison1 ,compt4 rend41 #eb1 #edi 7#ahfc7 7,stud474 #ee ,for instance in a test tube held in a horizontal position4 #ef ,by applying the corrections demanded by the kinetic theory 7van der ,waals's equation7 to gases even under ordinary pressures1 ,guye and ,d4 ,berthollet have obtained1 with the aid of ,avogadro's hypothesis1 values for the molecular weights of gases and for the atomic weights of their components1 which compare in accuracy with the best analytical work on solutions and solids4 #eg ,the usual experimental methods consist in determining the elevation of the boiling-point1 or the lowering of the freezing-point1 or the lowering of the vapor tension of a solvent by a solute1 methods which were discovered by ,raoult and used empirically until van 't ,hoff developed their relations to the ,avogadro principle4 ,the calculation of a molecular weight is much simplified by the use of the different specific constants expressing the lowering or elevation produced by one gram-molecule or mole1 dissolved either in one liter or in #ajj grams of each specific solvent4 #eh ,see ,arrhenius1 ,z4 phys4 ,chem41 #a1 #fca 7#ahhg74 #ei ,or1 on the basis of the accepted molecular weights1 abnormally high osmotic pressures1 abnormally great lowerings of the freezing-point1 raisings of the boiling-point1 etc41 were obtained4 ,van 't ,hoff1 originally1 on account of these discrepancies1 considered this extension of the ,avogadro ,hypothesis to hold only for the majority of substances in solution1 not for all 7,arrhenius1 loc4 cit474 ,it was considered to have universal application 7for dilute solutions7 only after ,arrhenius had explained the exceptions with the aid of his theory of electrolytic dissociation4 #fj ,that is1 hydrogen chloride1 in aqueous solution1 depresses the vapor tension and the freezing-point and elevates the boiling-point considerably more than an equimolecular quantity1 for instance1 of glucose does1 and gives a considerably higher osmotic pressure4 ,the differences are relatively greater1 the more dilute the solutions used4 #fa ,a fourth interpretation advanced at one time in opposition to the theory of ionization is that salts like sodium chloride and zinc chloride are hydrolyzed and thereby produce more solute molecules1 e4g4 ,na,cl ,h#b,o ,na,o,h ,h,cl4 ,aside from the fact that such hydrolysis of salts1 when it does occur 7,chapter ,x471 is easily detected1 and that it can be proved not to occur appreciably in the case of sodium chloride 7loc4 cit471 this interpretation fails utterly to account for the results obtained with acids1 e4g4 ,h,cl1 ,,hno#c1 ,h#b,,so#d1 and with bases1 e4g4 ,na,o,h1 ,ba7,,oh7#b1 which in aqueous solutions show an increase in the number of molecules as great as shown by salts4 ,this explanation is therefore untenable4 #fb ,z4 phys4 ,chem41 #a1 #fca1 7#ahhg74 ,previous papers were published in the transactions of the ,royal ,academy of ,sweden 7,stockholm74 ,for a history of the theory see ,ostwald1 ,z4 phys4 ,chem41 #fi1 p4 #a 7#aiji71 and ,arrhenius1 ,the ,willard ,gibbs ,address1 ,j4 ,am4 ,chem4 ,soc41 #aiaa 7,stud474 #fc ,in the case of double salts1 such as sodium-ammonium phosphate1 and similar compounds1 the dissociation leads to the formation of more than two products4 ,the molecules of two or more different products may then be charged positively and1 conversely1 there may be two or more different products of dissociation carrying negative charges4 ,we have1 for instance1 ,na7,,nh#d7;,,hpo#d ,na ,,nh#d ,h ,,po#dc and ,na7,,nh#d7;,,hpo#d ,na ,,nh#d ,,hpo#db4 ,in all cases the rule concerning the sum of all the charges1 as expressed in 7#b71 must be fulfilled1 the charge on the phosphate ion1 ,,po#dc1 being three times as great as that on a sodium1 ammonium1 or hydrogen ion2 that on the acid phosphate ion1 ,,hpo#db1 being twice as great4 #fd ,ion the going or the migrating particle4 #fe ,see ,washburn1 ,j4 ,am4 ,chem4 ,soc41 #ca1 #cbb 7#aiji71 in regard to the values of x and y1 the quantities of water carried by certain ions4 #ff ,vide ,j4 ,j4 ,thomson1 ,electricity and ,matter 7#aije7 and ,corpuscular ,theory of ,matter 7#aijg7 7,stud474 ,vide ,r4 ,a4 ,millikan1 ,science1 #cb1 #dcf 7#aiaj71 on the discrete or granular nature of electricity 7,stud474 #fg ,see ,millikan1 loc4 cit41 as to the exact value of this unit charge4 #fh ,cf4 ,mc,coy1 ,j4 ,am4 ,chem4 ,soc41 #cc1 ,march1 #aiaa1 in regard to electropositive1 composite 7i4e4 nonelementary7 metals4 #fi ,the symbol is used to designate an electron4 ,the loss of one electron by an atom leaves a unit positive charge on the particle4 #gj ,in ,chapter ,,xv 7q4 v47 the affinity of the elements for electrons and the reactions1 of the nature of oxidation and reduction1 depending on this affinity1 are discussed in detail4 #ga ,j4 ,j4 ,thomson1 ,corpuscular ,theory of ,matter1 p4 #abj4 #gb ,a4 ,a4 ,noyes 7,carnegie ,institution ,publications1 ,no4 #fc1 p4 #cea 7#aijg771 believes that we may have two kinds of molecules1 ,h,cl and ,h,cl1 as well as the ions ,h and ,cl4 #gc ,modern theory thus is reverting to the ,berzelius theory of chemical affinity ,vide ,meyer's ,history of ,chemistry 7translated by ,m',gowan7 #ahia1 #bbj-bfe1 or ,ladenburg's ,history of ,chemistry 7translated by ,dobbin7 #aijj1 #hf1 #hh1 etc4 #gd ,to a saturated solution of cupric nitrate may be added a small amount of a saturated solution of potassium permanganate1 sufficient to give a decided purple color to the mixture4 ,potassium chromate1 as recommended by ,a4 ,a4 ,noyes1 may be used in place of the permanganate4 7,cf4 ,noyes and ,blanchard1 ,j4 ,am4 ,chem4 ,soc41 #bb1 #gbf 7#aijj747 #ge ,exp42 cf4 ,eckstein1 ,j4 ,am4 ,chem4 ,soc41 #bg1 #gei 7#aije7 7,stud474 #gf ,w4 ,a4 ,noyes1 ,j4 ,am4 ,chem4 ,soc41 #bc1 #dfj 7#aija72 ,stieglitz1 ibid41 #bc1 #gif 7#aija72 ,walden1 ,z4 phys4 ,chem41 #dc1 #che 7#aijc74 #gg ,corpuscular ,theory of ,matter1 p4 #acj 7#aijg74 #gh ,the experiment is an adaptation of a similar one described by ,a4 ,a4 ,noyes and ,blanchard1 ,j4 ,am4 ,chem4 ,soc41 #bb1 #gbf 7#aijj74 #gi ,the copper electrodes are polarized by the formation of hydrogen on the cathode1 but1 in the course of a few seconds1 the current becomes rather constant and is then read4 ,the polarization may be considered as simply reducing the potential of the cell1 and since1 within the range of concentrations of acid used1--#d-molar to #a_/h-molar--the polarization current does not vary markedly1 as compared with the potential of the storage cell1 the total potential used through the series of dilutions may be considered sufficiently constant for the purposes of the experiment4 ,readings are made three or four seconds after each dilution1 when the polarization has been fully established4 ,polarization may be entirely avoided by the use of a silver nitrate solution and silver electrodes or of a cupric salt solution and copper electrodes 7,noyes and ,blanchard74 ,hydrochloric acid is used here in order to carry the discussion in the text as far as possible with this typical ionogen4 ,if one takes care to make readings as described1 the result is quite satisfactory1 as is shown by the comparison of the ratios of the readings with the ratios calculated from the known conductivities of the various dilutions 7see table below74 #hj ,current 7,potential ,difference7 _/ ,resistance1 or ,current 7,potential ,difference7 ,conductivity4 ,for a constant potential difference1 then1 ,current ,conductivity4 #ha ,the specific conductivity of a solution 7commonly designated by 7 is the conductivity of a cube of #a cm4 edge2 the molecular conductivity is the conductivity of a mole of the electrolyte2 the equivalent conductivity 7designated by 7 is the conductivity of a gram-equivalent of the electrolyte4 v1 where v is the volume1 expressed in cubic centimeters1 containing the gram-equivalent4 ,for instance1 the resistance of #j4a molar hydrochloric acid in a cube of #a cm4 edge is #bh4e ohms and its conductivity 77 therefore #a _/ #bh4e or #j4jcea reciprocal ohms4 ,since #aj liters or #aj1jjj c4c4 of #j4a-molar hydrochloric acid is the volume 7v7 containing one mole of the acid 7the molar and the equivalent conductivities1 for a monobasic acid being the same7 #j4jcea #aj1jjj1 or #cea4 #hb ,kohlrausch and ,holborn1 p4 #bjj4 #hc ,cf4 ,kahlenberg1 ,transactions of the ,faraday ,society1 #a1 #db 7#aije74 #hd ,clausius1 ,poggendorf's ,ann41 #aja1 #cdg 7#aheg7 7,stud474 ,his theory replaced the older one of ,grotthuss4 #he ,phil4 ,mag41 #e1 #gbi 7#aijc71 and ,transactions of the ,faraday ,society1 #a1 #ee1 7#aije74 #hf ,vide1 ,hudson1 ,j4 ,am4 ,chem4 ,soc41 #ca1 #aacf 7#aiji71 for a recent summary of results4 #hg ,lectures on ,physical ,chemistry1 #a1 p4 #aca4 #hh ,vide ,a4 ,a4 ,noyes and ,blanchard1 ,j4 ,am4 ,chem4 ,soc41 #bb1 #gbf 7#aijj74 #hi ,the concentrations are figurative1 but may be taken to represent actual concentrations1 such as #j4jae molar1 etc4 #ij ,kohlrausch and ,holborn1 loc4 cit41 p4 #bjj4 #ia ,raoult1 ,ann4 de ,chim4 et de ,phys4 7#f71 #b1 #hd 7#ahhd74 #ib ,the degree of ionization of mercuric chloride is based on ,raoult's freezing-point measurements and is subject to revision1 and the limit of the mobility of the mercuric-ion 7 ,hg7 is assumed to be #dh1 close to the values found for the ions of zinc and cadmium1 elements in the same family as mercury4 #ic ,lehfeldt's ,electrochemistry1 #aijd1 p4 #c4 #id ,see table1 p4 #ef4 #ie ,report of the ,british ,association for the ,advancement of ,science1 #ahhf1 p4 #chi4 #if ,with the aid of more elaborate apparatus rigorous demonstrations and measurements of such diffusion currents of so-called concentration cells are made4 #ig ,z4 phys4 ,chem41 #fc1 #agd 7#aijh74 ,the work was carried out in ,abegg's laboratory4 #ih ,report of the ,st4 ,louis ,congress of ,arts and ,sciences1 ,,iv1 #cad 7#aijd74 #ii ,am4 ,chem4 ,j41 #bj1 #ba1 #bc 7#ahih-aijj74 #ajj ,kablukoff1 ,z4 phys4 ,chem41 #d1 #dbi 7#ahhi74 #aja ,phil4 ,mag4 7#e71 #cf1 #cbj 7#ahic74 #ajb ,z4 phys4 ,chem41 #ac1 #eca 7#ahic74 #ajc ,walden1 ,z4 phys4 ,chem41 #ed1 #abi 7#aijf72 ,mc,coy1 ,j4 ,am4 ,chem4 ,soc41 #cj1 #ajgd 7#aijh74 #ajd ,z4 phys4 ,chem41 #ed1 #bbi 7#aijf74 #aje ,the degrees of ionization were always determined from the relation v _/ according to the method discussed on page #ej4 #ajf ,walden1 loc4 cit4 #ajg ,cf4 ,arrhenius1 ,theories of ,chemistry1 p4 #hc 7#aijg74 #ajh ,in hydrogen chloride1 the hydrogen and the chlorine atoms may be held in the molecules ,h,cl by the electric attraction of a positive charge on the hydrogen1 and a negative charge on the chlorine atom 7see p4 #dc74 #aji ,franklin and ,kraus1 ,am4 ,chem4 ,j41 #bc1 #cje 7#aijj7 7,stud47 #aaj ,it is very likely that in aqueous acids1 a large proportion1 at least1 of the hydrogen-ion is similarly combined with water4 7,lapworth1 ,j4 ,chem4 ,soc41 7,london7 #ic1 #bahg 7#aijh74 ,see ,chapter ,,xii47 #aaa ,vide the discussion on the ,constitution of ,water1 and the summary by ,j4 ,walker1 ,transactions of the ,faraday ,society1 ,,vi1 #ga-abc 7#aiaj74 #aab ,proc4 ,am4 ,acad41 #ahib2 ,liebig's ,ann4 #bhg1 #bfc 7#ahie74 #aac ,cf4 ,walden1 ,z4 phys4 ,chem41 #ee1 #fhc 7#aijf74 p#jfg ,,chapter ,v ,,the ,,theory ,,of ,,ionization4 ,,ii ,,ionization ,,and ,,osmotic ,,pressure4 ,,ionization ,,and ,,chemical ,,activity ,we will turn now to the consideration of evidence bearing on the theory of ionization1 found in the data on osmotic pressure4 ,the apparent molecular weight of hydrogen chloride is found to be smaller than #cf4e1 when determined in aqueous solution 7p4 #cg71 and it is found to approach the limit #ah4be as a more and more dilute acid is used4#aad ,the value found represents the average molecular weight of all the molecules in any solution1 the osmotic pressure1 freezing-point or boiling-point of which has been taken4 ,it is evident that1 if there is dissociation of hydrogen chloride into hydrogen and chloride ions1 the average values found for the molecular weight must be lower than #cf4e1 must be variable1 and must approach the limit #ah4be1 as the dissociation into the smaller molecules becomes more and more complete4 ,such a result is1 therefore1 what we would anticipate on the basis of the theory of ionization4 ,for a salt like potassium chloride ,k,cl1 a similar tendency toward a minimum1 average molecular weight of 7,k ,cl7 _/ #b or 7#ci4a #ce4e7 _/ #b #cg4c would be anticipated1 and1 as a matter of fact1 molecular weight determinations with potassium chloride in aqueous solution give results agreeing with such a tendency4#aae ,for a salt like calcium chloride1 on the other hand1 we would expect that its ionization into three ions1 according to the equation ,ca,cl#b ,ca#b #b ,cl1 would give a minimum1 not of one-half the formula weight1 but of one-third1 viz41 7,ca#b #b ,cl7 _/ #c or 7#dj #ga7 _/ #c #cg1 when the molecular weight determination is carried out in aqueous solution4 ,as a matter of fact1 with salts of this type1 the determinations1 by osmotic pressure methods1 indicate a dissociation into three smaller components1 as required by the theory4 ,it may be added that1 for p#jfh a salt1 sodium mellitate1 ,na#f7;,c#ab,o#ab71 the salt of a hexabasic acid1 ,taylor found average molecular weights tending to a minimum of one-seventh of the formula weight1 as we should expect from the ionization of the salt into seven smaller molecules1 7,c#ab,o#ab7,na#f #f ,na 7,c#ab,o#ab7f4 ,quantitative ,evidence4--,some of the most exact quantitative evidence bearing on these relations1 such as the results of investigations1 by ,griffith and by ,taylor1 on the freezing-point depressions of solutions of electrolytes1 may be briefly considered4 ,the depression of the freezing-point of a given solvent by a solute is proportional to the concentration of the solute or proportional to its osmotic pressure4 ,further1 according to the ,van 't ,hoff ,hypothesis 7p4 #ae71 the osmotic pressure at a constant temperature is dependent only on the number of molecules present in unit volume1 and not on the nature or composition of the molecules3 the freezing-point of the solvent is depressed1 likewise1 proportionally to the total concentration of the solute1 irrespective of the fact whether the solution contains only one1 or more than one molecular species4 ,the ratio1 observed depression _/ concentration1#aaf or _/ ,c1 should be constant1#aag therefore1 in a given solvent1 for dilute solutions of all kinds of solutes1 simple or mixed4 ,griffith#aah found1 for a solution of cane sugar1 a non-electrolyte1 in water1 the ratio of the freezing-point depression to the concentration to be #a4heh4 ,for instance1 the freezing-point of a #j4ja molar solution of cane sugar 7#c4db grams of cane sugar per liter2 ,c#ab;,h#bb,o#aa #cdb7 is found to be #j4jaheh1 and #j4jaheh _/ #j4ja #a4heh4 ,this ratio should be the same1 as stated above1 according to van 't ,hoff's theory of solutions1 for dilute aqueous solutions of all solutes4 ,but the ratio _/ ,c for an aqueous solution of potassium chloride1 an electrolyte1 was found to increase slowly and continuously until in #j4jjjc molar solution the ratio #c4gb was found1 which is exactly twice the value obtained with cane sugar4 ,the result indicates1 therefore1 a gradual dissociation of the potassium chloride with increasing dilution1 and a dissociation1 ultimately1 of each molecule of the salt into two new molecules1 in all respects exactly as demanded by the theory of ,arrhenius4 ,loomis#aai found in a similar way a ratio of #c4fa for ,h,cl1 #c4ga p#jfi for ,,koh1 #c4fj for ,k,cl1 #c4fg for ,na,cl1 #c4gc for ,,hno#c1 etc41 when #j4ja molar aqueous solutions were used4 ,for similar solutions of calcium chloride ,ca,cl#b1 magnesium chloride ,mg,cl#b1 and sodium sulphate ,na#b,,so#d1 the value #e4jg was found as the ratio between the depressions of the freezing-point and the concentration of the salts in extremely dilute solutions--a result showing1 plainly1 a dissociation of each salt into three smaller molecules4 ,the limit #e4fg for such a dissociation is not quite reached in these cases1 because salts of the types ,me,x#b and ,me#b,y ionize less readily than do the electrolytes ,me,x1 a fact also shown by their conductivities4 ,we thus find that the most exact work on molecular weight determinations in dilute aqueous solutions agrees excellently1 as does the conductivity of such solutions1 with the demands of the theory of ionization1 a fact which is particularly impressive because osmotic pressure and electrical conductivity are in no wise fundamentally related phenomena1 and yet each1 as a measure of ionization or electrolytic dissociation1 leads independently to the same conclusion4#abj ,the ,chemical ,composition of the ,ions of ,electrolytes4--,accepting the theory of ,arrhenius1 we may now inquire more closely than heretofore1 first1 what compounds are subject to electrolytic dissociation1 and then1 what the chemical composition of their ions is and how it is determined4 ,the compounds which are dissociated into ions1 by solvents which cause ionization 7p4 #fb71 comprise the salts1 the acids and the bases2 chemists are1 in fact1 more inclined now to invert the statement and say that those substances which have long been known as salts1 acids and bases1 owe the essential characteristics1 which led to their classification1 to the fact that they are ionizable 7see pp4 #gb-hb74 ,the composition of the ions1 formed from the simpler of these compounds1#aba may be expressed by saying that the metal component or metal-like component 7hydrogen1 ammonium7 forms the positive ion 7cation1 metal ion7 and all the rest of the p#jgj molecule forms the negative ion 7anion1 acid ion#abb74 ,thus1 sodium chloride1 nitrate1 sulphate1 phosphate yield the sodium-ion1 ,na1 and the chloride 7,cl71 nitrate 7,,no#c71 sulphate 7,,so#db71 or phosphate 7,,po#dc7 ions2 cupric nitrate ,cu7,,no#c7b dissociates into the cupric ion 7,cu#b7 and the nitrate ion1 calcium sulphate ,ca,s,o#d into the calcium-ion 7,ca#b7 and the sulphate-ion1 aluminium sulphate ,al#b7,,so#d7c into the aluminium-ion 7,al#c7 and the sulphate-ion4 ,but the question arises1 as to how we know that the salts mentioned produce ions of the given composition2 why1 for instance1 should sodium nitrate be considered to dissociate into sodium1 ,na1 and nitrate ions1 ,,no#c1 the nitrogen atom carrying all of the oxygen atoms with it in the negative ion8 ,illustration3 ,,fig4 #ac4 ,the composition of the ions of a salt can be determined experimentally#abc by devices of which the ,u-tube experiment 7p4 #de7 may be considered to be a simple type4 ,for instance1 if we wish to determine the composition of the ions of sodium nitrate1 we could cover a solution of sodium nitrate with a solution1 say1 of hydrochloric acid1 pass a current through the liquids1 and determine the composition of the components that have moved to the negative and positive poles1 respectively4 ,in practice1 the device could be elaborated for the sake of convenience4 ,stopcocks1 for instance1 might be placed in the ,u-tube1 at the points of separation of the nitrate solution and the hydrochloric acid 7see ,fig4 #ac71 the stopcocks being opened only during the passage of the current4 ,or porous plates or cells might be used1 in place of stopcocks1 at these p#jga points4 ,now1 if we assume sodium nitrate to be dissociated1 not into ,na and ,,no#c1 but let us say into positive ions ,na,o and negative ions ,,no#b1 the changes which would result from the passage of a current would be as follows3 starting with the action at the positive pole1 we should find chloride ions discharged and chlorine evolved at the pole 7the evolution of chlorine could be avoided1 if considered desirable1 by the use of a silver anode1 which would absorb the liberated chloride-ion to form insoluble silver chloride on the electrode74 ,at the same time1 hydrogen ions would move out of the space ,p1 being repelled by the positive pole1 and attracted by the negative4 ,at the boundary between the sodium nitrate solution and the hydrochloric acid1 the negative ions of sodium nitrate1 which we are supposing to have the composition ,,no#b1 would move up from ,b toward the positive pole 7cf4 exp41 p4 #de71 being attracted by its charge2 at any moment we should have in any part of ,p as many negative ions 7,cl and ,,no#b71 as there are hydrogen ions1 the solution showing no excess of free electricity at any point4 ,now1 if ,,no#b were the ion that moved up into the space ,p1 then we should presently find nitrous acid around the positive pole in space ,p1 ,h and ,,no#b combining to form nitrous acid1 ,,hno#b4 ,but1 as a matter of experiment1 although the tests for nitrous acid belong to the most sensitive ones in chemistry1 no trace of this acid is found there2 what we do find is nitric acid1 ,,hno#c1 resulting obviously from the presence in space ,p of both hydrogen ions and nitrate ions1 ,,no#c1 which have moved up from space ,b4 ,it is clear1 that the presence of nitric acid in the region around the positive pole means that the nitrogen atoms must have carried with them all three of the oxygen atoms of the nitrate--in a word1 that the composition of the negative ion of sodium nitrate is ,,no#c and not1 say1 ,,no#b4 ,similarly1 considering what happens in space ,n1 round the negative pole1 we have here an evolution of hydrogen1 a migration of some chloride ions out of ,n into the space ,c1 and1 at the same time1 a migration of the positive ions of space ,c into the division ,n4 ,on examining the solution in ,n1 we now find sodium chloride1 with unchanged hydrochloric acid1 exactly what we should expect from the migration of the ion ,na toward the negative electrode4#abd ,if the positive ion were1 say1 p#jgb ,na,o1 we should expect to obtain either some of the hypochlorite ,na,o,cl 7,na,o ,cl71 or1 at least1 an evolution of oxygen in this place1 since sodium chloride is formed4 ,as a matter of experiment1 no oxygen is evolved here1 and no trace of hypochlorite is found in ,n round the negative pole1 although the tests for hypochlorites are extremely sensitive4 ,comparatively simple methods1 in principle of the nature outlined1 enable us1 then1 to determine experimentally the composition of the ions into which ionizable compounds1 salts1 acids and bases1 dissociate4 ,whenever any doubt may exist about the composition of the ions of a given electrolyte1 this device may be employed to settle the matter1 and there will presently be occasion to employ the ,u-tube for such a purpose4 ,ionization and ,chemical ,activity4--,the fact that the theory of ionization gives us adequate explanations of the conductivity shown by dissolved electrolytes and of their abnormally high osmotic pressures1 would have been in itself of interest to chemists2 but1 if its applications were limited to these phenomena1 we should not be considering it in connection with qualitative chemical analysis1 nor would the theory1 presumably1 have greatly affected the development of chemistry1 as it has done4 ,it is the fact that the electrolytic dissociation of an electrolyte into its ions involves chemical changes of the most profound nature1 and most intimately affects chemical reactivity1 that has made it play1 in the last two decades1 such a leading rle in the development of chemistry1 and that makes it necessary to include its consequences in the consideration of analytical problems1 if one would understand1 as far as present knowledge permits1 the reactions involved in chemical analysis4 ,hydrogen chloride1 as a perfectly dry gas1 is a non-conductor of electricity and1 at the same time1 it is found to be chemically inactive--it does not combine1 for instance1 with dry ammonia#abe or act upon dry calcium carbonate#abf or on dry litmus4 ,hydrogen chloride1 subjected to great pressure at a low temperature1 is liquefied4 ,the liquid is also a very poor conductor of p#jgc electricity#abg and does not show the chemical activity of ordinary1 aqueous hydrochloric acid2 it does not combine with calcium oxide or attack marble1 zinc1 iron or even magnesium4#abg ,a solution of hydrogen chloride in a poorly ionizing medium1 like benzene or toluene1 is an extremely poor conductor4 ,there is an extremely small conductivity indicating only a trace of ionization4#abh ,,exp4 ,a solution of hydrogen chloride1 prepared by passing the dried gas into benzene or toluene 7thiophene-free benzene will not become discolored71 and kept anhydrous by means of fused calcium chloride1 is tested for its conductivity1 by dipping into it electrodes connected with a lighting circuit and a galvanometer4 ,such a solution behaves chemically1 also1 quite differently from the aqueous solutions of hydrogen chloride with which we are familiar3 dry steel nails1#abi dropped into it1 will remain almost unchanged--there is no marked evolution of hydrogen 7exp474 ,perfectly dried marble1 added to it1 will not give rise to the evolution of carbon dioxide#abi 7exp474 ,we find thus1 in all the cases discussed--the nonconducting dry gas1 the anhydrous liquefied hydrogen chloride and the anhydrous benzene solution--an absence of ionization1#acj as indicated by the lack of conductivity1 and1 along with this1 a lack of the familiar action of hydrochloric acid as an acid4 ,if we dissolve the gas in water1 we obtain a well-conducting solution 7exp471 in which1 according to molecular weight determinations1 the p#jgd hydrogen chloride is more or less largely ionized1 and this same solution has all the well-known chemical properties of hydrochloric acid--it evolves hydrogen liberally when given an opportunity to act upon zinc or iron 7exp471 it evolves carbon dioxide copiously when marble is brought into contact with it 7exp474 ,in such an aqueous solution we have both the ions of the acid and the more or less non-ionized hydrogen chloride1 the action 7,h,cl ,h ,cl7 being reversible4 ,now1 since in those cases in which we have admittedly only non-ionized hydrogen chloride1 there is no vigorous chemical action1 we are bound to conclude that1 in the aqueous solution where we have both the non-ionized and the ionized substance1 it must be the new components1 the ions of the acid1 which give this solution its new qualities1 the well-known properties of a pronounced acid4#aca ,this conclusion1 that the acid properties of hydrogen chloride in aqueous solution are due to the ionized hydrogen chloride1 rather than to the hydrogen chloride itself1 is one of fundamental importance4 ,dry ,salts and their ,aqueous ,solutions4--,if the study of the relation of ionization to chemical activity be extended1 it is found that a dry salt1 such as1 for example1 silver nitrate1 in crystals or finely pulverized1 is not perceptibly ionized1 for it is a non-conductor 7exp474 ,the same result is obtained with potassium chromate4 ,if the dry powders are intimately mixed1 there is no chemical action between them1 no perceptible change occurs4 ,the aqueous solutions of the salts are excellent conductors 7exp471 as are the aqueous solutions of almost all salts2 the dissolved salts are therefore largely ionized4 ,as soon as the ionizing medium1 water1 is added to the dry1 yellow mixture of silver nitrate and potassium chromate1 instantly a chemical change results--red silver chromate1 ,ag#b;,cr,o#d1 is precipitated 7exp474 ,now1 in the aqueous solution of these salts we have both non-ionized molecules and their ions3 ,ag,n,o#c ,ag ,,no#c1 ,k#b;,cr,o#d #b ,k ,cr,o#db4 ,since there is no interaction when the dry salts1 containing only the non-ionized substances1 are mixed1 and since there is interaction p#jge when the solutions are mixed1 in which both the non-ionized and the ionized salts are present1 one must conclude again that the formation of silver chromate is the result of the action of the silver ions on the chromate ions in the solution4 ,in point of fact1 there could hardly fail to be an action1 since the positive silver ions and the negative chromate ions1 moving in all directions through the solution1 must collide and be discharged1 or combine1 to form molecular silver chromate4 ,this salt happens to be very difficultly soluble1 and to be colored red1 as well1 so that silver chromate is precipitated and is immediately recognizable4 ,the two dry powders in the experiment were allowed to be in contact for only a few moments4 ,it is important to note1 therefore1 that dry sodium acid carbonate and dry potassium acid tartrate are also nonconductors 7exp471 and that the intimate mixture of these two powders is kept for years in the well-known form of baking powders without appreciable decomposition--yet best in tin vessels1 to exclude moisture4 ,the aqueous solutions1 however1 are good conductors 7exp471 and1 when dissolved1 these salts are more or less ionized4 ,the addition of water to the mixed salts 7exp47 leads at once to the well-known action1 carbon dioxide being liberated and sodium-potassium tartrate or ,rochelle salt being formed4 ,behavior of ,fused ,salts4--,it may be objected that there are common cases1 where dry salts are known to act upon each other2 barium sulphate is fused with sodium carbonate to convert the former into the carbonate1 ,ba,s,o#d ,na#b;,,co#c ,na#b,,so#d ,ba,c,o#c4 ,before one decides that this must be an instance of the action of non-ionized salts on each other1 the conductivity of dry salts under the conditions of the experiment1 namely at an elevated temperature1 must be examined4 ,there is no difficulty in recognizing that while dry sodium carbonate or potassium nitrate at ordinary temperatures does not conduct a current1 and is not perceptibly ionized1 each salt1 when fused1 becomes an excellent conductor 7exp41#acb with potassium nitrate74 ,it is1 in fact1 well known that1 in many electrolytic operations1 fused salts#acc are used in place p#jgf of solutions4 ,it must be added that the heat1 not the change of state1 causes the ionization1 careful work having shown that conductivity begins to be appreciable below the point of fusion4 ,,exp4 ,two platinum wires1 fused1 one inch apart1 into a glass rod1 are connected with a sensitive galvanometer and the lighting circuit4 ,when the glass is warmed1 a current is found to pass4 ,the action between barium sulphate and sodium carbonate at a high temperature does not mean1 then1 that the non-ionized salts interact2 on the contrary1 we find that1 under such conditions1 coincident with the evidence of reactivity1 we have also decided conductivity--again indicating decided ionization4 ,dry ,salts at ,ordinary ,temperatures4--,inasmuch as ordinary temperatures are still far removed from the absolute zero1 one must suppose that dry salts must be ionized1 minimally at least1 even at room temperature1 and should therefore react with each other4 ,presumably they do1 only so slowly1 as a result of the minimal degrees of ionization1 and of the few chances of collision between ions of opposite charges1 owing to the restricted range of the molecular motions1 that the total change is imperceptible4 ,critical work on the question is most desirable4 ,in this connection it maybe said that ,spring#acd found that dry salts do interact at ordinary temperature1 when subjected to great pressures1 provided the volume of the products is smaller than the volume of the initial substances4 ,whether this action is due to the ionization of the salts1 minimal as it is1 or whether we have here a case of interaction of non-ionized molecules1 has not1 it seems1 been determined2 it would require difficult quantitative work to settle the question4 ,influence of ,light and ,heat4--,it is apparent that heat1 a form of energy1 contributes to the dissociation of ionogens1 and it is natural that we should consider other forms of energy1 e4g4 light1 to have the same power4 ,one may speculate about the possibility of light inducing chemical action 7e4g4 in starting the combination of hydrogen and chlorine1 or in photography7 by its ionizing power1 and about the possibility that rapid combination of oxygen and hydrogen follows the application of a flame to the mixture1 as the result of increased ionization of the components at the elevated temperature of the flame and of the burning gases4 ,the experimental evidence shows that1 in some actions of this nature1 ionization is an important factor1 while in other instances it appears to be negligible4#ace p#jgg ,conclusions4--,it appears that we must accept the conclusion1 that the reactions of salts1 acids and bases 7ionogens7 in aqueous solution 7the so-called salt reactions7 are the reactions of the ions and not of the non-ionized molecules4 ,this conclusion is of the greatest and most practical importance in our science4 ,it is the natural inference from the results of the qualitative experiments described in the three preceding sections4 ,its final adoption1 however1 is based on the existence of a great mass of quantitative evidence1 and to the consideration of some of this we now turn4 ,quantitative ,relations4--,if the active components in aqueous solutions of acids1 bases and salts are the ions1 rather than the undissociated compounds1 then quantitative data supporting such a conclusion should be found4 ,such quantitative confirmation1 from the point of view of chemical activity1 is not lacking4 ,only a small part of the data can be considered here4 ,conductivity measurements1 and the lowering of freezing-points and the elevation of boiling-points1 show that there are very decided differences in the degrees of ionization of different acids and bases in solutions of equivalent concentration4 ,for instance1 potassium hydroxide is somewhat more ionized than is barium hydroxide1 and decidedly more so than ammonium hydroxide1 a fact that can readily be demonstrated by the conductivities of the solutions#acf3 ,,exp4 ,equivalent solutions 7#a _/ #aj normal7 of the three bases are introduced into three vertical tubes1 containing electrodes connected1 in parallel1 with a lighting circuit and with small electric lamps4 ,when the two electrodes in each of the three tubes are at equal distances from each other1 the lamp connected with the potassium hydroxide solution glows most brightly1 that connected with the barium hydroxide solution a little less brightly1 and the lamp connected with the ammonium hydroxide solution does not glow at all--not enough current is carried through the ammonium hydroxide solution to heat the filament in the corresponding lamp sufficiently to make it red4 ,now1 the current1 for a given fall of potential1 is proportional to the conductivity of a solution 7p4 #dh7 and1 in the equivalent solutions#acg the conductivity depends on the proportion of charged particles 7the degree of ionization7 of the base4 ,it is clear then1 that ammonium hydroxide is very much less ionized than are the two other bases4 p#jgh ,the resistance in a tube may be reduced1 and the conductivity increased1 by reducing the distance through which the current must be carried1 i4e4 by bringing the electrodes closer together4 ,in the solution of barium hydroxide1 we find that we must reduce the distance between the electrodes to about five-sixths the corresponding distance in the potassium hydroxide solution before we obtain1 approximately1 as bright a lamp from the current passing through it1 and in the case of ammonium hydroxide1 we must bring the electrodes so close together that they almost touch1 the distance being only one or two hundredths of the distance between the electrodes in the potassium hydroxide solution4 ,for the degrees of ionization of the three bases we have1 approximately1 the relation ,k 3 ,ba 3 ,,nh#d33 d,k 3 d,ba 3 d,,nh#d1 if we indicate by d,k1 d,ba1 d,,nh#d the distances between the electrodes in the three solutions when the lamps are of uniform brightness1 i4e4 when the same quantity of current passes through each solution4 ,in this deduction1 the conductivities of the bases at infinite dilution 77 are taken to be the same1 which is roughly true4 ,the experiment gives us a rough measure of the relative conductivities and the relative degrees of ionization of the three bases4 ,it shows that potassium hydroxide is somewhat more ionized than is barium hydroxide1 in equivalent solution1 and decidedly more than is ammonium hydroxide4 ,limiting the further discussion1 at this moment1 to potassium hydroxide and ammonium hydroxide1 we should find that1 since in equimolar solutions1 a larger portion of the former is ionized than of the latter1 the potassium hydroxide solution must contain the larger proportion or concentration of hydroxide-ion1 ,,ho1 which is the characteristic ion of bases4 ,it should1 therefore1 show the chemical characteristics of a base much more decidedly than the ammonium hydroxide solution4 ,that such is the case can be very simply shown by adding equal quantities 7#j4a c4c47 of the #j4a molar solutions to equal volumes 7#ej c4c47 of water#ach containing some phenolphthalen4 ,this is an indicator for bases and acids1 like litmus1 but it is less sensitive to hydroxide-ion than is litmus4 ,we find that the potassium hydroxide causes a very decided change1 producing a deep red color with the phenolphthalen1 whereas the ammonium hydroxide only produces a pink hue4#aci p#jgi ,in all the chemical changes produced by these alkalies1 the same difference in intensity of action is shown1 that is here exhibited towards indicators4 ,if1 for example1 we measure the rate of change in an action1 which is slow enough to be measured and which proceeds quantitatively in proportion to the concentration of hydroxide-ion1 we find that the measured rates of change indicate the same ratio in the concentrations of hydroxide-ion in potassium and ammonium hydroxide solutions1 as is indicated by quantitative conductivity measurements4 ,an action suitable for the purpose is the saponification of an ester1 such as ethyl acetate4 ,under the influence of an alkali1 like potassium hydroxide1 ethyl acetate is decomposed1 more or less rapidly1 into an acetate and alcohol3 we have1 for instance1 ,,ch#c;,,co#b;,c#b;,h#e ,,koh ,,ch#c;,,co#b,k ,c#b;,h#e,,oh4 ,the rate of saponification is found to be proportional to the concentration of hydroxide-ion1 and not to the total concentration of the base1 and the action may be formulated more accurately as follows3 ,,ch#c;,,co#b;,c#b;,h#e ,k ,,ho ,,ch#c;,,co#b ,k ,c#b;,h#e,,oh or ,,ch#c;,,co#b;,c#b;,h#e ,,ho ,,ch#c;,,co#b ,c#b;,h#e,,oh4 ,for ammonium hydroxide we have similarly1 ,,ch#c;,,co#b;,c#b;,h#e ,,nh#d ,,ho ,,ch#c;,,co#b ,,nh#d ,c#b;,h#e,,oh4 ,now1 ,arrhenius#adj proved that the rate of saponification of ethyl acetate by ammonium hydroxide1 which is very much slower than the rate of saponification by potassium hydroxide of equivalent concentration1 does agree quantitatively1 indeed1 with the rate demanded by the theory of ionization1 when the hydroxide-ion is considered the active component of the bases1 to which the saponification is due4 ,,exp4 ,a rough idea of the difference in the chemical actions of the two bases may be obtained by observing their effects on the ester1 methyl acetate1 which is decomposed into an acetate and methyl alcohol rather rapidly4 ,to #ej c4c4 of 7,,co#b free7 water containing some phenolphthalen1 #aj c4c4 of #j4a molar potassium hydroxide is added2 a similar mixture with #aj c4c4 of #j4a molar ammonium hydroxide solution is prepared4 ,to each of the solutions1 #b c4c4 7an excess7 of methyl acetate is added 7to the ammonium hydroxide solution first71 and the mixtures are shaken for a moment4 ,at room temperature1 the mixture containing potassium hydroxide will become pale pink in a few minutes1 and colorless soon thereafter1 while the mixture p#jha containing ammonium hydroxide will still be deep red at the end of #de minutes4#ada ,in the following tables are summarized some of the results which have been obtained in comparing the activity of bases1 in saponifying methyl acetate1 and the concentrations of the hydroxide-ion1 in the solutions of the bases1 as determined by conductivity measurements4 ,the comparisons are made by representing the activity of the hydroxide-ion in a solution of lithium hydroxide by #ajj and by expressing the ratio of the activity of a given base to that of the lithium hydroxide in percentages of the activity of the latter4 ,all the bases were used in #j4jbe molar concentration1 and their degrees of ionization are given in the last column of the table4 ,,chemical ,,activity ,,of ,,bases ,,and ,,their ,,ionization,a ,relative ,base4 ,activity4 ,concentration of ,,ho4 ,lithium hydroxide #ajj #ig ,potassium hydroxide #ih #ig ,sodium hydroxide #ih #ig ,ammonium hydroxide #b #b4e ,ethyl ammonium hydroxide #ab #af4 ,,table ,,note3 ,a4 ,whetham1 ,theory of ,solutions1 p4 #cch 7#aijb74 7,cf4 ,walker1 ,introduction to ,physical ,chemistry1 p4 #bgg 7#ahii747 ,an ester is decomposed also under the influence of acids1 in aqueous solution1 into an organic acid and an alcohol1 and cane sugar is similarly decomposed into glucose and fructose 7grape sugar and fruit sugar73 ,c#ab;,h#bb,o#aa ,h#b,o ,c#f;,h#ab,o#f ,c#f;,h#ab,o#f4 ,both actions are found to be caused by the influence of the hydrogen ions of the acids used and to proceed1 at a given temperature1 with a velocity proportional to the concentration of the hydrogen ions4 ,now1 in #j4a molar solution1 acetic acid is very little ionized 7#a4c71 as compared with hydrochloric acid 7#ia71 the degrees of ionization being determined by conductivity measurements 7p4 #ej72 the relation may easily be demonstrated with the aid of the conductivity apparatus used to show the difference in ionization between potassium hydroxide and ammonium hydroxide4 ,in the presence of #j4a molar hydrochloric acid1 the decomposition of cane sugar actually proceeds at #gi times the rate that it does in the presence of #j4a molar acetic acid4 ,the ratio of the concentrations of the hydrogen-ion in the two p#jhb solutions is1 in fact1 #gj 3 #a4 ,there is1 therefore1 close agreement#adb between the relative chemical activity of the two acids and the relation demanded1 if we assume1 on the basis of the theory of ionization 7p4 #gg71 that the chemically active components of the acids are their ions and particularly their hydrogen ions4 ,in the following table1 the relative activities of acids1 in accelerating the decomposition of methyl acetate by water1 are contrasted1 in a similar fashion1 with their relative conductivities4 ,the conductivities of acids depend to such an extent on the concentration of hydrogen-ion1 which moves five times1 or more1 faster than the anions and carries therefore the greater part of the current1 that the conductivities of acids1 in equivalent concentrations1 may be considered an approximate measure of their relative degrees of ionization and of the concentrations of hydrogen-ion4 ,for the purpose of comparison the activity and the conductivity of molar hydrochloric acid are both represented by #ajj4 ,all the acids were used in normal solutions4 ,,chemical ,,activity ,,of ,,acids ,,and ,,their ,,ionization4,a ,acid4 ,activity4 ,conductivity4 ,hydrochloric acid #ajj #ajj ,nitric acid #ib #ajj ,sulphuric acid #gd #fe ,acetic acid #j4c #j4d ,formic acid #a4c #a4g ,chloracetic acid #d4c #d4i ,tartaric acid #b4c #b4c ,,table ,,note3 ,a4 ,whetham1 ,theory of ,solutions1 p4 #cch4 ,in the following chapters and1 indeed1 throughout our further work1 we shall continually meet additional instances of the quantitative relation between chemical activity and ionization4 ,in fact1 the results obtained in the field of quantitative measurement of chemical action1 of which the above are single instances1 have demonstrated1 more than anything else1 the value of the theory of ionization to chemistry and the necessity of taking it into account in expressing the results of chemical action in mathematical terms4 p#jhc ,summary4--,measurements made1 then1 in three great and independent fields of investigation1 electrical conductivity1 osmotic pressure and the allied relations1 and chemical activity1 bring independent testimony to the correctness of the fundamental assumptions of ,arrhenius's theory of ionization4 ,in the quantitative study of solutions of electrolytes1 wherever secondary disturbing influences are eliminated or are taken into account as far as possible1 the three lines of investigation give results which agree satisfactorily#adc as to the degree of ionization of the electrolytes under examination4 ,with the aid of this theory1 predictions of the course of chemical action may now be made more definitely and with more assurance than ever before in the history of chemistry4 ,chemical ,activity of ,non-ionized ,molecules4--,the conclusion reached1 on the basis both of qualitative and1 particularly1 of quantitative evidence1 that the reactions of salts1 acids and bases 7ionogens7 in aqueous solutions 7the so-called salt reactions7 are the actions of the ions and not of the non-ionized molecules1 does not necessarily mean that the non-ionized molecules are altogether inactive chemically4 ,some chemists believe that ions have only the advantage of an enormously greater degree of reactivity4#add ,if the atoms in a molecule carry electric charges even prior to their separation 7ionization71 as expressed for instance by the formula ,h,cl for hydrogen chloride 7p4 #dc71 it can be readily seen that an action#ade resulting from the collision of a molecule of hydrogen chloride with a molecule of potassium hydroxide ,h,cl ,,ho,k ,k,cl ,,ho,h would1 in some respects1 resemble the ionic action ,h ,cl ,k ,,ho ,k ,cl ,,hoh4 ,the latter would probably have the advantage of a considerably smaller resistance to the action1 and consequently of a far greater speed4 ,but the question of supreme importance and interest to chemistry is the question as to which actions are found experimentally to be of moment in any given case4 ,now1 a great mass of corroborative evidence shows that for the interactions of ionogens in aqueous solutions the ionic actions1 probably on account of their enormous speeds1 are the important ones4 p#jhd ,on the other hand1 there are large numbers of compounds1 especially among organic substances1 which do not appear to ionize to a measurable extent and whose actions1 in large part at least1 appear to be the actions of non-ionized molecules4 ,it is characteristic that most of these actions take place at slow1 very frequently easily measurable1 rates of speed4 ,critical study shows that even for such actions ionization often plays a very important rle1 at least in some of their stages1 and throughout the field of organic chemistry the intimate relations between electrical phenomena and chemical activity can be readily recognized4#adf ,but these relations are not obvious ones and do not1 as yet1 play a dominant rle4 ,it is because analytical chemistry deals predominantly with the reactions of ionogens1 that the study of the reactions of ions will demand our extended attention4 ,reactions in ,non-aqueous ,solutions4--,kahlenberg#adg has made some interesting and important1 although not conclusive1 contributions to the problem of chemical activity of ionogens in non-aqueous solutions4 ,he has found1 for instance1 that zinc1 left in contact with a benzene solution of hydrogen chloride carefully freed from moisture1 displaces hydrogen4#adh ,cadmium1 aluminium and magnesium1 on the other hand1 do not evolve hydrogen in such a solution4#adi ,the solution shows an enormous resistance to the passage of an electric current1 and the conclusion is drawn by ,kahlenberg that the liberation of hydrogen is due to the action of non-ionized hydrogen chloride on the zinc4 ,it is evident1#aej from ,walden's equation showing the relation between the ionizing power and the dielectric constant of a solvent 7p4 #fc71 that the presumption is that hydrogen chloride in benzene solution is not absolutely non-ionized1 but rather that it is ionized in traces4#aea ,no exact measurements of the p#jhe degrees of ionization of hydrogen chloride in benzene solution have been made2 that the solution shows an enormous resistance to the passage of the electric current and can be1 at best1 very little ionized1 is all that has been established4 ,in default of exact data1 the semiquantitative determination by ,kablukoff1 showing that a #j4be molar solution of hydrogen chloride in benzene has a resistance of #abj #ajf ohms1 is of interest4 ,from the meager data concerning the dimensions of the electrodes used1 one may calculate 7with the aid of a not unreasonable assumption as to the limiting value of the conductivity1 at infinite solution7 that the degree of ionization of the acid in the solution is perhaps of the order #e;,e#i1 and the concentration of hydrogen-ion1#aeb consequently1 roughly #aji4 ,now1 the evolution of hydrogen by means of zinc1 in aqueous solutions1 takes place according to the equation ,zn 1 #b ,h ,zn#b ,h#b 1 and depends on a ratio of the concentrations of zinc-ion and hydrogen-ion#aec 7,chapters ,,xiv and ,,xv1 q4v474 ,even if the concentration of hydrogen-ion is very small1 zinc will liberate hydrogen1 provided the conditions are such that the concentration of zinc-ion cannot reach a large enough value to satisfy the equilibrium ratio1 and stop the action4 ,now1 in an alkaline solution1 zinc-ion is converted into zincate-ion 7,zn#b #d ,,ho ,zn,o#bb #b ,,hoh7 and a large concentration of zinc-ion cannot accumulate4 ,the consequence is that zinc liberates hydrogen freely even from alkaline solutions1 for instance from molar solutions of potassium hydroxide1 in which the concentration of hydrogen-ion1 roughly #ajad1 is very much smaller than that calculated for the benzene solution of hydrogen chloride 7namely1 #aji74 ,now1 although the values of the solution-tension constants of elements change most decidedly with a change of solvent1 it seems likely#aed that their ratios1 on which their mutual displacement depends1 will not be found materially altered4 ,zinc chloride being insoluble in benzene1 the ratio for equilibrium may not be fulfilled for zinc in contact with a benzene solution of hydrogen chloride4 ,hence1 with that solvent1 the evolution of hydrogen may1 so far as it goes1 very well be due to precisely the same machinery as that operating in aqueous solution4 ,the liberation goes on until the metal is protected against any further action by a film of the solid chloride4 ,it seems1 therefore1 at least possible1 that the evolution of hydrogen observed by ,kahlenberg and his collaborators#aee is a purely ionic action1 the same as the similar p#jhf action in aqueous solution has been proved to be by quantitative measurements4#aef ,only exact measurements1 comparable with those made in aqueous solutions1 can settle the question at issue1 and until such quantitative evidence is forthcoming1 a definite conclusion that the action of hydrogen chloride in benzene solution is or is not an ionic action is not warranted by the facts4 ,equally interesting are ,kahlenberg's observations of interaction between hydrogen chloride in benzene solution and a similar solution of copper oleate4 ,each solution shows absence of appreciable conductivity1 yet1 when the solutions are mixed1 precipitation of copper chloride occurs instantly4 ,whether we have here an instantaneous action between non-ionized molecules1 as claimed by the observer1 or whether the minimal ionization#aeg of the hydrogen chloride and copper oleate1 the existence of which we have a right to assume1 is sufficient to account for this rapid action1 both components being in solution and intimately mixed1 is a question of the greatest interest4 ,but until quantitative measurements of all the factors involved in chemical actions in benzene solution are obtained1 a very difficult1 but necessary task1 which the discoverer of the action omitted to perform1 no definite conclusion whatever can be based on such results1 interesting as they are4 ,water1 although it is only minimally ionized 7tables1 ,chapter ,,vi71 hydrolyzes salts like potassium cyanide and aluminium chloride almost instantly1 and it has been rigorously proved that the resulting condition of equilibrium involves the ions of water#aeh 7,chapter ,x74 ,with the possibility that the well-known enormous speeds of action of ions may completely offset the tremendous reduction in concentration of the hydrogen-ion1 in a benzene solution of hydrogen chloride as compared with an aqueous solution1 further analysis of the relations is imperative4#aei ,until such investigations have been carried out1 we must consider p#jhg it possible that the reactions of hydrogen chloride in benzene solution may be reactions of its non-ionized molecules or reactions of its ions4 ,in view of the undoubted minute concentrations of the latter1 as compared with aqueous solutions1 and in view of the inertness of non-ionized hydrogen chloride in aqueous solutions as compared with the activity of its ions1 a benzene solution of hydrogen chloride should show far less ionic activity than an aqueous solution1 and that such is the case is brought out clearly by ,kahlenberg's interesting experiments4 ,some ,applications of the ,chemical ,activity of ,ions to ,qualitative ,analysis4--,the knowledge that aqueous solutions of ionogens show the reactions of the ions contained in them1 gives us a clear1 sharply defined interpretation of many of the simpler facts of qualitative analysis4 ,the elementary observation that a large number of hydrogen derivatives show acid properties and a considerable number of others do not 7at least not to a sufficient extent to be appreciable71 finds its simplest explanation in the fact that all solutions showing acid properties have these properties as the result of the presence of a common component1 namely the hydrogen-ion4 ,the acid properties are1 in fact1 the properties of this one substance and no other4 ,thus hydrochloric1 nitric1 sulphuric1 carbonic acids are acids because they are dissociated more or less1 liberating hydrogen ions2 and compounds like marsh-gas ,,ch#d1 ammonia ,,nh#c1 benzene ,c#f;,h#f1 in spite of the presence of a great deal of hydrogen in their molecules1 are not acids1 because they do not1 to an appreciable extent1#afj ionize as do the first compounds mentioned4 ,in the same way1 glycerine ,c#c;,h#e7,,oh7#c1 although it is a trihydroxide1 does not show the characteristic actions of the hydroxides of potassium1 barium1 aluminium1 of the metal hydroxides in general--the latter are more or less ionized1 forming the characteristic ion of bases1 the hydroxide-ion ,,ho2 but glycerine does not appear to ionize into ,c#c;,h#ec and ,,ho4 ,the well-known observation of qualitative analysis1 that potassium chlorate solutions do not precipitate silver chloride from silver nitrate1 while potassium chloride and other chlorides do so at once1 is now understood as being the result of the fact that the chlorates produce the chlorate-ion ,cl,o#c 7see page #gj for the method of determining its composition71 while the chloride-ion p#jhh is required for the precipitation of silver chloride4 ,chlorplatinic acid ,h#b,pt,cl#f1 in spite of the large proportion of chlorine in its composition1 does not precipitate silver chloride1 but rather silver chlorplatinate1#afa a yellow salt1 insoluble in ammonia1 and it does so because its ions#afb are ,h and 7,pt,cl#fb74 ,perhaps the most instructive case of this kind1 that we can study1 is that of iron in ferrous and ferric salts4 ,exceedingly sensitive tests are known for the ferrous and the ferric ions4 ,thiocyanates produce an intensely red salt1 ,fe7,,scn7#c1 when added1 for instance1 to ferric chloride2 potassium ferrocyanide1 ,k#d;,fe7,,cn7#f1 precipitates ferric ferrocyanide1 ,fe#d;,fe7,,cn7#fc1 ,prussian blue1 from ferric chloride solutions2 ammonium hydroxide precipitates quantitatively the insoluble red ferric hydroxide 7exps474 ,with ferrous salts1 potassium ferricyanide ,k#c;,fe7,,cn7#f precipitates ferro-ferricyanide ,fe#c;,fe7,,cn7#fb1 ,turnbull's blue2 ammonium sulphide precipitates black ferrous sulphide 7exps474 ,now1 in two of the reagents used1 potassium ferro- and ferricyanide1 iron is present according to the formul given4 ,if one should attempt to demonstrate its presence by means of these tests--among the most sensitive and most reliable tests known in analysis--one would fail utterly4 ,thiocyanates do not produce even the faintest tinge of pink in potassium ferricyanide solution#afc2 ammonium hydroxide does not precipitate any ferric hydroxide 7exps474 ,ammonium sulphide does not precipitate the least trace of a black sulphide from a ferrocyanide solution1 and when the latter is mixed with the ferricyanide solution1 no trace1 either of ,prussian or ,turnbull's blue1 is shown 7exps474 ,the contrast between the behavior of these salts and ferrous and ferric salts is now sharply and definitely interpreted1 as being the result of the contrast in their ionization1--the color tests we use are extremely sensitive tests only for the ferric and ferrous ions1 ,fe#c and ,fe#b1 respectively1--but potassium ferrocyanide ionizes into potassium ions and the negative ferrocyanide ions ,fe7,,cn7#fd1 and shows the actions of ferrous ions as little as chlorate ions ,cl,o#c exhibit the reactions of chloride ions ,cl4 ,potassium ferricyanide1 in turn1 gives rise to trivalent1 negative ferricyanide ions ,fe7,,cn7#fc and not to ferric p#jhi ions4#afd ,if any doubts arise on this point1 one can decide the question readily by experiment4 ,when a concentrated solution of potassium ferricyanide is placed in a ,u-tube under a solution of some colorless electrolyte1 such as sodium sulphate1 and plates connected with a battery are inserted1 there is no difficulty 7exp47 in seeing that the yellow ion1#afe containing the iron1 moves to the positive pole and not to the negative4 ,the iron is1 therefore1 as a matter of experiment1 part of a negatively charged substance4 ,that iron is really present in these compounds can be shown most effectively if we destroy the salts3 ,,exp4 ,dry1 pulverized potassium ferrocyanide is intimately mixed with dry potassium carbonate and the mixture heated in a hard glass test tube4 ,when the whole mass has become red-hot1 insuring complete decomposition1 the hot 7not red-hot7 tube is plunged into water2 the salts are extracted and particles of metallic iron are left undissolved4 ,the action is ,k#d;,fe7,,cn7#f ,k#b;,,co#c #f ,,kcn ,fe,c,o#c ,fe,c,o#c ,fe,o ,,co#b and ,fe,o ,,kcn ,,kcno ,fe4 ,if the iron is dissolved in a little dilute hydrochloric acid and oxidized to the ferric condition1 by the addition of a few drops of bromine water1 the intensely red solution characteristic of ferric salts may be readily obtained1 when a thiocyanate is added to the solution4 ,,footnotes3 #aad ,loomis4 7,cf4 ,whetham1 ,theory of ,solution1 p4 #cbj 7#aijb747 #aae ,loomis2 and ,e4 ,h4 ,griffith4 7,cf4 ,whetham1 loc4 cit47 #aaf ,expressed in moles per liter4 #aag #a 3 #b444 ,c#a 3 ,c#b444 or #a _/ ,c#a #b _/ ,c#b a constant4 #aah ,cf4 ,whetham1 loc4 cit41 pp4 #adg1 #aeh4 #aai ,ibid41 p4 #cbj4 #abj ,in regard to the degrees of ionization1 as shown by freezing-point depressions and conductivities of salts1 see also ,a4 ,a4 ,noyes1 ,report of the ,congress of ,arts and ,sciences1 ,st4 ,louis1 #aijd1 ,vol4 ,,iv1 p4 #cac4 #aba ,see ,chapter ,,xii1 in regard to so-called complex ions and their salts4 #abb ,the term acid ion is used to designate the acid radical1 when it exists1 in solution1 as an independent charged particle or ion4 ,acid ion is thus a convenient synonym for anion1 just as metal ion1 designating the metal or metal-like radical of a salt1 is used as a synonym for cation4 ,the term1 acid ion1 has been found to convey more quickly and definitely to the student's mind1 than does the term anion1 which component of an acid or salt is referred to4 ,while it is not1 in some respects1 an ideal term1 yet its use seems justified by its very close relation to the term acid radical and by its practical advantages4 #abc ,the principle was first applied by ,hittorf4 #abd ,this does not preclude the possibility that the ion is combined with more or less water and is ,na7,h#b,o7x2 see pp4 #db1 #fe4 #abe ,baker1 ,j4 ,chem4 ,soc4 7,london71 #fe1 #faa 7#ahid71 #gc1 #dbb 7#ahih74 ,on page #fbc of the first article is given a list of chemical actions for which the effect of the presence of moisture has been investigated 7,stud474 #abf ,hughes1 ,phil4 ,mag41 #cd1 #aag 7#ahib7 7,stud474 #abg ,gore1 ,proc4 ,royal ,soc41 #ad1 #bjd 7#ahda74 ,gore found that aluminium was dissolved and that sodium and potassium were attacked by the gas1 even before its liquefaction4 ,it is uncertain whether these positive reactions are reactions of absolutely anhydrous hydrogen chloride or the result of the presence of moisture in the experiments in question1 since ,cohen ,chem4 ,news1 #ed1 #cje 7#ahif71 drying the gas more carefully than did ,gore1 found1 in contrast to the latter1 that metallic sodium may be exposed for several weeks to dry hydrogen chloride gas and retain its lustre4 ,in all experiments demanding the rigorous exclusion of moisture1 more weight must be attached to negative results 7showing lack of activity7 than to positive results4 ,cf4 the controversy between ,baker1 loc4 cit41 and ,gutmann1 ,liebig's ,ann41 #bii1 #c 7#ahih74 #abh ,nernst's ,theoretical ,chemistry1 p4 #cge4 ,kablukoff1 ,z4 phys4 ,chem41 #d1 #dcj 7#ahhi74 #abi ,in regard to the behavior of zinc1 see below1 p4 #hd4 7,cf4 ,kahlenberg1 ,j4 ,phys4 ,chem41 #f1 #ac 7#aijb7 7,stud4747 #acj ,for a fuller discussion of the benzene solution see p4 #hd4 #aca ,the acid character1 in particular1 is due to the hydrogen-ion1 ,h2 see below4 #acb ,the fusion is conveniently made in a platinum dish2 the dish and a platinum cathode are connected with the lighting circuit and an electric lamp4 #acc ,see ,smith1 ,inorganic ,chemistry1 pp4 #eej1 #efi1 #egh1 #ehh1 #fjh1 #faj1 #fhc3 ,college ,chemistry1 #cfa1 #cgc1 #chj1 #chi1 #djd1 #dje1 #ddc 7,stud474 #acd ,j4 ,chem4 ,soc4 7,abstracts7 7,london71 #dj1 #ejd 7#ahha74 #ace ,for positive evidence of the ionizing power of light1 see ,haber1 ,z4 ,elektrochem41 #aa1 #hdg 7#aije74 ,for evidence as to the negligible rle of ionization in the combination of chlorine and hydrogen1 see ,mellor1 ,chemical ,statics and ,dynamics 7#aijd71 p4 #bij4 #acf ,the apparatus described by ,a4 ,a4 ,noyes and ,blanchard for comparing acids is used ,j4 ,am4 ,chem4 ,soc41 #bb1 #gcg 7#aijj74 #acg ,the conductivity depends in this case chiefly on the migration of the fast moving hydroxide ions 7p4 #ef71 common to the three bases4 ,there is little difference in the rates at which the cations move4 #ach ,the water should be free from carbonic acid4 #aci ,the various indicators show different1 specific degrees of sensitiveness to acids 7to hydrogen ions7 and to bases 7to hydroxide ions74 ,that is1 different concentrations of hydrogen-ion or of hydroxide-ion are required to change their colors4 ,as they are particularly useful in demonstrating varying concentrations of these ions1 they will frequently be used in illustrating conclusions reached in the course of our work1 just as they are used extensively in practical analysis4 ,the following tables are intended to give some definite information on this valuable quality4 ,the fourth column of the first table shows the concentration of hydrogen-ion1 required to change the color of the indicator from the tint given in the second column to the tint given in the third column4 ,the second table gives1 similarly1 the concentrations of hydroxide-ion required to produce the changes of tint indicated4 ,the tables refer to results obtained when #j4a c4c4 7about two drops7 of a #j4a to #j4ae solution of the indicator is added to #aj c4c4 of the solution examined4 ,,table ,,of ,,sensitiveness ,,to ,,acids 7,,to ,,hydrogen-,,ion7 ,indicator4 ,from to ,concentration ,h4 ,phenolphthalen ,pink ,colorless #aj;,e#i ,azolitmin,a 7litmus7 ,violet ,violet pink #a;,e#f ,methyl orange ,yellow ,reddish orange #a;,e#c - #j4a;,e#c ,,table ,,note3 ,a4 ,azolitmin is an important component of litmus4 ,,table ,,of ,,sensitiveness ,,to ,,bases 7,,to ,,hydroxide-,,ion7 ,indicator4 ,from to ,concentration ,,ho4 ,phenolphthalen ,colorless ,pink #aj;,e#f ,azolitmin ,violet ,violet blue #a;,e#f - #j4a;,e#f ,methyl orange ,orange ,yellow #a;,e#i ,it is clear that of the three indicators given in the table1 phenolphthalen is the most sensitive to acids1 methyl orange the most sensitive to bases4 ,an extended table of the sensitiveness of many indicators1 on which the above tables are based1 is given by ,salm1 ,z4 phys4 ,chem41 #eg1 #dga 7#aijg74 ,the theories 7of ,ostwald1 ,bernthsen1 and others7 regarding the color changes1 and the theory 7of ,ostwald7 concerning the sensitiveness of indicators1 are discussed 7with references to the literature7 by ,stieglitz1 ,j4 ,am4 ,chem4 ,soc41 #be1 #aaag 7#aijc74 ,later modifications of the views on color changes are discussed in papers by ,stieglitz1 ,am4 ,chem4 ,j4 #ci1 7#aijh71 and by ,acree1 ibid41 #cg1 #ci1 #db1 and in these papers references to the literature will be found4 ,for investigations on the sensitiveness of indicators1 see ,mc,coy1 ibid41 #ca1 #ejh 7#aijd71 ,salm1 loc4 cit41 and ,a4 ,a4 ,noyes1 ,j4 ,am4 ,chem4 ,soc41 #cb1 #hae 7#aiaj74 #adj ,z4 phys4 ,chem41 #b1 #bhi 7#ahhh74 ,note the remarks in the footnote following4 #ada ,the formation of an ammonium salt in the latter action still further reduces the concentration of the hydroxide-ion 7,chapter ,,vi7 and retards the action2 but the solution1 in equal measure1 becomes less active toward the indicator1 phenolphthalen 7p4 #aad74 ,the experiment shows1 therefore1 rather fairly1 the relative activities of the bases4 ,the exact work of ,arrhenius included consideration of the effect of the ammonium salt1 and the clearing up of the mystery of this effect 7p4 #aad7 formed one of the greatest triumphs of his theory4 #adb ,arrhenius1 ,electro-chemistry1 p4 #ahd 7#aijb74 ,a second accelerative factor1 the so-called salt effect 7,chap4 ,,vi1 q4 v471 is more pronounced in the case of #j4a molar hydrochloric acid than in that of #j4a molar acetic acid1 as the result of which the activity of the hydrochloric acid should be increased about ten per cent2 the ratio1 therefore1 of the speeds of reaction1 both the degrees of ionization of the acids and the salt effect being considered1 should be approximately #hc 3 #a1 whereas the ratio found by experiment is #gi 3 #a4 #adc ,vide also ,a4 ,a4 ,noyes1 ,report of the ,congress of ,arts and ,science1 ,vol4 ,,iv1 p4 #caa 7#aijd74 #add ,haber1 ,z4 fr ,elektrochem41 #aj1 #gge 7#aijd72 see ,chapter ,,xii4 #ade ,this is1 essentially1 the old ,berzelius view of chemical action4 #adf ,vide1 for instance1 ,stieglitz1 ,report of the ,congress of ,arts and ,sciences1 ,st4 ,louis1 ,,iv1 #bgf 7#aijd72 ,w4 ,a4 ,noyes1 ,ibid41 #bhe2 ,nef1 ,j4 ,am4 ,chem4 ,soc41 #cj1 #fde 7#aijh74 ,for the application of the electron theory to organic compounds1 see ,falk and ,nelson1 ,school of ,mines ,quarterly1 #cj1 #agi1 and ,j4 ,am4 ,chem4 ,soc41 #cb1 #afcg 7#aiaj74 7,cf4 also ,chapter ,,xv47 #adg ,j4 ,phys4 ,chem41 #f1 #a 7#aijb71 and other papers in the same ,journal4 #adh ,cf4 ,patten1 ibid41 #g1 #afh 7#aijc71 and ,falk and ,waters1 ,am4 ,chem4 ,j41 #ca1 #cih 7#aijc74 ,according to the latter investigators1 the evolution of hydrogen is slow and weak4 #adi ,patten1 loc4 cit4 #aej ,students will not be capable of following the argument given in the succeeding passages and would better omit this part until ,chapter ,,xv has been studied4 #aea ,kablukoff1 ,z4 phys4 ,chem41 #d1 #dcj 7#ahhi74 ,see also ,nernst1 ,theoretical ,chemistry1 p4 #cgc4 #aeb ,in view of the low order of accuracy of the data1 and of the approximate method of calculation1 this result is only qualitative1 but even with an error of #ajb to #ajd the argument in the text would hold4 #aec ,for hydrogen under atmospheric pressure1 the equilibrium ratio1 ,zn#b _/ ,h#b1 is1 approximately1 #ajbg4 #aed ,vide ,sackur1 ,z4 ,elektrochem41 #aa1 #chg 7#aije74 ,kahlenberg holds a different view2 ibid4 #aee ,the negative results obtained with aluminium and magnesium are possibly more interesting than the positive action observed with zinc1 but their inactivity may be due to thin films of protective chloride or oxide or to a passive condition 7vide ,smith's ,inorganic ,chemistry1 pp4 #gbc1 #gec2 ,college ,chemistry1 p4 #dge74 #aef ,the work of ,ostwald1 ,arrhenius1 ,nernst and many others shows conclusively that the liberation of hydrogen by metals and the precipitation of metals by one another is a function of ion concentrations 7,chapter ,,xiv74 ,vide ,nernst1 ,theoretische ,chemie 7#aije71 p4 #bde4 #aeg ,see above4 #aeh ,in a #j4a molar solution of potassium cyanide1 the potassium hydroxide formed by the decomposition of the cyanide by water is approximately #j4jjac molar and the concentration of hydrogen-ion is reduced to #ajaa 7,chapter ,x71 a value roughly of the same order as that calculated above as a possible concentration of hydrogen-ion in a benzene solution of hydrogen chloride4 ,in spite of this small concentration of hydrogen-ion in the cyanide solution1 the reactions in which it is involved are1 as far as known1 completed in a few moments4 ,only for much smaller concentrations of ions have any doubts as to their direct action been aroused2 in ,chapter ,,xii this question1 as raised by ,haber1 is discussed for concentrations of ions of the order of #ajbc4 ,haber considers that ionic concentrations of #ajad can still account for very fast actions4 #aei ,cf4 ,abegg41 ,theorie der ,elektrolytischen ,dissociation 7#aijc71 #bee2 ,lehfeldt1 ,electro-chemistry 7#aijd71 #hg4 #afj ,there is probably minimal ionization in all these cases1 especially in the case of ammonia 7,,nh#c ,,nh#b ,h71 but not enough to yield a sufficient supply of hydrogen-ion to show its common properties4 #afa ,vide ,jorgensen1 ,j4 prakt4 ,chem41 #af1 #cdi 7#ahgg74 #afb ,see ,chapter ,,xii in regard to the stability of 7,pt,cl#fb7 as a complex ion4 #afc ,freshly prepared solutions must be used4 #afd ,see ,chapter ,,xii as to the decomposition of the complex ions4 #afe ,k and ,,cn are colorless ions4 ,the yellow color of the ion moving to the positive electrode shows the presence of the iron in it--a fact that can be confirmed by testing the solution round the anode for ferricyanide by the method discussed further on in the text4 p#jij ,,chapter ,,vi ,,chemical ,,equilibrium4 ,,the ,,law ,,of ,,mass ,,action ,the theory of ionization1 as studied so far1 gives us simple1 rational explanations of many of our qualitative reactions--explanations which agree with phenomena taken from separate fields of investigation4 ,but1 if our study of the theory ceased at the present stage without further elaboration1 we should fail to find in it a satisfactory explanation of a number of other important facts of analysis--notably1 why certain reactions1 the occurrence of which we might anticipate1 do not take place4 ,for instance1 the addition of a soluble carbonate to a barium chloride solution precipitates almost all the barium as barium carbonate 7exp472 we have #b ,na ,,co#cb ,ba#b #b ,cl ,ba,c,o#c #b ,na #b ,cl4 ,but the addition of carbonic acid to barium chloride solutions fails to produce the slightest precipitate 7exp471 although carbonic acid also gives rise to the carbonate-ion1 ,,co#cb4 ,in the same way silver nitrate readily precipitates silver phosphate from sodium phosphate solutions 7exp471 but not from a solution of phosphoric acid 7exp474 ,hydrogen sulphide precipitates zinc sulphide from a zinc sulphate solution 7exp471 ,zn#b ,,so#db #b ,h ,s#b ,zn,s #b ,h ,,so#db2 but the addition of hydrochloric acid effectually prevents the precipitation 7exp471 although the hydrogen sulphide is still ionized1 as is apparent from the precipitation of copper sulphide when copper sulphate is added to the mixture 7exp474 ,in the negative results1 we have instances of a very large number of cases which require closer study1 and a further development of the theory1 if we wish to interpret them satisfactorily4 ,the line of development to be followed is indicated perhaps most sharply by the following experiment4 ,,exp4 ,some sodium tetraborate 7borax7 is dissolved in a little water and silver nitrate is added to a small part of the solution4 ,a pure white precipitate 7silver borate7 results4 ,another portion of the borate solution is diluted with a large quantity of water1 and then silver nitrate is added2 quite a different result is obtained--a brown precipitate 7silver oxide7 is formed4 p#jia ,the change in the quantity of water brought about the difference in result--the quantitative relations were altered thereby4 ,in order to follow intelligently this and the other actions referred to1 the study of reactions in solutions must be taken up from the quantitative side--the development heretofore has been essentially qualitative in character4 ,on several occasions we have found that all electrolytes do not ionize equally well1 and that the intensity of their action1 demonstrated1 for instance1 for potassium and ammonium hydroxides1 varies accordingly4 ,we shall now have to study these relations in greater detail4 ,for our purpose1 the study of two of the fundamental quantitative laws governing action in solution and of their application to analytical phenomena1 will be sufficient3 these are1 the law of chemical or homogeneous equilibrium1 in which the law of mass action is included1 and the law of physical or heterogeneous equilibrium4 ,the ,law of ,chemical ,equilibrium4--,the law of chemical equilibrium may be expressed1 for a simple case1 by saying that if two substances ,a and ,b interact at a constant temperature to give two compounds ,c and ,d and1 vice versa1 ,c and ,d interact with each other to produce ,a and ,b1 then equilibrium will be reached when the ratio of the product of the concentrations of ,a and of ,b to the product of the concentrations of ,c and of ,d has a definite1 constant value1 which is a value characteristic of the equilibrium between the compounds involved1 at the given temperature4 ,the action may be expressed in the chemical equation ,a ,b ,c ,d1 in which ,a1 ,b1 ,c and ,d represent four different substances reacting in the molecular proportions indicated by their symbols1 which as usual represent molecular weights4 ,and the condition for equilibrium may be expressed in the mathematical equation ,a ,b _/ 7,c ,d7 k4 ,a1 ,b1 ,c and ,d are used to represent the concentrations#aff of p#jib the four reacting substances and k is some definite number1 called the equilibrium constant4 ,the law was discovered by ,guldberg and ,waage in #ahfg1 and1 with certain limiting conditions 7see below7 it has been fully established by extensive experimental work4#afg ,the significance of the law may be interpreted on the basis of the following considerations4 ,if we start with the two substances ,a and ,b alone and have one mole of each in one liter 7as gas or in solution7 at a given temperature1 then1 all the conditions being given1--the temperature1 the concentrations1 and the nature of the substances1--the reaction ,a ,b ,c ,d1 leading to the formation of ,c and ,d1 will proceed with a perfectly definite velocity4 ,the molecules of ,a and of ,b move in all directions 7kinetic theory of gases and solutions71 and molecules of ,a will collide with molecules of ,b a definite number of times in unit time and will form a definite number#afh of molecules of ,c and ,d per minute4 ,the velocity of chemical change of a given substance 7chemical velocity7 is also measured in terms of moles1 and is represented by the number of moles or the fraction of a mole changed per minute4 ,if v#a stands for the velocity of the action between ,a and ,b1 under the given conditions1 then v#a k#a1 where k#a is some number4 ,now1 if the concentration of one of the components1 e4g4 ,a1 should be doubled1 then the chances for collision and for action between molecules of ,a and ,b will be twice as great as before and the velocity of the action will be doubled4 ,if only one-tenth of the concentration of ,a 7one-tenth mole7 is used1 the velocity will only be one-tenth as great as originally1 and1 in general terms1 if ,a moles of ,a are used per liter1 the velocity of the change will be proportional to ,a1 and equal to k#a ,a4 ,if the concentration of the other reacting component1 ,b1 is now doubled1 the chances for action are again doubled1 and1 in general1 the velocity of the action will be proportional also to the concentration p#jic ,b of the second reacting substance4 ,for the velocity1 v#a of the action for any concentrations1 ,a and ,b1 of ,a and ,b at any moment at a given temperature1 we have v#a k#a ,a ,b4 ,hence1 if by the symbols ,a and ,b the concentrations at any given moment are represented1 we may say that the velocity of the formation of ,c and ,d at that moment#afi is proportional to the product of the concentrations of ,a and ,b1 and to some constant1 which is characteristic of the interaction of ,a and ,b4 ,the validity of this conclusion has been fully verified by experiment4#agj ,the case is an instance of the law of mass action1 which states that in chemical changes the velocity of the action is proportional at any moment to the molecular concentrations#aga of the reacting components1 and to a constant1 which is characteristic of the chemical nature of the reacting components 7and of the temperature74 ,if we start with the reversed action ,a ,b ,c ,d1 the relation may be developed in the same way4 ,thus the two substances ,c and ,d will react upon each other1 at the given temperature1 with a velocity proportional to a constant1 k#b1 and1 at any given moment1 proportional also to their respective concentrations at that moment3 v#b k#b ,c ,d4 ,equilibrium will be reached when the substances ,a and ,b are formed at any moment from ,c and ,d just as rapidly as they are used up to produce ,c and ,d1 and vice versa4 ,such is the case1 p#jid when the velocities of the two opposite reactions are equal to each other4 ,for the condition of equilibrium1 then1 v#a must be equal to v#b and therefore k#a ,a ,b k#b ,c ,d or ,a ,b _/ 7,c ,d7 k#b _/ k#a kequilibrium4 ,in this way the meaning of the fundamental law of chemical equilibrium may be developed from the consideration of the velocities of the reversible actions1 such as are involved in all conditions of equilibrium1 and the equilibrium constant represents the ratio of the velocity constants of the two opposite reactions4 ,this conclusion has been fully verified by experiment1 the equilibrium constant being1 as a matter of fact1 found equal to the ratio of the velocity constants4#agb ,the relations1 so far considered1 have been those of the simplest type of reversible reaction4 ,we may now discuss the modifications required for other types of reaction by the law of equilibrium4 ,when two molecules of any reacting component take part in a reaction--for instance1 in ,a #b ,b ,c ,d--the concentration of this component is raised to the second power in the mathematical expression of the law of equilibrium2 when three molecules of a component take part1 its concentration is raised to the third power1 etc4 ,for instance1 hydrogen iodide is decomposed1 reversibly1 into hydrogen and iodine1 according to #b ,,hi ,h#b ,i#b4 ,a condition of equilibrium is reached1 at a given temperature when ,h#b ,i#b _/ ,,hi#b ,k4 ,at #ddj1 the results given in the following table were obtained by ,bodenstein4 ,the concentrations are expressed in moles per liter4#agc ,the constant is calcuated according to the equation just given4 ,analytical errors affect the value of the constant most in the first and last experiments1 as a result of the very small concentrations of one component1 ,i#b or ,h#b4 p#jie ,h#b ,i#b ,,hi ,k #j4jbfh #j4jjjaij #j4jagg 7#j4jaf7 #j4jjihf #j4jjbjc #j4jcbh #j4jai #j4jjcjh #j4jjghc #j4jccg #j4jba #j4jjage #j4jaad #j4jcae #j4jbj #j4jjjfec #j4jbjd #j4jbcf #j4jbd #j4jjjbfe #j4jbdb #j4jbjb 7#j4jaf7 ,the mechanical significance of the raised powers of the concentrations of components1 two or more molecules of which take part in a reaction as indicated1 will be discussed further on1 in connection with a case of equilibrium between an electrolyte and its ions 7,chapter ,,vi1 p4 #ajb74 ,limitations to the ,law of ,chemical ,equilibrium4--,quite in agreement with the interpretation of the law of chemical equilibrium from the view-point of the kinetic theory1 it is found that1 in its applications1 one must take into consideration the possibility1 that molecular attractions 7p4 #bg7 or other important forces of attraction or repulsion 7e4g4 electrical7 of a more than negligible magnitude exist between the molecules of the components in a reversible reaction4 ,if such forces are involved1 suitable allowance must be made for them1 so that the mathematical formulation of the law may express the facts of observation4#agd ,for these reasons1 the law1 in its simplest terms1 which1 alone1 can be considered here1 holds for the relations obtaining in dilute systems#age 7dilute solutions or gases that are not too strongly compressed71 and in systems involving only nonelectrolytes or only weak ionogens1 more generally than for the relations in concentrated solutions 7or strongly compressed gases7 or in systems1 in which electrically charged particles 7ions7 are present in large proportions 7see below1 p4 #ajh74 ,the ,factors of the ,law of ,chemical ,equilibrium4--,inspection of the mathematical expression of the law of chemical equilibrium 7p4 #ia7 shows that there are two significant kinds of factors in it3 first1 the equilibrium constant1 whose value depends only on the nature of the substances involved and on the temperature4#agf ,in p#jif the second place1 we have concentration factors1 which1 to a large extent1#agg may be varied at will4 ,the following experiments may be used to illustrate the significance of the two classes of factors3 ,phosphorus pentabromide is partially decomposed by heat into the tribromide and bromine 7a case of gaseous dissociation73 ,p,br#e ,p,br#c ,br#b4 ,phosphorus trichlordibromide is decomposed more or less1 in a similar fashion1 into the components phosphorus trichloride and bromine1 according to the equation ,p,cl#c;,br#b ,p,cl#c ,br#b4 ,for the condition of equilibrium in the two cases we have ,p,br#c ,br#b _/ ,p,br#e k#a and ,p,cl#c ,br#b _/ ,p,cl#c;,br#b k#b4 ,,exp4 ,two tubes containing equivalent quantities of the two bromides are placed side by side in warm water4#agh ,the tube containing the trichlordibromide is found to be much more intensely colored by free bromine than that containing the pentabromide4 ,the intensity of the color of the bromine vapor shows that the concentration of bromine1 ,br#b1 in the ,p,cl#c;,br#b tube1 is greater than the corresponding concentration1 ,br#b1 in the ,p,br#e tube4 ,as a molecule of pentahalide ,,px#e dissociates into one molecule of ,,px#c and one molecule of ,x#b1 ,p,cl#c equals ,br#b and is greater than ,p,br#c1 which is equal to ,br#b4 ,further1 more of the pentabromide than of the trichlordibromide must be left undecomposed1 i4e4 ,p,cl#c;,br#b is smaller than ,p,br#e4 ,since the factors in the numerator of the second equation are both larger1 and the factor in the denominator smaller1 than the corresponding factors in the first equation1 k#b must be greater than k#a4 ,these constants are thus seen to be a measure of the chemical stability of these pentahalides4 ,it is evident1 too1 that in reactions which depend on the presence of free bromine1 such as the bromination of many organic compounds1 the trichlordibromide should be more effective than the equivalent quantity of the pentabromide4 p#jig ,in the second place1 if we were to introduce into either tube1 for instance into the tube containing the phosphorus trichlordibromide1 an excess of one of the dissociation products1 say an excess of phosphorus trichloride1 then the condition of equilibrium would necessarily be disturbed3 y ,p,cl#c ,br#b _/ ,p,cl#c;,br#b k#b1 in which the bracketed symbols represent the concentrations of the first experiment4 ,the velocities of the two opposite reactions would be no longer equal1 the combination of trichloride with bromine would be accelerated by the increased concentration of the former4 ,here1 equilibrium would only be restablished when the trichloride and bromine had combined to a sufficient extent to make 7y ,p,cl#c x7 7,br#b x7 _/ 7,p,cl#c;,br#b x7 k#b1 in which x represents the number of moles of additional phosphorus trichlordibromide formed in unit volume by the combination of bromine with phosphorus trichloride4 ,the net result is seen to be that an increase in the concentration of the one dissociation product eo ipso reduces the concentration of the other dissociation product4 ,,exp4 ,a third tube charged with the same quantity of phosphorus trichlordibromide as the tube mentioned above1 and with an added excess of phosphorus trichloride1 is placed in the warm water next to the tube containing the trichlordibromide4 ,its color is much paler than that of the latter1 owing to the suppression of free bromine4#agi ,the concentration of the free bromine1 7,br#b x71 under the new conditions of equilibrium1 is smaller than the original concentration ,br#b--;a result confirmed by experience4 ,it is in our power1 therefore1 arbitrarily to change the concentration of a reacting component1 in a case of equilibrium1 and thus to affect the reactivity of the system2 for instance1 for brominating purposes1 the new system would be less effective than the original one1 and it might be of especial service where bromination is to be avoided4 ,in the cases studied1 are found the two fundamentally important relations expressed by the law of equilibrium3 the equilibrium constant is a measure of the stability of a certain system and1 in a way1 of its reactivity at a given temperature2 and the p#jih concentration factors are variables1 which we may change to a very considerable extent1 so as1 to a certain degree1 to subject the system to our own purposes4 ,we shall repeatedly have occasion to refer to these two fundamental relations and we shall use them again and again in our analytical work4 ,chemical ,equilibrium of ,electrolytes4--,ionization of an electrolyte is a reversible chemical action and its relation to the law of chemical equilibrium will now be discussed4 ,for acetic acid1 ionization into hydrogen and acetate ions occurs thus3 ,,ch#c;,,co#b;,h ,,ch#c;,,co#b ,h1 and1 in accordance with the law of equilibrium1 at a given temperature1 the following relation would hold3 ,h ,,ch#c;,,co#b _/ ,,ch#c;,,co#b;,h ,kionization4 ,if the total concentration of the acid is known1 the concentrations of the ions and of the non-ionized acid may be calculated from the conductivity of the solution4 ,for instance1 if #fj grams of acetic acid 7#a mole7 is dissolved in sufficient water to make #aj liters1 the equivalent conductivity of the solution 7p4 #ej7 is found to be #d4fg reciprocal ohms at #ah4 ,the maximum conductivity of one mole of acetic acid1 at infinite dilution1 when all the acid would be ionized1 would be #cdg4 ,therefore1 in the acid under examination1 #d4fg _/ #cdg1 or #a4cd per cent1 is ionized 7p4 #ej74 ,since the total concentration of the acid is #j4a mole per liter and #a4cd per cent is ionized1 the concentration of the hydrogen-ion1 ,h1 is #j4a #j4jacd1 and that of the acetate-ion1 ,,ch#c;,,co#b1 is the same4 ,the concentration of the non-ionized acetic acid1 ,,ch#c;,,co#b;,h1 is #j4a #j4ihff4 ,if these values are inserted in the equation for the condition of equilibrium1 we have 7#j4a #j4jacd7b _/ 7#j4a #j4ihff7 ,kionization #ah4b;,e#f4 ,from this experimental result1 the equilibrium constant1 which is called the ionization constant of the acid1 is found to have the value #ah4b;,e#f4 ,if the ratio ,h ,,ch#c;,,co#b _/ ,,ch#c;,,co#b;,h really is a constant1 the same value1 within the limits of experimental errors1 should be obtained from acetic acid in other concentrations4 ,now1 if the above solution is diluted to ten times its volume1 the concentration of the acid is made #j4ja mole per liter1 the conductivity p#jii is found to have increased to #ad4e reciprocal ohms1 and the percentage of ionized acid is then #ad4e _/ #cdg1 or #d4ag4 ,here1 ,h and ,,ch#c;,,co#b #j4ja #j4jdag and ,,ch#c;,,co#b;,h #j4ja #j4iehc4 ,inserting these values in our general equation and calculating the result1 we obtain #ah4a;,e#f as the value of the constant4 ,in the following table#ahj are given the molar conductivities1 7column #b71 of acetic acid of varying concentrations1 m 7column #a74 ,the degrees of ionization1 1 and the ionization constant1 calculated according to the equilibrium equation1 are given in columns #c and #d4 ,,ionization ,,of ,,acetic ,,acid4 #cdg4 m4 4 #ajj 4 ,k4 #j4a #d4fg #a4cd #ah4b;,e#f #j4jh #e4bb #a4ej #ah4c;,e#f #j4jc #h4ej #b4de #ah4e;,e#f #j4ja #ad4ej #d4ag #ah4a;,e#f ,it is evident1 that a constant value is found for the ratio ,h ,,ch#c;,,co#b _/ ,,ch#c;,,co#b;,h and that the ionization of acetic acid1 in these dilute solutions1 obeys the law of chemical equilibrium4#aha ,the equilibrium constant expresses in definite1 quantitative terms the tendency of acetic acid to ionize in dilute solution4 ,examination of other acids shows that there is an enormous range in the values found for their respective ionization constants4 ,the constants are the best measure of the strength of the acids as acids4 ,obviously1 the more readily acids in equivalent solutions ionize1 the greater will be the concentration of the hydrogen-ion to which the characteristic acid properties are due1 and the more pronounced 7stronger7 will be the exhibition of these properties4 ,from the ionization constants one may calculate1 for instance1 the proportion in which two competing acids will neutralize a base1 when the latter is used in quantity insufficient to neutralize both acids4 p#ajj ,inspection of the equation for acetic acid1 which is the typical equilibrium equation for all monobasic acids1 shows that the greater the degrees of ionization of acids are in equivalent solutions1 i4e4 the greater the concentrations of the hydrogen-ion which their ionization produces in equivalent solutions1 the larger will be the values of their ionization constants4 ,the acids with the larger constants are1 then1 the stronger acids4 ,the ,ionization of ,various ,acids4--,the table given on page #ajd shows the ionization constants for a number of acids of interest in analysis4 ,before proceeding to give the table1 we must consider further two important points4 ,in the first place1 for the strongest acids1 such as hydrochloric1 nitric1 hydrobromic and similar acids1 chemists have been unable to determine ionization constants on the basis of the law of chemical equilibrium4 ,strong acids1 strong bases and most salts 7see pp4 #ajf-h1 below71 the three classes comprising all the very readily ionizable electrolytes1 do not give constants when the values of the equilibrium ratio1#ahb ,cation ,anion _/ ,molecules1 are calculated for different concentrations1 and they therefore do not ionize simply in accordance with the law of chemical equilibrium4 ,the reasons for this abnormal behavior will be discussed presently 7p4 #ajh71 when other necessary facts are before us4 ,in order to have1 at least1 a rough basis for comparison of these strong acids with the weak ones1 which do obey the law of chemical equilibrium1 the table will give for the strong acids the value of the above ratio as calculated from their ionization in #j4a molar solutions4 ,the ,ionization of ,polybasic ,acids4--,in the second place1 the meaning of the constants for polybasic acids1 such as sulphuric1 phosphoric1 carbonic and similar acids1 requires explanation4 ,the relations for carbonic acid will be first developed1 as representing a typical case4 ,carbonic acid1 in ionizing1 forms the carbonate-ion ,,co#cb1 and the hydrogen-ion1 as expressed in the p#aja equation#ahc ,h#b;,,co#c #b ,h ,,co#cb4 ,according to the law of chemical equilibrium for the case where a product 7here the hydrogen-ion7 appears twice on one side of the reaction equation1 we have1 for the condition of equilibrium 7p4 #id7 ,h#b ,,co#cb _/ ,h#b;,,co#c ,k4 7#a7 ,we may ask1 however1 whether both the hydrogen atoms of carbonic acid show the same tendency to ionize1 or1 since there is a vast difference in the ease of ionization of different acids1 whether there is not also a difference in the ease of ionization of the different hydrogen atoms in a polybasic acid4 ,as a matter of experiment1 we find that a molecule of carbonic acid does ionize1 first1 and more readily1 into one hydrogen ion and an acid carbonate ion ,,hco#c1 according to ,h#b;,,co#c ,h ,,hco#c4 ,for this reversible reaction we have#ahd ,h ,,hco#c _/ ,h#b;,,co#c ,k#a4 7#b7 ,the value of this constant1#ahe called the primary ionization constant of carbonic acid1 is #j4c;,e#f4 ,the acid carbonate-ion ,,hco#c1 in turn1 is ionized to a certain extent1 producing another hydrogen ion and the carbonate-ion1 ,,co#cb4 ,we have ,,hco#c ,h ,,co#cb1 and ,h ,,co#cb _/ ,,hco#c ,k#b4 7#c7 ,the value of this constant#ahf1 called the constant of the p#ajb secondary ionization of carbonic acid1 is #j4jg;,e#i1 which has about one four-thousandth of the value of the constant for the primary ionization4 ,if we combine equations 7#b7 and 7#c7 we have ,h ,,hco#c ,h ,,co#cb _/ 7,h#b;,,co#c ,,hco#c7 ,k#a ,k#b 7#d7 or ,h#b ,,co#cb _/ ,h#b;,,co#c ,k4 ,this is equation 7#a71 derived originally by the application of the law of mass action to the relation between the carbonate-ion1 ,,co#cb1 the hydrogen-ion1 and carbonic acid1 ,h#b;,,co#c4 ,this relation1 and1 in particular1 the significant squaring of the concentration of the hydrogen-ion1 an ion which appears twice in the equation for the formation of carbonic acid from carbonate and hydrogen ions1 7#b ,h ,,co#cb ,h#b;,,co#c71 may now be interpreted mechanically 7p4 #ib7 as follows3 ,for the formation of carbonic acid from a carbonate ion and two hydrogen ions1 a carbonate ion must collide and combine first with one hydrogen ion1 and the velocity for the formation of this intermediate product1 ,,hco#c1 will be proportional to the 7total7 concentration of the hydrogen ions2 the product1 ,,hco#c1 to form ,h#b;,,co#c1 must collide and combine with a hydrogen ion once more1 and this combination will proceed with a velocity again proportional to the 7total7 concentration of the hydrogen ions4 ,so the velocity for the transformation of ,,co#cb into ,h#b;,,co#c will be proportional twice over to the 7total7 concentration of the hydrogen ions--as well as1 in the usual fashion1 to the concentration of the carbonate ions present at any moment4 ,it is a general principle that the primary ionization of polyvalent acids occurs more readily than the secondary1 and this in turn more readily than the tertiary 7if a third ionizable hydrogen atom is present in the acid74 ,in the case of phosphoric acid1 for instance1 the primary ionization into the hydrogen-ion and the dihydrogen-phosphate-ion1 ,h#b,,po#d1 takes place so readily that phosphoric acid reacts strongly acid#ahg to methyl orange1#ahh the p#ajc concentration of hydrogen-ion being sufficiently great to affect this indicator 7see ,,exp4 below74 ,when phosphoric acid is neutralized by one equivalent of a base1 say of sodium hydroxide1 the salt formed1 sodium dihydrogen-phosphate1 ,na,h#b,,po#d1 yields sodium-ion and dihydrogen-phosphate-ion1 ,h#b,,po#d4 ,the latter is ionized somewhat into ,h and the bivalent hydrogen-phosphate-ion1 ,,hpo#db4 ,the ionization of the ion ,h#b,,po#d is now the chief source of supply of hydrogen-ion 7the further ionization of ,,hpo#db is practically negligible here7 and it is ionized so little that the solution of ,na,h#b,,po#d no longer changes the color of methyl orange 7see ,,exp4 below74 ,the solution is1 however1 acid to the indicator phenolphthalen1 which is much more sensitive to the hydrogen-ion and will show the presence of much smaller concentrations of it than will methyl orange4 ,the addition of a second equivalent of sodium hydroxide to the solution converts ,na,h#b,,po#d into ,na#b;,,hpo#d4 ,this salt gives sodium-ion and the hydrogen-phosphate-ion ,,hpo#db1 which1 in turn1 is ionized only very slightly1 producing phosphate-ion ,,po#dc1 and again hydrogen-ion4 ,the ionization of ,,hpo#db is so slight1 however1 and the concentration of the hydrogen-ion1 therefore1 so minute1 that the solution does not react acid even to the sensitive indicator phenolphthalen4 ,,exp4 ,methyl orange 7very little7 is added to #aj c4c4 of a #j4a molar solution of phosphoric acid and #aj c4c4 of #j4a molar sodium hydroxide solution is added to the mixture2 the color will be found to change from the acid to the neutral tint just as the last drop or two of the alkali are added4 ,phenolphthalen is then added to the mixture and #aj c4c4 more of the #j4a molar sodium hydroxide solution are required to change the color of the mixture to a pronounced pink 7alkaline7 tint4 ,even sulphuric acid1 although its two hydrogen atoms are ionized very easily1 making sulphuric acid a strong acid1 shows a difference in the ease of ionization of the two hydrogen atoms4 ,since ionization1 in general1 is favored by dilution1 we find that in the case of such a strong acid the difference is most marked in more concentrated solutions1 the smaller amount of water starting the ionization in the more favored direction and producing first1 chiefly1 hydrogen-sulphate ions1 ,,hso#d4 ,when the solution is diluted1 the hydrogen-sulphate ions are to a very considerable extent dissociated into sulphate ions and hydrogen ions4 ,the described change in ionization can be roughly followed with the aid of an insoluble sulphate like barium sulphate4 ,barium sulphate1 while very insoluble in water1 dissolves in rather strong sulphuric acid to form the acid sulphate1 ,ba7,,hso#d7b1 the ,,so#db ion of the sulphate being more or less suppressed by uniting with hydrogen-ion4 ,we have the action ,ba,s,o#d ,ba#b ,,so#db and ,ba#b ,,so#db ,h ,,hso#d ,ba#b #b ,,hso#d4 ,if the solution of the acid sulphate is poured into a large volume of water1 barium sulphate is immediately reprecipitated1 the hydrogen-sulphate-ion being dissociated1 in the dilute solution1 into hydrogen-ion and sulphate-ion1 ,,so#db1 whose barium salt is so difficultly soluble3 ,ba#b #b ,,hso#d ,ba#b #b ,h #b ,,so#db ,ba,s,o#d #b ,h ,,so#db4 p#ajd ,,exp4 ,finely divided barium sulphate is warmed for a moment with a few cubic centimeters of concentrated sulphuric acid in a test tube1 the mixture is allowed to settle1 and some of the clear acid is carefully decanted into a large beaker full of water4 ,it may be added1 that while the primary ionization of sulphuric acid does not yield an equilibrium constant for the ratio ,h ,,hso#d _/ ,h#b,,so#d1 even such a strong acid as is sulphuric acid is found to give a fairly good constant#ahi for ,h ,,so#db _/ ,,hso#d4 ,the value of this constant#ahi is #j4jc4 ,the ,ionization ,constants,a of ,acids ,acid4 ,equilibrium ,ratio4 ,k4 ,hydrochloric ,h,cl_/,h,cl 7#a7 ,hydrobromic ,h,br_/,h,br 7#a7 ,hydroiodic ,h,i_/,,hi 7#a7 ,nitric ,h,,no#c_/;,,hno#c 7#a7 ,chromic,b ,h,h,cr,o#d_/;,h#b;,cr,o#d 7#a7 ,h,cr,o#db_/;,h,cr,o#d #j4f;,e#f ,sulphuric,c,d ,h,,hso#d_/;,h#b,,so#d 7#a7 ,h,,so#db_/;,,hso#d #j4c;,e#a ,oxalic,e ,h,c#b,o#d_/;,h#b;,c#b,o#d #c4h;,e#b ,h,c#b,o#db_/;,,hc#b,o#d #j4e;,e#d ,phosphoric,f ,h,h#b,,po#d_/;,h#c,,po#d #j4a;,e#a ,h,,hpo#db_/;,h#b,,po#d #j4b;,e#f ,h,,po#dc_/;,,hpo#db #j4d;,e#ab ,arsenic,d ,h,h#b;,as,o#d_/;,h#c;,as,o#d #j4e;,e#b ,nitrous,b ,h,,no#b_/;,,hno#b #j4e;,e#c ,acetic,g ,h,,ch#c;,,co#b_/;,,ch#c;,,co#b;,h #a4h;,e#e ,carbonic,h,i ,h,,hco#c_/7;,h#b;,,co#c ,,co#b7 #j4c;,e#f ,h,,co#cb_/;,,hco#c #j4g;,e#aj ,h#b,s,j,k ,h,,sh_/,h#b,s #j4i;,e#g ,h,s#b_/,,sh #j4a;,e#ad ,boric,b ,h,h#b;,,bo#c_/;,h#c;,,bo#c #j4g;,e#i ,hydrocyanic ,h,,cn_/,,hcn #j4g;,e#i ,arsenious ,h,h#b;,as,o#c_/;,h#c;,as,o#c #j4f;,e#i ,water,l,c ,h,,ho_/,h#b,o at #be #j4b;,e#ae at #ajj #j4i;,e#ad ,h,,ho at #be #a4b;,e#ad at #ajj #j4e;,e#aa ,,table ,,notes3 ,a4 ,as explained on p4 #ajj1 the bracketed values given for the strong acids are not constants1 but express the values of the ratios ,h ,anion _/ ,acid for #j4a molar solutions4 ,b4 ,see references1 ,noyes1 ibid41 #cb1 #hfj 7#aiaj74 ,c4 ,noyes and ,eastman1 ,carnegie ,institution ,publications1 #fc1 #bgd 7#aijg74 ,d4 ,luther1 ,z4 ,elektroch1 #ac1 #bif 7#aijg74 ,e4 ,chandler 7,mc,coy71 ,j4 ,am4 ,chem4 ,soc41 #cj1 #gac 7#aijh74 ,f4 ,abbot and ,bray1 ibid41 #ca1 #gfj 7#aiji74 ,g4 ,see above1 p4 #ii4 ,h4 ,walker1 ,j4 ,chem4 ,soc41 7,london71 #gg1 #e 7#aijj74 ,i4 ,mc,coy1 ,am4 ,chem4 ,j41 #bi1 #dee 7#aijc72 ,stieglitz1 ,carnegie ,institution ,publications1 #ajg1 #bdc 7#aiji74 ,j4 ,auerbach1 ,z4 phys4 ,chem41 #di1 #bbj 7#aijd74 ,k4 ,knox1 in ,abegg's laboratory1 ,trans4 ,faraday ,soc41 #d1 #dc 7#aijh74 ,l4 ,vide p4 #ff4 p#aje ,the difference in the tendencies of acids to ionize1 as expressed in the table1 may be recognized in equivalent solutions by any of the properties dependent on the ionization1 such as the conductivity1 the chemical activity1 the osmotic pressure and allied effects1 and so forth4 ,if the conductivities of equal volumes of equivalent 7e4g4 normal7 solutions of hydrochloric1 phosphoric and acetic acids are compared 7exp47#aij1 it is readily seen that hydrochloric acid is the best conductor1 phosphoric acid a much poorer one1 and acetic acid an exceedingly poor one 7the conductivity of normal acetic acid is about #a _/ #bjj that of normal hydrochloric acid1 and the conductivity of normal phosphoric acid is about #a _/ #ad that of normal hydrochloric acid74 ,since the conductivity is approximately proportional to the concentration of the hydrogen-ion#aia in each of the solutions1 it is evident that the hydrochloric acid is ionized to a considerably greater extent than either of the other acids--than acetic acid1 in particular4 ,similarly1 if a drop 7#j4je c4c47 of molar hydrochloric acid and a drop of molar acetic acid are added to equal volumes 7#ej c4c47 of a very dilute solution of methyl orange 7exp471 the color will be changed decidedly by the hydrochloric acid to a bright pink1 but by the acetic acid only to an orange hue4 ,again1 if a precipitate of barium chromate or calcium oxalate is treated with some strong acid1 hydrochloric or nitric1 for instance1 it dissolves readily1 while a considerable excess of acetic acid 7exp47 only dissolves traces of either precipitate4#aib ,in this way1 the chemical behavior of these acids differs in degree1 as a result of the different tendencies to ionize1 which are expressed in the constants of the table4 ,advantage is taken1 in analysis1 of such differences4 ,acetic acid1 for instance1 is used when only a slight degree of acidity is desired--as in recognizing barium-ion by its chromate1 or oxalic acid by means of its calcium salt4 ,hydrochloric or nitric acid is used when decided acidity is required--as in the separation of groups by hydrogen sulphide 7,chap4 ,,xi74 ,the ,ionization of ,bases4--,the same relations hold for bases as for acids3 the weaker bases give ionization constants as p#ajf do the weaker acids2 the strong bases1 again1 as was mentioned above1 do not give constants4 ,the values for strong bases1 stated in the following table1 are bracketed1 and refer to the ionization in #j4a molar solutions of the bases4 ,polyvalent bases1 like polybasic acids1 ionize in stages1 and the primary ionization is usually stronger than the secondary ionization1 and so forth4 ,for instance1 a study of ferric chloride solution shows that the third hydroxide group of ferric hydroxide1 ,fe7,,oh7#c1 must have the smallest ionization constant4#aic ,the ,ionization ,constants,a of ,bases ,base4 ,ratio4 ,k4 ,potassium hydroxide ,k,,ho_/,,koh 7#a7 ,sodium hydroxide ,na,,ho_/,na,o,h 7#a7 ,barium hydroxide ,ba#b;,,ho#b_/;,ba7,,oh7#b 7#j4jc7 ,strontium hydroxide ,sr#b;,,ho#b_/,sr7,,oh7#b 7#j4jc7 ,calcium hydroxide,b ,ca#b;,,ho#b_/;,ca7,,oh7#b 7#j4jc7 ,ammonium hydroxide,c,d ,,nh#d;,,ho_/ 7,,nh#d,,oh,,nh#c7 #a4h;,e#e ,hydrazine,e ,n#b;,h#e;,,ho_/ 7,n#b;,h#e,,oh,n#b;,h#d7 #j4c;,e#e ,aniline,f ,c#f;,h#e,,nh#c;,,ho_/ 7,c#f;,h#e,,nh#c,,oh ,c#f;,h#e,,nh#b7 #j4e;,e#i ,water ,h,,ho_/,h#b,o at #be #j4b;,e#ae at #ajj #j4i;,e#ad ,h,,ho at #be #a4b;,e#ad at #ajj #j4e;,e#aa ,,table ,,notes3 ,a4 ,as explained above1 the bracketed values under ,k for strong bases are not constants1 but express the values of the ratios for #j4a molar solutions only4 7,for the alkaline earths #j4je molar solutions are referred to47 ,b4 ,estimated value4 ,c4 ,vide page #afj4 ,d4 ,corrected value1 from ,bredig's data1 ,z4 phys4 ,chem41 #ac1 #cbb 7#ahid74 ,a4 ,a4 ,noyes1 ,carnegie ,institution1 ,publication ,no4 #fc1 p4 #agh1 finds the value #ag4c;,e#f for #ah4 ,e4 ,uncorrected value1 ,bredig1 ibid4 ,f4 ,bredig1 ibid42 ,stieglitz and ,derby1 ,am4 ,chem4 ,j41 #ca1 #deg 7#aijd74 ,while the constants of a large number of organic bases#aid have been determined few constants of inorganic bases are as yet known4 ,the fact that the majority of inorganic bases are polyvalent and difficultly soluble has made their examination in this respect more difficult4 ,from the study of the decomposition of salts by water 7see ,chapter ,x71 the trivalent bases1 such as p#ajg ferric hydroxide and aluminium hydroxide1 are found to be much weaker than bivalent bases like cadmium1 zinc and lead hydroxides1#aie but the data are not sufficient for the calculation of any constants1 or for distinguishing between the ionization of the first1 second and third hydroxide groups4 ,the difference in ionization and in chemical activity between a strong base1 like sodium or potassium hydroxide1 and a weak base1 like ammonium hydroxide1 has already been discussed and illustrated 7see p4 #gg74 ,in analysis1 advantage is frequently taken of these relations4#aif ,the ,ionization of ,salts4--,while we read and hear a good deal about strong and weak acids1 and strong and weak bases1 the expression strong or weak salt is never heard2 as a matter of fact1 all salts1 with very few exceptions1 ionize exceedingly readily--about as readily as the strongest acids and bases4 ,there are minor differences1 but none of great moment--none of the kind indicated by the wide range of constants for the acids and bases4 ,there are only a few important exceptions to this general rule--the most important ones1 among the common salts1 being mercuric chloride and mercuric cyanide3 their exceptional behavior in regard to ionization1 as indicated by their conductivities 7see below71 is found side by side with an exceptional chemical behavior1 exactly as the theory of ionization would lead us to anticipate1 and it renders necessary certain precautions1 particularly in analytical work1 which will be discussed later 7,chap4 ,,vi74 ,ordinary salts are all ionized readily3 for instance1 whereas acetic acid in molar solution is ionized only to the extent of #j4cg per cent1 its salts are highly ionized1 the degree of ionization of sodium acetate1 for example1 being #eb4h in molar solution4 ,as in the case of the strong acids and bases1 salts of the type ,me,x1 which ionize according to the equation ,me,x ,me ,x and which1 according to the law of chemical equilibrium1 might be expected to give a constant ratio ,me,x _/ ,me,x1 do not give a constant ratio4 ,that is1 when the values obtained for the concentrations of the ions and of the nondissociated molecules1 in solutions of various p#ajh strengths1 are substituted in this formula1 different values are obtained4#aig ,for potassium chloride1 we have the following relations3 ,molar ,per cent ,ratio4 ,concentration4 ,conductivity4 ,ionized4 #j4 #aca4b #ajj -- #j4jja #abg4f #ig4c #j4jce #j4ja #abb4e #ic4d #j4acj #j4je #aae4i #hh4d #j4cce #j4aj #aaa4i #he4a #j4dhe #j4bj #ajg4g #hb4a #j4ged #j4ej #ajb4c #gg4i #a4ch #a4jj #ih4b #gd4i #b4bc ,the ,ionization of ,strong ,electrolytes and the ,law of ,chemical ,equilibrium4--,the fact that the ionization of good electrolytes does not seem to conform to the law of chemical equilibrium is an exceedingly important one--it is1 perhaps1 the most important problem demanding rigorous investigation1 which is before chemists at the present time4 ,it has been used as an argument against the whole theory of ionization1 and is the most important objection that has been urged against it4 ,but1 to the impartial observer1 this single discrepancy1 between observation and what we might have anticipated1 will only prove a stronger stimulus to keener investigation and to more rigorous analysis of relations1 since the latter are more complex than was at first expected4 ,without considering the mass of evidence in favor of the theory1 found in other fields of chemistry and in physics1 a part of which has been given above1 we must remember that this fundamental law of chemical equilibrium has already decided unequivocally in favor of the theory in hundreds of cases of the ionization of weak acids and weak bases#aih and that these are the cases where the conditions are most simple4#aii p#aji ,it would lead too far from our subject to enter into a full discussion of this important question4 ,it will be sufficient here to indicate two directions of inquiry1 which promise to lead to an explanation of the apparent contradiction between the demands of the law of chemical equilibrium and the ionization of strong electrolytes4 ,in the first place1 the law of chemical equilibrium is based thermodynamically1 i4e4 from the point of view of the ultimate energy relations involved1 on the assumption that none but negligible forces of attraction or repulsion exist between the molecules1 whose concentrations are factors in the equilibrium equations 7cf4 p4 #ie74bjj ,now1 in solutions of electrolytes this condition is not strictly fulfilled under any circumstances2 the attractions between ions of opposite charge and the repulsions of ions of like charge1 as well as the effect of charged particles on neutral molecules1 come into play4 ,for strong electrolytes1 where the proportion of charged particles is always a large one1 the deviations from the simpler conditions to which alone the law is really applicable must be very much greater than for weak electrolytes4 ,it is1 therefore1 probable that these electrical forces#bja are the source of the deviation of the ionization of strong electrolytes from the law of chemical equilibrium3 although ionization is a reversible reaction1 forces come into play which make the simple law inapplicable1 and it is altogether likely1 therefore1 that we shall find1 when all the factors have been investigated1 that strong electrolytes should not and cannot obey this law alone4#bjb ,in confirmation of this conclusion1 recent careful calculations#bjc have shown that entirely analogous deviations from the equilibrium law become perceptible in rather concentrated solutions of weak electrolytes1 such as acetic acid1 in which there is an accumulation of charged particles1 more nearly akin to that present in dilute solutions of strong electrolytes4 ,so it appears more and more certain that the deviations are a result of the presence of electrically charged components in the solutions1 the amount of deviation depending on their concentration4 ,the ,salt ,effect4--,in the second place1#bjd it seems possible that the presence of strong electrolytes in a solution may modify the ionizing power of the solvent in such a way as to increase it1 and to increase it the more1 the more concentrated the ions are in the solution4#bje ,the ionizing power of solvents1 as has been explained1 is intimately connected with their dielectric properties4 p#aaj ,now1 solid salts have higher dielectric constants than has#bjf solid water1 and the dielectric constant of a compound is usually much higher in the liquid than in the solid form4#bjg ,it is possible1 therefore1 that the presence of salts in the solution increases the dielectric or1 at any rate1 the ionizing power of the solvent and there are many facts which would be explained by such a behavior4 ,unfortunately for any decision of the question1 determinations of the dielectric constants of salt solutions have given contradictory results2 the more recent1 and possibly more reliable results of ,drude#bjh indicate that salt solutions show approximately the same dielectric behavior as water itself4 ,smale1 in ,nernst's laboratory1 on the other hand1 obtained results indicating that salt solutions have decidedly higher dielectric constants than pure water4#bji ,a final decision in the matter would be of great importance4#baj ,but1 as explained before 7p4 #fd71 there are other properties of a solvent which seem to be intimately related to its ionizing power and which may be modified by the presence of salts1 i4e4 of strong electrolytes4 ,the value obtained for the proportion ,me ,x _/ ,me,x grows rapidly with increasing concentration1 indicating a disproportionately large ionization in the more concentrated solutions--which is what one would expect1 if electrolytes or their ions in some way increased the ionizing power of the medium4 ,in agreement with such a conclusion1 ,arrhenius found#baa that the ionization of weak acids1 like acetic acid1 is increased by the presence of foreign neutral salts1 such as sodium chloride4 ,this means1 of course1 that the strength of acetic acid1 as an acid1 is increased likewise4 ,,exp4 #j4e c4c4 of #j4a molar acetic acid is added to #ajj c4c4 of a dilute solution of methyl orange in each of three test glasses4 ,when some solid sodium chloride 7#c grams1 and then #c grams more--altogether #j4a mole7 is added to the one solution1 a plain increase in the intensity of the acid tint is observed4#bab ,the addition of cane sugar to a second solution has no such effect4 ,the addition of sodium chloride to a fourth portion of the methyl orange1 to which no acetic acid has been added1 shows that its color remains unchanged3 the effect on the indicator in the first case1 then1 is the result of the action of the salt on the acetic acid4#bac p#aaa ,the so-called salt-effect on the ionization of ammonium hydroxide may be illustrated in a similar way4 ,,exp4 #j4e cc of #j4a molar ammonium hydroxide is added to each of two portions 7#ajj c4c47 of a dilute solution of phenolphthalen4 ,when some sodium chloride solution is then added to one of the two portions1 the basicity of the solution is distinctly increased4 ,the addition of sodium chloride to a third portion of the phenolphthalen solution shows that its own reaction to the indicator is neutral4 ,if the ionizing power of a solvent is changed by the presence of an electrolyte1 then the law of chemical equilibrium1 in its simple form1 would not apply to the ionization of such electrolytes in varying concentrations--as little as we should expect to obtain the same constant for acetic acid in aqueous solution and in alcoholic solution1 the ionizing power of alcohol being much smaller than that of water4 ,the deviation from the law1 naturally1 would be most marked in the case of those electrolytes which ionize so easily as readily to produce high concentrations of ions4 ,it may be said that laws based on the electrical properties of salt solutions seem to be the predominating laws governing the ionization of electrolytes and modifying1 in certain cases1 the chemical laws based on the study of non-electrolytes4#bad ,for the purposes of qualitative analysis1 it will suffice to bear in mind the fact that the ionization#bae of salts1 strong acids and strong bases does not conform to the laws of mass action1 and the fact that practically all salts 7with the notable exceptions1 among common salts1 given on p4 #ajg7 are very readily ionized in aqueous solution1 namely to the extent of #dj to #he in solutions of such moderate concentration as #j4a molar4#baf ,some ,applications of the ,law of ,chemical ,equilibrium4--,according to the discussions given above1 for the ionization of acetic acid1 ,,ch#c;,,co#b;,h ,,ch#c;,,co#b ,h we have the relation ,,ch#c;,,co#b ,h _/ ,,ch#c;,,co#b;,h ,kionization4 p#aab ,if the concentrations of the components are modified in any way1 the condition of equilibrium is disturbed and change will result1 always toward the restoration of equilibrium4 ,the changes1 in the case of purely ionic actions1 are found to take place with an enormous velocity1 equilibrium being restored almost instantly4 7#a7 ,if the solution of acetic acid1 represented in the above equation1 is diluted by an equal volume of water1 the condition of equilibrium is disturbed3 ,,ch#c;,,co#b ,h _/ 7 ,,ch#c;,,co#b;,h7 ,kionization4 ,the ratio is smaller than that required for equilibrium1 and there will be a change towards increasing the ratio4 ,the acid will ionize more rapidly than it will be formed from the acetate and hydrogen ions 7which collide less frequently in the diluted solution7 and a new condition of equilibrium will be reached1 when more of the acid is ionized4 ,we found1 as a matter of fact1 that the more a solution of acetic acid is diluted1 the larger is the proportion of ionized acid 7see p4 #ii74 7#b7 ,if the concentration of the acetate-ion is increased in the solution by the addition of a salt of acetic acid1 say sodium acetate1 we have x ,,ch#c;,,co#b ,h _/ ,,ch#c;,,co#b;,h ,kionization4 ,the ratio is larger than allowed by the equilibrium law1 and the acetate ions will combine with the hydrogen ions to form acetic acid more rapidly than the ions are formed from it1 until equilibrium is restablished4 ,in a molar solution of acetic acid1 #j4db of the acid is ionized1 and we have ,,ch#c;,,co#b ,h _/ ,,ch#c;,,co#b;,h #j4jjdb #j4jjdb _/ #j4iieh #a4h;,e#e4 ,if an equivalent quantity of sodium acetate should be added1 i4e4 one mole or #hb grams of the salt per liter1 the salt being ionized to the extent of #ec1 we would have #j4ecd #j4jjdb _/ #j4iieh #a4h;,e#e4 ,the equilibrium constant will be satisfied 7and the velocity of ionization of the acetic acid will become equal to the velocity of its p#aac formation from its ions7 when#bag ,,ch#c;,,co#b #j4ec1 ,h #j4jjj1jcd and ,,ch#c;,,co#b;,h #j4iii1iff4 ,if we use two characteristic places in the decimals1 we have 7#j4ec #j4jjjjcd7 _/ #a #a4h;,e#e4 ,the most significant fact in the new condition of equilibrium is the extremely small concentration of hydrogen-ion in the solution4 ,since the acid properties of acetic acid are due to its forming hydrogen-ion1 we would conclude that such properties of acetic acid are very much weakened by the presence of its own salts4 ,this conclusion has been fully verified by careful quantitative measurements and can be demonstrated as follows#bah3 ,,exp4 ,to two of three portions of a dilute solution of methyl orange equal quantities of acetic acid are added 7e4g4 #j4e c4c4 molar acid71 the third portion being reserved to show the color of the neutral solution of the indicator4 ,now1 if into one of the solutions1 to which acetic acid has been added1 a few crystals of sodium acetate are gradually dropped1 the color reverts gradually to the color of the original neutral solution2 the concentration of hydrogen-ion becomes so small1 that it does not visibly affect this indicator1 which is not very sensitive to acids1 7,h74#bai ,the solution1 according to the views expressed1 should still be very slightly acid1 and by the use of an indicator 7litmus paper7 which is much more sensitive to the hydrogen-ion than is methyl orange1 no difficulty is found in recognizing this fact also4 ,as a matter of experiment1 then1 an acid like acetic acid is very much weaker in the presence of its own salts than in their absence1 and the equilibrium constant and the concentrations of the components used determine the extent to which the hydrogen-ion is suppressed4 ,the same must be true for all weak acids and similar relations must p#aad hold for all weak bases#bbj--;in general1 weak acids and weak bases are very much weakened by the addition of their own salts4 ,the importance of recognizing such changes1 in considering analytical reactions1 may be illustrated as follows3 ,,exp4 ,a solution of ferrous acetate 7ferrous chloride with an equivalent quantity of sodium acetate7 is treated with hydrogen sulphide2 a precipitate of black ferrous sulphide is formed4 ,a second portion of the solution is first decidedly acidified with acetic acid3 hydrogen sulphide does not precipitate any ferrous sulphide4 ,some crystals of sodium or ammonium acetate are added to the mixture and a black precipitate of iron sulphide immediately appears around the salt as it dissolves1 and on mixing the contents a heavy precipitate of the sulphide throughout the vessel is formed4 ,it is evident that the addition of a neutral salt1 containing the same negative ion as the added acid1 may completely reverse the net result of a test with hydrogen sulphide4 7#c7 ,if the concentration of the hydrogen ions in the solution of acetic acid is increased by the addition of hydrochloric1 or some other strong acid1 equilibrium between the acetic acid and its ions will likewise be disturbed and the new condition of equilibrium will show a suppression of the acetate-ion4 ,instances of such action of a strong acid in suppressing the characteristic ions of weaker acids will be discussed in detail in connection with the analytical applications of hydrogen sulphide 7,chap4 ,,xi71 where the action is of peculiar importance4 ,strong bases have a similar effect on weak bases4 7#d7 ,if one of the ions of acetic acid is suppressed by the addition of some agent1 equilibrium is again destroyed and the resulting change is always in the direction of restablishing a condition of equilibrium on the basis of the law of equilibrium4 ,instances of this common case1 such as the neutralization of acetic or any other acid by a base1 or the driving out of a weak acid1 from its salts1 by a strong acid1 or of a weak base by a strong base1 considered from the point of view of the equilibrium law1 should be worked out by the student4#bba p#aae 7#e7 ,the displacement of an acid 7or base7 in salts by another acid 7or base7 is subject always to the law that equilibrium is reached1 when all the equilibrium constants are satisfied in the system4 ,very frequently1 the application of the law will lead1 apparently1 to the incorrect conclusion that the stronger acid 7or base7 will always displace1 more or less completely1 the weaker#bbb--;an inference1 out of which grew1 indeed1 the characterization of acids and bases as strong and weak4 ,yet1 when the laws of equilibrium1 as the result of the peculiar values of constants1 demand that1 on the contrary1 a strong acid or base should be displaced by a weak1 or even a feeble one1 we find that the change in this direction occurs with equal ease4 ,numerous instances will be given where a weak acid 7or a weak base7 does this to a certain extent 7,chap4 ,x71 and others where precipitation of salts facilitates the action of weaker acids greatly by the introduction of new1 physical constants4 ,the following case of the liberation of hydrochloric acid by the exceedingly weak acid1 hydrocyanic acid1 is important because it shows a reversal of the common action without the formation of any precipitate1 and especially because it brings out most strikingly the relations between ionization and chemical activity in a case of special importance to analytical chemists4 ,the ,exceptional ,ionization of ,mercuric ,cyanide and ,its ,consequences4--,we have found that practically all salts are very readily ionized4 ,but it was mentioned that there are a few exceptions to this rule1 and mercuric chloride and especially mercuric cyanide were named as the most important exceptions from the point of view of analytical chemistry4 ,the difference in ionization between these two salts and ordinary salts may be shown readily by the apparatus previously used to demonstrate the difference in the ionization of various bases and acids4 ,,exp4 ,into the parallel tubes of the conductivity apparatus 7p4 #gg7 equivalent quantities#bbc of solutions of mercuric cyanide#bbd ,hg7,,cn7#b1 mercuric chloride p#aaf ,hg,cl#b1 and barium chloride ,ba,cl#b1 are introduced4 ,the barium chloride represents an ordinary salt of the same type as the mercury salts1 and the current passing through its solution makes the little lamp glow4 ,the electrodes in the mercuric chloride solution must be brought quite close together before sufficient current will pass through the solution to bring its little lamp to redness4 ,in the case of the cyanide we can1 at most1 get a faint1 dull glow by bringing the electrodes together as closely as we can1 without allowing them to touch each other and short-circuit the current4 ,it is evident that these mercury salts are not as readily ionizable as are ordinary salts4 ,this difference1 as may be anticipated1 shows itself also in the chemical behavior of their solutions and makes necessary special precautions on the part of the analyst in examining mercury compounds4 ,for instance1 whereas mercuric oxide is readily precipitated by the addition of sodium hydroxide to solutions of the nitrate and even of the moderately ionized chloride1 one fails to get a precipitate of oxide from the cyanide solution 7exp471 and if we relied on this test1 we should overlook the mercury entirely4 ,that traces of the mercuric-ion are present1 as indicated by the minimal conductivity of the cyanide1 is confirmed by the fact that from the cyanide solution the sulphide1 which is much less soluble than is the oxide1 may be precipitated by the addition of ammonium sulphide 7exp474 ,that the sulphide is in fact less soluble#bbe than the oxide is shown by the conversion of the latter into the former by the action of ammonium sulphide 7exp474 ,as a further result of the abnormally slight ionization of these mercury salts1 the analyst1 unless he is on his guard1 may also have difficulty in discovering the presence of their negative ions4 ,thus1 while sodium chloride readily gives hydrogen chloride when treated with concentrated sulphuric acid1 mercuric chloride1 although it is a soluble salt1 does not 7exp471 and reliance on this test alone might lead to a gross error4#bbf ,in the case of the cyanide1 it is correspondingly difficult to recognize the p#aag cyanide-ion 7see the laboratory experiment1 ,part ,,iii74 ,the ordinary tests fail to show its presence until the mercury has been removed from the solution by precipitation as a sulphide4 ,mercuric cyanide being a deadly poison which analysts are liable to meet and have met with in criminal cases1 it is clear that a knowledge of these facts is vital to analytical accuracy4 ,now1 the very slight ionization of mercuric cyanide enables us to realize1 in the following experiment1 the case where an exceedingly weak acid without the formation of any precipitate involving physical constants1 may displace a much stronger acid from its salts4 ,hydrocyanic acid is one of the weakest acids 7table1 p4 #ajd71 the constant for the ratio ,h ,,cn _/ ,,hnc being #j4g;,e#i4 ,it is so weak an acid that the addition of a dilute solution to methyl orange will not redden the indicator1 but will have only a barely perceptible effect on it 7exp474 ,mercuric chloride solutions also are almost neutral to methyl orange 7exp47 7very slight decomposition of the salt by water makes the solution very slightly acid1 not enough to produce more than an orange color with methyl orange74 ,now1 mercuric chloride1 while it is not very easily ionized1 is1 we found1 very much more readily ionized than is mercuric cyanide4 ,the consequence is that when we add hydrocyanic acid to a mercuric chloride solution1 the equilibrium between mercuric chloride and its ions and between hydrocyanic acid and its ions will be decidedly displaced1 the mercuric-ion combining with the cyanide-ion to form the scarcely ionizable mercuric cyanide4 ,as a result1 more and more of the molecular mercuric chloride and hydrocyanic acid will be ionized2 and since the other ions1 the chloride and the hydrogen ions1 form a readily ionizable electrolyte1 hydrochloric acid1 these ions 7,h and ,cl7 will accumulate in the solution and we shall have sufficient ionized hydrochloric acid liberated to make the solution decidedly acid4 ,,exp4 ,when the two solutions described above are mixed1 a strongly acid solution1 colored a bright pink1 results4 ,in the following equations the dark arrows indicate the direction in which the action goes when the solutions are mixed3 ,hg,cl#b ,hg#b #b ,cl #b ,,hcn #b ,,cn #b ,h #b ,,cn ,hg#b ,hg7,,cn7#b #b ,cl #b ,h #b ,h,cl ,,footnotes3 #aff ,concentrations are usually measured in moles or gram-molecular weights per liter1 and a gram-molecular or molar weight of a compound is its molecular weight expressed in grams4 ,hence the number of grams of a given substance in a liter divided by its molecular weight represents its concentration4 #afg ,nernst1 ,theoretical ,chemistry1 #dbc1 #dcc2 ,ostwald1 ,lehrbuch1 ,,ii#b1 #ajd1 etc41 #bif2 ,walker1 ,introduction to ,physical ,chemistry 7#aiji71 #bei1 etc4 #afh ,not every collision of a molecule of ,a with one of ,b is supposed to result in a chemical interaction1 but the number of collisions with such a result is considered to be directly proportional to the total number of collisions4 ,van 't ,hoff1 ,lectures on ,physical ,chemistry1 ,i1 #ajd4 #afi ,since in any chemical action1 which has not reached a condition of equilibrium1 the concentrations of the reacting substances change continuously1 the relation between the velocity of the action and the concentrations1 for any moment1 is found by the application of the calculus to the experimental data4 7,cf4 ,elements of ,calculus1 by ,young and ,linebarger 7#aijj71 #afh1 #aha1 #bdj2 ,mellor1 ,higher ,mathematics for ,students of ,chemistry and ,physics 7#aijb71 #aig47 #agj ,nernst1 loc4 cit41 #eda1 etc42 ,ostwald1 loc4 cit41 #ajg1 etc42 ,walker1 loc4 cit41 #beg2 ,smith1 loc4 cit41 #bej1 and #ahj 7,stud474 #aga ,if a component takes part more than once in the action1 its concentration is raised to the power corresponding to the coefficient expressing the number of its molecules taking part in the action4 ,for instance1 for ,a #b ,b ,c ,d1 v#a k#a ,a ,b#b2 7see below74 #agb ,cf4 ,van 't ,hoff1 loc4 cit41 ,i1 #bjf4 #agc ,the concentrations are calculated from the data given by ,bodenstein1 ,z4 phys4 ,chem41 #bb1 #af 7#ahig74 7,cf4 ,van 't ,hoff loc4 cit41 ,i1 #aaj47 #agd ,the fundamental meaning of the law is most accurately defined in thermodynamic terms1 that is1 in terms of the work or energy relations connected with changes of gaseous or osmotic pressures4 #age ,van 't ,hoff1 loc4 cit41 ,i1 #ajd1 #aei1 etc4 #agf ,in regard to the variations of the equilibrium constant with changes of temperature and the relations which govern these changes see ,smith's ,inorganic ,chemistry 7#aiji71 p4 #bfj4 #agg ,the limitations are indicated in the preceding section4 #agh ,stieglitz1 ,am4 ,chem4 ,j41 #bc1 #djf 7#aijj74 #agi ,vide ,stieglitz1 loc4 cit4 #ahj ,the table is based on the results of ,noyes and ,cooper1 given in ,the ,electrical ,conductivity of ,aqueous ,solutions1 ,carnegie ,institution ,publications1 ,no4 #fc1 pp4 #ach1 #ada 7#aijg74 #aha ,ostwald ,z4 phys4 ,chem41 #b1 #bgh 7#ahhh71 was the first to develop this relation from the conductivity data for so-called weak acids1 and the law of chemical equilibrium1 holding in such and similar cases1 is often called ,ostwald's ,law of ,dilution4 #ahb ,the equilibrium ratio1 used as an illustration in the text1 is the equilibrium ratio for monobasic acids4 ,for polybasic acids1 the ratio would have the form demanded by the rule given p4 #id4 ,for instance1 for ,h#b,x #b ,h ,x#b1 the expression ,h#b ,x#b _/ ,h#b,x should be constant1 provided the ionization occurs according to the law of chemical equilibrium in its simplest terms4 ,in point of fact1 for strong acids1 this ratio holds as little as does the equilibrium ratio for the monobasic acids4 #ahc ,owing to the instability of carbonic acid1 which breaks down into carbon dioxide and water 7,h#b;,,co#c ,h#b,o ,,co#b71 the carbonic acid is1 in turn1 in equilibrium with the carbon dioxide4 ,for the sake of simplicity1 this relation is not included in the detailed discussion1 and wherever the symbols ,h#b;,,co#c and ,h#b;,,co#c are used1 they are intended to represent the total carbonic acid1 present as such and as carbon dioxide4 ,the detailed discussion of the complication mentioned will be given in connection with the analogous case of ammonium hydroxide and ammonia1 and1 as will be shown there1 with the significance just attached to the symbols1 the relations developed in the text are a rigorous expression of the facts4 #ahd ,h1 in all the equations used1 represents as usual1 the total concentration of hydrogen-ion4 #ahe ,walker and ,cornack1 ,j4 ,chem4 ,soc4 7,london71 #gg1 #bj 7#aijj74 #ahf ,mc,coy1 ,am4 ,chem4 ,j41 #bi1 #dcg 7#aijc72 ,stieglitz1 ,carnegie ,institution ,publications1 ,no4 #ajg1 p4 #bde 7#aiji74 #ahg ,in a solution of phosphoric acid1 all the possible forms of ionization1 described in the text1 occur simultaneously1 but the secondary and tertiary forms of ionization1 as far as the concentration of the hydrogen-ion is concerned1 are entirely subordinate to the primary ionization4 #ahh ,vide footnote1 p4 #gi4 #ahi ,luther1 ,z4 ,elektrochem41 #c1 #bif 7#aijg74 ,noyes and ,eastman1 ,carnegie ,institution ,publications1 #fc1 #bgd 7#aijg74 ,noyes and ,stewart1 ,j4 ,am4 ,chem4 ,soc41 #cb1 #aacc 7#aiaj74 #aij ,the apparatus described on p4 #gg is used4 ,vide ,noyes and ,blanchard1 loc4 cit4 #aia ,hydrogen ions move five to ten times as fast as the anions and carry #hj-ij per cent of the current2 see p4 #ef4 #aib ,the solution of these salts is due to the action of hydrogen ions on their anions2 see ,chap4 ,,viii4 #aic ,goodwin1 ,z4 phys4 ,chem41 #ba1 #a 7#ahif74 #aid ,see ,kohlrausch and ,holborn1 loc4 cit41 p4 #aid4 ,their values for ,k 7last column7 must be divided by #ajj to express the constants in terms of the same units as those used in the above table4 #aie ,j4 ,h4 ,long1 ,j4 ,am4 ,chem4 ,soc41 #ah1 #fic 7#ahif74 ,ley1 ,z4 phys4 ,chem41 #cj1 #cbb 7#ahii72 ,bruner1 ibid41 #cb1 #acc 7#aijj72 ,walker1 ,j4 ,chem4 ,soc41 7,london71 #fg1 #ehe 7#ahie74 #aif ,instances are found in the laboratory experiments1 ,parts ,,iii and ,,iv4 #aig ,the ionization of salts of other types1 e4g4 ,me,x#b1 ,me#b,y1 etc41 likewise fails to conform to the law of chemical equilibrium4 #aih ,see below 7pp4 #aab-d71 also1 further1 confirmatory evidence1 derived from the application of the same law to the influence upon the degree of ionization of weak acids and weak bases1 exerted by the presence of their own salts4 #aii ,see below1 in regard to evidence that the disturbing factors1 predominant with strong electrolytes1 are exhibited in much slighter1 but perceptible measure in the case of the weak electrolytes4 #bjj ,see also the interpretation of the law of chemical equilibrium from the viewpoint of the kinetic theory1 ,nernst1 ,theoretical ,chemistry1 p4 #dbh4 #bja ,for a more detailed discussion of these views1 see ,lehfeldt's ,electrochemistry 7#aijd71 pp4 #gh1 #gi4 #bjb ,various empirical laws1 expressing the behavior of strong electrolytes1 have been suggested3 see ,nernst1 ,theoretical ,chemistry1 p4 #dih1 as to ,rudolphi's and van 't ,hoff's rules2 see also ,a4 ,a4 ,noyes1 ,report of the ,congress of ,arts and ,science1 ,,iv1 p4 #caf 7#aijd74 #bjc ,wegscheider1 ,z4 phys4 ,chem41 #gj 7,i71 #fjc 7#aiji74 #bjd ,it is possible that this effect is only another form of expressing the very relation discussed in the preceding paragraph4 #bje ,arrhenius1 ,z4 ,elektrochem41 #f1 #aj 7#ahii72 ,z4 phys4 ,chem41 #ca1 #aig 7#ahii74 #bjf ,salts have constants averaging about #g1 and running from #e to #bh2 the constant for ice is about #c4 ,landolt1 ,brstein1 ,meyerhoffer1 ,tabellen1 p4 #gff 7#aije74 #bjg ,we have3 ,ice1 #c1 water 7at #j71 #hj2 glacial acetic acid1 #b4h1 acetic acid 7liquid71 #aj2 cane sugar1 #d1 cane sugar in aqueous solution 7#dj71 #fg4e1 7#f4e71 #de4c4 ,ibid4 #bjh ,z4 phys4 ,chem41 #bc1 #bhj 7#ahig74 #bji ,wiedemann's ,ann41 #fj1 #fbe 7#ahig74 #baj ,see ,walden1 ,z4 phys4 ,chem41 #fa1 #fcf 7#aijh71 in regard to the difficulties of the problem4 #baa ,loc4 cit4 #bab ,cf4 ,szyszkowski1 ,z4 phys4 ,chem41 #eh1 #dbj 7#aijg74 #bac ,arrhenius made a calculation of the effect1 taking into account all the rather involved changes produced by the salt4 ,loc4 cit4 #bad ,for instance1 the principle of isohydric solutions1 discovered by ,arrhenius1 has been established empirically and it involves relations which are in marked disagreement with the demands of the law of chemical equilibrium4 ,vide ,a4 ,a4 ,noyes1 ,report of the ,congress of ,arts and ,sciences1 ,,iv1 p4 #cah 7#aijd74 #bae ,the most reliable estimates of the concentrations of ions in these solutions are based on determinations of the degrees of ionization by means of conductivity measurements 7see ,chap4 ,,iv1 and the previous footnote74 #baf ,salts ,me,x ionize more readily 7#hj-he in #j4a molar solution7 than do salts ,me,x#b or ,me#b,x 7#ej to #gj in #j4a molar solution71 and these1 again1 more readily than salts ,me,x 7about #dj in #j4a molar solution74 #bag ,the calculation of the condition of equilibrium can be made1 with sufficient accuracy for our purpose1 as follows3 ,the denominator #j4iieh in the original proportion1 being near its limit 7its highest possible value is #a in a molar solution71 cannot change appreciably4 ,consequently1 when the one factor in the numerator1 ,,ch#c;,,co#b1 is made #j4ec _/ #j4jjdb1 or #abf times as large as it was1 the other factor1 ,h1 to maintain a constant proportion1 must be made #a _/ #abfth of its original value and #j4jjdb _/ #abf #j4jjj1jcd4 ,for more exact work1 the new concentrations of the three components may be found by solving a simple quadratic equation4 #bah ,kster1 ,z4 fr ,elektrochem41 #d1 #aaj 7#ahig74 #bai ,see note1 p4 #gi4 #bbj ,see ,part ,,iii for the application of this principle to ammonium hydroxide and its experimental confirmation4 7,cf4 ,arrhenius1 ,z4 phys4 ,chem41 #b1 #bh 7#ahhh72 ,stieglitz1 ,am4 ,chem4 ,j41 #bc1 #djf 7#aijj747 #bba ,for instance1 in the first place1 the action of #j4a mole of ,h,cl on #j4a mole of ,c#b;,h#c,o#b,na1 dissolved in a liter of water1 and1 in the second place1 the action of #j4a mole of ,na,o,h on #j4a mole of ,,nh#d;,cl1 in a liter of water1 may be considered4 ,the strong electrolytes 7,h,cl1 ,c#b;,h#c,o#b,na1 ,na,cl1 ,,nh#d;,cl1 ,na,o,h7 may be taken to be 7roughly7 #hj ionized4 ,from the concentrations given and the constants involved1 the direction and the presumable intensity of the main change in each of the two cases should be determined4 #bbb ,instances of such displacement are given in the footnote of the previous paragraph4 #bbc ,e4g4 #ej c4c4 of #j4b molar solutions4 #bbd ,mercuric cyanide and mercuric chloride are largely present in aqueous solution as ,hg7,,cn7#bb and ,hg,cl#bb2 see ,chap4 ,,xii4 #bbe ,see ,chapter ,,viii in regard to this proof that mercuric sulphide is less soluble than mercuric oxide and in regard to the question how1 by a continuous disturbance of the equilibrium conditions1 all the mercury may be precipitated from the cyanide solution as the sulphide1 in spite of the very slight degree of ionization of the cyanide4 #bbf ,the chloride is1 however1 sufficiently ionized to make possible the precipitation of the very insoluble silver chloride1 when silver nitrate is added to its solution4 p#aah ,,chapter ,,vii ,,physical ,,or ,,heterogeneous ,,equilibrium4--,,the ,,colloidal ,,condition ,the law governing physical or heterogeneous equilibrium applies to all cases where1 at a constant temperature1 one and the same chemical substance is present in two or more physical conditions1 or phases1 in contact and in equilibrium with each other4 ,we have1 for instance1 the common case of a liquid1 say water1 in contact with its vapor1 or the liquid in contact with its solid phase 7ice7 and its vapor2 or1 we may have a gas1 say oxygen1 in contact with its solution in some solvent like water4 ,we may have a solid1 like cane sugar1 in contact with its solution4 ,we may also have a substance like bromine1 which is soluble both in chloroform and in water1 present in both solutions at the same time1 the two solutions being in contact but immiscible4 ,these cases represent the most common types of systems to which the law of physical equilibrium may be applied1 although the list has by no means been exhausted4 ,the law of physical or heterogeneous equilibrium states that when one and the same chemical compound is present in two physical states or phases1 as expressed in the equation ,s#a ,s#b1 then when equilibrium is reached1 at a given temperature1 the ratio of the concentrations of the substance in the two phases is some constant number3 ,s#a 3 ,s#b k4 ,the bracketed symbols denote concentrations4 ,it should be noted that the condition of equilibrium is independent of the total quantity#bbg of substance present in either phase or in both phases2 that is1 provided the ratio of the concentrations is maintained constant at a given temperature1 the quantity of substance present in both phases or in either phase is variable4 ,for instance1 the condition of equilibrium between water and p#aai water vapor is independent of the quantity of water or of water vapor present3 in a closed liter bottle containing water and water vapor1 the ratio of the concentrations is maintained1 irrespective of the question whether the bottle contains #aj c4c4 of water and #iij c4c4 of vapor or #iij c4c4 of water and #aj c4c4 of vapor4 ,the law is one of experience2 instances of its application are given below4 ,its probable theoretical significance may be explained mechanically with the aid of the kinetic theory of gases and solutions1 as follows3 ,if chloroform is added to a solution of bromine in water1 the chloroform takes up part of the bromine and1 if the mixture is vigorously shaken1 a condition of equilibrium and a definite distribution of bromine between the two solvents will result 7exp4#bbh74 ,now1 if one imagines a liter of the aqueous solution to contain one mole of bromine at some given temperature and to cover a liter of chloroform1 the whole system being left to itself1 then all the conditions affecting the migration of the bromine into the chloroform will be definite ones--the concentration of the bromine1 the temperature1 the surface between the two solvents--and bromine will pass from the aqueous solution into the chloroform solution at a definite speed4 ,we may call the quantity 7in moles7 of bromine which would enter the chloroform in one minute1 if the concentration of the bromine in the water were kept constant 7one mole7 throughout the minute1 the velocity of migration of the bromine--this velocity1 like chemical velocity1 representing a quantity1 not a distance4 ,the velocity being a definite one under these conditions1 we have v#a k#a4 ,now1 if all the conditions are left unaltered1 except that the concentration of the bromine is changed1 say kept at one-hundredth its original value1 then only one one-hundredth as many molecules of bromine as in the first case will come into contact with the chloroform surface in unit time4 ,the chances for migration are one one-hundredth as great1 and the quantity entering the chloroform in unit time--the velocity of the p#abj change--will be one one-hundredth of the original velocity4 ,in general1 the velocity will be proportional to the concentration of the bromine ,braq4 in the water at any moment and to the characteristic constant k#a4 v#a ,braq4 k#a4 ,on the other hand1 if a solution of bromine in chloroform is covered with water1 bromine enters the water 7exp474#bbi ,we would find1 by the method of analysis used before1 and for the same conditions1 that the velocity of migration1 v#b1 of the bromine into the water is also proportional to a characteristic constant1 k#b1 and to the concentration of the bromine in the chloroform ,brch44 ,we have1 therefore v#b ,brch4 k#b4 ,equilibrium between the two solutions will be reached when v#a v#b or ,braq4 k#a ,brch4 k#b1 from which follows that#bcj for the condition of equilibrium ,braq4 _/ ,brch4 k#b _/ k#a k4 ,applications of the ,law of ,physical ,equilibrium4--7#a7 ,the law of physical equilibrium may be applied first to the case of a liquid1 say chloroform1 in contact with its vapor4 ,for the condition of equilibrium at a fixed temperature ,c,h,cl#cvap4 3 ,c,h,cl#cliq4 k4 ,now1 at a fixed temperature1 a pure liquid has a fixed concentration1 its specific gravity being a definite one4 ,hence1 for a fixed temperature1 the second term of the constant ratio being definite1 the first term1 ,c,h,cl#cvap41 representing the concentration of the vapor1 must also have a fixed1 constant value for the condition of equilibrium1 i4e4 when the space above the liquid is saturated with its vapor4 ,this is in agreement with well-known facts4 ,the concentration of the vapor is usually expressed in terms of its p#aba pressure1 and is called the vapor pressure or vapor tension of the liquid at the temperature in question4 ,tables giving the definite vapor pressures of important liquids at the various fixed temperatures are in common use4 7#b7 ,for oxygen in equilibrium with its saturated solution1 say in water1 at a fixed temperature1 we have1 according to the law1 ,o#b;gas 3 ,o#bsolut4 k4 ,if the oxygen is under a given pressure at a definite temperature1 its concentration ,o#b;gas is fixed1 and consequently the second term1 ,o#bsolut41 of the ratio1 the concentration of the dissolved oxygen1 or its solubility1 must also be definite1 i4e4 oxygen must have a definite solubility in water at a given temperature under a given pressure4 ,if the pressure on the gas is doubled1 its concentration is doubled and1 to maintain the constant ratio1 its solubility must also be doubled--which is in agreement with the facts 7,henry's law74 ,if air of the same pressure is taken1 in place of pure oxygen1 then the concentration of the oxygen 7first term of the above ratio7 is only about one-fifth as great as for the pure gas1 and the water must be saturated with oxygen when it has taken up only one-fifth 7second term of the ratio7 as much as it would from the pure gas 7,dalton's law73 ,each gas in a mixture is soluble in proportion to its own partial pressure or concentration4 7#c7 ,for sugar in equilibrium with its solution in water1 i4e4 in contact with its saturated solution1 at a given temperature1 we should have ,c#ab;,h#bb,o#aa;aq4 3 ,c#ab;,h#bb,o#aasolid k4 ,since a pure solid like sugar at a given temperature has a definite specific gravity1 the concentration of the sugar in the solid condition should also be a definite one4 ,consequently1 according to the law under discussion1 the first term1 ,c#ab;,h#bb,o#aa;aq41 of the ratio1 the concentration of the sugar in its saturated solution in contact with the solid phase1 must also have a definite value4 ,this is in agreement with fact1 the concentration of the sugar in the saturated solution1 termed its solubility1 being a definite one for a given temperature4 7,see below1 p4 #abc1 in regard to the solubility of fine powders47 ,supersaturated ,solutions4-- ,it is well known1 however1 that by dissolving a substance1 such as sugar1 in hot water and carefully p#abb cooling the solution1 we may obtain a solution of sugar containing much more sugar in unit volume than is represented by its solubility at the lower temperature4 ,the concentration of the sugar at the temperature in question1 instead of having the definite value represented by ,c#ab;,h#bb,o#aa;aq41 can easily have a value several times as large4 ,this phenomenon is not at variance with the law of physical equilibrium1 inasmuch as the law states that1 when a given compound is present in two physical states or phases1 then a constant ratio between the concentrations of the substance in the two phases is established when equilibrium is reached at a given temperature4 ,in the solution prepared as described1 we have the substance present only in one phase1 and we have what may be called a metastable condition1 as long as the second phase is not introduced4 ,as soon as a minute crystal of the solid phase is added or is formed in the solution1 change immediately ensues1 and the excess of solid is deposited4 ,if the mixture be kept perfectly quiet1 the excess will in most cases be deposited on the surfaces of the added crystal1 which thereby grows larger 7rock-candy manufacture74 ,,exp4 ,supersaturated solutions of sodium sulphate and sodium thiosulphate1 into which crystals of the salts are dropped1 show how the crystal starts crystallization4 ,the crystals develop as branches from the crystal first introduced and from the new crystals formed4 ,this phenomenon of supersaturation is one which analytical chemists must always take into consideration4 ,tests which involve the precipitation of substances that are merely difficultly soluble1 rather than exceedingly insoluble1 or of substances present only in very small quantities1 may well lead to entirely wrong conclusions1 if precautions are not taken against the possibility of the failure of a precipitate to appear as a consequence of persistent supersaturation4 ,for instance1 a common test for the presence of potassium salts consists in the precipitation of potassium acid tartrate by the addition of tartaric acid to the solution of a potassium salt 7exp474 ,the tartrate is somewhat soluble and tends to form supersaturated solutions2 if we proceed without due regard for this phenomenon1 we may readily have a quantity of potassium salt present and fail to obtain the test for it4 ,simply mixing tartaric acid and potassium chloride solutions 7exp47 may fail to p#abc give any precipitate1 and if the test is thrown away and potassium reported absent1 a glaring blunder is committed4 ,to insure against the error of supersaturation1 we try to start crystallization by the common devices of shaking the solution or scratching the walls of the vessel1 the object being to facilitate the formation of the first crystal4 ,the surest method is to inoculate a small portion of the mixture with a minute crystal of the substance we expect to be formed4 ,if no precipitate results in a short time1 the solution is not supersaturated--it may be too dilute and may require further concentration1 but the error of supersaturation has been excluded4 ,the relation between supersaturated solutions and crystals brings out sharply the fact that physical equilibrium is essentially a condition of equilibrium between the substance at the surface of the solid and the substance in its dissolved state4 ,in terms of the molecular theory1 equilibrium is established when the molecules of the crystal surface dissolve as rapidly as molecules from the solution are deposited on the surface4 ,if the concentration of the dissolved molecules is reduced below the point required for equilibrium1 the velocity of deposition is diminished4 ,the velocity of solution will then be greater than the velocity of deposition and solution will result4 ,the reversed relations hold when the concentration of the solution is greater than that demanded by equilibrium3 the velocity of deposition will be the greater than that of solution and precipitation follows4#bca ,solubility of ,fine ,powders4--,consideration of the surface forces1 acting between crystals and the liquids wetting them1 led to the interesting prediction#bcb that the more minute crystals of a given specimen would not only dissolve more rapidly1 on account of the larger surface exposed1 but would also be more soluble than the larger crystals1 and for the same reason4 ,surface tension always tends to produce the smallest possible free surface of a liquid1 and the free surface between a liquid and a given weight of solid material in a fine powder is much larger than between the liquid and the same weight in larger crystals4 ,the surface tension p#abd will therefore tend to convert the smaller crystals into larger ones1 and it can do so only by means of a greater degree of solubility of the former4 ,this prediction has now been fully verified by experiments on the solubility of barium sulphate and of gypsum4#bcc ,the solubility of barium sulphate in a very fine powder 7with an average diameter of #ajd mm47 is almost twice as great as the solubility of a coarser material 7#ah;,e#d mm4 average diameter74 ,the application of these relations to analysis is as follows3 ,if a crystalline precipitate is in contact with a solvent1 e4g4 if barium sulphate is in contact with the liquid from which it has been precipitated1 then this liquid must be continually in a state of change1 not of equilibrium1 with respect to the solution and the deposited barium sulphate4 ,the more minute crystals1 being a little more soluble than the larger ones1 will supersaturate the solution in respect to the larger crystals and the excess will be deposited on these larger crystals and make them grow still larger4 ,this deposition will make the solution unsaturated with respect to the smaller crystals and more of these will dissolve4 ,the process is obviously a continuous one1 and must lead in time to the disappearance of the minute crystals and the growth of the larger ones4 ,that is a result which analysts aim to attain1--which in quantitative work it is in fact necessary to attain1 since the more minute crystals are likely to pass through filters and be lost in the analysis4 ,the views expressed1 and the experimental confirmation of the conclusion reached1 form the theory of what is called the digesting of precipitates before they are brought on filters4 ,it is clear that every condition facilitating contact between solvent and solid will accelerate the desired change and continuous stirring is therefore desirable4 ,heating is1 as a rule1 also to be desired for very insoluble precipitates1 as it will1 in the majority of cases1 facilitate the solution of the undesirable1 finer crystals4 ,in conclusion1 these considerations will also indicate the precautions to be observed in the precipitation of difficultly soluble substances4 ,if this is not properly carried out1 endless trouble in p#abe the analytical laboratory results4 ,except when heating is1 for some special reason1 undesirable--as inducing a chemical change 7like hydrolysis7 that is not wanted--solutions are brought to the boiling-point1 and the precipitant added drop by drop1 in order not to supersaturate the solution too strongly4 ,the solution is thus allowed time to deposit its excess as far as possible on the first crystals formed1 which it will do rather than to form new1 minute ones 7see supersaturation1 p4 #aba74 ,constant stirring is prescribed in order to bring older crystals1 as far as possible1 into contact with all parts of the slightly supersaturated solution4 ,after the precipitation is complete1 it is usually desirable to allow the mixture to digest for some time1 for the reasons given above--stirring and a high temperature during the process being desirable4 7,see further ,chap4 ,,viii1 p4 #adg1 in regard to the use of an excess of precipitant47 ,,the ,,colloidal ,,condition ,when a difficultly soluble substance is formed in a solution beyond the point of saturation of the solution1 the substance in question separates from the solution in a new phase1 according to the principles just laid down4 ,ordinarily1 if the substance is a solid1 a precipitate is formed2 if a gas1 a gas escapes2 if a liquid1 a liquid separates out1 which is immiscible with the solution in which it is formed4 ,occasionally1 the condition of supersaturation which precedes the separation is somewhat persistent1 but this resistance to the separation of the phase may be overcome by vigorous agitation of the solution or1 as in the case of supersaturation with a crystallizable salt1 by inoculation of the solution with a particle of the new phase 7p4 #abc74 ,under certain conditions1 however1 a difficultly soluble substance may be produced in a solution1 in a concentration far beyond its solubility1 without the separation of a precipitate 7evolution of a gas or formation of a separate liquid7 and also without the formation of a supersaturated solution4 ,thus1 when hydrogen sulphide is passed into an aqueous solution of arsenious oxide1 the liquid acquires the yellow to orange color of arsenious sulphide and becomes opalescent4 ,but no precipitate is seen 7exp471 in spite of the fact that the sulphide is extremely insoluble and is formed practically quantitatively according to the equation ,as#b,o#c #c ,h#b,s ,as#b,s#c #c ,h#b,o4 ,the orange liquid passes through a p#abf filter unchanged 7exp474 ,but if some hydrochloric acid or a salt 7e4g4 sodium chloride7 solution is added to a portion of it1 a heavy precipitate of arsenious sulphide is immediately produced 7exp472 its quantity is a good indication of the great amount of sulphide that is not precipitated before the addition of the acid or salt4 ,if some pure arsenic sulphide 7solid7 is added to another portion of the orange liquid1 in order to overcome any possible condition of supersaturation1 the liquid is found to remain clear 7but opalescent71 excepting for the few particles of added sulphide 7exp472 even when it is vigorously shaken 7exp471 or allowed to stand for days1 no precipitate is formed4 ,we are therefore not dealing with a case of supersaturation4 ,a liquid1 in which a very insoluble substance appears thus to be in solution far beyond its usual degree of solubility1 and yet does not show at all the behavior of a supersaturated solution1 is said to contain the substance in the colloidal condition4 ,after a few more instances of the colloidal condition have been presented1 the significance of the condition and the meaning of the term used to designate it will be explained4 ,colloidal ,gold4--,when a solution of gold chloride#bcd is treated with a solution of stannous chloride which contains a little stannic chloride1#bce a purple-red1 flocculent precipitate--the purple of ,cassius--is formed2 in extremely dilute solutions only a purple-red liquid#bcf may be produced4 ,if the precipitate is collected on a filter1 washed with water and then treated1 on the filter1 with a few drops of ammonium hydroxide solution and some water 7exp471 it is seen to dissolve and a beautifully colored liquid1 of purple-red or claret-red tint1 is found to pass through the filter4 ,in spite of the extreme insolubility of metallic gold1 the red ammoniacal solution 7as well as the first red precipitate7 contains metallic gold1 in the colloidal condition1 formed according to the equation#bcg #b ,au#c #c ,sn#b #b ,au #c ,sn#d4 ,by the careful p#abg reduction of gold chloride with phosphorus1#bch or with formaldehyde in dilute1 slightly alkaline solution1#bci brilliant red liquids1 containing metallic gold in the colloidal condition1 may be prepared1 which remain clear for months4 ,the passage of an electric current1 in the form of an arc1 between two gold points under pure water produces similar red liquids#bdj containing metallic gold4 ,colloidal ,silver4--,further1 although silver is likewise an extremely insoluble metal1 solid preparations of silver are known which1 on treatment with water1 form apparently perfectly clear 7opalescent7 liquids or solutions 7exp474#bda ,from these silver is not deposited1 even in the course of months4 ,if a little of the black solid is heated on the lid of a porcelain crucible1 the metal may be readily recognized by its white color and luster4#bdb ,colloidal ,ferric ,hydroxide4--,further1 if to a solution of ferric chloride an excess of ammonium hydroxide is added1 the well-known1 rust-red precipitate of very difficultly soluble ferric hydroxide is formed3 ,fe,cl#c #c ,,nh#d,,oh ,fe7,,oh7#c #c ,,nh#d;,cl4 ,the precipitate is so insoluble that it is a favorable form for precipitating the ferric-ion in quantitative analysis4 ,if1 however1 a solution of ferric chloride be carefully neutralized with ammonium carbonate#bdc and be then placed in a vessel 7called a dialyzer71 in such a way that it is separated1 by an animal membrane or by parchment1 from pure water1 ferric hydroxide is obtained in an apparently soluble form4 ,the ammonium chloride1 as well as hydrochloric acid which is formed by the decomposition of the chloride by water 7,fe,cl#c #c ,,hoh ,fe7,,oh7#c #c ,h,cl1 see ,chapter ,x71 are found to pass through the membrane readily1 while the ferric hydroxide produced does not pass through such p#abh membranes#bdd and is retained in the dialyzer without forming a precipitate4 ,the acid and salt pass through such membranes in either direction1 indeed1 but flow mainly from their solutions of higher concentration to those of lower concentration4 ,the water on the outside of the dialyzer is1 therefore1 continuously renewed1 in order to insure a concentration of these substances on the outside of the dialyzer lower than that within it4 ,as the hydrochloric acid is thus removed through the membrane1 the condition of equilibrium between the ferric chloride1 water1 ferric hydroxide and acid is continuously disturbed and1 in the reversible reaction1 expressed in the above equation1 the action is carried more and more towards the right1 and more and more ferric hydroxide is formed4 ,the salt is1 at last1 practically all decomposed and a clear red opalescent liquid1 which contains ferric hydroxide in enormous excess beyond its solubility in water1 is left in the dialyzer4 ,exactly as in the case of the other liquids discussed above1 in which very insoluble substances appear to be in solution far beyond their usual degree of solubility1 so the present liquid does not show the behavior of a supersaturated solution and it is said to contain the ferric hydroxide in the colloidal condition4#bde ,solution ,theory of the ,colloidal ,condition4--,for many years the belief was prevalent among chemists that these liquids represent true solutions of difficultly soluble substances1 in the form of soluble 7colloidal7 modifications of the substances4 ,like ordinary p#abi solutions1 the liquids are found1 indeed1 to show a certain osmotic pressure1 but1 unlike ordinary solutions1 the osmotic pressure is exceedingly small in proportion to the quantity of the substance present4 ,since the osmotic pressure is proportional to the number of molecules in unit volume 7,chap4 ,,ii71 this observation proved the presence of a relatively very small number of molecules in solution1 and chemists were led to assign1 therefore1 a relatively very great weight to each4 ,hence1 the data led to the assumption that the colloidal modifications consist of molecules of very large1 sometimes enormous molecular weight4 ,from the fact that colloids are unable to traverse membranes1 through which crystalloids readily pass1 ,graham had reached the same conclusion4 ,the following measurements of osmotic pressures may be given3#bdf ,osmotic ,substance4 ,concentration ,pressure4 ,per cent4 ,cm4 ,hg4 ,gum arabic #a #f4i ,dextrin #a #af4f ,as#b,s#c #d #a4g ,fe7,,oh7#c #a4a #j4h #b4j #b4h #c4j #e4f #e4c #ab4e #h4i #bb4f ,the last results1 obtained with special care to exclude soluble impurities1 are more reliable than the older results on gum arabic and dextrin4 ,for the purpose of comparison it may be said that a #a solution of cane sugar 7molecular weight #cdb7 has an osmotic pressure of #ec cm4 ,hg at #ah1 a #e solution a pressure of #bfe cm4 ,the ,suspension ,theory of the ,colloidal ,condition4--,on the other hand1 a number of chemists considered the colloidal liquids to represent1 essentially1 suspensions of minute solid particles#bdg in an extreme state of subdivision1 or1 in some instances1 perfect p#acj emulsions of difficultly miscible liquids4#bdh ,observations with the ultramicroscope#bdi finally proved1#bej beyond question1 the correctness of this theory of the colloidal condition4 ,thus1 the colloidal solutions of gold are seen to contain minute solid particles of gold1 the diameter of which varies#bea between 7approximately7 #fj and #f and the color of which varies with their size4 ,still finer subdivisions1 the diameter of whose particles cannot be measured1 are also found to exist4 ,colloidal silver1 platinum1 arsenious sulphide and other colloidal metals and sulphides have also been shown1 in the same way1 to be suspensions of solid particles4 ,the ,general ,character and the ,definition of the ,colloidal ,condition4--,recent investigations have shown that the colloidal condition is possible1 not only for a limited class of substances1 but is1 in general1 possible for all substances4#beb ,thus1 even such an eminently crystallizable1 readily soluble 7in water7 substance as sodium chloride may be obtained1 under certain conditions1 in colloidal suspension in benzene1#bec in which it is insoluble4 ,for our purposes it will be sufficient to define the colloidal condition1 on the basis of these results1 as the condition of an insoluble substance in which1 as far as ordinary observation and the common methods for separation of heterogeneous phases 7filtration1 sedimentation1 etc47 are concerned1 the substance appears to be present in a homogeneous clear solution1 whereas in reality it is present in a heterogeneous mixture4 ,an extremely finely divided solid suspended in a liquid1 or an emulsified liquid suspended in another liquid1 are the most common types#bed of such mixtures4 p#aca ,relations to ,analysis4--,since the colloidal condition of insoluble substances interferes with the precipitation of the latter1 and with their separation by filtration from the liquids in which they are suspended1 and since the majority of the separations and tests of analytical chemistry depend on the successful formation of precipitates and on their successful separation by filtration1 analytical chemistry is primarily#bee concerned with the colloidal condition as a condition that is to be avoided as completely as possible in order to escape error4 ,in other fields of chemistry1 notably in physiological chemistry and in some branches of technical chemistry1 it is a source of effects so momentous and specific that a new branch of chemistry1 the chemistry of colloids1#bef has grown out of the investigations of its relations and laws4 ,the present discussion will be limited to the presentation of such of the fundamental facts concerning the colloidal condition as are of chief importance in analytical work4#beg ,electrical ,conditions of ,colloids4--,one of the most important discoveries made on colloids is the observation that the suspended particles of a large class of colloids carry electrical charges1 so that there is a potential difference between the particles and the liquid in which the suspension exists4#beh ,thus1 in the colloidal suspension of arsenious sulphide 7prepared as described on p4 #abe7 the sulphide particles carry negative charges1 and the solution bathing them is positive4 ,conversely1 colloidal ferric hydroxide 7p4 #abg71 in water1 is charged with positive1 the water with negative1 electricity4 ,the existence and character of these charges may be readily demonstrated by the passage of a current of electricity through the colloidal suspension in ,u tubes 7exp474#bei ,colloidal arsenious sulphide is found to migrate toward the positive pole1 ferric hydroxide p#acb to the negative pole1 the movement being easily followed by the color of the suspended particles4 ,the following colloids1 which are of interest in analytical chemistry1 are found to carry a negative charge in pure water3 ,colloidal acids 7silicic1 stannic71 sulphides 7,as#b,s#c1 ,as#b,s#e1 ,cd,s1 etc471 salts 7,ag,i1 ,ag,cl7 and metals 7,au1 ,pt1 ,ag74 ,it is noteworthy that the suspensions of finely divided clay1 kaolin1 quartz1 carbon1 carry the same charge as these colloidal suspensions4 ,on the other hand1 metal hydroxides 7ferric1 aluminium1 chromic71 and basic substances in general1 carry positive charges4 ,on the other hand1 the colloids of one important group are found to be almost without any electric charges2#bfj the passage of an electric current through their suspensions has little or no effect on them4 ,perfectly neutral albumen and gelatine are common representatives of this group4 ,the charge on a colloid seems to be liable to variation with the nature of the liquid in which it is suspended4 ,colloidal platinum in water is negative1 in a mixture of water and alcohol1 positive4#b ,of peculiar interest and importance is the fact that some colloids change the character of their charge when the liquid1 in which they are suspended1 is made to pass from an acid to an alkaline condition1 and vice versa4#bfa ,for instance1 albumen#bfb1 colloidal silicic acid#bfc and colloidal stannic acid#bfd are negative in alkaline liquids1 positive in acid4 ,the relation of these facts to the chemical nature of the substances will be discussed presently4 ,the ,source of the ,electrical ,charges on ,colloids4--,different views are held as to the source of electrification of colloidal suspensions4 ,only the two views of most direct interest in analysis can be considered here4 ,in the first place1 it is possible that partial ionization of the colloidal suspension produces the electrical charge4 ,it is a significant fact that basic colloids 7metal hydroxides1 some basic dyes7 receive a positive charge1 such as would be left1 if they were slightly ionized as bases 7or salts of bases7 and insoluble 7suspended7 p#acc positive ions were retained by the particles4 ,that would be the case1 for instance1 if particles of colloidal ferric hydroxide1 ,fe7,,oh7#cx1 sent a few hydroxide ions into solution and the suspended particles included positive insoluble ions4 ,acid colloids1 on the other hand1 assume a negative charge1 as would be expected from this point of view4 ,then1 the behavior of silicic acid is particularly suggestive2 in alkaline or slightly acid liquids1 in which its ionization as a weak acid is favored or predominant 7,chapter ,x71 it carries a negative charge1 the charge that would be left on it1 if it ionized1 in part1 as an acid or its salt4 ,silicic acid shows some slight tendency to ionize also as a base 7see ,chapter ,x7 and the basic form of ionization would be favored by the presence of a strong acid 7,chapter ,x74 ,colloidal silicic acid1 as stated above1 changes its charge from negative to positive as the solution passes from an alkaline to a 7strong7 acid reaction1#bfe just as if1 in the acid liquid1 it ionized slightly as a base 7salt of a base7 and retained a difficultly soluble positive ion4 ,albumen1 which has the property of being both a base and an acid1#bff shows the same change of charge#bfg in the colloidal condition and the change has been ascribed#bfh to the change of basic and acid functions4 ,according to the other of the two theories1 here considered1 the electrification of the colloid may result from what is known as contact or surface electricity4#bfi ,at the surface of two different substances there is always a potential difference4#bgj ,in the case of finely divided suspensions1 like the colloids1 the contact surfaces are enormous1 as compared with the surfaces involved in ordinary contact4 ,whether metals 7,au1 ,pt1 ,ag7 owe their charges to simple contact effects or to their 7minimal7 tendency to ionize 7,chapters ,,xiv and ,,xv7 is not known4 ,in fact1 no exact knowledge of the source of electrification of any colloid has yet been obtained4 ,precipitation of ,colloids by ,electrolytes and by ,colloids4--,substances in the colloidal condition1 which carry an electrical charge1 are readily precipitated by the addition of electrolytes to the colloidal suspensions 7see the behavior of arsenious sulphide1 p4 #abf74 ,negatively charged colloids are precipitated by the action of positive ions1 positively charged colloids by the action of negative ions 7,hardy's rule#bga74 ,the precipitated colloid carries p#acd with it a part of the precipitating ion#bgb 7adsorption7 and the weights of ions1 carried down by a given quantity of a given colloid1 are proportional to the equivalent weights of the ions4#bgc ,the precipitation thus appears to be intimately associated with the neutralization of the charge on the colloid4 ,in accordance with this conclusion1 it has also been found that a colloid may be precipitated by a colloid carrying the opposite charge4#bgd ,thus1 colloidal arsenious sulphide1 carrying a negative charge1 and colloidal ferric hydroxide1 carrying a positive charge1 mutually precipitate each other 7exp4#bge74 ,the purple precipitate 7purple of ,cassius71 which is formed when stannous chloride is added to gold chloride 7p4 #abf71 contains colloidal gold1#bgf which1 in suspension1 is charged with negative electricity1 and colloidal stannic acid1#bgf which in acid solution1 presumably1 carries a positive charge#bgg3 these two colloids mutually precipitate each other in the presence of hydrochloric acid4#bgh ,when the precipitate is treated with an alkaline liquid 7ammonium hydroxide solution71 the charge on the stannic acid becomes negative1 both colloids acquire the same charge and the precipitate dissolves1 to form the beautifully tinted suspensions of colloidal gold 7p4 #abf74 ,in this condition the colloids 7gold and stannic acid7 are sensitive to precipitating electrolytes1 and the solution is more sensitive to a mixture of magnesium nitrate and ammonium nitrate than to ammonium nitrate alone 7exp471 as is to be expected from a negative suspension 7see below74 ,the characteristic difference in behavior between ortho-1 pyro- and metaphosphoric acids toward albumen1 which is used as a characteristic analytical test to distinguish metaphosphoric acid from the other two acids1#bgi appears to be due to similar relations#bhj3 metaphosphoric acid1 which precipitates 7coagulates7 albumen1 is colloidal1 ortho- and pyrophosphoric acids are not4 ,the p#ace coagulation seems to be the result of the union of the negative colloid metaphosphoric acid 7or a complex negative colloidal ion thereof7 with the positive colloid albumen 7or a positive colloidal ion thereof74 ,the ,precipitating ,power of ,electrolytes and the ,valence of their ,ions4--,the complete precipitation of colloids1 which carry electric charges1 depends on the concentrations of the colloid and the electrolyte2 in this connection the important observation has been made that the precipitating power of electrolytes increases decidedly with the valence of the precipitating ions 7,h4 ,schulze's rule#bha74 ,bivalent ions are far more efficient than univalent2 trivalent1 in turn1 still more effective than bivalent4 ,thus1 colloidal ,as#b,s#c1 carrying a negative charge1 is precipitated by the positive ions of added electrolytes4 ,the addition of a few drops of a molar solution of ammonium nitrate 7the precipitating ion is ,,nh#d7 to #bj c4c4 of the colloidal suspension#bhb produces a slight precipitate2 complete precipitation requires #c4e to #c4f c4c4 of the ammonium nitrate solution4#bhc ,only #j4jf c4c4 of an equivalent solution#bhd of magnesium nitrate 7the precipitating ion is ,mg#b7 is required1 and as little as #j4jae c4c4 of an equivalent solution of aluminium nitrate#bhe 7the precipitating ion is ,al#c7 has the same effect 7exp474 ,an increase in valence of the negative ion1 which is not the precipitating ion in this case1 does not affect the result appreciably3 #c4e c4c4 of a solution#bhf of ammonium sulphate1 7,,nh#d7b,,so#d1 equivalent to the solution of ,,nh#d,,no#c1 is also required for the complete precipitation of the colloidal ,as#b,s#c 7exp471 although the one contains the univalent ion1 ,,no#c1 the other the bivalent ion1 ,,so#db4 ,conversely1 a positively charged colloid1 like ferric hydroxide1 may be precipitated by much smaller quantities#bhg of bivalent negative ions than of univalent ions1 etc4 p#acf ,nonprecipitation of ,nonelectrified ,colloids by ,electrolytes4--,colloids which do not carry any electric charges of moment 7see p4 #acb7 are also not precipitated by dilute solutions of electrolytes4 ,heat1 the addition of concentrated salt solutions in great excess 7whose effect is probably a dehydrating one71 or of other solvents 7e4g4 alcohol71 are the agents most commonly used to effect coagulation in such cases4 ,protective ,action of ,colloids on ,other ,colloids4--,colloids1 particularly such as are not sensitive to precipitation by electrolytes1 increase in a remarkable degree the stability of the colloidal condition of substances1 that carry electrical charges and1 ordinarily1 would be very sensitive to precipitation4 ,thus1 small quantities of albumen are used to render colloidal silver preparations more stable4 ,tannic acid1 gelatine and albumen and related compounds are frequently used as such protective agents4 ,it is supposed that they form protecting films around the colloidal particles4 ,applications in ,analysis4--,from the preceding discussion we may now draw the following conclusions concerning the consideration that is to be given to the colloidal condition as a factor in qualitative analysis4 ,the absence of electrolytes in solution must favor the production of the colloidal condition1 which would result in the nonprecipitation or solution and consequent loss of substances1 which it is intended to precipitate4 ,such absence of electrolytes in solution is most likely to be met with1 in the first place1 in the washing out of precipitates4 ,when the larger part of the mother liquor is washed away by the use of pure water1 many precipitates show a tendency to run through a filter1 forming colloidal suspensions in the pure water in the filter and being again precipitated as the colloid mixes with the electrolytes in the filtrate4 ,precipitates1 showing this tendency to assume the colloidal condition1 are therefore washed with appropriate solutions of electrolytes1 rather than with pure water4 ,ammonium nitrate solution is most frequently available in qualitative analysis1 because neither the ammonium-ion nor the nitrate-ion tends to interfere with the subsequent examination of the solution4 ,when chloride-ion is not likely to interfere1 ammonium chloride may be used4 ,thus1 the sulphides of the arsenic1 copper and zinc groups are washed with solutions containing ammonium nitrate 7the p#acg chloride may be used for the zinc group#bhh7 rather than with pure water 7or pure hydrogen sulphide water#bhh74 ,in quantitative analysis1 aluminium hydroxide is also washed with ammonium nitrate solution1 silver chloride with acidulated 7nitric acid7 water1 lead sulphate with dilute sulphuric acid1 etc4 ,in the second place1 if precipitations are attempted either in rather dilute solutions or in solutions of little ionized substances 7arsenious acid and hydrogen sulphide71 the addition of an electrolyte is frequently required to insure precipitation4 ,thus1 the presence of ammonium chloride1 or nitrate1 in excess1 is helpful in the precipitation of the sulphides of the zinc group2 the addition of hydrochloric acid 7or other electrolyte7 is required to effect the precipitation of arsenious sulphide from a solution of the oxide 7p4 #abf74 ,in the next place1 account must be taken1 in analytical work1 of the fact that colloids carry down with them the precipitating ion by which they are coagulated1 a fact which may lead to the loss of ions which1 it is intended1 should be kept in solution4 ,to a certain extent1 this loss may also be avoided by insuring the presence of electrolytes 7acids1 ammonium salts7 in sufficient concentration to cause the coagulation without the aid of the ions which1 it is intended1 should not be precipitated4 ,in view of the much weaker precipitating power of univalent ions 7of hydrochloric acid1 ammonium nitrate and chloride71 as compared with that of polyvalent ions1 which may be present1 the acid and ammonium salts must not be used in too small concentrations4 ,in quantitative analysis1 when conditions permit it1 ammonium or sodium sulphate is frequently substituted for the ammonium salts of the univalent monobasic acids4 ,the washing of the precipitated colloid with such salt solutions gradually removes#bhi the ions which are precipitated with the colloid and forms a further safeguard against their loss4 ,but this source of loss is avoided only with great difficulty and is seldom absolutely removed4 ,finally1 the presence of protective colloids1 especially of the p#ach gelatine and albumen type1 may interfere so decidedly with the common precipitation tests for ions1 that their destruction is imperative1 before these tests can be applied with any degree of confidence4 ,thus1 the mixing of solutions 7#j4a molar7 of silver nitrate and hydrochloric acid1 each containing one per cent of gelatine1 fails to produce the ordinary1 characteristic precipitate#bij of silver chloride1 the reaction which is used to determine the presence of the silver-ion in systematic analysis4 ,the mixture is opalescent and1 in reflected light1 looks opaque-white2 on somewhat prolonged standing a white milk is produced1 but no precipitate4 ,when the mixture is boiled1 the same deep white milk is formed1 but no coagulated precipitate1 the mixture running unchanged through a filter4 ,hydrogen sulphide converts the mixture into a similar suspension of the black sulphide4 ,,footnotes3 #bbg ,the ratio is affected somewhat by the fineness of division of liquids and solids as a result of surface tension phenomena1 as explained below4 #bbh ,an aqueous solution of iodine and potassium iodide shaken with chloroform gives similar results1 and the difference in color between the two layers is an advantage for a lecture experiment4 ,but the iodine is partially combined with the iodide1 according to ,,ki ,i#b ,,ki#c1 or ,i ,i#b ,i#c1 and the theoretical relations are not so simple as for bromine in aqueous and chloroform solutions4 #bbi ,to accelerate the action1 the mixture is shaken vigorously4 ,after the separation of the layers1 the bromine may be recognized in the aqueous layer by its color1 or by the addition of potassium iodide 7liberation of iodine74 #bcj ,braq4 and ,brch4 are used to express the actual concentrations at any given moment we wish to consider1 for instance at the moment equilibrium is reached4 ,the ratio k#b _/ k#a for any substance ,s is found to be equal to the ratio of the solubilities of the substance in the two solvents4 ,that it must be so can be proved by applying the law of physical equilibrium to the mixed solvents in contact with an excess of the substance1 i4e4 to its saturated solutions 7see below74 #bca ,similar relations hold for the condition of equilibrium between a liquid and its vapor4 #bcb ,curie1 ,bull4 ,soc4 ,min41 #h1 #ade 7#ahhe72 ,ostwald1 ,grundlagen der ,anal4 ,chem41 p4 #bb 7#ahid74 #bcc ,hulett1 ,z4 ,phys4 ,chem41 #cg1 #chd 7#aija74 ,see also ,ostwald1 ibid41 #cd1 #die 7#aijj71 on the solubilities of finely divided mercuric oxide 7yellow oxide7 and of larger crystals 7red oxide74 #bcd ,a #a _/ #ajjj solution of ,au,cl#c1 #b aq41 and a #a4b _/ #ajjj solution of ,sn,cl#b1 #b aq41 may be used conveniently4 ,when equal volumes of the solutions are mixed1 the desired precipitate is formed4 #bce ,stannous chloride is usually sufficiently contaminated with stannic salt4 ,add a few drops of bromine- or chlorine-water to #ajj c4c4 of a pure stannous chloride solution4 #bcf ,the action is an exceedingly sensitive qualitative test for gold4 ,by a modification of the test ,donau was able to detect as little as #b;,e#i gram of gold 7,monatshefte f4 ,chem41 #be1 #ede 7#aijd774 #bcg ,the nature of the reduction reaction is discussed in ,chapters ,,xiv and ,,xv4 #bch ,faraday1 ,proc4 ,royal ,soc41 #h1 #cef 7#aheg71 ,phil4 ,mag4 7#d71 #ac1 #dja 7#aheg7 7,stud474 #bci ,zsigmondy1 ,liebig's ,annalen1 #cja1 #cj 7#ahih74 #bdj ,bredig1 ,z4 f4 ,elektrochem41 #d1 #ead1 #edg 7#ahih71 and ,anorganische ,fermente1 #aija4 ,colloidal preparations of platinum1 silver and many other metals may be prepared in the same way4 ,in ether1 colloidal preparations of the alkali metals may be made 7,svedberg1 ,ber4 d4 chem4 ,ges41 #ch1 #cfaf 7#aije71 #ci1 #agjh 7#aijf774 #bda ,argentum ,cred may be conveniently used4 ,it contains1 with the metallic silver1 a small percentage of albumen1 which is added for reasons discussed below4 ,brown solutions are formed at once4 #bdb ,first a thin film of black carbon is produced round the metal1 then the latter appears in the form of a filigree of silver4 #bdc ,for details of the preparation1 see ,a4 ,a4 ,noyes1 ,j4 ,amer4 ,chem4 ,soc41 #bg1 #id 7#aije74 #bdd ,this process of separation of substances1 which do not pass through membranes1 from such as do1 is called dialysis4 ,it was first used by ,graham1 ,trans4 ,royal ,soc41 ,london1 #aea1 #ahc-bbd 7#ahfa7 7,stud474 #bde ,graham made the first extended investigations in this field3 ,trans4 ,royal ,soc41 #aea1 #ahc 7#ahfa72 ,j4 ,chem4 ,soc4 7,london71 #ag1 #cah 7#ahfd7 7,stud474 ,he found that amorphous1 gelatinous bodies like ferric hydroxide1 aluminium hydroxide1 silicic acid1 gelatine1 glue1 dextrin1 caramel1 albumen and similar bodies do not pass through membranes and may be obtained by dialysis in the colloidal condition4 ,such substances were called colloids by ,graham1 the name referring to the ,latin for gelatine4 ,substances which pass through membranes readily were found by ,graham to resemble in behavior such bodies as are crystallizable when solid2 such compounds were classified by him as crystalloids4 ,that liquids containing substances in the colloidal condition 7e4g4 arsenious sulphide1 gold1 silver and many other substances7 may be prepared by methods other than dialysis1 was found later by many investigators and1 in a few cases1 previous to ,graham1 e4g4 by ,faraday1 loc4 cit4 ,a brief history of the chemistry of colloids is found as an introduction to ,wo4 ,ostwald's ,kolloidchemie1 pp4 #a-fc 7#aiji74 #bdf ,cf4 ,wo4 ,ostwald1 loc4 cit41 p4 #aic4 #bdg ,before ,graham's time1 and for the few colloidal liquids then known1 this view was held by such men as ,j4 ,b4 ,richter1 ,berzelius and ,faraday 7loc4 cit47 7cf4 ,wo4 ,ostwald1 loc4 cit41 p4 #ai74 ,the first extended experimental investigation in support of it was made by ,barus and ,schneider1 ,z4 phys4 ,chem41 #h1 #bgh 7#ahia74 ,bredig was also an early and consistent champion of this view 7vide his ,anorganische ,fermente1 #aija74 #bdh ,cf4 ,wo4 ,ostwald1 loc4 cit41 pp4 #ajb-aad4 ,graham considered colloidal silicic acid a liquid miscible with water in all proportions4 ,according to modern ideas1 no true miscibility exists1 but a suspension or emulsion is formed 7see ,ostwald1 p4 #bcg74 #bdi ,siedentopf and ,zsigmondy1 ,drude's ,annalen1 #aj1 #a 7#aijc74 ,zsigmondy1 ,colloids and the ,ultramicroscope 7#aiji71 ,chapter ,v4 #bej ,zsigmondy1 ,z4 fr ,elektrochem41 #h1 #fhd 7#aijb72 ,siedentopf and ,zsigmondy1 loc4 cit4 #bea ,zsigmondy1 loc4 cit41 p4 #afa4 ,a is #a;,e#f mm4 ,the hydrogen molecule is considered to have a diameter of #j4a 7,o4 ,e4 ,meyer71 the alcohol molecule one of #j4e 7,zsigmondy1 loc4 cit41 plate ,,iv1 p4 #aeg74 #beb ,weimarn1 ,chem4 ,zentralblatt1 #aijg1 ,,ii1 p4 #abic4 #bec ,paal1 ,ber4 d4 chem4 ,ges41 #ci1 #adcf1 #bhei 7#aijf74 #bed ,other varieties of heterogeneous colloidal mixtures are tabulated by ,wo4 ,ostwald1 loc4 cit41 p4 #if4 #bee ,the ,cassius' purple test for gold is an instance where the colloidal condition is used in analysis for a positive test4 ,see ,wo4 ,ostwald1 loc4 cit41 p4 #fh1 for other1 similar applications for positive tests4 #bef ,vide ,wo4 ,ostwald's ,kolloidchemie1 #aiji1 and the references given by ,noyes1 loc4 cit41 p4 #hf4 #beg ,a general discussion of the preparation and properties of colloidal mixtures is given by ,a4 ,a4 ,noyes1 ,j4 ,am4 ,chem4 ,soc41 #bg1 #hf-ajd 7#aije7 7,stud474 #beh ,picton and ,linder1 ,j4 ,chem4 ,soc4 7,london71 #fa1 #afj 7#ahib71 #fg1 #fc 7#ahie71 #ga1 #efh 7#ahig71 etc41 and others4 ,wo4 ,ostwald1 loc4 cit41 p4 #bdj1 gives a list of references4 #bei ,the arrangement of the experiment is described by ,noyes1 loc4 cit41 p4 #ih4 #bfj ,cf4 ,wo4 ,ostwald1 loc4 cit41 p4 #ajh4 ,billitzer has found that gelatine is positive in acid solution1 negative in alkaline1 ,z4 phys4 ,chem41 #ea1 #adg 7#aije74 ,the charges are1 however1 relatively small ones4 #bfa ,billitzer1 ,z4 f4 ,elektrochem41 #h1 #fch 7#aijb74 ,this is probably true of all amphoteric colloids 7,chapter ,x72 it is also true of many other substances1 which are not pronouncedly amphoteric4 7,cf4 ,perrin1 ,comp4 rend41 #acf1 #achh 7#aijc72 ,billitzer1 ,z4 phys4 ,chem41 #ea1 #aeg 7#aije747 #bfb ,hardy1 ,j4 of ,physiology1 #bd1 #bhh 7#ahii72 ,z4 phys4 ,chem41 #cc1 #chg 7#aijj74 #bfc ,billitzer1 loc4 cit41 p4 #aei2 ,mller's ,allgemeine ,chemie der ,kolloide1 #aijg1 p4 #gi4 #bfd ,see below1 p4 #acd4 #bfe ,in a slightly acid solution colloidal silicic acid is negatively charged2 in a strong acid solution1 positively--a relation which agrees with its predominantly acid character4 #bff ,the general class of substances1 showing both basic and acid properties1 of which albumen is a derivative1 is described in a footnote on glycocoll1 ,chapter ,x1 p4 #ahh4 #bfg ,hardy1 loc4 cit4 #bfh ,j4 ,loeb1 ,university of ,california ,publications1 ,physiology1 #b1 #adi 7#aijd74 #bfi ,very little is known about the nature of contact electricity4 ,it is even doubtful whether it is different1 in principle1 from ionization4 #bgj ,w4 ,ostwald1 ,lehrbuch der ,chem41 #b1 7#a7 #eec 7#aijc74 #bga ,hardy1 ,proc4 ,royal ,soc41 #ff1 #aaj 7#ahii72 ,z4 phys4 ,chem41 #cc1 #cia 7#aijj74 #bgb ,picton and ,linder1 ,j4 ,chem4 ,soc4 7,london71 #fg1 #fc 7#ahie74 #bgc ,whitney and ,ober1 ,j4 ,am4 ,chem4 ,soc41 #bc1 #heb-hef 7#aija7 7,stud474 #bgd ,picton and ,linder1 loc4 cit4 #ga1 #egb 7#ahig72 ,lottermoser1 ,anorganische ,kolloide1 p4 #gf2 ,biltz1 ,ber4 d4 chem4 ,ges41 #cg1 #ajie 7#aijd74 #bge ,precipitation is complete only when the colloids are used in the proportions required to neutralize each other's charges ,billitzer1 ,z4 phys4 ,chem41 #ea1 #adj 7#aije74 ,the proportions to be used must be determined in each case1 most simply by trial 7,noyes1 loc4 cit41 p4 #aja71 but quantitative methods for determining the charges1 by titration1 are also known 7cf4 ,billitzer1 loc4 cit474 #bgf ,e4 ,a4 ,schneider1 ,z4 anorg4 ,chem41 #e1 #hj 7#ahid74 #bgg ,see the above discussion on silicic acid4 ,stannic acid has a greater tendency to form a base than has silicic acid4 #bgh ,zsigmondy1 ,liebig's ,annalen1 #cja1 #cfa 7#ahih74 #bgi ,cf4 ,fresenius1 p4 #ccd1 or ,smith's ,inorganic ,chemistry1 p4 #dfh4 #bhj ,mylius1 ,ber4 d4 chem4 ,ges41 #cf1 #gge 7#aijc72 ,biltz1 ibid41 #cg1 #aaaf 7#aijd74 #bha ,j4 fr prakt4 ,chem41 #be1 #dca 7#ahhb74 #bhb ,the suspension used is prepared by saturating1 with hydrogen sulphide1 an aqueous solution of arsenious oxide4 ,the latter is saturated on a steam bath1 cooled to #bj1 filtered and diluted with an equal volume of water before it is used4 #bhc ,eight grams of ,,nh#d,,no#c per #ajj c4c4 #bhd #j4f c4c4 of a tenth-normal solution is used1 containing #a4bh gram ,mg7,,no#c7b1 #f aq41 in #ajj c4c4 ,precipitation was found to be incomplete with #j4e c4c4 #bhe #j4ae c4c4 of a tenth-normal solution is used1 containing #a4b gram ,al7,,no#c7c1 #d aq41 in #ajj c4c4 ,precipitation was found to be incomplete with #j4a c4c4 of the solution4 #bhf #c4c grams 7,,nh#d7b,,so#d in #ajj c4c4 #bhg ,freundlich found1 for instance1 that ,na,cl1 ,k,cl1 ,ba,cl#b1 in equivalent concentrations1 had practically the same effect on colloidal ferric hydroxide1 but only one-fortieth as much of a sulphate 7the precipitating ion is ,,so#db versus ,cl7 was required2 ,z4 phys4 ,chem41 #dd1 #abi 7#aijc74 #bhh ,for other reasons 7e4g4 to prevent oxidation of the sulphides71 hydrogen sulphide is also used in the solution for washing the arsenic group1 and ammonium sulphide in that for the zinc group 7see ,lab4 ,manual1 pp4 #aja and #aaj74 #bhi ,picton and ,linder1 loc4 cit41 and ,whitney and ,ober1 loc4 cit4 #bij ,a4 ,a4 ,noyes describes a similar experiment with sodium chloride and silver nitrate1 loc4 cit4 p#aci ,,chapter ,,viii ,,simultaneous ,,chemical ,,and ,,physical ,,equilibrium4--,,the ,,solubility- ,,or ,,ion-,,product4 ,it frequently happens that we have to deal1 simultaneously1 with conditions of chemical and of physical equilibrium1 obtaining in the same system4 ,for instance1 a gas like carbon dioxide1 in contact with its saturated solution in water1 is in equilibrium with the dissolved carbon dioxide1 and this1 in turn1 is in equilibrium with its hydrate1 carbonic acid4 ,a substance may be distributed between two solvents and show a different molecular weight in the two 7see p4 #ah72 it may exist1 in the one1 primarily in polymeric form1 and only to a slight extent in the simple form1 the two forms being in equilibrium 7chemical equilibrium74 ,in the other solvent1 it may exist only in its simple molecular form1 and this will be in equilibrium with the same simple molecular form in the first solvent 7physical equilibrium74 ,in matters dealing with the solubility of electrolytes in water1 and1 therefore1 in questions of their precipitation or solution1 such simultaneous conditions of chemical and physical equilibrium are constantly occurring4 ,since qualitative analysis deals to a very considerable extent with just such precipitates of salts1 acids and bases1 these cases are of particular importance to us4 ,earlier ,derivation of the ,solubility-,product ,principle4--,a very simple relation was derived by ,nernst#bia for the combined conditions of chemical and of physical equilibrium1 where difficultly soluble electrolytes 7precipitates7 were concerned4 ,we shall develop the relation first for a simple salt1 such as silver acetate4 ,when water is added to solid silver acetate1 the salt will dissolve4 ,if an excess of the acetate is used1 equilibrium will result between the solid salt and its solution1 when the solution is saturated at the temperature used4 ,as the salt dissolves1 it is more or less ionized1 and in the saturated solution we have a p#adj condition of chemical equilibrium between the salt and its ions3 ,,ch#c;,c,o,o,ag ,,ch#c;,,coo ,ag4 7#a7 ,if the law of chemical equilibrium is applied to this reversible action1 we have 7p4 #ih7 ,,ch#c;,,coo ,ag _/ ,,ch#c;,c,o,o,ag ,k,ionization4 ,i ,the nonionized silver acetate is present in two phases1 in the solid phase and also in solution3 ,,ch#c;,c,o,o,ag ,,ch#c;,c,o,o,ag4 7#b7 ,applying the law of physical equilibrium to this system1 we have further 7p4 #aba7 ,,ch#c;,c,o,o,ag _/ ,,ch#c;,c,o,o,agsolid ,k4 ,,ii ,the concentration of a pure solid1 as we have seen1 may be considered a constant at a given temperature4 ,consequently1 if we consider the question of the size of the solid particles as a minor factor and negligible1 we shall conclude1 that1 for saturated solutions of silver acetate1 the concentration of the solid silver acetate being a constant1 the concentration of the nonionized or molecular silver acetate1 the first term of our constant ratio ,,ii1 must also have some definite1 constant value at a given temperature4 ,we may call this concentration the molecular solubility of silver acetate and may put ,,ch#c;,c,o,o,ag ,kmol4 sol4 ,,iii for a saturated solution of silver acetate in water at the given temperature4 ,now1 since the concentration of the nonionized silver acetate1 ,,ch#c;,c,o,o,ag1 in the saturated solution also forms the second term of equation ,i1 representing the condition of chemical equilibrium between the acetate and its ions1 we obtain1 by combining ,i and ,,iii1 ,,ch#c;,,coo ,ag ,k,ionization ,kmol4 sol4 ,k,solubility-,product4 ,,iv ,further1 if the assumption is made that the presence of foreign electrolytes1 in not too concentrated solutions1 does not affect either the molecular solubility1 ,kmol4 sol41 of silver acetate or its tendency to ionize--as expressed in ,k,ionization--then1 the p#ada relation1 which has been developed1 would hold for saturated aqueous solutions of silver acetate in the presence of foreign electrolytes1 as well as for a saturated1 pure1 aqueous solution4 ,a single1 simple equation would thus express the conditions for simultaneous chemical and physical equilibrium between a difficultly soluble ionogen1 of the type of silver acetate1 and its saturated solutions1 at a given temperature1 in the presence or the absence of foreign electrolytes4 ,the ,solubility- or ,ion-,product ,principle4--,we may formulate this important conclusion by stating1 that1 in saturated solutions of silver acetate1 the product of the concentrations of its ions has a constant value at a given temperature4 ,analogous relations may be developed for the saturated solutions of other difficultly soluble ionogens4 ,the constant has been called the solubility-product constant or the ion-product constant of the ionogen4 ,for salts like lead iodide ,pb,i#b1 silver chromate ,ag#b;,cr,o#d1 etc41 each molecule of which forms more than one of a given ion1 the concentration of such an ion is raised1 in the solubility-product1 to the power corresponding to the number of ions of this kind formed from a single molecule of the electrolyte4#bib ,thus1 lead iodide ionizes according to the equation ,pb,i#b ,pb#b #b ,i and1 for a saturated solution of lead iodide#bic at a given temperature1 ,pb#b ,i#b ,k4 ,for silver chromate1 ionizing according to the equation ,ag#b;,cr,o#d #b ,ag ,cr,o#db1 the form of the solubility-product equation is ,ag#b ,cr,o#db ,k4 ,in general1 for a saturated solution of a difficultly soluble salt at a given temperature the product of the ion concentrations1 each raised to the power corresponding to the number of that kind of ion formed from the ionization of one molecule of the salt1 is a constant4 ,criticism of the ,derivation of the ,principle4--,nernst developed this important relation in #ahhi1 shortly after the theory of ionization was formulated4 ,since then1 however1 the soundness of the theoretical development1 on which it was based1 has been rendered open to question in a way that could hardly have been foreseen at that early stage in the development of the theory of ionization4 ,in the first place1 it is known now that the ionization of easily ionizing substances 7strong electrolytes7 does p#adb not conform to the law of chemical equilibrium 7vide p4 #ajh72 as far as our present knowledge goes1 the ratio in equation ,i is not a constant1 but grows larger with an increasing total concentration of good electrolytes4 ,in the present case1 this total concentration may be increased by the introduction of foreign salts4#bid ,in the second place1 the second fundamental principle used1 the principle of the constant solubility of the dissolved molecular or non-ionized salt1 as expressed in equation ,,iii1 was questioned and disproved by ,arrhenius in #ahii4 ,the molecular solubility depends on the total concentration of salts in the solution and1 in general1 decreases with increasing concentration of the total dissolved salts4 ,this result does not invalidate the law of physical equilibrium2 it merely means that the presence of salts1 especially in appreciable quantities1 modifies the nature of the solvent and changes its dissolving power1 much as we have different dissolving power shown by different pure solvents1 such as water and alcohol4 ,it appears1 however1 that while the soundness of this theoretical development of the relations expressed by the solubility-product must be questioned1 nevertheless as a matter of experiment1 the product of the ion concentrations of a difficultly soluble salt is found1 in dilute solutions1 to be a constant1 or sufficiently close to a constant to satisfy all but the most rigorous requirements4#bie ,it is1 in fact1 quite evident1 that a decreasing value for the second term of the ratio ,i--namely1 for ,,ch#c;,c,o,o,ag1 the molecular solubility of the salt--as the total concentration of the electrolytes present increases1 together with an increasing value for the whole ratio ,i under the same conditions1 are not incompatible with a constant value of the first term of the ratio4 ,that is1 the product of the ion concentrations1 ,,ch#c;,,coo ,ag1 may well remain constant 7equation ,,iv71 or approximately constant1 in dilute salt solutions1 even if equations ,i and ,,iii do not hold for salt solutions4 p#adc ,whether in the case of all difficultly soluble salts1 as the total salt concentration increases1 the increasing values of the chemical equilibrium ratio 7equation ,i7 will be so nicely balanced by the decreasing values of the molecular solubility1 that the first term of the first ratio 7the solubility-product7 will always be constant1 is a question demanding further extended investigation4#bif ,the range of the investigation must be extensive1 because it must include several other classes#big of salts 7e4g4 ,me#b,x1 ,me,y#b1 etc471 for which the first equation has a different form2 for instance1 for ,me#b,x1 ,me#b ,x#b _/ ,me#b,x ,k4 ,for the present we must remain content with the result of the past investigations and consider the principle of the constant solubility-product to be essentially an empirical one4 ,it is an extremely convenient condensation1 into a very simple mathematical form1 of the main factors involved in the precipitation and solution of difficultly soluble salts1 acids1 and bases4 ,it should be used with due knowledge of its character and limitations4 ,washburn#bih derives the principle of the constancy of the solubility-product1 without involving in his derivation the relation between ions and nonionized molecules--a relation which1 as was stated above1 deviates from the law of chemical equilibrium4 ,the deviation1 it will be recalled 7p4 #aji71 is generally supposed to be due to the fact that the fundamental kinetic assumption which must be made to derive the law of chemical equilibrium from the kinetic theory1 the assumption that there should be none but negligible forces of attraction and repulsion between the molecules 7of a gas or solute7 which are in equilibrium1 is not fulfilled in the case of solutions of strong electrolytes 7p4 #aji74 ,according to ,washburn1 if it is assumed that the ions of an electrolyte fulfill this fundamental condition and that only the nonionized molecules do not--the latter causing the deviation from the law of chemical equilibrium--then the principle of the solubility-product constant follows4#bii ,he sees an approximate confirmation of the assumption made1 in the fact that the principle is found1 empirically1 to be true1 and that other relations1 developed on the basis of the same assumption1 agree with the observations made4 p#add ,this theoretical derivation of the principle1 like the derivations of the law of chemical equilibrium and of all our laws of dilute solutions1 assumes#cjj that the nature of the solvent1 and consequently of the solution-process1 is not changed by added substances1 for instance by an excess of the precipitating ionogen4 ,there can be no question1 however1 that the nature of the solvent must change1 as a continuous function1 by the addition of electrolytes to solutions4 ,the changed solubilities of inert gases in salt solutions1#cja and a mass of other evidence1#cjb lead to this conclusion4 ,the addition of a half mole of sodium chloride to a liter of water reduces the dissolving power of the liquid towards oxygen at #be by #ae1 i4e4 by #cj per mole of salt4 ,a weak electrolyte1 such as acetic acid1 has practically no effect at this concentration1 and so the effect must be chiefly due to the ions of sodium chloride2 since the salt1 in half-molar solution1 is ionized #gc1 the reduction in the dissolving power would be #cj _/ #j4gc #da per mole of fully ionized salt4 ,the principle of the constant solubility-product cannot be considered as established for solutions more concentrated than #j4b to #j4c molar2 but it is evident that1 in any comprehensive theoretical formulation of the principle for the range in which it is found empirically to hold1 the change in the nature of the solvent1 which in some cases is conspicuous in #j4e molar solution1 must be taken into consideration as a factor even in more dilute solutions 7say #j4je to #j4c molar74 ,it seems at present1 quite possible1 perhaps even probable1 that the constancy1 in all but the most dilute solutions1 is the result of the approximate balancing of two 7or more7 opposing factors4#cjc ,when we leave the range of concentrations mentioned1 and go to more concentrated solutions1 these factors seem to be less well balanced and the validity of the principle ceases4#cjd ,for the present it will be safe to consider the principle as an empirical one1 holding for solutions of total salt content up to #j4be or #j4c molar4#cje ,for quite dilute solutions the effect of the electrolyte on the solvent would be negligible1 and only to such solutions would the theoretical derivation brought forward by ,washburn be applicable4 ,influence of a ,common ,ion4--,for a saturated aqueous solution of silver acetate at a given temperature1 the product of p#ade the ion concentrations may be considered a constant1 ,,ch#c;,,coo ,ag ,k,s4,p44 ,in such an aqueous solution1 containing no foreign salts1 the concentration of the silver-ion is equal to the concentration of the acetate-ion1 since a molecule of silver acetate1 when it ionizes1 gives one silver ion for every acetate ion formed4 ,the numerical value of the solubility-product may then be calculated1 if the solubility of the salt and its degree of ionization are known4 ,for instance1 at #af one liter of water dissolves #aj4jg grams of silver acetate1 that is1 #aj4jg _/ #afg1 or #j4jfjc gram-molecule 7mole74 ,conductivity measurements show that #gj4h of the salt is ionized in such a solution1 and consequently the concentration of the silver-ion is #j4gjh #j4jfjc1 or #j4jdbg4 ,the concentration of the acetate-ion is the same1 and the value of the solubility-product constant1 obtained by inserting these quantities in the above equation1 is ,k,s4,p4 #j4jdbg #j4jdbg #j4jjahb4 ,now1 if1 to the saturated solution of the silver acetate1 there are added a few drops of a concentrated solution of sodium acetate or some crystals of solid sodium acetate1 the concentration of the acetate-ion is thereby increased and the condition of equilibrium in the solution is disturbed3 x ,,ch#c;,,coo ,ag ,k,s4,p44 ,the concentration of the acetate-ion having been increased1 the ion will combine more rapidly than before with the silver-ion1 and the concentration of the nonionized salt will be increased4 ,the solution being already saturated with nonionized silver acetate1 the excess formed must be precipitated4 ,as a matter of fact1 a precipitate of silver acetate is readily obtained in this way 7exp474 ,precipitation will cease when sufficient silver acetate has crystallized out to make the product of the concentrations of the ions again equal to the solubility-product constant4 ,if1 after the crystallization is complete and equilibrium has been restablished1 the acetate-ion is x times as concentrated as it was in the pure aqueous solution1 the concentration of the silver-ion must be reduced to #a _/ x its original value3 x ,,ch#c;,,coo ,ag _/ x ,k,s4,p44 ,precipitation4--,we see thus that precipitation of a difficultly soluble ionogen will result when the product of the ion concentrations p#adf is made greater than the value of the solubility-product constant for that substance4 ,in the second place1 it is seen that the concentration of an ion of an insoluble salt1 which can be present in the saturated solution of the salt1 is dependent on the concentration of the other ion 7or ions7 of the salt4 ,this fact is a very important one in analytical chemistry and it is taken advantage of in many ways1 as we shall presently see4 ,it is clear that a corresponding result should be obtained when1 to the saturated aqueous solution of silver acetate1 an excess of the silver-ion is added--for instance by the addition of solid silver nitrate or of a little of a concentrated solution of this salt 7exp474 ,here again1 the product of the ion concentrations is greater than the constant1 i4e4 ,,ch#c;,,coo y ,ag ,k,s4,p41 and precipitation results4 ,silver acetate therefore crystallizes out1 until 7,,ch#c;,,coo _/ y7 y ,ag ,k,s4,p44 ,the following table shows the relations when sodium acetate is added to the saturated solution of silver acetate4 ,column #a gives the concentration of the sodium acetate in the solution saturated with silver acetate1 column #b the percentage of the sodium acetate that is ionized1 column #c the total concentration of silver acetate in the saturated solution1 column #d the percentage of it which is ionized1 column #e the concentration of the acetate-ion1 column #f the concentration of the silver-ion and column #g the value of the solubility-product4 #a #b #c #d #e #f #g ,na-,acet4 #ajj p4 ,ag-,acet4 #ajj p4 acetate4 ,ag4 ,k,s4,p44 #j 4444 #j4jfjc #gj4h #j4jdbg #j4jdbg #j4jjahb #j4jfa #gh4f #j4jcib #fd4e #j4jgce #j4jbeh #j4jjahe #j4aai #ge4h #j4jbh #ei4g #j4ajfe #j4jafg #j4jjagi #j4bci #gj4h #j4jbjh #eb4c #j4agbg #j4jaji #j4jjahh ,the second table shows the relations when an excess of the silver-ion is present1 silver nitrate having been added to the saturated silver acetate solution4 ,the columns have the same significance as in the first table1 excepting that the first column gives the concentration of silver nitrate present and the second column its degree of ionization4#cjf ,it is clear from these results that a difficultly soluble salt is rendered less soluble 7see column #c of the tables7 by the presence of another salt1 when the p#adg latter has an ion in common with the former4 ,this conclusion has been well established#cjg for a considerable number of salts4#cjh #a #b #c #d #e #f #g ,ag,n,o#b4 #ajj p4 ,ag-,acet4 #ajj p4 acetate4 ,ag4 ,k,s4,p44 #j4 4444 #j4jfjc #gj4h #j4jdbg #j4jdbg #j4jjahb #j4jfa #hb4j #j4jdag #fd4j #j4jbfg #j4jgfg #j4jjbjd #j4aai #gh4d #j4jcda #eh4f #j4jbjj #j4aadb #j4jjbbg #j4bci #gd4j #j4jaie #ea4g #j4jajj #j4ahji #j4jjahb ,applications in ,analysis4--,a few instances of the application of this relation in analysis follow4 ,the determination of the sulphate-ion is based on the precipitation of barium sulphate from solutions of sulphates4 ,the solubility of barium sulphate in water at #ah is #j4jjbc gram1 or #j4jjbc _/ #bcc #a;,e#e mole per liter4 ,in such an extremely dilute solution1 the salt may be considered to be completely ionized1 and the value of the solubility-product constant is found from ,k,s4,p ,ba#b ,,so#db 7#a;,e#e7b1 or #a;,e#aj4 ,now1 the amount of sulphate-ion left in solution1 which would be about one milligram per liter of the aqueous solution1 may be reduced by the use of a small excess of the precipitant1 barium chloride4 ,an excess of as little as #j4b gram or #j4jja mole of ,ba,cl#b per liter would increase the concentration of the barium-ion about one hundredfold1 and barium sulphate would be precipitated1 until the concentration of the sulphate-ion had been reduced about one hundredfold4 ,the loss of the sulphate-ion is thus reduced to approximately #j4ja milligram per liter4 ,in passing1 we may ask what the approximate loss of dissolved nonionized barium sulphate would amount to4 ,the value of the ratio 7,ba#b ,,so#db7 3 ,ba,s,o#d1 representing the ionization of barium sulphate1 is unknown for the extreme dilution represented p#adh by the saturated solution4 ,if we assume it to be roughly of the order #bjjj 3 #a1cji the solubility of nonionized barium sulphate at #ah would be roughly #j4je milligram per liter4 ,as a rule1 then1 in the absence of complicating conditions1#caj an excess of the precipitant promotes the complete precipitation of an ionogen4 ,washing of ,precipitates4#caa--,when barium sulphate has been brought on the filter and the excess of precipitant is to be washed out1 then1 as the excess of barium chloride is removed1 the sulphate becomes more soluble again4 ,it is advisable1 therefore1 to wash the precipitate as effectively as possible with a very small volume of water--as a rule1 the water is used in a very fine stream or is applied drop by drop4 ,such precautions are still more important in the case of precipitates which are somewhat more soluble than is barium sulphate1 and in such cases the question must be considered1 whether as a washing fluid1 some solution may not be used1 which contains an ion in common with the precipitate1 and which has1 therefore1 according to the principle of the solubility-product1 a very much smaller dissolving power for the precipitate in question than pure water4 ,that is a resource of the analyst to which recourse is occasionally taken4 ,lead sulphate1 for instance1 is washed with a very dilute solution of sulphuric acid1 rather than with pure water2#cab potassium cobaltinitrite1 ,k#c;,co7,,no#b7f1 which is used in the separation of cobalt from nickel1 is washed#cac with a ten per cent solution of potassium acetate1 containing a little potassium nitrite4 ,ammonium phosphomolybdate1 used in determinations of phosphates1 is washed with a solution of ammonium nitrate4 p#adi ,the use of such solutions for washing precipitates is limited by the necessity1 first1 of avoiding salts which interfere with subsequent operations 7e4g4 which would leave nonvolatile residues in the subsequent ignition of a precipitate1 that is to be weighed after ignition7 and1 second1 of avoiding the loss of precipitate by the formation of complex ions between an ion of the precipitate and a component of the washing mixture 7see p4 #adh74 ,but wherever such complications can be excluded1 the method is a desirable one4 ,it has sometimes been recommended to wash a precipitate with a saturated aqueous solution of the precipitate itself1 in place of with pure water4 ,it was reasoned that the solution1 being already saturated with the salt1 would not be able to dissolve any of the precipitate obtained4 ,that is true2 but if a saturated solution of a salt1 ,me,x1 is placed on a filter still holding an excess of the precipitant1 i4e4 one of the ions1 say ,x1 of the precipitate1 then this excess may cause supersaturation of the saturated washing fluid and some of the salt may be precipitated out of the washing fluid4 ,the method1 as commonly employed1 has therefore the inherent fault1 theoretically at least1 of being liable to give too high results4 ,if it is to be employed without error1 precautions must be taken first to remove1 from the precipitate and filter1 the mother liquor 7containing the excess of precipitant7 as completely as possible4 ,if in a given case this can be accomplished1 then the danger of precipitating any of the salt 7,me,x7 from the saturated solution is avoided1 and the precipitate 7,me,x 7 may then be further washed with a saturated solution of the same salt 7,me,x71 with advantage1 in certain cases4 ,thus1 in the ,lindo-,gladding method#cad of determining potassium in the form of potassium chloroplatinate1 the source of error1 just discussed1 has been avoided in the following way3 the excess of precipitant1 chloroplatinic acid ,h#b,pt,cl#f1 which has the ion ,pt,cl#fb in common with the precipitate1 is first removed from the precipitate by thorough washing of the precipitate with alcohol2 subsequently1 other impurities1 e4g4 sulphates1 soluble in water but not in alcohol1 are washed out with an aqueous solution of ammonium chloride#cae that has been saturated with potassium chloroplatinate4 ,the method gives good results4 ,the ,solubility-,product in ,volumetric ,analysis4--,a final instance of the application of the solubility-product principle to the ordinary methods of analytical chemistry1 may be taken from the field of quantitative1 volumetric analysis4 ,a particularly accurate method of determining silver consists in precipitating it as silver chloride by means of a standardized solution of sodium chloride4 ,the aim of the method is to recognize1 as exactly as p#aej possible1 the point where the action ,ag,n,o#c ,na,cl ,ag,cl ,na,n,o#c has just completed itself1 i4e4 where one equivalent of sodium chloride has been added for just one equivalent of silver nitrate present4 ,a very sensitive method#caf depends on the fact that silver chloride can be made to coagulate by the vigorous shaking of its suspensions1 and that the coagulated chloride settles rapidly1 leaving a clear supernatant liquid1 in which the appearance of the faintest turbidity may be recognized1 when the sodium chloride solution is carefully added to the silver nitrate solution under investigation4 ,now1 when sodium chloride solution is added in this way to silver nitrate1 a point is reached 7called the neutral point71#cag where the addition of a further drop or two of sodium chloride solution will still produce a precipitate1 and where one would be inclined to decide that too little of the chloride had been used to complete the action4 ,but1 at the same time1 the addition of a few drops of silver nitrate solution to the solution at the neutral point also produces a precipitate of silver chloride1 seemingly indicating that an excess of sodium chloride had been used1 and apparently contradicting the previous result4 ,as a matter of fact1 such a behavior is exactly what is to be expected from a solution1 when exactly equivalent quantities of silver nitrate and sodium chloride have been brought together in solution4 ,the solution is then saturated with silver chloride1 ,k,s4,p4 ,ag ,cl and ,ag ,cl1 and the further addition either of the silver-ion 7silver nitrate7 or of the chloride-ion 7sodium chloride7 should produce a precipitate1 according to the principle of the solubility-product4 ,the correct end-point in the determination is1 thus1 the neutral point1 for at that point the quantity of silver present is equivalent to the quantity of sodium chloride added4 ,effect of ,electrolytes with ,no ,ion in ,common with the ,precipitate4--,in the precipitation of silver acetate from its saturated solution by the addition of sodium acetate 7p4 #ade71 it is the acetate-ion1 according to the principle of the solubility-product1 which is effective--the sodium-ion has no part in the action4 ,also1 in a similar way1 the precipitation produced by the addition of silver nitrate is ascribed to the increased concentration of the silver-ion--the nitrate-ion has no share in the action4 ,we may ask1 what the effect on the solubility of silver acetate will be1 if a salt1 sodium nitrate1 yielding only foreign ions1 and no common one1 is added to its saturated solution4 ,the presence of sodium and of nitrate ions will not increase the concentration of either of the ions of silver acetate1 will not increase the value of either factor in the product of ion concentrations2 the addition of sodium nitrate1 therefore1 should not lead to the precipitation of any silver acetate1 and as a matter of experiment it does not 7exp474 ,a closer study p#aea of the conditions will show1 in fact1 that it renders silver acetate somewhat more soluble4 ,the addition of the sodium-ion will lead to the suppression of some of the acetate-ion1 nonionized sodium acetate being formed to a certain extent2 the nitrate-ion will combine with some of the silver-ion to form nonionized silver nitrate3 thus the concentrations of both of the ions of silver acetate are reduced1 and the product of ion concentrations is rendered smaller than the solubility-product constant1 7,,ch#c;,,coo x7 7,ag y7 ,k,s4,p44 ,since the concentrations of both the silver and the acetate ions are reduced1 they will not combine as rapidly as before to form nonionized silver acetate1 and the conditions of equilibrium between the latter and its ions must be disturbed4 ,the nonionized salt ionizes1 for a moment1 more rapidly than it is formed and its concentration will thus be reduced4 ,we1 therefore1 might expect the solution to become unsaturated in respect to the nonionized form1 and the solid salt1 if present1 should go into solution4 ,in other words1 the addition of a salt with two foreign ions should increase the solubility of a difficultly soluble salt 7it is understood that no salt is used which would precipitate a new1 less soluble salt74 ,this expectation has also been fully confirmed by careful quantitative determinations1 especially by ,a4 ,a4 ,noyes and his collaborators4 ,the effect may be demonstrated more easily by the addition to silver acetate of an electrolyte which will very thoroughly suppress one of its ions4 ,nitric acid is such an agent4 ,the hydrogen-ion will very decidedly reduce the concentration of the acetate-ion1 acetic acid being a weak acid 7table1 p4 #ajd74 ,there is no difficulty in recognizing the anticipated effect 7exp474 ,solution of ,precipitates4--,we find1 then1 that when the product of the ion concentrations of a difficultly soluble salt becomes smaller than the solubility-product constant1 the solution is unsaturated in regard to the salt1 and the solid salt1 if present1 will go into solution4 ,summary4--,the conclusions concerning the application of the solubility-product constant may be summarized as follows3 ,a solution is saturated with a difficultly soluble ionogen when the product of the concentrations of the ions of the ionogen is equal to the characteristic solubility-product constant 7at the given temperature74 ,a solution is supersaturated and precipitation will follow1 if the product of the ion concentrations is greater than the constant4 p#aeb 7,see p4 #abb in regard to precautions against prolonged supersaturation47 ,a solution is unsaturated1 and the ionogen1 if present1 will dissolve when the product of the ion concentrations is smaller than the constant4 ,further ,considerations ,concerning ,precipitation and ,solution4--,it is further evident that precipitation is favored1 if the precipitating agent contains an electrolyte which produces the precipitating ion readily2 for instance1 carbonic acid does not precipitate any barium carbonate from a solution of barium chloride 7exp47--carbonic acid being an exceedingly weak acid and producing only a minute concentration of the carbonate-ion ,,co#cb1 necessary for the precipitation2 but sodium carbonate1 a readily ionized salt1 will precipitate the barium carbonate quantitatively 7p4 #ij74 ,if some alkali is added to the mixture of barium chloride and carbonic acid 7exp471 the latter is converted into a readily ionized salt1 the concentration of the carbonate-ion is thus decidedly increased1 and the precipitate forms instantly4 ,in the same way1 if hydrogen sulphide--a still weaker acid 7table1 p4 #ajd71 which forms only minute quantities of sulphide and hydrosulphide ions 7,s#b and ,,hs7--is passed through a solution of ferrous sulphate1 it fails to precipitate ferrous sulphide2 but a salt of hydrogen sulphide1 ammonium sulphide1 for instance1 precipitates ferrous sulphide quantitatively 7exp474 ,on the other hand1 solution of an ionogen is evidently favored and its precipitation rendered more difficult1 if we suppress one 7or both7 of its ions4 ,thus barium phosphate1 calcium carbonate1 silver borate1 and many salts of weak acids1 that are very difficultly soluble in water1 are quite easily soluble in strong acids1 which suppress the anions by converting them into little ionized acids4 ,when a precipitate is dissolved by the addition of a reagent1 such as an acid1 an alkali1 ammonia1 ammonium sulphide--chemical solvents most frequently used in analytical work--we may1 as a general principle1 consider that the reagent must affect one or both of the ions of the precipitate in question1 suppressing it 7or them7 and thereby making solution possible4 ,the problem of determining in what way the suppression of the ion is effected1 must then be faced4 ,many occasions to determine such questions#cah will arise4 p#aec ,we have1 therefore1 a certain degree of control over the precipitation and solution of electrolytes1 the control depending upon1 and being limited by1 the fact that the factors of the product of ion concentrations are variables4 ,on the other hand1 we have little control1 in a given solvent1 over the question of solution or precipitation as affected by the value of the ion product constant1 the remaining term in the equation of the solubility-product for saturated solutions4 ,these constants cover a very wide range of values for the various salts1 which are most frequently used in analytical work for the precipitation of the common ions4#cai ,they are subject to variation with the temperature1 and1 as a rule1 as most salts are more soluble at higher than at lower temperatures1 the values of the constants increase with the temperature4 ,for exceedingly difficultly soluble salts1 the increase is commonly of no practical moment in analytical work1 when1 by an excess of the precipitant1 the ion1 which is to be precipitated1 can be precipitated quantitatively2 the solubility of the nonionized salt1 that is precipitated1 is so minute 7see p4 #adh7 in this case1 even at high temperatures1 that it is altogether negligible for ordinary purposes4#cbj ,on the other hand1 precipitates are often used which are not at all extremely insoluble but merely rather difficultly soluble2 they are used in spite of their relatively slight insolubility because they are the best available forms for our purposes4 ,such salts are1 for instance1 lead chloride1 magnesium-ammonium phosphate1 potassium chloroplatinate4 ,when these are precipitated1 not only must the fact that they are appreciably soluble at ordinary temperature be taken into account1 but also the fact that they are very much more soluble at higher temperatures4 ,lead chloride and potassium chloroplatinate are1 for instance1 quite soluble in hot water4 ,as a rule1 we select for the form in which a given ion is to be precipitated1 a form which1 in a saturated aqueous solution1 shows the smallest concentration of the ion in question4 ,but if no form is p#aed known which is sufficiently insoluble to give satisfactory quantitative results1 then we have recourse to a change in the solvent4 ,solubility and ,solvent4--,for instance1 a mixture of alcohol and water may be used1 or water be excluded altogether2 and either absolute 7water-free7 alcohol or a mixture of alcohol and ether may be employed4 ,in the quantitative treatment of potassium chloroplatinate1 the last-named mixture is used in place of water4 ,the change of solvent affects the solubility by a change both in the solubility of the ionized portion of a salt and in that of the nonionized salt4 ,an important quantitative relation between the solubility of a given ionogen in different solvents and the ionizing powers of the solvents1 as determined by their dielectric constants 7p4 #fc71 was predicted1 on the basis of theoretical considerations1 by ,malstrm#cba and by ,baur4#cbb ,walden#cbc has furnished experimental confirmation of the relation3 ,the degree of ionization of a salt is found to be the same in its saturated solutions in different solvents1 when the solutions are saturated at the same temperature4 ,if this relation is combined with that discussed on page #fc1 according to which the degree of ionization of a given salt1 in different solvents1 is the same1 when the cube roots of its concentrations are directly proportional to the dielectric constants of the solvents 7e#a 3 c#a e#b 3 c#b a constant71 then we find1 that in saturated solutions of a given salt1 in different solvents1 the cube roots of the concentrations1 or solubilities1 are directly proportional to the dielectric constants of the solvents1 or1 the solubilities are proportional to the third powers of the dielectric constants4 e#a 3 c#a e#b 3c#b a constant1 or e#ac 3 e#bc c#a 3 c#b1 c#a and c#b representing the solubilities1 in molar concentrations1 in two solvents of dielectric constants e#a and e#b4 ,the following table illustrates the relations for a salt examined by ,walden1 a derivative of ammonium iodide1 namely tetraethyl ammonium iodide 7,c#b;,h#e7d,,ni4 ,the first column gives the name of the solvent1 the second the solubility or concentration in the saturated solution1 in terms of the proportion of moles of the solute to the total number of moles present#cbd p#aee 7solute solvent72 the third column gives the dielectric constant1 under comparable conditions1 and the last column gives the relation e 3 c4 ,solvent4 ,solubility4 e#e e 3 c ,water #j4jccb #ge4j #ej4e ,nitrobenzene #j4jjbj #cb4b #ed4h ,ethyl alcohol #j4jjbja #bf4f #de4e ,acetone #j4jjjgb #ba4h #eb4h ,amyl alcohol #j4jjjca #ae4j #dh4 ,in view of the difficulties in determining the values for the dielectric constant1 the agreement in the values of the last column must be considered satisfactory4#cbe ,this important principle forms another striking instance of the supreme influence of electrical relations in determining the behavior of ionogens in solution 7see p4 #aaa74 ,since1 in solutions saturated at the same temperature with a given ionogen1 the degree of ionization of the ionogen is the same in both solvents1 the proportion of nonionized to ionized salt is also the same4 ,if a salt1 e4g4 calcium sulphate1 is less soluble in alcohol than in water1 the alcohol must hold less of the nonionized form1 as well as less of the ionized salt1 than does an equal volume of water at the same temperature4 ,the development of further relations1 of fundamental importance to analytical chemistry1 with the aid of the laws of chemical and physical equilibrium and of the principle of the solubility-product1 will be taken up in the study of the reactions of the various analytical groups of ions4 ,,footnotes3 #bia ,z4 phys4 ,chem41 #d1 #cgb 7#ahhi74 ,see also van 't ,hoff1 ibid41 #c1 #dhd 7#ahhi74 #bib ,cf4 page #id4 #bic ,a4 ,a4 ,noyes1 ,z4 phys4 ,chem41 #i1 #fah 7#ahib72 ,findlay1 ibid41 #cd1 #dji 7#aijj74 #bid ,as foreign salts affect the ionization of poor electrolytes 7p4 #aji71 the ratio of equation ,i would hold as little for poor electrolytes1 and would grow larger with an increased concentration of the foreign salts4 #bie ,cf4 ,a4 ,a4 ,noyes1 ,congress of ,arts and ,sciences 7,st4 ,louis71 #d1 #cba 7#aijd7 and ,stieglitz1 ,j4 ,am4 ,chem4 ,soc41 #cj1 #idf 7#aijh7 7,stud471 and the references to literature given there4 ,the empirical relation seems to hold for dilute solutions1 the total electrolyte concentration of which is not greater than #j4b to #j4c gram-equivalent per liter1 and1 roughly1 for concentrations not greater than #j4e gram-equivalent per liter4 #bif ,see ,stieglitz1 loc4 cit4 #big ,since the writing of this it has been learned that such investigations have been carried out by ,harkins4 ,cf4 ,j4 ,am4 ,chem4 ,soc41 #aiaa4 #bih ,j4 ,am4 ,chem4 ,soc41 #cb1 #dhh 7#aiaj74 #bii ,otherwise a perpetuum mobile of the second class 7footnote #c1 p4 #ab7 could be constructed1 which is at variance with experience4 #cjj ,this sentence is quoted from a letter from ,dr4 ,washburn1 who is at present investigating moderately concentrated solutions of electrolytes1 to determine the range of concentrations in which it is possible to apply the laws of ideal solution4 #cja ,cf4 ,geffcken1 ,z4 ,phys4 ,chem41 #di1 #beg 7#aijg71 and the references given there4 #cjb ,cf4 ,arrhenius1 loc4 cit41 and similar investigations on the salt effect 7p4 #aji74 #cjc ,vide ,geffcken1 loc4 cit41 #bie1 and ,stieglitz1 loc4 cit41 and p4 #adb4 #cjd ,see also ,hill1 ,j4 ,am4 ,chem4 ,soc41 #cb1 #aahf 7#aiaj74 ,hill attacks the principle as a whole1 but brings no evidence against its validity for solutions of concentrations up to #j4c4 #cje ,the limit of concentration depends1 for constancy1 upon the nature of the salts4 ,the calculations1 on which the data in the tables on pp4 #adf-g are based1 involve extrapolations which prevent the results1 especially for the more concentrated solutions1 being considered as final4 #cjf ,for further illustrations1 vide ,stieglitz1 ,j4 ,am4 ,chem4 ,soc41 #cj1 p4 #idg 7#aijh71 and the references given there to the work of ,noyes1 ,findlay1 etc4 #cjg ,some instances are known where the solubility of a salt is increased by the addition of a salt with a common ion4 ,in such cases it is extremely likely that an ion of the salt in question forms a complex ion with a component of the solution4 ,vide ,a4 ,a4 ,noyes1 ,z4 phys4 ,chem41 #f1 #bda 7#ahij71 and #i1 #fjc 7#ahib74 ,in ,chapter ,,xii we shall discuss1 in detail1 instances of this nature where the formation of complex ions is particularly susceptible of exact experimental verification4 #cjh ,especially by ,noyes1 loc4 cit41 and later papers2 ,findlay1 loc4 cit4 #cji ,this is the value for a similar ratio for ,k,cl of the same concentration as found1 by extrapolation1 from the data in the table on p4 #ajh4 #caj ,owing to the possibility of the formation of complex ions 7,chapter ,,xii71 each individual case must be considered by itself and the most favorable conditions for the complete precipitation determined experimentally4 ,the rule mentioned is to be used as a guide1 and the reference to the possibility of the formation of complex ions considered as a warning1 in the planning of such investigations4 #caa ,cf4 p4 #acf1 concerning precautions used to prevent precipitates from assuming the colloidal state4 #cab ,fresenius1 ,quantitative ,analysis1 ,i1 #cee 7#aijd74 #cac ,ibid41 ,i1 #cjg4 #cad ,official ,methods of ,analysis1 ,bulletin #ajg1 p4 #aa1 ,u4 ,s4 ,dept4 of ,agriculture4 #cae ,the excess of chloroplatinic acid is first washed out of the precipitate primarily to avoid subsequent precipitation of ammonium chloroplatinate1 but its removal also avoids the error discussed in the text4 #caf ,gay-,lussac's method4 #cag ,mulder4 ,see ,sutton's ,volumetric ,analysis1 p4 #cjd 7#aijd74 #cah ,vide ,chapters ,,xii and ,,xiii4 #cai ,a table of exact solubilities is given at the end of the ,lab4 ,manual1 q4v4 #cbj ,in the most exact quantitative work1 as demanded in the determinations of atomic weights1 every known loss must1 as far as possible1 be measured and taken into account4 ,beautiful instances of such work are found in ,t4 ,w4 ,richards' classic determinations of atomic weights4 ,see1 for instance1 ,richards1 ,carnegie ,institution ,publications1 ,no4 #abe 7#aiaj71 ,determinations of the ,atomic ,weights of ,silver1 ,lithium and ,chlorine 7,stud474 #cba ,z4 ,elektrochem41 #aa1 #gig 7#aije74 #cbb ,ibid41 #aa1 #icf 7#aije71 and #ab1 #gbe 7#aijf74 #cbc ,z4 phys4 ,chem41 #ee1 #gjg 7#aijf71 and #fa1 #fch 7#aijg74 #cbd ,if n is the number of moles of solute dissolved in ,n moles of solute1 the concentration of the solute may be expressed as n _/ 7n ,n71 which is called its mole fraction4 ,this form of expressing concentrations is in many particulars preferable to the mole _/ liter form4 ,for very dilute solutions 7n is very small compared with ,n7 the two forms become practically identical1 but they are not so for more concentrated solutions1 and the mole-fraction expression is then easier to treat rigorously4 #cbe ,see ,walden1 loc cit41 for more extended data4 p#aeg ,,part ,,ii ,,systematic ,,analysis ,,and ,,the ,,application ,,of ,,fundamental ,,principles ,,chapter ,,ix ,,systematic ,,analysis ,,for ,,the ,,common ,,metal ,,ions4 ,,the ,,ions ,,of ,,the ,,alkalies ,,and ,,of ,,the ,,alkaline ,,earths4 ,,order ,,of ,,precipitation ,,of ,,difficultly ,,soluble ,,salts ,,with ,a ,,common ,,ion ,in systematic analysis it is most convenient to make separate examinations for the metal and for the acid ions4 ,the examination for metal ions usually precedes that for the acid ions1 and the scheme of analysis for the former will be considered first4 ,the analytical grouping of the metallic elements is not a natural one1 as far as their chemical behavior is concerned4 ,such a grouping is found in the ,periodic ,system of ,mendeleff and is used in systematic inorganic chemistry4#cbf ,the groups in analysis are based chiefly1 but not exclusively1 on the physical property of greater or smaller solubility of certain salts of the metals4 ,according to the salts chosen1 different systems vary somewhat in detail4 ,frequently elements of the same natural family are also found in the same analytical group1 relationship in chemical properties being often coincident with relationship in the physical behavior of the salts of the metals4 ,in the following list1 the common metal ions are arranged in groups1 which are given in the order in which they are precipitated in the method of systematic analysis adopted4 ,in each case1 a group name and the characteristic reagents used in separating a group from those following it1 are given4 ,the ,silver ,group4--,ions whose chlorides are insoluble in dilute acid solutions4 ,the precipitating agent is ,h,cl4 p#aeh ,pb#b 7the chloride is somewhat soluble71 ,ag1 ,hg4 ,the ,copper and the ,arsenic ,groups4--,ions whose sulphides are insoluble in dilute acids4 ,the precipitating agent for the two groups is ,h#b,s1 in acid solution4 ,the sulphides of the arsenic group are soluble in a mixture of 7,,nh#d7b,s and 7,,nh#d7b,sx and are separated thereby from the sulphides of the copper group4 ,the ,copper ,group4--,hg#b1 7,pb#b71 ,bi#c1 ,cu#b1 ,cd#b4 ,the ,arsenic ,group4--,as#c1 ,as#e1 ,sb#c1 ,sb#e1 ,sn#b1 ,sn#d1 ,pt#b1 ,pt#d1 ,au1 ,au#c4 ,the ,aluminium and the ,zinc ,groups4--,ions whose sulphides or hydroxides are insoluble in neutral or slightly alkaline 7ammonium hydroxide7 solutions4 ,the two groups are precipitated together by a mixture of ,,nh#d;,cl1 ,,nh#d,,oh1 7,,nh#d7b,s4 ,the aluminium group may be separated from the zinc group by treatment of solutions of the chlorides or nitrates with barium carbonate4 ,the ,aluminium ,group4--,fe#c1 ,al#c1 ,cr#c4 ,the ,zinc ,group4--,fe#b1 ,ni#b1 ,co#b1 ,mn#b1 ,zn#b4 ,the ,alkaline ,earth ,group4--,ions whose carbonates and phosphates are insoluble in neutral or alkaline solutions4 ,the precipitating agent is ,,nh#d;,cl1 ,,nh#d,,oh1 7,,nh#d7b;,,co#c for ,ba#b1 ,sr#b1 ,ca#b1 and 7,,nh#d7b;,,hpo#d for ,mg#b4cbg ,the ,alkalies4--,ions whose chlorides1 sulphides1 hydroxides1 carbonates and phosphates are soluble4 ,k1 ,na1 ,,nh#d4 ,in considering the analytical reactions and the analysis of these groups of metal ions1 we shall take up the groups in the order reversed to that given in the table4 ,we shall begin with the group of alkali metals1 follow this group with the alkaline earths1 then take the aluminium and zinc groups1 the copper and silver groups1 and finish with the arsenic group4 ,this order is chosen because the chemistry of the reactions involved is simplest in the groups to be studied first and grows more complicated as we advance to those to be studied later4 ,it is not intended to discuss in detail all the reactions and methods2 our attention will be limited rather to the study of typical general relations1 and the student is expected to acquire the power to apply the general conclusions reached1 to any specific case demanding it4 p#aei ,the ,alkali ,group4--,the group includes the ions of sodium and potassium1 the most common and most important of the alkali metals1 and the ammonium-ion4 ,characteristic of the ions of the group is the fact that all of their common salts are easily soluble in water4 ,they remain in solution in systematic analysis1 while other metal ions are removed in the form of various insoluble precipitates4 ,the ammonium-ion is recognized1 and may be removed from a mixture of the salts of the group1 on the basis of a fundamental distinction in its chemical behavior1 namely its instability and the instability of its compounds4 ,sodium-ion and potassium-ion1 are recognized1 and separated from each other1 by physical methods4 ,all ammonium compounds1 ,,nh#d,x1 decompose more or less readily into ammonia and the free acids1#cbh according to the reversible reaction1 ,,nh#d,x ,,nh#c ,,hx4 ,the stronger the acid combined with ammonia1 the more stable is the salt1 and the higher is the temperature1 at which the salt decomposes readily and rapidly4 ,ammonium chloride1 one of the most stable of the salts1 is decomposed rapidly only at about #cej1 which is1 however1 still below red heat2 ammonium carbonate1 the salt of a very much weaker acid1 decomposes appreciably at ordinary temperatures1 and exposed to the air1 it gradually disappears as ammonia1 carbon dioxide and water4 ,if the acid of the salt is volatile at the dissociation temperature of the salt1 the whole salt is volatilized1 and if the ammonia and volatile acid vapor reach a colder space1 recombination to form the original solid salt occurs to a considerable extent 7the smoking off of ammonium chloride74 ,if the acid is not volatile1 the salt1 nevertheless1 loses its ammonia at temperatures below red heat1 while the acid remains4 ,sodium-ammonium phosphate1 for instance1 when heated1 loses its ammonia1 and sodium-dihydrogen phosphate is left as a nonvolatile residue4 ,ammonium happens to form salts which closely resemble the corresponding salts of potassium in physical properties1 such as p#afj solubility and insolubility1 salts which could readily be mistaken for potassium salts4 ,advantage is taken of the chemical instability of the ammonium salts1 just described1 to remove ammonium completely from mixtures1 by ignition1 before tests for potassium are made4 ,water is a far weaker acid 7see table1 p4 #ajd7 than carbonic acid and it is not surprising to find the compound formed by water and ammonia1 ammonium hydroxide1 one of the least stable of the ammonium compounds4 ,even at ordinary temperature1 the hydroxide is more or less decomposed1 according to a reversible reaction of the same type as that found for the ammonium salts1 ,,nh#d,,oh ,,nh#c ,,hoh4 ,chemists have always been interested in the problem of the exact degree of stability of ammonium hydroxide1 and1 more particularly1 in the problem whether ammonia gives solutions in water showing very much weaker basic strength#cbi than equivalent solutions of potassium and sodium hydroxides1 primarily because only a small proportion of the ammonia is combined with water to form the real base1 ammonium hydroxide 7which would be present then in much more dilute solution than the alkali metal hydroxides are in the solutions with which the comparison is made71 or chiefly because ammonium hydroxide is much less readily ionizable than potassium or sodium hydroxide4 ,for the reversible action ,,nh#c ,,hoh ,,nh#d,,oh we would have1 at a constant temperature1 according to the law of chemical equilibrium1 ,,nh#c ,,hoh _/ ,,nh#d,,oh k4 ,for a dilute solution at a given temperature the concentration of the water may be considered a constant1 and therefore ,,nh#c _/ ,,nh#d,,oh k _/ ,,hoh k,,nh#c4 7,i7 ,for the ionization of ammonium hydroxide1 ,,nh#d,,oh ,,nh#d ,,ho1 we would have in turn1 ,,nh#d ,,ho _/ ,,nh#d,,oh kbase4 7,,ii7 ,this constant represents the real ionization constant of ammonium hydroxide as a base1 and its approximate value has only recently been determined by ,moore#ccj and found to be about #e;,e#e4 ,the ratio ,,nh#c _/ ,,nh#d,,oh was found to be approximately #b at #bj4 ,according to this result1 ammonium hydroxide is really a much weaker1 less readily ionized base than potassium or sodium hydroxide4 ,the efficiency of ammonium hydroxide as a base depends p#afa on both conditions of equilibrium2 the first equation states what proportion of ammonium hydroxide can exist1 as such1 in solution1 if a given amount of ammonia is dissolved in a given amount of water1 and the second equation shows the proportion of the hydroxide1 which is ionized4 ,the equations may be combined#cca into one expression1 ,,nh#d ,,ho _/ 7,,nh#d,,oh ,,nh#c7 ,k4 7,,iii7 ,that is1 the ratio of ,,nh#d ,,ho to the total concentration of nonionized ammonium hydroxide and ammonia1 is a constant4 ,this constant has the value #j4jjj1jah at #ah 7as given in the table1 p4 #ajf7 and1 as said1 comprises in a single expression a statement measuring the efficiency1 as a base1 of a solution of ammonium hydroxide and ammonia in aqueous solutions4 ,the concentration of the hydroxide-ion1 on which the efficiency as a base depends1 can be ascertained directly from the expression1 provided we know the total concentration of the ammonia and ammonium hydroxide and the concentration and degree of ionization of any ammonium salt1 which may be present with the base 7see p4 #afa74 ,these data are easily obtained by direct measurement4 ,the instability of ammonium hydroxide is used as a means for detecting ammonium-ion in its salts4 ,the latter are treated with some strong base1 such as sodium or calcium hydroxide1 and the ammonia1 liberated by the decomposition of its hydroxide1 is recognized by its odor or by the more sensitive test of its action on moist litmus4 ,the delicacy of the test is dependent on the conditions expressed in the equilibrium equation 7p4 #afj74 ,sodium and potassium resemble each other so profoundly in the chemical behavior of their compounds1 that they are recognized1 and separated from each other1 by physical methods4 ,a very simple physical test is based on the color of their heated vapors1 the color imparted to the nonluminous bunsen flame by the introduction and volatilization of their salts4 ,the sodium flame is so intense that1 if sodium is present in any quantity1 the color of its flame easily masks the faint color of potassium vapor4 ,the color of the flame is best examined1 in such a case1 with the aid of a spectroscope1 in which the light emitted by the two elements may be readily recognized side by side1 or with the aid of cobalt glass1 which absorbs the sodium light4 p#afb ,the ions of the two metals may be separated and identified by means of difficultly soluble salts4 ,there are so few of these in the case of both ions1 that recourse must be taken to the salts of comparatively uncommon acids4 ,potassium chloroplatinate ,k#b,pt,cl#f1 precipitated by the addition of chloroplatinic acid ,h#b,pt,cl#f to concentrated solutions of potassium salts1 gives very satisfactory results1 both in qualitative and in quantitative work4 ,the acid tartrate1 ,,khc#d;,h#d,o#f1 the picrate1 ,,kc#f;,h#b,n#c,o#g1 and the cobaltinitrite1 ,k#c;,co7,,no#b7f1ccb are difficultly soluble and are sometimes used to identify potassium-ion4 ,the corresponding ammonium salts are also difficultly soluble and resemble the potassium salts1 and ammonium-ion must therefore be removed1 as stated above1 if present1 before any of these precipitates may be used for the identification of potassium-ion4 ,in the case of sodium-ion1 recourse is taken to the salt of a still more uncommon acid2 pyroantimonate of sodium1 ,na#b;,h#b,sb#b,o#g1 #f aq41 is sufficiently difficultly soluble and characteristic to be used as a means of identifying sodium-ion4 ,the ,alkaline ,earth ,group4--,this group includes magnesium1 calcium1 strontium1 and barium4 ,chemically1 the analogous compounds of the four alkaline earths resemble one another so much1 that physical differences alone are used in their separation and identification4 ,for qualitative work1 the colors of their heated vapors1#ccc especially when examined in the spectroscope1 give us sensitive and reliable tests for their presence4 ,the alkaline earth ions1 especially the ions of barium1 strontium and calcium1 form a great number of insoluble salts1 which may be used to separate them from each other4 ,salts used for this purpose and the methods of employing them are considered in detail in the laboratory work 7see ,part ,,iii74 ,here some general principles1 only1 will be considered in connection with the behavior of some of the most important of the precipitates4 ,there is a very wide range in the degree of the insolubility of such precipitates as are used in analysis4 ,in the table at the end of ,part ,,iv1 the exact solubilities of the most important p#afc precipitates of the alkaline earths are given1 for #ah1 in grams and moles per liter4 ,the values are instructive in a number of respects4 ,inspection of the table shows which are the least soluble 7in molar terms71 and therefore the best salts1 for precipitating barium1 strontium and calcium1 in order to insure the use of the most sensitive tests for the ions of each of these metals4 ,it also shows which salts must be treated with special precautions to escape error4 ,it is further seen1 that if the carbonates of these alkaline earths are precipitated by a moderate excess of ammonium carbonate1 the addition of a sulphate 7for instance ammonium sulphate71 to the filtrate from the precipitated carbonates1 will only precipitate barium sulphate1 the only sulphate whose solubility 7and solubility-product7 is smaller than that of the corresponding carbonate4 ,in the same way1 calcium oxalate is the only oxalate of these three alkaline earths that will be precipitated by ammonium oxalate in the filtrate from the carbonates 7see ,part ,,iii in regard to precautions against difficultly soluble double oxalates of magnesium74 ,again1 calcium sulphate is the only one of the sulphates1 which is sufficiently soluble in water to give an immediate heavy precipitate1 when the sulphates are shaken for a few moments with water and the filtered solution is treated with a few drops of ammonium oxalate solution4 ,fractional ,precipitation4#ccd--;,if sulphuric acid is added to a #j4e molar solution of the chloride either of barium1 of strontium or of calcium1 the corresponding sulphate is precipitated4 ,we may ask which sulphate will be precipitated first1 when sulphuric acid is added1 drop by drop1 to a solution containing the three chlorides4 ,this problem1 a case of the fractional precipitation of salts containing a common ion1 may be treated from the point of view of the solubility-product principle as follows1 the problem being limited1 for the sake of simplicity1 to only two of the sulphates1 those of barium and strontium4 ,for a saturated solution of barium sulphate1#cce at #ah1 in contact with the solid salt1 we have1 according to the principle of the solubility-product1 ,k,ba,s,o#d ,ba#b ,,so#db #a;,e#aj1 p#afd and for a saturated solution of strontium sulphate1 we have similarly#ccf ,k,sr,s,o#d ,sr#b ,,so#db #b4e;,e#g4 ,now1 we may ask what the conditions are under which both precipitates can be present together in a condition of equilibrium with a supernatant saturated solution4 ,in such a solution we have simultaneously ,k,ba,s,o#d ,ba#ba ,,so#dba1 ,k,sr,s,o#d ,sr#ba ,,so#dba4 ,new symbols1 ,ba#ba1 etc41 are used for expressing the concentrations1 as they are not the same as in the pure aqueous solutions4 ,the much more soluble strontium sulphate makes the concentration of the sulphate-ion very much greater than it is in the saturated solution of pure barium sulphate and diminishes the concentration of the barium-ion proportionately 7p4 #ade74 ,the concentration1 ,,so#dba1 of the sulphate-ion1 representing the actual 7total7 concentration of the ion in the solution saturated with both salts1 appears in both of the new equations4 ,combining the two equations1 we have1 for the condition of equilibrium between the two precipitates and the supernatant liquid1 ,ba#ba _/ ,sr#ba ,k,ba,s,o#d _/ ,k,sr,s,o#d #a _/ #bejj4 ,that is1 in a solution in equilibrium with both precipitates at #ah1 the strontium-ion must be about #bejj times as concentrated as is the barium-ion4 ,if we start with equivalent quantities of barium and strontium chlorides1 say in #j4a molar solutions1 and gradually add sulphuric acid or ammonium sulphate1 barium sulphate will be precipitated alone1#ccg until the strontium-ion is in the excess p#afe indicated by the ratio given4 ,after that1 strontium sulphate will be precipitated1 with traces of barium sulphate1 the ratio expressed in the equilibrium equation being maintained in the supernatant liquid4 ,on the other hand1 if we start with a solution containing a very large excess of a strontium salt1 more than is required by the equilibrium ratio1 then strontium sulphate will be precipitated first1 until the ratio given is reached4 ,even should the more soluble salt be precipitated first from a solution containing1 say1 equal concentrations of barium and strontium ions1 it could not remain in equilibrium with the supernatant liquid and would be converted into the less soluble one1 before equilibrium was reached in the system4 ,we can follow similar relations1 experimentally1 by using precipitates of different colors4 ,silver chromate ,ag#b;,cr,o#d is an intensely red precipitate1 that is rather difficultly soluble in water 7exp472 a liter of water dissolves#cch #j4jbeb gram or #h;,e#e mole at #ah4 ,the concentration of the silver-ion in the saturated solution is then #j4jjjaf mole4#cci ,silver chloride ,ag,cl1 a white salt1 is still less soluble in water1 a liter of water at #ah dissolving #j4jjacd gram or #a;,e#e mole1 and the concentration of the silver-ion in the saturated solution is1 therefore1 only #a;,e#e mole1 as compared with #a4f;,e#d in the saturated silver chromate solution4 ,if a mixture of potassium chromate and potassium chloride1 containing approximately equal 7#j4ja molar7 concentrations of the two salts1 is prepared and silver nitrate solution added1 drop by drop1 to the mixture1 the first permanent precipitate is the white silver chloride 7exp474 ,however1 as the silver nitrate solution strikes the surface of the liquid1 a red precipitate of the chromate1 mixed with chloride1 is momentarily seen1 where the silver nitrate temporarily produces a local excess of the precipitant4 ,but the red precipitate disappears rapidly and gives way to the white precipitate of the less soluble chloride4 ,the quantitative relations1 which may be developed with the aid of the principle of the solubility-product 7see below71 are such that1 if little chromate is used1 it may serve as an p#aff indicator to determine quantitatively the moment when all the chloride1 within the limits of allowed quantitative error1 is precipitated1 the first permanent tinge of pink 7solid ,ag#b;,cr,o#d71 mixed with the yellow color of the solution1 being used as the indication that the precipitation of the chloride is complete4 ,potassium chromate is used as a favorite indicator in quantitative analysis1 for this purpose4 ,the quantitative relations#cdj for the precipitation may be developed as follows3 ,for a supernatant liquid in which a precipitate of silver chromate just appears permanently1 together with the chloride1 i4e4 for the condition of saturation with both silver salts at #ah1 we have ,k,ag,cl ,ag ,cl 7#a;,e#e7b #a;,e#aj and ,k,ag#b;,cr,o#d ,ag#b ,cr,o#db 7#a4f;,e#d7b 7#h;,e#e7 #b;,e#ab1 and therefore3 ,cl#b _/ ,cr,o#db 7,k,ag,cl7#b _/ ,k,ag#b;,cr,o#d 7#a;,e#aj7b _/ #b;,e#ab #a _/ #b;,e#h4 ,for a solution containing one or two drops 7#j4a c4c47 of saturated potassium chromate solution per #ajj c4c41 a proportion frequently used in quantitative analysis1 the concentration of the chromate-ion is approximately #b4e;,e#c and the chloride-ion will consequently be precipitated until ,cl #c;,e#f4 ,the chief source of error in the method1 then1 will not be due to the incompleteness of the prior precipitation of the chloride1 but rather to the use of the small excess of silver nitrate required to precipitate sufficient chromate to be visible4 ,this error may be avoided1 and is avoided in very accurate work 7e4g4 in water analysis71 by determining1 in a blank test1 the amount of silver nitrate required to show the change of tint of a pure chromate solution of the concentration to be used in the titration and by titrating to this tint in the determination of the chloride3 the volume of silver nitrate 7e4g4 #j4b c4c4 of a #j4ja molar solution71 required to produce the tint in the blank test1 is subtracted from the total volume of silver nitrate used in the chloride determination4 ,we find thus1 that the order of precipitation of difficultly soluble salts1 which contain a common ion 7fractional precipitation71 is subject to the equilibrium conditions derived from the application of the principle of the solubility-product to the salts in question4#cda ,it should be further noted that the condition of equilibrium between two precipitates1 containing a common ion1 and a supernatant liquid1 depends on the concentrations in the supernatant liquid1 in the liquid phase1 and not on the quantities of the solids p#afg present4 ,this conclusion was first reached by ,guldberg and ,waage1 to whom we owe the law of mass action1 and was fully confirmed by them4 ,the modern treatment of the subject substitutes ion concentrations1 i4e4 the concentrations of the active components1#cdb for the total concentrations used by these investigators4#cdc ,that the condition of equilibrium is dependent on the liquid phase can easily be demonstrated if mercurous chloride and mercurous hydroxide are selected as the two precipitates1 in order that we may follow changes of concentration in the liquid phase by color changes4 ,for the condition of equilibrium between the two precipitates and the supernatant liquid we may develop the relation ,,oh _/ ,cl ,k,hg,o,h _/ ,k,hg,cl ,k4 ,,exp4 ,a few drops of phenolphthalen are added to #ajj c4c4 of a very dilute solution of potassium hydroxide 7#a _/ #ejj molar72 the usual indication of the presence of the hydroxide-ion is shown and the intensity of the color will be a measure of its concentration4 ,three identical solutions are prepared and then a pinch of calomel is added to two of the solutions1--their pink color fades decidedly4 ,some of the calomel is decomposed into dark-colored mercurous oxide1 which is precipitated1 and sufficient potassium chloride is formed to bring the ratio ,,oh _/ ,cl1 in the solution1 down to the value required by the constant ,k4 ,since no chloride-ion is present at the start1 this result can be brought about only by the change indicated4 ,now1 some chloride1 say a little of a concentrated solution of potassium chloride1 which reacts perfectly neutral1 is added to one of the mixtures of the hydroxide and chloride4 ,the concentration of the chloride-ion is increased in the solution1 the ratio ,,oh _/ ,cl is made much too small and the condition of equilibrium is disturbed4 ,consequently1 mercurous oxide reacts with potassium chloride1 as expressed in the equation ,hg,o,h ,k,cl ,hg,cl ,,koh1 until the ratio ,,oh _/ ,cl p#afh has the value required by the constant ,k4 ,the phenolphthalen is colored by the increased concentration of the hydroxide-ion and shows the direction of the change4#cdd ,precipitation by a ,weak ,base in the ,presence of its ,salts4--,magnesium1 in contrast to the other alkaline earth metals1 forms very few difficultly soluble compounds4 ,magnesium-ammonium phosphate1 ,mg7,,nh#d7,,po#d1 a double salt1 is the most characteristic precipitate for identifying it4 ,magnesium hydroxide1 as the table of solubilities shows1 is also very difficultly soluble4 ,it is readily precipitated by potassium or sodium hydroxide1 but ammonium hydroxide1 at best1 precipitates it only incompletely#cde from solutions of its salts1 and very commonly does not precipitate it at all--namely1 when ammonium salts in sufficient quantity are present 7exp474 ,this peculiar behavior of ammonium salts1 in interfering with the precipitation of magnesium hydroxide1 puzzled chemists for many years1 and a number of theories were offered in explanation of it4 ,but they all proved untenable1 and the first adequate explanation1 the one in accord with all the facts1 was only found after the development of the theory of ionization4 ,its quantitative application to the case in question gives a perfect insight into the relations1 and brings important confirmation of the correctness of its fundamental assumptions4#cdf ,the fact that ammonium salts prevent the precipitation of magnesium hydroxide was formerly explained as being due to the formation of double salts1 such as ,mg,cl#b1,,nh#d;,cl4 ,it is true that such double salts exist1 but1 if their formation should prevent the precipitation of magnesium hydroxide1 possibly by including the magnesium as part of a negative ion or radical1#cdg ,mg,cl#c1 then the corresponding double salts of magnesium chloride with potassium and sodium chloride 7e4g4 ,mg,cl#b1,k,cl71 which are just as stable as the ammonium salts1 should show the same behavior2 but1 as a matter of fact1 the addition of potassium chloride does not interfere with the precipitation of the hydroxide by either p#afi potassium hydroxide or ammonium hydroxide 7exp474 ,so the explanation is untenable4 ,obviously1 a specific interference of ammonium salts with the precipitating power of ammonium hydroxide is involved4 ,but that is exactly what the law of chemical equilibrium1 applied to the ionization of ammonium hydroxide1 would demand3 ,as a weak base1 which is little ionized in pure aqueous solutions1 it is very much weaker as a base1 produces a far smaller concentration of the hydroxide-ion1 when readily ionizable salts of ammonium are added to the solution1#cdh and the precipitation of magnesium hydroxide1 and of metal hydroxides in general1 depends on the concentration of the hydroxide-ion1 which is a factor in the solubility-products of bases4 ,the precipitation of magnesium hydroxide1 in particular1 depends on the relation of the product ,mg#b ,,ho#b to the solubility-product constant of magnesium hydroxide4 ,for the saturated aqueous solution1 the product ,mg#b ,,ho#b is equal to the solubility-product constant1 and from the solubility of magnesium hydroxide 7see the table7 the value of the constant is found to be #ae;,e#ab at #ah4 ,the concentration of magnesium-ion is #j4jjj1aed in this solution4 ,in a #j4a molar solution of magnesium sulphate1 which is ionized to the extent of #cg4c1 the concentration of magnesium-ion is #j4jcgc1 and it would require a concentration greater than #b;,e#e of hydroxide-ion to precipitate any magnesium hydroxide4#cdi ,now1 the concentration of the hydroxide-ion1 in an ammoniacal solution1 can easily be reduced far below this value by the addition of ammonium chloride1 nitrate1 sulphate or other readily ionizable ammonium salt to the solution1 and then magnesium hydroxide will not be precipitated4 ,in solutions of ammonium hydroxide the concentration of hydroxide ion for #ah is found from the relation ,,nh#d ,,ho 3 7,,nh#d,,oh ,,nh#c7 #ah;,e#f 7p4 #afa74 7#a7 ,for ammonium hydroxide1 for instance in #j4b molar solution1 and in the absence of any ammonium salt1 ,,ho ,,nh#d #j4jjai4cej ,this concentration of the hydroxide-ion should be more than sufficient to precipitate magnesium hydroxide in a #j4a molar solution of the sulphate4#cea ,,exp4 #ajj c4c4 of a mixture which should contain magnesium sulphate in #j4a molar solution would require #bdf _/ 7#aj #aj7 or #b4df grams of ,mg,s,o#d1 #g ,h#b,o4 p#agj ,this weight of the salt is dissolved in #ej c4c4 of water and #ej c4c4 of #j4d molar solution of ammonium hydroxide is added to it4 ,magnesium hydroxide is precipitated4 7,the precipitation is incomplete because the ammonium sulphate1 formed in the reaction1 reduces the ionization of ammonium hydroxide47 7#b7 ,in the presence of #j4be molar ammonium chloride1 the chloride being dissociated to the extent of #hj1ceb the concentration of the hydroxide-ion in a #j4b molar ammonium hydroxide solution is reduced to #ah;,e#f4cec ,according to the above calculation this is too small a concentration to precipitate magnesium hydroxide in a #j4a molar solution of the sulphate4 ,,exp4 #a4ce grams ammonium chloride 7the weight corresponding to #ajj c4c4 of a mixture containing ammonium chloride in #j4be molar solution7 is dissolved in #ej c4c4 of #j4d molar ammonium hydroxide and #b4df grams of magnesium sulphate1 dissolved as before in #ej c4c4 of water1 is added to the mixture4 ,no precipitate of magnesium hydroxide is formed4 ,in a similar fashion and for the same reason1 ammonium salts interfere more or less with the precipitation of other hydroxides1 for instance with the precipitation of manganous1 nickelous1 cobaltous1 ferrous1 zinc1 cupric and cadmium hydroxides4 ,but ammonium salts do not prevent the precipitation of aluminium1 chromium and ferric hydroxides1 which are much less soluble than the hydroxides just mentioned1 and as much weaker bases1 7,chap4 ,x7 are also much less readily ionized4 ,they are precipitated by smaller concentrations of the hydroxide-ion than are the hydroxides of the first group1 and their precipitation may be made quantitative4 ,,exp4 ,ferric hydroxide is readily precipitated when #b4g grams of ferric chloride ,fe,cl#c1 #f ,h#b,o1 the weight of the chloride required to give #ajj c4c4 of a #j4a molar solution1 is dissolved in as little water as possible4 ,the solution is added to the mixture of magnesium sulphate1 ammonium chloride and ammonium hydroxide obtained in the previous experiment1 in which no magnesium hydroxide was precipitated4 ,,footnotes3 #cbf ,see ,smith1 ,general ,inorganic ,chemistry1 p4 #dad1 ,general ,chemistry for ,colleges1 p4 #bgg2 ,remsen1 ,inorganic ,chemistry 7advanced course71 p4 #aeh4 #cbg ,mg#b may also be precipitated as a carbonate with the other ions of the group 7see ,part ,,iii74 #cbh ,in the case of ammonium nitrate a different form of decomposition1 namely into nitrous oxide and water1 predominates1 and1 in the case of ammonium nitrite1 decomposition into nitrogen and water takes place so readily1 that the decomposition of the salt takes that direction chiefly4 #cbi ,table1 p4 #ajf4 #ccj ,t4 ,s4 ,moore1 ,j4 ,chem4 ,soc4 7,london71 #ia1 #acgi 7#aijg74 #cca ,from equation 7,i7 we obtain directly1 by the application of a simple mathematical transformation1 that ,,nh#c ,,nh#d,,oh _/ ,,nh#d,,oh k,,nh#c #a k1 and1 therefore1 ,,nh#d,,oh ,,nh#c ,,nh#d,,oh _/ k4 ,inserting this value for ,,nh#d,,oh in equation 7,,ii7 and transferring k1 we have ,,nh#d ,,ho _/ 7,,nh#c ,,nh#d,,oh7 kbase _/ k ,k4 #ccb ,water of crystallization1 found in many of the precipitates used in qualitative analysis1 will1 as a rule1 be indicated only in the formulas used in ,part ,,iii1 in the study of the reactions of ions4 #ccc ,see ,part ,,iii as to the method of vaporizing magnesium4 #ccd ,cf4 ,findlay1 ,z4 phys4 ,chem41 #cd1 #dji 7#aijj74 #cce ,the solubility of barium sulphate at #ah1 according to the table1 is #j4jjbc _/ #bcc1 or #a;,e#e mole per liter1 and the salt may be considered completely ionized at this dilution4 #ccf ,the solubility 7see the table7 is #j4aad _/ #ahc4f1 or #f4b;,e#d mole per liter1 #hd of which is ionized 7according to conductivity determinations1 ,kohlrausch and ,holborn1 loc4 cit41 p4 #bjj74 ,hence ,sr#b ,,so#db #j4jjjfb #j4hd #j4jjje4 #ccg ,to establish equilibrium1 prolonged digesting is sometimes required4 ,double salts1 solid solutions and mechanical enclosures are liable to interfere with the completeness of such separations by fractional precipitation4 ,resolution and reprecipitation will then usually effect a sufficiently accurate separation for most purposes4 ,on account of the possibility of such complications1 the conditions for a successful separation1 within limits such as those described in the text1 must in all cases be investigated4 #cch ,see the table at the end of ,part ,,iv4 #cci ,the salt may be considered completely ionized at this dilution4 ,each molecule of silver chromate forms two silver ions when it is ionized4 ,see p4 #ada in regard to the form the solubility-product takes in the case of a salt of this type4 #cdj ,the complication1 resulting from the hydrolysis of the chromate1 is not included in this calculation4 #cda ,cf4 ,findlay1 loc4 cit4 #cdb ,even ,guldberg and ,waage considered the active mass to be the fundamental factor and simply considered the total concentrations to be proportional to the active masses1 since they had no means of determining the proportion of active substances in the total concentrations4 #cdc ,see ,nernst1 ,theoretical ,chemistry1 p4 #ecc1 for a fuller discussion of the relations between the new and the old views on this subject4 #cdd ,dietrich and ,whler1 ,z4 anorg4 ,chem41 #cd1 #aid 7#aijc74 #cde ,on account of the formation of an ammonium salt in the reaction4 #cdf ,loven1 ,z4 ,anorg4 ,chem41 #aa1 #djd 7#ahif72 ,herz and ,muks1 ibid41 #ch1 #ach 7#aijd74 #cdg ,in that case the salts would be called complex salts1 salts of a complex ion1 ,mg,cl#c4 ,see ,chapter ,,xii4 ,they are really double salts2 cf4 ,smith1 ,general ,inorganic ,chemistry1 p4 #ecf4 #cdh ,see p4 #aad1 and recall the laboratory experiments 7,lab4 ,manual1 p4 #i1 #f71 which may be given as lecture experiments at this point4 #cdi ,calling x the concentration of the hydroxide-ion1 required to saturate a #j4a molar magnesium sulphate solution with magnesium hydroxide1 we have #j4jcgc x#b #ae;,e#ab and x #b;,e#e4 #cej ,putting ,,ho ,,nh#d y1 we have y#b 3 7#j4b y7 #ah;,e#f4 ,then y #j4jjai4 #cea #j4jcgc #j4jjaib #j4ac;,e#f1 which is considerably larger than the solubility-product constant for magnesium hydroxide1 #ae;,e#ab4 #ceb ,kohlrausch and ,holborn1 p4 #aei4 ,minor changes in the degrees of ionization of ,mg,s,o#d and ,,nh#d;,cl 7and consequently of ,,nh#d,,oh7 occur1 when the salts are present together4 ,in a rigorous treatment1 the ionization of each salt in the mixture would be calculated with the aid of ,arrhenius's principle of isohydric solutions4 #cec ,vide the analogous calculation on p4 #aac4 p#aga ,,chapter ,x ,,aluminium2 ,,amphoteric ,,hydroxides2 ,,hydrolysis ,,of ,,salts4 ,,the ,,aluminium ,,and ,,zinc ,,groups ,the chemistry of the analytical reactions of the alkalies and alkaline earths is extremely simple1--it is essentially the chemistry of well-defined bases and their salts1--and the separations and identifications1 as we have seen1 depend almost entirely on physical differences rather than on chemical contrasts4 ,in the aluminium and zinc groups1 which are precipitated together and which will be discussed together1 the chemistry of the reactions becomes very much more complex4 ,therefore1 we shall not1 as yet1 consider the groups as a whole1 but shall first discuss the important analytical reactions of some compounds of aluminium4 ,aluminium ,hydroxide an ,amphoteric ,hydroxide4--,whereas the hydroxides of the alkali and alkaline earth metals are bases1 pure and simple1 aluminium hydroxide shows the properties both of a base and of an acid2 it is an amphoteric hydroxide1 the term amphoteric indicating the combination of acid with basic properties in any compound4 ,aluminium hydroxide dissolves in acids4 ,from its solution in hydrochloric acid1 an aluminium salt1 aluminium chloride ,al,cl#c1 #f ,h#b,o1 is obtained4 ,it also combines with strong bases1 dissolving for instance in a solution of sodium hydroxide and forming an aluminate1 ,na,al,o#b4 ,the two salts mentioned are typical representatives of the two series of salts1 which aluminium hydroxide is capable of forming4 ,this dual character of the hydroxide raises a number of interesting questions1 which one meets with quite frequently in the study of analytical reactions4 ,one may ask1 first1 how aluminium hydroxide can ionize both as an acid and as a base2 second1 whether any reason can be given1 why it should show the dual nature2 and third1 if it is both base and acid1 why it does not neutralize itself4 ,according to the best knowledge we have on the subject1 the molecule of aluminium hydroxide has the following structure or arrangement of its atoms3 ,al7--,o--,h7#c4 ,it is readily seen that the cleavage of the molecules may produce1 p#agb either aluminium and hydroxide ions1 characteristic ions of a base1 or aluminate#ced and hydrogen ions1 characteristic ions of an acid3 ,al#c #c ,,oh ,al7--#j--;,h7#c ,al,o#b ,h ,h#b,o4 ,the ionization of the hydroxide both as an acid and as a base is1 thus1 quite possible on the basis of the molecular structure assigned to it4 ,in fact1 all of the so-called oxygen acids are considered to be hydroxides--we have sulphuric acid1 ,o#b,s7,,oh7#b1 phosphoric acid1 ,,op7,,oh7#c1 etc41--exactly as the bases1 ,mg7,,oh7#b1 etc41 are hydroxides4 ,that brings us to the second question1 why aluminium hydroxide should show this dual character1 whereas1 for instance1 sodium and magnesium hydroxides1 which have similar structures1 do not show it4 ,the best answer to this question is found when we consider the properties of the elements and their derivatives in connection with their position in the periodic or natural system of elements1 which shows the properties as 7periodic7 functions of the atomic weights4 ,in the second series of the elements1#cee omitting the zero group element neon and taking the elements in the order of increasing atomic weights1 we have sodium 7#bc71 magnesium 7#bd71 aluminium 7#bg71 silicon 7#bh71 phosphorus 7#ca71 sulphur 7#cb71 and chlorine 7#ce4e74 ,one of the properties that are shown to be functions dependent on the atomic weight1 is the property under discussion1 namely the tendency of the 7highest7 hydroxides of the elements to ionize as bases or acids1 respectively4 ,it is clear that the hydroxides of the elements with the lowest atomic weights in the series1 sodium and magnesium1 show the most pronounced tendency to ionize as bases2 the hydroxides of the elements with the highest atomic weights show the most pronounced tendency to ionize as acids--perchloric acid1 7,,ho7,cl,o#c1 and sulphuric acid1 7,,ho7#b,,so#b1 belong to the strongest acids4 ,in accordance with the underlying principle of the periodic system1 the change of p#agc properties1 in going from one extreme to the other1 is a function of the increase in atomic weight and is not sudden but gradual4 ,and so the basic function1 the tendency to produce the hydroxide-ion1 is found to grow weaker as one goes from sodium to magnesium and then to aluminium1 hydroxide2 and the acid function1 the tendency to produce the hydrogen-ion1 grows markedly stronger1 as one goes from phosphoric to sulphuric and perchloric acids4 ,it is not surprising to find the two functions existing together1 but in rather weak form1 in the case of the intermediate hydroxides1 notably in aluminium hydroxide and1 to some degree1 in silicic acid1 the acid character beginning before the basic function has ceased4 ,in accordance with this view1 aluminium hydroxide is found to be only a weak1 slightly ionized base1 and a very weak1 even less readily ionizable acid4 ,in the case of silicic acid1 which is the next hydroxide one meets as one goes toward the acid end of the series1 the conditions are reversed4 ,as the name indicates1 it is primarily an acid1 but it is a very weak one1 and a critical scrutiny of its behavior shows it to have very weak basic functions1 much weaker than those of aluminium hydroxide4 ,the question may1 indeed1 be raised1 whether either the basic or the acid properties really die out altogether in the hydroxides1 from one end of the series to the other4 ,in view of the small tendency toward sudden changes found in nature1 one might suspect traces of basic character to be preserved right through the series to the strongest acids1 like perchloric acid4 ,as a matter of fact1 later 7see ,chapter ,,xv71 we shall be obliged to consider possible basic functions of the strongest oxygen acids1 such as nitric1 perchloric1 permanganic acids1 and one of their most important properties1 their behavior as oxidizing agents1 will be found to be probably intimately associated with this remnant of basic ionization4 ,on the other hand1 fused sodium hydroxide will dissolve sodium with evolution of hydrogen1 sodium oxide1 ,na--,o--,na1 being formed2 and it can readily be shown1#cef that in the fused hydroxide there must be at least a few ions ,na,o1 besides ,,ho1 ,h1 ,o#b1 and ,na4 p#agd ,the position of aluminium in the periodic system adequately accounts1 then1 for the amphoteric character of its hydroxide4#ceg ,common ,occurrence of ,amphoteric ,hydroxides4--,if we consider the question of amphoteric behavior a little longer--its consequences are used extensively in analytical work--we find1 in the periodic system1 two other regular changes concerning acid and basic functions1 only one of which we shall discuss here4#ceh ,while in a series of elements the acid character of the hydroxides increases with the atomic weight1 in a family of elements the reverse relation holds4 ,from nitrogen to bismuth1 in the nitrogen family of the sixth column of the periodic system1 the acid character of the hydroxides grows steadily weaker1 the basic character increases1 and we find1 again1 that the intermediate elements1 notably arsenic and antimony1 produce hydroxides1 which show markedly amphoteric character4 ,if1 in the second series of the periodic group1 one goes back from aluminium to magnesium hydroxide1 in accordance with the first general principle laid down a much stronger base is found2 and if one then goes1 in the magnesium family1 to the hydroxide of the element of next lower atomic weight1 glucinum or beryllium1 one again meets1 in accordance with the second principle laid down1 a weaker basic and more acidic hydroxide than magnesium hydroxide2 in other words1 the basic and acid functions revert closely to those exhibited by aluminium hydroxide4 ,glucinum hydroxide is a pronounced amphoteric hydroxide and resembles aluminium hydroxide so closely that1 in the early history of chemistry1 it was mistaken for the latter4 ,if one goes from glucinum back to lithium1 in the same series of the periodic system1 and from lithium to the element with the next lower atomic weight in the same group1 one comes to hydrogen1 which forms one of the most important and interesting of the p#age amphoteric hydroxides1 water4 ,the ionization of water1 slight as it is1 yields hydrogen-ion and hydroxide-ion1 the ions characteristic of acids and of bases1 and water is placed among the weakest of the acids 7see table1 p4 #ajd7 as well as among the weakest of the bases 7table1 p4 #ajf74 ,we shall return to these relations1 presently1 and shall find that the apparent weakness of water1 as a base and as an acid1 is seemingly very largely due to the fact that water represents only an extremely dilute solution 7see p4 #ff7 of the real hydroxide1 ,,hoh1 or hydrol1 and consists very largely of a compound 7,h#b,o7#b4 ,h#b,o1 or hydrol1 is1 perhaps1 not very much weaker as an acid or as a base1 than is aluminium hydroxide4 ,lower oxides of elements in the higher 7acid-forming7 groups show a less pronounced acid-forming character than the higher oxides1 and a greater tendency to produce bases as well as acids1 and are often amphoteric4 ,chromium hydroxide is of this type4 ,in view of all these facts1 and in view1 also1 of the fact that the majority of the seventy-odd elements cannot lie at the ends of the periodic system but are found in the middle1 it is not surprising to find that pronounced amphoterism is shown by a large number of metal hydroxides2 it is1 perhaps1 the rule rather than the exception4 ,a considerable number of the elements in the middle of the system are rare elements and that is perhaps the chief reason why this relation does not stand out more prominently in the consideration of the common acids and bases4 ,amphoteric ,character of ,hydroxides ,considered in ,analysis4--,the amphoteric character of hydroxides is frequently made use of in analytical work in the separation and identification of various elements and1 when present1 it must always be considered1 in order to escape possible error4 ,the following hydroxides of the common elements show pronounced amphoteric character3 aluminium1 chromic1 zinc1 lead1 stannous1 antimonous hydroxides and arsenious1 platinic1 auric1 antimonic and stannic acids4 ,arsenic acid1 ferric hydroxide and silicic acid show exceedingly slight1 but perceptible1 amphoteric character1 sufficient to affect1 to a certain degree1 their analytical behavior4#cei p#agf ,self-,neutralization of ,amphoteric ,substances4#cfj--,we may turn now to the third question raised in connection with aluminium hydroxide1 to the inquiry 7p4 #aga71 why aluminium hydroxide1 the acid1 does not neutralize aluminium hydroxide1 the base4 ,in fact1 the base must and does form a salt with the acid4 ,but the salt is formed only to a minimal extent1 as the result of the fact that the base is a very weak base1 the acid an exceedingly weak acid4 ,such exceedingly weak bases and acids show little tendency to combine with each other to form salts in the presence of water1 especially if one or both are difficultly soluble in water1 as in the present instance4 ,the behavior of aluminium hydroxide1 in this respect1 is part of a much larger and more general question1 growing out of the fact that water is a very weak acid and base1 as has been seen1 and1 to a greater or lesser extent1 reacts as such with salts1 which are dissolved in it4 ,this action of water plays an important rle in many analytical reactions1 and especially1 also1 in the reactions of aluminium salts4 ,we shall1 first1 discuss this larger question of the action of water1 as an ionogen1 on salts1 and then return 7p4 #ahg7 to the problem of the self-neutralization of an amphoteric hydroxide4 ,,hydrolysis ,,of ,,salts ,ionization of ,water4--,we may first consider1 very briefly1 the evidence that water is ionized even to the extent indicated by the ionization constants given in our tables4 ,it may be said that the purest water ever prepared#cfa shows a minimal conductivity1 from which the concentrations of its hydrogen and hydroxide ions and the value of the ionization constant may be calculated4 ,for the ionization of water we have ,h ,,ho _/ ,nonionized water ,k,ion4 ,as the concentration of pure water1 or of the water in dilute solutions1 may be considered nearly a constant1 we may put ,h ,,ho ,k,h#b,o4 ,this is the relation most commonly1 and most conveniently1 used4 ,it is free from all assumptions as to the molecular weight of the nonionized water1 the calculation of the concentrations p#agg ,h and ,,oh being independent of any such assumption4 ,the value of ,k,h#b,o increases decidedly with an increase in the temperature1#cfb whereas the ionization constant of an ordinary acid1 such as acetic acid1 is affected very little by changes in temperature4 ,this peculiar increase of the ionization of water at higher temperatures is undoubtedly due to the increasing dissociation of the complex water molecules into hydrol molecules 7see p4 #ff71 which1 presumably1 are most easily ionized4 ,now1 the value of the constant ,k,h#b,o1 at any temperature1 may be determined in some half a dozen different and independent ways1 including the conductivity method mentioned1 and one of the most remarkable developments of the theory of ionization is that all of these methods lead to concordant results4#cfc ,aside from considerations based on its ionization1 water may be shown1 by its chemical behavior1 to have the functions of an acid and of a base1 and the conclusions reached are in complete accord with those reached with the aid of the theory of ionization4 ,water is ,an ,acid4--,if the oxide of a metal such as copper1 lead or calcium1 is treated with an acid1 a salt is formed by the combination of the two2 for instance1 we have ,pb,o ,h,cl ,pb7,,oh7,cl1 ,pb7,,oh7,cl ,h,cl ,pb,cl#b ,h#b,o1 ,pb,o #b ,h,cl ,pb,cl#b ,h#b,o1 ,ca,o #b ,h,cl ,ca,cl#b ,h#b,o4 ,water will combine with a number of oxides very much in the same manner and sometimes with such vigor1 that considerable heat is evolved1 as in the slaking of lime 7exp473 ,ca,o ,,hoh ,ca7,,oh7#b4 ,water in this1 and similar actions1 takes the place of and plays the rle of1 an acid1 and the metal hydroxides or bases appear as its salts4#cfd ,it is a very weak acid1 which can easily be driven out of its salts by any stronger acid 7neutralization of bases71 but that does not alter the conclusions reached4 ,considered from the point of view of the theory of ionization1 the relation p#agh would be expressed by saying that in the common bases the positive hydrogen ion of water has been replaced by some other positive or metal ion4 ,the salt of any acid could be defined in exactly the same way4 ,water as a ,base4--,acid oxides1 such as carbon dioxide1 silicon dioxide1 arsenious oxide1 combine more or less readily with bases1 such as sodium hydroxide1 to form salts3 ,,co#b ,na,o,h ,na,h,c,o#c1 ,as#b,o#c #b ,na,o,h #b ,na,as,o#b ,h#b,o4 ,a number of acid oxides combine with water in exactly the same manner1 and sometimes with such tremendous vigor1 that great care must be taken in bringing the two together1 as is the case when sulphur trioxide or phosphorus pentoxide are added to water 7,exp474 ,we have ,p#b,o#e ,,hoh #b ,,hpo#c4 ,it is evident that in such actions water may take the place of1 and play the rle of1 an ordinary base1 forming the acids1 which may well be defined as hydrogen salts4#cfe ,it is true that the basic properties of water are so weak1 that the metal ion of even a weak base1 like ammonium hydroxide1 will replace the hydrogen-ion in its salts1 the acids1 quite readily 7,h,cl ,,nh#d,,oh ,,nh#d;,cl ,h#b,o74 ,but such a weak base1 in turn1 will have to give way1 of course1 to still stronger bases2 for instances1 ,,nh#d;,cl ,na,o,h ,na,cl ,,nh#d,,oh4 ,from the point of view of the theory of ionization1 the hydrogen-ion is positive1 like all the other metals ions whose hydroxides are bases4 ,there should be no difficulty1 therefore1 in considering water to have the chemical properties of a base as well as of an acid4 ,its chemical activities as such1 weak as they may be1 must be satisfied whenever it is present4 ,these activities lead to the hydrolysis or the decomposition of salts by water1 in greater or lesser degree1 whenever water is used as a solvent for salts4 ,action of ,water on a ,salt of a ,strong ,base and a ,strong ,acid4--,if sodium chloride1 a typical salt formed from a strong base and a strong acid1 is dissolved in water1 it is ionized to a considerable extent4 ,considering the solution from a mechanical point of view1 we would expect that the sodium ions1 moving in all directions1 would collide occasionally with hydroxide ions1 which are formed from the water and are present in minute but definite quantity4 ,some of the collisions must result in the formation of sodium hydroxide1 as we have no reason to suppose that the result would differ from that in other cases where positively charged particles meet with negatively charged ones4 ,however1 since sodium hydroxide is an ionogen1 with a very great tendency to ionize1 and since there is present only a minute concentration of the hydroxide-ion1 the p#agi equilibrium conditions will be satisfied when only traces of the nonionized hydroxide are formed4 ,in a similar manner1 we must expect to have traces1 and only traces1 of nondissociated hydrochloric acid formed by the union of chloride ions with some of the hydrogen ions of the water4 ,since hydrogen chloride and sodium hydroxide show practically the same tendency to ionize 7tables1 pp4 #ajd and #ajf71 the two kinds of ions which water forms1 the hydrogen-ion and the hydroxide-ion1 will be used up to a very slight and practically equal extent to form nonionized sodium hydroxide and hydrogen chloride1 but the ions will be immediately regenerated1 and in equal concentrations1 from the nonionized water which is present4 ,all the equilibrium requirements will be satisfied when traces of sodium chloride have been converted into nonionized sodium hydroxide and hydrogen chloride4 ,such a solution1 containing no excess of the hydrogen- or the hydroxide-ion1 would react neutral4 ,the action may be expressed by the equation#cff ,na,cl ,na ,cl ,h#b,o ,,ho ,h ,na ,,ho ,na,o,h ,cl ,h ,h,cl4 ,the decomposition of sodium chloride by water1 which one may predict on the basis of these theoretical considerations1 may be demonstrated1 slight as it is1 by the following experiment4#cfg ,,exp4 ,a pinch of sodium chloride is brought into a platinum crucible1 which is previously heated in a blast lamp to a bright yellow heat 7#aajj72 then #a c4c4 of water is introduced1 drop by drop4 ,a steam cushion is formed at once 7,leidenfrost's phenomenon74 ,after about half of the water has been evaporated 7half a minute71 the water is poured into a solution colored with blue litmus2 it is changed to red by an excess of hydrochloric acid in the water4 ,the crucible is cooled1 and the salt remaining in it is dissolved in a little water and the solution poured into a red litmus solution2 the latter turns blue4 ,the sodium chloride has obviously been partially decomposed1 by the water1 into its base and its acid2 the decomposition is favored by the high temperature and by the fact that the hydrogen chloride p#ahj formed can pass through the steam cushion into the water1 while the sodium hydroxide is left behind4 ,the removal of a product of the decomposition would favor its progress 7see4 p4 #aad74 ,the conclusions concerning salts of the type of sodium chloride may then be summarized in the statement1 that salts formed by the union of a very strong base with an equally strong acid are only very slightly decomposed by water and their solutions show a neutral reaction4 ,the decomposition of a salt by water into its component base and acid is called hydrolysis and the salt is said to be hydrolyzed in the action4 ,action of ,water on the ,salt of a ,strong ,base with a ,weak ,acid4--,the relations are similar in principle1 but quite different in degree and in net result1 when the salt of a very strong base1 combined with a weak acid1 is dissolved in water4 ,potassium cyanide is a typical salt of this kind1 and the study of its hydrolysis will illustrate the behavior of this class of salts4 ,the hydrolysis takes place according to the equations ,,kcn ,k ,,cn ,,hoh ,,ho ,h ,k ,,ho ,,koh ,,cn ,h ,,hcn4 ,when the cyanide is dissolved in water1 we must obtain1 for the same reasons as were developed in the discussion of the hydrolysis of sodium chloride1 a little nonionized potassium hydroxide1 from the union of potassium ions with hydroxide ions1 formed by the water4 ,potassium hydroxide being a strong1 easily ionizable base1 there will be only a slight tendency towards this union4 ,hydrocyanic acid1 on the other hand1 is an exceedingly weak acid4 ,the value of its ionization constant ,k,,hcn ,h ,,cn _/ ,,hcn is only #g;,e#aj1 as compared with a similar ratio approximating #a for potassium hydroxide 7,k ,,ho _/ ,,koh #a2 see the tables1 p4 #ajd and p4 #ajf and see pp4 #ajf-g74 ,the hydrogen-ion1 formed from the water1 must therefore combine with cyanide-ion1 to form nonionized hydrocyanic acid1 much more completely than the hydroxide-ion combines with potassium-ion4 ,with the disappearance of the ions of water1 in this case notably of its hydrogen ions1 more water must ionize to satisfy the ionization constant p#aha for water 7p4 #agf71 and the formation of hydrocyanic acid will continue1 towards the satisfying of its own constant4 ,it is important to note that1 for the reasons given1 the hydrogen-ion of water is used up to a far greater extent than is the hydroxide-ion2 the latter therefore accumulates1 and this accumulation results in the formation of smaller and smaller concentrations of the hydrogen-ion1 by the water4 ,since ,h ,,ho #a4b;,e#ad 7at #be2 p4 #ajd71 as ,,ho grows larger1 ,h must grow proportionally smaller4 ,the suppression of the hydrogen-ion by the accumulation of the hydroxide ion will1 ultimately1 make ,h so small1 that the equilibrium ratio ,h ,,cn _/ ,,hcn will equal the equilibrium constant4 ,since the union of the hydrogen-ion with the cyanide-ion1 to form little ionized hydrocyanic acid1 is the main moving cause for the changes1 the latter will then come to a standstill and equilibrium will be established4 ,the net result of the action of water on potassium cyanide may be said to consist in the formation of practically nonionized hydrocyanic acid and the liberation of 7chiefly7 ionized potassium hydroxide1 until all the equilibrium constants of the system are satisfied4 ,we note that potassium cyanide solution must react strongly alkaline 7exp47 and that a free acid 7e4g4 ,,hcn7 may well exist in the presence of a free base 7e4g4 ,,koh71 provided the acid is present in a nonionized1 and therefore chemically inactive1 condition 7inactive as an acid74 ,ignoring the 7practically7 unimportant formation of small quantities of nonionized potassium hydroxide1 we may summarize the action in a single equation1 which shows the main action3 ,,cn ,,hoh ,,hcn ,,ho4 ,whereas water1 as an acid and as a base1 is so exceedingly weak1 that it can form but traces of its own salts1 sodium hydroxide and hydrochloric acid1 when acting on sodium chloride and competing for the base with such a strong acid as hydrochloric acid and for the acid with such a strong base as sodium hydroxide 7see p4 #agi71 the result1 evidently1 is quite different when water competes for a base with so weak an acid as hydrocyanic acid4 ,in this case1 we note that a considerable quantity of 7ionized7 potassium hydroxide1 the salt of water in its rle of an acid1 is formed as a result of the action of water on potassium cyanide4 p#ahb ,the theory of ionization1 with the aid of the law of chemical equilibrium1 gives us the means for accurately defining the relative concentrations of the products1 in the final condition of equilibrium4#cfh ,for the weak acid1 hydrocyanic acid1 we have the condition of equilibrium ,h ,,cn _/ ,,hcn ,k,,hcn #g;,e#aj4 ,the symbols ,h1 ,,cn and ,,hcn denote the final concentrations for the condition of equilibrium1 indicated in the equations on p4 #ahj2 in such a mixture ,h is not equal to ,,cn1 as it is in pure solutions of hydrocyanic acid in water4 ,,cn1 representing the total concentration of the cyanide-ion1 is very much larger than ,h1 since the salt1 potassium cyanide1 produces the cyanide-ion in large concentrations4 ,for water1 we have ,h ,,ho ,k,,hoh #a4b;,e#ad1 at #be4 ,here1 again1 the symbols represent the final1 total concentrations of the ions in the mixture and ,,ho is much larger than ,h1 since hydroxide-ion is formed in large quantities1 as described above4 ,combining the two equations1 we have3 ,,cn _/ 7,,hcn ,,ho7 ,k,,hcn _/ ,k,,hoh ,k,hydrolysis4 ,the cyanide-ion1 whose concentration is expressed by ,,cn1 is formed practically altogether by the ionization of potassium cyanide1 which is an easily ionizable and almost entirely ionized salt2 the hydroxide-ion1 whose concentration is expressed by ,,ho1 is formed by the ionization of potassium hydroxide1 which is an easily ionizable base1 ionized to practically the same degree as is the potassium cyanide in the solution4 ,if we represent the total concentration of the potassium cyanide1 ionized and nonionized1 at the point of equilibrium1 by ,,kcn and its degree of ionization by #a1 and if we represent1 similarly1 the total concentration of potassium hydroxide by ,,koh and its degree of ionization by #b1 the equilibrium equation may be written3 #a,,kcn _/ 7,,hcn #b,,koh7 ,k,,hcn _/ ,k,,hoh ,k,hydrolysis4 ,since the degrees of ionization of the two strong electrolytes are practically the same1 we have further simply ,,kcn _/ 7,,hcn ,,koh7 ,k,,hcn _/ ,k,,hoh ,k,hydrolysis4 ,the mathematical equations give us a measure of the extent to which water must decompose or hydrolyze the salt in question1 as expressed in the chemical equations 7p4 #ahj74 ,the extent of the hydrolysis1 clearly1 depends on the relative ionization constants of hydrocyanic acid and water1 the two acids competing for the base4 ,from the known values of the constants1 one may calculate that1 at #be1 in a solution of #f4e grams potassium cyanide in a liter 7#j4a molar71 almost #a4c of the cyanide is decomposed into potassium hydroxide and hydrocyanic acid4 ,since every molecule of hydrolyzed salt forms one molecule of p#ahc the hydroxide and one molecule of the acid1 we may put ,,koh ,,hcn x and ,,kcn #j4a x4 ,the ionization constant1 ,k,,hcn #g;,e#aj1 and ,k,,hoh #a4b;,e#ad1 at #be4 ,inserting these values into the equation ,,kcn _/ 7,,hcn ,,koh7 ,k,,hcn _/ ,k,,hoh we have3 7#j4a x7 _/ x#b #g;,e#aj _/ #a4b;,e#ad4 ,here x #j4jjac4 ,this is #a4c of the #j4a mole of cyanide used4 ,one may convince himself1 as follows1 that the constants are satisfied when the decomposition of the cyanide has proceeded to this point3 the degrees of ionization of the potassium cyanide and potassium hydroxide1 #a and #b1 may be taken as #he 7the same as the degree of ionization of the similar electrolyte ,k,cl in #j4a molar solution74 ,then ,,ho #j4he #j4jjac #j4jjaa2 ,,cn #j4he 7#j4a #j4jjac7 #j4jhc2 ,h #a4b;,e#ad _/ ,,ho #a4a;,e#aa4 ,for ,h ,,cn _/ ,,hcn we have then3 7#a4a;,e#aa #j4jhc7 _/ 7#j4jjac7 or #g;,e#aj1 the value for the ionization constant of hydrocyanic acid4 ,it should be noted that1 whereas in pure water at #be ,h ,,ho 7#a4b;,e#ad7 #a4a;,e#g1 in the solution under consideration ,,ho has increased to the value #j4jjaa and ,h is only #a4a;,e#aa4 ,the relation developed for the hydrolysis of potassium cyanide is a general one1 holding for the hydrolysis of salts1 of the type ,me,x1 of a weak acid with a strong base4 ,it may be expressed in general as follows3 for the hydrolysis of a salt according to ,me,x ,,hoh ,me,o,h ,,hx1 where ,,hx is a weak acid and ,,meoh a strong base1 we have3#cfi ,salt _/ 7,acid ,base7 ,k,acid _/ ,k,,hoh4 ,it is clear1 from the equation1 that the weaker the acid of the salt 7measured by the ionization constant ,k,acid1 the numerator on the right71 the more will water1 ceteris paribus1 be able to drive it out of its salt and form its own salt1 the base 7the smaller the numerator on the right1 the larger must be the denominator on the left74 ,the conclusions may be summarized in the statement that the salts of strong bases with weak acids are more or less decomposed by water 7hydrolyzed7 and the resulting solutions must react alkaline4 ,we find1 as a matter of fact1 that aqueous solutions of potassium cyanide1 sodium carbonate1 sodium sulphide1 borax 7see the table1 p4 #ajd71 all react strongly alkaline to litmus 7exp474 ,conversely1 it may be said1 that if the sodium or potassium salt of an acid dissolves in water with a decidedly alkaline reaction1 it is the salt of a weak1 poorly ionized acid4#cgj p#ahd ,action of ,water on a ,salt of a ,strong ,acid with a ,weak ,base4--,exactly similar relations obtain in the case of salts of strong acids with weak bases3#a they are decomposed1 to a greater or less extent1 into the free1 strong1 largely ionized acid and the free1 scarcely ionized weak base1 the decomposition being stopped by the accumulation of the free strong acid 7more exactly1 of the hydrogen-ion74 ,such solutions react strongly acid1 as in the case of the chloride1 nitrate1 sulphate of aluminium1 of iron 7ferric71 of chromium1 and of similar salts of weak bases4 ,for ,me,x ,,hoh ,me,o,h ,,hx1 where ,me,o,h is a weak base and ,,hx a strong acid1 we have as before3#cga ,me _/ 7,h ,me,o,h7 ,salt _/ 7,acid ,base7 ,k,base _/ ,k,,hoh4 ,action of ,water on a ,salt of a ,base and an ,acid1 ,both of which are ,weak4--,we will now turn to the consideration of the action of water on the fourth class of salts1 the salts of a weak base with a weak acid4#cgb ,like all salts1 such a salt1 say ,me,x1 would ionize very readily1 when dissolved in water 7the few exceptions to readily ionizable salts are not under consideration71 and1 in this case1 both the positive and the negative ions would have to combine respectively with the hydroxide and the hydrogen ions of water to form the nonionized weak base and the nonionized weak acid1 and satisfy two very small constants1 ,k,base and ,k,acid3 ,me ,,ho _/ ,me,o,h ,k,base and ,h ,x _/ ,,hx ,k,acid4 ,both the hydrogen and the hydroxide ions of water would disappear1 and in approximately equal quantity1 if the base and acid were approximately equally weak1 and the ions would be regenerated from water with no accumulation of either one to suppress the other1 as in the two previous cases considered4 ,under these circumstances1 the decomposition by water must proceed very much further than in the previous cases4 ,for instance1 in the hydrolysis of potassium cyanide in #j4a molar solution1 at #be1 we find the concentration of the hydrogen-ion ,h reduced#cgc from #a4a;,e#g1 its p#ahe value in pure water1 to #a4a;,e#aa1 as a result of the accumulation of potassium hydroxide 7the hydroxide-ion71 and only this small value for ,h appears in the equation for the formation of the free acid1 ,,hcn 7first equation1 p4 #ahb2 vide the calculation1 p4 #ahc74 ,but1 in the present case1 the factors ,,ho and ,h1 in the equations on p4 #ahd1 maintain practically their original value1 about the same as in pure water1 and the formation of nonionized ,me,o,h and ,,hx must go correspondingly further to satisfy the constants ,k,base and ,k,acid4 ,just how far the action must proceed1 can be formulated with the aid of the theory of ionization and the law of chemical equilibrium1#cgd much in the same way as for the hydrolysis of potassium cyanide4 ,the final equation1 as developed by ,arrhenius1 reads3 ,me ,x _/ 7,,hx ,me,o,h7 #b ,salt#b _/ 7,acid ,base7 7,k,acid ,k,base7 _/ ,k,,hoh ,k1 in which ,k,acid and ,k,base represent the ionization constants of the acid and the base1 as given in the tables 7pp4 #ajd and #ajf71 and is the degree of ionization of the salt4 ,for the cyanide of a base1 which is as weak a base as hydrocyanic acid is an acid1 we find that the decomposition by water1 at #be in a #j4a molar solution1 must comprise #ii4cecge of the salt1 in order to establish equilibrium4 ,in the case of potassium cyanide1 in #j4a molar solution1 only #a4c of the salt is decomposed 7p4 #ahb74 ,now1 if both the free base and the free acid are very difficultly soluble1 then the concentrations ,me,o,h and ,,hx1 respectively1 in the solution cannot go beyond a certain minute limit4 ,in view1#cgf then1 of the very small value1 ,k,base1 of the ratio ,me ,,ho _/ ,me,o,h and the minute value that the second term ,me,o,h has under these conditions1 the first term ,me ,,ho must have a correspondingly smaller value4 ,it is clear1 therefore1 that in such a solution neither the nonionized base1 ,me,o,h1 nor its ion1 ,me1 can exist in more than minute quantities when the equilibrium constants are satisfied4 ,the same conclusion is reached regarding the p#ahf possibility of the existence of the difficultly soluble acid ,,hx and its ion ,x1 in more than minimal quantities4 ,since1 then1 neither the ion ,me nor the ion ,x can be present in more than traces1 their salt1 ,me,x1 which is considered readily ionizable1 also cannot exist in aqueous solutions1 except in traces4 ,the quantitative relations are evident from the equilibrium equation 7p4 #ahe73 ,me ,x _/ 7,,hx ,me,o,h7 #b ,salt#b _/ 7,acid ,base7 7,k,acid ,k,base7 _/ ,k,,hoh ,k4 ,it is evident that the concentration of the salt1 ,salt1 which is capable of existence in aqueous solution1 is1 in the first place1 the smaller the smaller the values for ,k,acid and ,k,base are1 i4e4 the weaker the acid and the base are2 and1 in the second place1 it is the smaller the smaller the values for ,acid and ,base are1 which1 in the present instance1 represent the concentrations of the difficultly soluble acid and base in saturated solution1 i4e4 their solubilities4 ,we reach the conclusion that salts of very weak bases and very weak acids are very considerably decomposed by water1 and1 if both the acid and the base are difficultly soluble in water1 the decomposition is practically complete4 ,conversely1 such a very weak1 difficultly soluble base will not combine with a very weak1 difficultly soluble acid to form a salt in the presence of water4 ,an instance of the first kind is found in the case of aluminium sulphide1 the salt of a very weak1 difficultly soluble base1 aluminium hydroxide1 with a rather little soluble1 weak acid1 hydrogen sulphide 7see table1 p4 #ajd74 ,we find that when a piece of aluminium sulphide1 prepared by dry methods1 is dropped into water 7exp471 a precipitate of aluminium hydroxide is immediately formed and evolution of hydrogen sulphide occurs4 ,we have ,al#b,s#c #b ,al#c #c ,s#b1 #f ,,hoh #f ,,ho #f ,h #b ,al#c #f ,,ho #b ,al7,,oh7#c #c ,s#b #f ,h #c ,h#b,s 4 ,an instance where a very weak insoluble acid will not combine1 appreciably1 with a very weak insoluble base1 is found in the case of aluminium hydroxide4 ,a development of the equilibrium equations for its ionization as a base and its ionization as an acid would show1 that all the constants would be readily satisfied1 when a very minute quantity of dissolved ionized aluminium aluminate is formed4 p#ahg ,self-,neutralization of ,amphoteric ,hydroxides4--,we may consider a saturated solution of aluminium hydroxide1 in contact with the solid hydroxide4 ,for the acid ionization1#cgg ,al7,,oh7#c ,al,o#b ,h ,h#b,o1 we have ,al,o#b ,h _/ ,al7,,oh7#c ,k,acid4 ,similarly1 for the basic ionization1#cgh ,al7,,oh7#c 7,al,o7 ,,ho ,h#b,o1 we have ,al,o ,,ho _/ ,al7,,oh7#c ,k,base4 ,the formation of traces of nonionized 7basic7 aluminium aluminate would satisfy the equilibrium requirements for ,al,o ,al,o#b ,al,o7,al,o#b71 since the aluminate1 like other aluminates1 is presumably readily ionizable in aqueous solutions4 ,aluminium hydroxide1 as a base and as an acid1 would yield in the first moment greater concentrations of the hydroxide and hydrogen ions than would satisfy the equilibrium constant for water 7p4 #agf72 the excess of these ions must combine to form water1 until the product of their concentrations is equal to the ionization constant of water4 ,the neutralization of these first quantities of hydrogen and hydroxide ions would destroy the momentary condition of equilibrium between aluminium hydroxide and its ions and would lead to its further ionization1 both as a base and as an acid1 and to the solution of some aluminium hydroxide 7see the above equilibrium equations74 ,however1 since ,al,o and ,al,o#b remain practically uncombined and therefore accumulate in the solution1 the concentrations of the hydroxide and hydrogen ions formed grow smaller and smaller2 for an increasing excess of the ion ,al,o will allow only smaller and smaller values for ,,ho1 according to the equilibrium equation for ,k,base1 and1 similarly1 an increasing excess of the ion ,al,o#b will permit ,h to reach only smaller and smaller values1 according to the equilibrium equation for ,k,acid4 ,when the values for ,,ho and ,h have in this way become small enough to make ,,ho ,h ,k,,hoh1 equilibrium is reached4 ,it is evident that in such a solution1 in the condition of equilibrium1 ,,ho is not equal to ,al,o1 as it would ordinarily be1 according to the ionization equation ,al7,,oh7#c ,al,o ,,ho ,h#b,o1 but is much smaller4 ,similarly1 ,h is much smaller than ,al,o#b4 ,just how much aluminium aluminate must be formed by a self-neutralization of the amphoteric hydroxide will depend on the values for ,k,base and ,k,acid and on the solubility of aluminium hydroxide 7nonionized ,al7,,oh7#c74 ,the two equilibrium equations may be combined3 ,al,o ,al,o#b ,h ,,ho _/ ,al7,,oh7#cb ,k,base ,k,acid4 p#ahh ,since ,h ,,ho ,k,,hoh1 and since ,al,o and ,al,o#b may be taken to represent each the concentration of the practically completely ionized aluminium aluminate ,al,o7,al,o#b71 we have#cgi ,alum4 ,aluminate#b _/ ,alum4 ,hydroxide#b 7,k,base ,k,acid7 _/ ,k,,hoh1 or ,alum4 ,aluminate _/ ,alum4 ,hydroxide 7,k,base ,k,acid7 _/ ,k,,hoh4 ,it is clear1 that the smaller the ionization constants ,k,base and ,k,acid are1 and the smaller the solubility of nonionized aluminium hydroxide ,alum4 ,hydroxide is1 the smaller must be the concentration of the aluminate formed to satisfy the conditions for equilibrium4 ,aluminium hydroxide is a typical amphoteric hydroxide1 and the relations developed may be applied1 mutatis mutandis1 to the conditions of equilibrium for analogous amphoteric hydroxides1 such as zinc1 lead1 chromic hydroxides1 and so forth4 ,salt formation or self-neutralization will depend1 in every instance1 on the strength of the base and the acid formed1 and on the solubility of the hydroxide4#chj ,with the aid of the preceding considerations the analytical reactions of aluminium1 which are used to separate it from other elements and to identify it1 may be readily understood4 ,they will be discussed in connection with the analysis of the ,aluminium and ,zinc ,groups4 ,the ,analysis of the ,aluminium and ,zinc ,groups4--,the groups of metals which are here called the p#ahi ,aluminium and ,zinc ,groups consist of two groups1 which ordinarily are precipitated together in qualitative analysis1 and which are then separated from each other4 ,we may distinguish the ,aluminium ,group of trivalent metal ions1 including aluminium1 ferric and chromium ions1 and the ,zinc ,group of bivalent metal ions1 including zinc1 nickelous1 cobaltous1 manganous and ferrous ions4 ,of the two groups1 the ions of the second group1 in agreement with their lower valence 7see p4 #agb71 form the stronger bases1 and1 as such1 they are all capable of forming comparatively stable salts even with such very weak acids as hydrogen sulphide and carbonic acid4 ,ammonium sulphide1 added to a solution of a salt of any one of the ions of the zinc group1 precipitates the corresponding sulphide1 sodium or ammonium carbonate precipitates the corresponding carbonate4#cha ,we have1 for instance3 ,fe,cl#b 7,,nh#d7b,s ,fe,s #b ,,nh#d;,cl1 ,fe,cl#b ,na#b;,,co#c ,fe,c,o#c #b ,na,cl4 ,only one member of this group1 zinc1 forms an amphoteric hydroxide and advantage is taken of this in identifying zinc4 ,the members of the aluminium group form hydroxides1 which are much weaker bases than are the hydroxides of the bivalent group just considered4 ,their salts with strong acids are considerably hydrolyzed and react strongly acid1 and their salts with very weak acids1 like carbonic acid and hydrogen sulphide1 are decomposed so readily by water1 that only ferric sulphide is capable of existence in its presence4 ,when the sulphide1 ,al#b,s#c1 prepared by heating aluminium with sulphur1 is added to water1 it is totally decomposed into the hydroxide and hydrogen sulphide 7p4 #ahf72 and if aluminium chloride is treated with ammonium sulphide in aqueous solution1 aluminium hydroxide1 and not its sulphide1 is precipitated4 ,the latter result may be interpreted in two ways1 both of which1 in the ultimate analysis1 mean that hydrogen sulphide is too weak an acid to form a stable sulphide with aluminium hydroxide in the presence of water1 the difficult solubility of aluminium hydroxide and the limited solubility of hydrogen sulphide being favoring factors 7see p4 #ahf74 ,in a solution of aluminium chloride1 the salt of a very weak base with a strong p#aij acid1 more or less of the salt is hydrolyzed1 and we have a condition of equilibrium as expressed in the equation ,al,cl#c #c ,h#b,o ,al7,,oh7#c #c ,h,cl4 ,the addition of ammonium sulphide to such a solution would neutralize the free hydrochloric acid1 and the action would proceed to completion towards the right1 hydrogen sulphide being liberated1 by the action of the acid on the ammonium sulphide4 ,as hydrogen sulphide is too weak an acid to combine1 appreciably1 with aluminium hydroxide1 and as the latter is difficultly soluble1 the hydroxide is precipitated4 ,according to the degree of dilution1 more or less of the hydrogen sulphide also escapes4 ,besides this interpretation of the precipitation of aluminium hydroxide under these conditions1 we may also consider the following3 any aluminium sulphide1 formed the first moment1 would remain largely ionized and would be immediately converted1 by the ions of water1 into aluminium hydroxide and hydrogen sulphide4 ,the net result of the action is the precipitation of aluminium hydroxide and the evolution of hydrogen sulphide3 #b ,al,cl#c #c 7,,nh#d7b,s #f ,h#b,o #b ,al7,,oh7#c #f ,,nh#d;,cl #c ,h#b,s or #b ,al#c #c ,s#b #f ,,hoh #b ,al7,,oh7#c #c ,h#b,s 4 ,a similar result is obtained when the solution of a chromium salt is treated with a solution of ammonium sulphide4 ,only ferric hydroxide is capable of forming a sulphide1 ferric sulphide1 ,fe#b,s#c1 which is precipitated when solutions of ferric salts are treated with ammonium sulphide4#chb ,ammonium sulphide will1 consequently1 precipitate aluminium and chromium hydroxides and ferric1 ferrous1 nickel1 cobalt1 manganese and zinc sulphides1 from a solution of the chlorides of the metals4 ,now1 both the sulphides and the hydroxides of the alkaline earths and alkalies are sufficiently soluble not to be precipitated by ammonium sulphide1 or by a mixture of it with ammonium hydroxide1 if ammonium chloride be added to the mixture to prevent the precipitation of magnesium hydroxide 7see p4 #afh71 which is the least soluble of the hydroxides of the alkaline earth group4 p#aia ,a mixture of ammonium sulphide1 ammonium hydroxide and ammonium chloride will1 therefore1 precipitate the aluminium and zinc groups together1 separating them from the alkaline earth and alkali groups4#chc ,separation of the ,aluminium ,group from the ,zinc ,group by ,means of ,ammonium ,chloride and ,ammonium ,hydroxide4--,the precipitation of the two groups together makes their subsequent separation necessary4 ,some analysts attempt to avoid the extra operations involved1 by making use of the fact that the hydroxides of the bivalent group1 although difficultly soluble1 are1 like magnesium hydroxide1 still sufficiently soluble not to be precipitated by ammonium hydroxide in the presence of sufficient ammonium chloride1 while the hydroxides of the trivalent metals of this group are so insoluble that they may be precipitated quantitatively by such a mixture 7p4 #agj74 ,the trivalent hydroxides may be first precipitated by ammonium hydroxide1 in the presence of ammonium chloride1 and1 subsequently1 the sulphides of the bivalent metals may be precipitated by ammonium sulphide1 the two precipitates being collected separately4 ,the method has the disadvantage that it is not always accurate4 ,the acid character of aluminium and chromium hydroxides 7and even of ferric hydroxide1 see p4 #aie71 as well as of zinc hydroxide1 leads1 to a certain extent1 to the precipitation1 from such alkaline solutions1 of salts of these amphoteric hydroxides with the basic hydroxides of the bivalent group2 the latter are thus liable to be lost in the analysis4 ,it will be recalled1 that the equilibrium conditions in alkaline solutions favor the ionization of amphoteric substances in the acid form 7,part ,,iii71 and alkaline solutions would favor the precipitation of aluminates1 chromites1 etc41 of the ions of the zinc group4 ,methods have1 therefore1 been devised to separate the two groups in neutral1 or very slightly acid1 media1 and they give quantitative separations and are preferable to the method just described4 ,the separation by means of suspended barium carbonate1 in which carbonic acid is liberated and the solution is practically neutral1 will be discussed below on page #aic4 ,a second method1 frequently used in quantitative analysis1 is based on the p#aib decomposition of the acetates of the aluminium group by boiling water1 acetic acid being liberated4#chd ,separation of ,cobalt and ,nickel from the ,other ,members of the ,zinc and ,aluminium ,groups4--,when the aluminium and zinc groups are precipitated together1 by means of a mixture of ammonium sulphide1 hydroxide and chloride1 the precipitate1 obtained from a solution containing1 say1 the chlorides of all the ions of the groups1 would consist of the following compounds3 ,aluminium ,group3 ,fe#b,s#c1 ,al7,,oh7#c1 ,cr7,,oh7#c4 ,zinc ,group3 ,ni,s1 ,co,s1 ,fe,s1 ,mn,s1#che ,zn,s4 ,if such a precipitate is treated1 in the cold1 for a short time with quite dilute 7#a to #a4b molar7 hydrochloric acid1 all of the hydroxides and sulphides dissolve1 excepting the greater part of the nickel and cobalt sulphides1 which dissolve very much more slowly than do the other compounds4 ,advantage is taken of this fact1 to separate these two elements from the remaining members of these groups1 and if the treatment is carried out with care1 the separation is usually satisfactory4 ,in all cases1 however1 since it is a question of delayed solution only1 at least traces1 and sometimes considerably more than traces1 of the sulphides of nickel and cobalt go into solution with the other compounds4 ,no sacrifice of analytical accuracy is involved1 if this possible loss is kept in mind and provision made for the later detection of these small quantities of nickel and cobalt4 ,the question of the slow solution1 or apparent lack of solubility1 of nickel and cobalt sulphides in dilute hydrochloric acid has formed an interesting problem for investigation4 ,while nickel and cobalt sulphides are precipitated by ammonium sulphide1 these sulphides1 in common with those of all the other members of the zinc group1 are not precipitated by hydrogen sulphide in the presence of a small excess of hydrochloric acid4#chf ,we would have p#aic ,ni,cl#b x ,h,cl ,h#b,s ,ni,s 7x #b7 ,h,cl as representing the condition of equilibrium1 if we start with nickel chloride1 hydrochloric acid and hydrogen sulphide2 the amount of sulphide ,ni,s1 formed1 is insufficient to supersaturate the solution and form a precipitate4 ,in reversible reactions the final condition of equilibrium must be independent of the order in which components are mixed 7p4 #ia71 a conclusion which is borne out by experience4 ,one should expect1 then1 that nickel sulphide1 when treated with dilute hydrochloric acid1 would dissolve and give nickel chloride1 hydrogen sulphide and an excess of acid1 and thus produce the same system1 found to be in equilibrium1 when one starts with the chloride1 hydrogen sulphide and hydrochloric acid4 ,as a matter of fact1 the same condition of equilibrium is finally reached1 only it is reached slowly1#chg much more slowly than ordinarily in such cases1 much more slowly1 for instance1 than with ferrous sulphide1 hydrochloric acid and hydrogen sulphide 7exp474 ,by taking advantage of this slow return to equilibrium and by working with the system during the process of slow change 7collecting the undissolved nickel and cobalt sulphides on a filter71 one can separate the sulphides of nickel and cobalt from the other components of the mixed precipitate1 which dissolve much more rapidly4 ,separation of the ,aluminium and ,zinc ,groups by ,means of ,barium ,carbonate4--,the solution1 obtained by treating the mixture of the sulphides and hydroxides of the aluminium and zinc groups with dilute hydrochloric acid 7p4 #aib71 contains aluminium1 chromium1 manganous1 zinc and ferrous chlorides1 all the iron being now present in the ferrous condition because of the reducing action of hydrogen sulphide on the ferric-ion 7,part ,,iii74 ,the chlorides of nickel and cobalt are also present in small quantities 7see above74 ,the further treatment of the solution is directed toward a separation of the bivalent ions of the zinc group from the trivalent ions of the aluminium group1 and the intention is to have all the iron go with the trivalent metals4 ,the ferrous is1 therefore1 oxidized to the ferric-ion4 ,after a part of the solution has been tested to show the presence or absence of ferric salts1 the two groups are separated by means of a suspension1 in water1 of finely p#aid divided barium carbonate4 ,the theory of the separation may be developed as follows3 ,when zinc chloride1 which may be taken as a representative of the bivalent group1 is treated with sodium carbonate1 a difficultly soluble carbonate is precipitated1 since zinc hydroxide1 like the remaining bivalent hydroxides1 is a sufficiently strong base to form a fairly stable carbonate4#chh ,when ferric chloride1 a representative of the trivalent group1 is treated with a solution of sodium carbonate1 ferric hydroxide1 mixed with some basic ferric carbonate#chi ,fe#b7,,oh7#d;,,co#c1 is precipitated and carbon dioxide escapes 7exp474 ,the trivalent hydroxides are too weak bases#cij to form stable salts with so weak an acid as carbonic acid4 #b ,fe,cl#c #c ,na#b;,,co#c #f ,h#b,o #b ,fe7,,oh7#c #c ,h#b;,,co#c #f ,na,cl #c ,h#b;,,co#c #c ,h#b,o #c ,,co#b 4 ,since the bivalent metal ions are precipitated by sodium carbonate as carbonates and the trivalent ones as hydroxides1 the reagent1 obviously1 cannot be used to separate the two groups4 ,but barium carbonate is so little soluble in water that it will not precipitate manganous1 zinc1 nickel1 cobalious and ferrous carbonates#cia from solutions of their chlorides or nitrates4 ,we have1 for instance1 ,zn,cl#b ,ba,c,o#c ,ba,cl#b ,zn,c,o#c4 ,barium carbonate has1 however1 the same effect on ferric chloride 7exp47 and on the other chlorides of the trivalent group1 as has sodium carbonate1 i4e4 it precipitates their hydroxides4 ,by means of barium carbonate p#aie we can1 therefore1 precipitate the hydroxides of the aluminium group without precipitating the ions of the zinc group4 ,the separation is carried out in a1 practically1 neutral medium 7free carbonic acid in excess is evolved2 barium carbonate alone1 when treated with water1 is slightly alkaline7 and thus avoids the error of facilitating the precipitation of the bivalent metals in the shape of salts of the acidic forms of the trivalent metals1 i4e4 as aluminates1 chromites1 and so forth4 ,manganous salts are liable to oxidation to manganic salts1 when exposed to the air1 especially in alkaline1 neutral or slightly acid solutions1 and prolonged exposure of the barium carbonate mixture to the air may result in the precipitation of manganic hydroxide1 ,mn7,,oh7#c1 with the other trivalent hydroxides4 ,provision is made for its detection in the systematic analysis4 ,analysis of the ,aluminium ,group4--,the precipitate of the aluminium group may contain aluminium1 chromium and ferric hydroxides 7possibly traces of manganic hydroxide7 and their basic carbonates4 ,a color test for ferric-ion has already been made 7see p4 #aic7 and chromium 7and manganese7 is readily found and identified by oxidation to the intensely colored salts of chromic 7and manganic7 acid 7,part ,,iii1 q4v474 ,in ascertaining whether aluminium hydroxide is present or not1 advantage is taken of its amphoteric character4 ,chromium hydroxide1 like aluminium hydroxide1 is amphoteric2 but1 in agreement with the greater atomic weight of chromium1 it is an even weaker acid than is aluminium hydroxide4 ,its sodium salt1 sodium chromite1 is completely decomposed by boiling water1 chromium hydroxide being precipitated in a less hydrated1 insoluble form4 ,ferric hydroxide1 whose metal has the highest atomic weight of the three elements under consideration1 has so little acid character1 that it is not perceptibly soluble in solutions of potassium or sodium hydroxide4 7,that it has slight acidic properties is shown by its capacity to form ferrites1 e4g4 ,me7,fe,o#b7b1 which may best be obtained by dry methods1 and of which ferrous ferrite or magnetic iron ore1 ,fe#c,o#d or ,fe7,fe,o#b7b1 is the most important representative47 ,of the three hydroxides1 aluminium hydroxide is1 therefore1 the only one that will dissolve in boiling sodium hydroxide4 ,in this solution we can best identify it1 by converting the aluminate into an aluminium salt1 by means of an excess of acid1 p#aif and by a final precipitation of aluminium hydroxide with ammonium hydroxide4 ,aluminium hydroxide is too weak an acid to form a stable aluminate with so weak a base as ammonium hydroxide1 when the latter is used only in slight excess 7p4 #ahf74 ,if we attempt to prepare ammonium aluminate1 by adding ammonium chloride to a solution of sodium aluminate1 a precipitate of aluminium hydroxide is obtained 7exp474 ,for exact work1 an excess of ammonium hydroxide is to be avoided and its strength as a base should be weakened by the addition of some ammonium chloride or nitrate 7pp4 #aad1 #afi and ,lab4 ,manual1 p4 #i1 #f74 ,we have1 in this instance1 the case of a very weak1 difficultly soluble acid1 aluminium hydroxide1 forming a salt with a weak1 soluble base1 ammonium hydroxide4 ,the conditions determining the solubility of aluminium hydroxide in ammonium hydroxide1 as an aluminate ,,nh#d;,al,o#b1 may be shown as follows3 for the acid ionization of aluminium hydroxide1 ,al7,,oh7#c ,al,o#b ,h ,h#b,o 7p4 #agb72 the solubility-product for a saturated solution is ,al,o#b ,h ,k,ac4,s4,p44 ,further1 from ,h ,,ho ,k,,hoh1 we find ,h ,k,,hoh _/ ,,ho4 ,then ,al,o#b ,,ho ,k,ac4,s4,p4 _/ ,k,,hoh1 which shows that the solubility of aluminium hydroxide1 as aluminate1 is proportional to the concentration ,,ho of the hydroxide-ion in the solution4 ,for ,,nh#d,,oh we have ,,nh#d ,,ho _/ 7,,nh#c ,,nh#d,,oh7 #j4jjj1jah 7p4 #afa71 and consequently1 ,,ho #j4jjj1jah 7,,nh#c ,,nh#d,,oh7 _/ ,,nh#d4 ,then ,,ho is the smaller1 the smaller the excess of ammonium hydroxide used 7which is approximately equal to 7,,nh#c ,,nh#d,,oh77 and the greater the concentration ,,nh#d of the ammonium-ion1 i4e4 of the added ammonium salt4 ,the solubility of ,al7,,oh7#c1 as aluminate1 in ammonium hydroxide and ammonium chloride is1 therefore1 directly proportional to the excess of ammonium hydroxide1 and indirectly proportional to the concentration of the ammonium salt present4#cib ,the ,favorable ,conditions for a ,maximum ,precipitation of an ,amphoteric ,hydroxide4--,the precipitation of aluminium hydroxide depends also on the solubility-product of aluminium hydroxide1 ionized as a base4 ,for ,al7,,ho7#c ,al#c #c ,,ho1 in a saturated solution1 ,al#c ,,ho#c ,k,bas4,s4,p44 ,it is evident1 that an excess of the precipitating hydroxide-ion would be favorable to the precipitation in this form1 and that the reduction of the concentration of the hydroxide-ion1 while acting favorably1 as just shown1 in preventing the solution of the hydroxide as an aluminate1 must be1 to some extent1 detrimental to a maximum precipitation of the hydroxide as a base4 ,one may ask1 therefore1 what the most favorable concentration of the hydroxide-ion must be for a quantitative precipitation of aluminium hydroxide4 ,the problem may be treated as follows3 ,according to the solubility-product relation for the basic ionization1 we have1 in a solution saturated with aluminium hydroxide1 p#aig ,al#c ,k,bas4,s4,p4 ,,ho#c4 ,i ,for the sake of a certain simplicity in the result1 we will1 for the moment1 consider aluminium hydroxide to ionize as an acid according to ,al7,,ho7#c ,al,o#cc #c ,h1 which would resemble the basic ionization4 ,then we would have ,al,o#cc ,h#c ,k,ac4,s4,p41 and1 using the relation ,h ,k,,hoh _/ ,,ho1 we have ,al,o#cc ,,ho#c ,k,ac4,s4,p4 ,k,,hoh#c4 ,,ii ,adding equations ,i and ,,ii we find ,al#c ,al,o#cc ,k,bas4,s4,p4 ,,ho#c ,,ho#c ,k,ac4,s4,p4 ,k,,hoh#c ,,iii ,aluminium hydroxide will be most completely precipitated when ,al#c ,al,o#cc is a minimum1 the values ,al#c and ,al,o#cc measuring the solubility of aluminium as aluminium-ion and as aluminate-ion4 ,if we put ,al#c ,al,o#cc y and ,,ho x1 we can find the value x 7the concentration of the hydroxide-ion7 for which y is a minimum4 ,we have y ,k,bas4,s4,p4 x#c x#c ,k,ac4,s4,p4 ,k,,hoh#c1 and find1 by means of the calculus1#cic that y is a minimum1 when x 7,k,,hoh#c ,k,bas4,s4,p4 _/ ,k,ac4,s4,p47#a_/f4 ,if aluminium hydroxide were as strong an acid as it is a base1 i4e4 if ,k,bas4,s4,p4 ,k,ac4,s4,p41 we would have1 simply1 x ,,ho 77#a4b;,e#ad7c7a_/f 7#a4b;,e#ad7 7at #be71 which is the concentration of the hydroxide-ion in pure water at #be 7p4 #agf74 ,in other words1 a perfectly neutral solution would then give us the conditions for as complete a precipitation as possible4 ,but aluminium hydroxide is a stronger base than acid1 ,k,bas4,s4,p4 ,k,ac4,s4,p41 and consequently we find for x ,,ho 7,k,,hoh#c ,k,bas4,s4,p4 _/ ,k,ac4,s4,p47#a_/f1 a value somewhat greater than the concentration of the hydroxide-ion in pure water1 i4e4 we must use a slightly alkaline medium--which agrees with common practice4 ,in other words1 there is less danger of losing aluminium hydroxide in the form of aluminate1 owing to the weaker acid character of the hydroxide1 than there is of losing it in the form of aluminium-ion4 ,the most favorable degree of alkalinity for the precipitation would depend on the relation of ,k,bas4,s4,p44 and ,k,ac4,s4,p44 ,the exact values for ,k,bas4,s4,p4 and ,k,ac4,s4,p41 the two solubility-product constants1 and for the corresponding ionization constants1 which would show the same ratio1 are still not known4 ,but1 if1 for the sake of an illustration1 we take recourse to assumed values for these constants1 we find that the solubility of aluminium1 as aluminium-ion and as aluminate-ion1 is1 by calculation1 as anticipated1 a minimum for a solution1 which contains the concentration of ,,ho calculated 7for x7 in the manner indicated above4 ,and the further interesting conclusion is reached that this minimum loss of aluminium p#aih hydroxide would occur when ,al#c ,al,o#cc--which would correspond to a saturated solution of aluminium aluminate1 ,al7,al,o#c74 ,when the ionization of aluminium hydroxide1 as an acid1 is considered to take place according to ,al7,,oh7#c ,al,o#b ,h ,h#b,o1 which agrees best with its real behavior 7p4 #agb71 we can find1 similarly1 that ,al#c ,al,o#b is a minimum1 when aluminium hydroxide is precipitated in such a way1 that an excess x of the hydroxide-ion is used1 and x ,,ho 7#c ,k,,hoh ,k,bas4,s4,p4 _/ ,k,ac4,s4,p47#j4be1--where ,k,ac4,s4,p4 represents the solubility-product constant for ,al,o#b ,h4 ,that a minimum loss of aluminium hydroxide would be suffered when the favorable excess of the hydroxide-ion 7x7 is calculated on the basis of the equation as given1 may readily be seen by again assuming definite values for ,k,bas4,s4,p4 and ,k,ac4,s4,p44 ,it also appears that this minimum loss#cid of aluminium includes one-third as many ,al#c ions1 as ,al,o#b ions--a relation corresponding1 again1 to a saturated solution of aluminium aluminate1 ,al7,al,o#b7c4 ,,footnotes3 #ced ,when all three of the hydrogen atoms in the hydroxide are ionized1 an aluminate ion1 ,al,o#cc is formed3 ,al7,,oh7#c ,al,o#cc #c ,h4 ,but1 as in the case of other weak polybasic acids1 a single hydrogen atom is far more readily ionized than are the remaining two 7p4 #ajb71 and the ion ,al7,,oh7#b,o1 which is formed by the primary ionization1 readily loses water and forms the anhydride ion ,al,o#b4 ,the most important aluminates are derivatives of this ion4 #cee ,see the table at the back of ,smith's ,inorganic ,chemistry1 or p4 #adi of ,remsen's ,inorganic ,chemistry4 #cef ,the displacement of hydrogen by a metal1 like sodium1 is the result of the displacement of the hydrogen-ion 7see ,chapters ,,xiv and ,,xv74 ,the hydrogen-ion in fused sodium hydroxide is probably formed chiefly by the secondary ionization of the hydroxide-ion 7,,ho ,h ,o#b7 7see ,chap4 ,,xiii74 ,we cannot have positive ions1 ,na1 with negative ions1 ,o#b1 without having some ions ,na,o4 7,o#b ,na ,na,o71 ,na,o,h1 undoubtedly1 is much too weak an acid to form salts with bases in the presence of water4 ,such salts would be decomposed by water 7see below1 p4 #ahj71 as sodium oxide1 indeed1 is decomposed2 we have ,na--,o--,na ,,hoh #b ,na,o,h 7see ,chapter ,,xiii for a detailed discussion of this action74 ,these relations sufficiently account for the fact that salts of sodium hydroxide1 in which it has the functions of an acid1 are not commonly formed4 7,cf4 ,abegg1 ,anorganische ,chemie1 ,,ii1 7#a7 p4 #bdg47 #ceg ,see ,j4 ,j4 ,thomson1 ,corpuscular ,theory of ,matter1 pp4 #ajc-ada4 #ceh ,see ,mendeleff1 ,principles of ,chemistry1 ,i1 #bb 7#ahia71 in regard to the rle of even and uneven series in the system4 #cei ,in regard to the indications of the amphoteric character of stronger acids1 see ,chapter ,,xv4 #cfj ,an elaborate treatment of this problem is given by ,walker1 ,z4 phys4 ,chem41 #di1 #hb 7#aijd71 #ea1 #gjf 7#aije74 #cfa ,kohlrausch and ,heydweiller1 ,z4 phys4 ,chem41 #ad1 #cag 7#ahid74 #cfb ,see the table1 p4 #ajd4 #cfc ,see p4 #ec and van 't ,hoff's remarks1 ibid4 #cfd ,this suggests a much broader1 natural definition of a base than the conventional one4 ,all salts of very weak acids1 to a certain degree1 which is determined by the weakness of their acids1 do exactly what the ordinary bases do1 e4g4 neutralize acids4 ,metal derivatives of acids weaker than water1 metal amides1 like ,zn7,,nh#b7b1 metal alkyls1 like zinc methyl1 ,zn7,,ch#c7b1 react more vigorously than the hydroxides do1 e4g4 in neutralizing acids1 and water attacks them and acts upon them1 exactly as ordinary acids interact with metal hydroxides4 ,we have1 for instance1 ,zn7,,ch#c7b #b ,,hoh ,zn7,,oh7#b #b ,,ch#d4 #cfe ,see footnote1 p4 #agg4 ,similar considerations apply to the conventional definition of an acid4 #cff ,the symbols in heavy type indicate the chief components of the final system4 ,vide ,smith's ,general ,chemistry for ,colleges and ,inorganic ,chemistry1 for the form of equations used4 #cfg ,emich1 ,ber4 d4 chem4 ,ges4 #dj1 #adhb 7#aija74 #cfh ,arrhenius1 ,z4 phys4 ,chem41 #e1 #af 7#ahij72 ,shields1 ibid41 #ab1 #afg 7#ahic74 #cfi ,see below for the corresponding equation1 developed by ,walker for a salt of a weak base and a strong acid4 #cgj ,potassium sulphate1 ,k#b,,so#d1 reacts faintly alkaline in aqueous solution1 the secondary ionization of sulphuric acid 7table1 p4 #ajd7 being somewhat weaker than the ionization of potassium hydroxide4 ,we have3 ,k#b,,so#d ,,hoh ,,khso#d ,,koh or ,,so#db ,,hoh ,,hso#d ,,ho4 #cga ,walker1 ,z4 phys4 ,chem41 #d1 #cai1 7#ahhi72 ,arrhenius1 loc4 cit42 ,bredig1 ibid41 #ac1 #cba 7#ahid74 #cgb ,arrhenius1 loc4 cit4 #cgc ,see p4 #ahc4 #cgd ,arrhenius developed the relation for aniline acetate1 loc4 cit4 #cge ,putting x ,acid ,base1 we have ,salt 7#j4a x71 and 7#j4a x7#b _/ x#b 7#g;,e#aj7b _/ #a4b;,e#ad4 ,then 7#j4a x7 _/ x #j4jjfd and x 4#jiice1 which is #ii4ce of the total salt used4 ,the degree of ionization1 1 of the salt1 in the extremely dilute solution1 is taken to be #ajj4 #cgf ,see the equations for ,k,base and ,k,acid1 on p4 #ahd1 and their premises4 #cgg ,see p4 #agb4 ,the concentration of water may be considered a constant and is included in ,k,acid 7and ,k,base1 below74 #cgh ,only the primary ionization 7of aluminium hydroxide7 is considered in the text1 because only that is involved1 as a rule1 in the neutralization of very weak bases by very weak acids 7see footnote #b1 p4 #aid74 ,the relations are also simpler and clearer1 if we limit the discussion to the formation of a salt ,al,o7,al,o#b74 #cgi ,see the similar equation1 p4 #ahe4 #chj ,amphoteric substances of a different class are also known1 which have1 at the same time1 moderately strong acid and moderately strong basic functions4 ,glycocoll1 ,h#b,n4,,ch#b;,,cooh1 a derivative of acetic acid and ammonia1 contains an acid group1 the --,,cooh group1 the hydrogen of which is approximately as ionizable as the hydrogen in the corresponding group in acetic acid1 ,,ch#c;,,cooh4 ,the ammonia residue1 ,h#b,n--1 in glycocoll1 forms with water a hydroxide1 corresponding to ammonium hydroxide1 which likewise is approximately as ionizable as is ammonium hydroxide4 ,in the hydroxide of glycocoll we have1 consequently1 both a moderately strong acid1 and a moderately strong basic1 group4 ,in this1 and in similar cases1 salt formation between the acid and the basic groups of the amphoters takes place to as great an extent as if the functions were attributes of distinct compounds4 ,glycocoll in aqueous solution is present1 then1 chiefly in the form of a salt1 for instance1 ,h#c,n4,,ch#b4;,,coo1 corresponding to ammonium acetate1 ,,ch#c;,,coonh#d4 ,for an elaborate discussion of the equilibrium conditions in solutions of amphoteric compounds vide ,walker1 ,z4 phys4 ,chem41 #di and #ea4 #cha ,the carbonates are occasionally partially hydrolyzed to basic carbonates4 #chb ,stokes1 ,j4 ,am4 ,chem4 ,soc41 #bi1 #cjd 7#aijg74 #chc ,a complication1 which leads to the precipitation of alkaline earths1 along with these groups1 as phosphates and similar insoluble salts 7not as hydroxides or sulphides71 when phosphate or certain other acid ions are present1 is treated in ,part ,,iv 7q4v47 under the systematic analysis of the groups4 #chd ,cf4 ,fresenius1 ,quantitative ,analysis4 #che ,ammonium sulphide usually precipitates a pink hydrated sulphide of manganese1 probably ,mn7,,sh77,,oh74 ,under certain conditions of concentration and temperature1 the dark green sulphide ,mn,s is precipitated4 ,in quantitative work the chemist aims to precipitate this green sulphide1 which is more easily collected on a filter4 7,cf4 ,fresenius1 ,quantitative ,analysis47 #chf ,we shall find that this property of the whole zinc group makes it possible to separate the following groups1 the copper and arsenic groups1 from the zinc group 7see p4 #aeh74 ,the theory of the separation will be discussed in detail in ,chapter ,,xi4 #chg ,vide ,noyes1 ,bray and ,spear1 ,j4 ,am4 ,chem4 ,soc41 #cj1 #dhc 7#aijh74 #chh ,see footnote1 p4 #ahi4 #chi ,the comparative stability of this basic salt represents an instance of the different ionizing power1 or basic strength1 of the three hydroxide groups of a trivalent base 7see p4 #ajf74 ,the hydrolysis of ferric chloride seems to involve1 primarily1 only the third or least ionizable of the hydroxide groups of ferric hydroxide1 and the hydrolysis1 except in extreme dilution1 proceeds chiefly according to ,fe#c #c ,cl ,,hoh ,fe7,,oh7#b #c ,cl ,h4 ,vide ,goodwin1 ,z4 phys4 ,chem41 #ba1 #a 7#ahif74 ,in the case of the salt of the much weaker acid1 carbonic acid1 the hydrolysis goes further1 involving two hydroxide groups of ferric hydroxide and1 to some extent1 all three4 #cij ,the extreme insolubility of ,al7,,oh7#c1 ,fe7,,oh7#c and ,cr7,,oh7#c1 together with their weakness as bases1 facilitates their precipitation 7see pp4 #ahe-f74 #cia ,there is a small degree of hydrolysis 7see footnote1 p4 #ahi71 but the hydroxides of the zinc group are not sufficiently insoluble to be precipitated under these conditions4 #cib ,cf4 ,a4 ,a4 ,noyes1 ,bray and ,spear1 ,j4 ,am4 ,chem4 ,soc41 #cj1 #dif 7#aijh74 #cic ,cf4 ,the ,elements of the ,differential and ,integral ,calculus1 based on ,nernst and ,schnflies's ,lehrbuch1 etc41 by ,young and ,linebarger1 pp4 #cfc and #cfd 7#aijj74 #cid ,losses due to the tendency of aluminium hydroxide to assume the colloidal condition 7p4 #acf7 must be guarded against by other precautions 7loc4 cit474 p#aii ,,chapter ,,xi ,,the ,,copper ,,and ,,silver ,,groups4 ,,precipitation ,,with ,,hydrogen ,,sulphide ,the sulphides of the metal ions of the zinc group are readily precipitated by ammonium or sodium sulphide1 but hydrogen sulphide1 in the presence of a small excess of a strong acid1 such as hydrochloric acid1 does not precipitate any of these sulphides 7or any of the sulphides of the aluminium1 the alkaline earth and the alkali groups74 ,under the same conditions the sulphides of the metal ions of the silver group1 ,ag1 ,hg1 ,pb#b1 of the copper group1 ,hg#b1 ,pb#b1 ,bi#c1 ,cu#b1 ,cd#b1 and also of the arsenic group1 ,as#c1 ,as#e1 ,sb#c1 ,sb#e1 ,sn#b1 ,sn#d1 ,pt#b1 ,pt#d1 ,au1 and ,au#c1 are precipitated4 ,advantage is taken of these relations in the following way1 in systematic analysis3 after the separation of the silver group1 by precipitation of the difficultly soluble chlorides1 hydrogen sulphide1 in the presence of an excess of acid1 is used to precipitate the sulphides of the ions of the copper and the arsenic groups1 the two groups being precipitated together4 ,hydrogen sulphide1 under these conditions1 does not precipitate any sulphides of the zinc group or those of any of the remaining groups4 ,hydrogen sulphide is used1 in this way1 as one of the most valuable reagents in analytical work1 enabling the analyst to separate whole groups of metal ions from other groups4 ,there is also no other agent1 equally important1 which is more likely to be used in a wrong way and to lead to error4 ,the ,ionization of ,hydrogen ,sulphide4--,before taking up the theory of the separation of these groups by precipitation with hydrogen sulphide in the presence of a strong acid1 a discussion of some of the characteristics of the reagent will be in place4 ,hydrogen sulphide1 like carbonic acid and other dibasic acids1 ionizes in two stages2 it produces first hydrogen-ion and hydrosulphide-ion1 ,,hs1 and this ion in turn dissociates1 producing hydrogen-ion and sulphide-ion1 ,s#b4 p#bjj ,for the first dissociation1 ,,hsh ,h ,,hs1 we have ,h ,,hs _/ ,h#b,s ,k#a 7,i7 ,the value of the constant#cie for this primary ionization of hydrogen sulphide is #j4ia;,e#g4 ,it is apparent that hydrogen sulphide1 even in the primary ionization1 is a very weak acid and produces a very small concentration of hydrosulphide-ion4 ,in a solution1 saturated at #be1 the total concentration of hydrogen sulphide is approximately #j4a molar1 and the concentration of hydrosulphide-ion1 therefore1 in the absence of any foreign acid1 at most#cif #j4ie;,e#d4 ,the concentration of the dissolved1 nonionized hydrogen sulphide1 ,h#b,s1 is practically a constant1 if solutions saturated with hydrogen sulphide under a given pressure1 say under atmospheric pressure1 are considered4 ,for such solutions1 then1 we may put more simply#cif ,h ,,hs k 7#j4ie;,e#d7b #j4i;,e#h4 7,,ii7 ,the concentration of hydrosulphide-ion is1 therefore1 inversely proportional to the concentration of hydrogen-ion4 ,it is clear that the addition of a strong acid1 readily yielding concentrations of hydrogen-ion very much greater than #j4ie;,e#d 7the value of ,h in a saturated aqueous solution of hydrogen sulphide7 will1 as the result of the greatly increased total hydrogen-ion concentration1 reduce the concentration of hydrosulphide-ion to correspondingly low values4 ,for instance1 the presence of #j4a molar hydrochloric acid will increase the concentration of hydrogen-ion close to a thousandfold and will reduce the concentration of hydrosulphide-ion to #j4i;,e#g4 ,for the secondary ionization 7see p4 #aja7 of hydrogen sulphide1 ,,hs ,h ,s#b1 we have ,h ,s#b _/ ,,hs ,k#b4 7,,iii7 ,the value of this constant has recently been determined#cig and found to be #a4b;,e#ae4 ,recalling the fact that the concentrations ,h and ,,hs of hydrogen-ion and hydrosulphide-ion1 p#bja respectively1 resulting from the primary ionization1 are each#cih #j4ie;,e#d1 we have for the concentration of the sulphide-ion1 in aqueous solution saturated with hydrogen sulphide at atmospheric pressure and #be1 ,s#b #a4b;,e#ae4 ,combining equations 7,,ii7 and 7,,iii71 we have1 further3#cii ,h#b ,s#b k ,k#b k#b #a4a;,e#bc1 7,,iv7 which shows1 directly1 the relation between the concentration of the sulphide-ion and that of the hydrogen-ion1 the relation of primary importance in considering the precipitation of metal sulphides in acid solutions4 ,the concentration of the sulphide-ion is1 thus1 inversely proportional to the square of the concentration of the hydrogen-ion4 ,a thousandfold increase in the concentration of the latter1 which is very nearly the effect produced by the presence of #j4a molar hydrochloric acid 7,h #j4jia71 reduces the concentration of sulphide-ion in the saturated aqueous solution a millionfold3 ,if we call ,s#b;,ac4 the concentration of the sulphide-ion in the acid solution1 ,s#b;,ac4 7#a4a;,e#bc7 _/ 7#j4jia7b #a4c;,e#ba1 whereas1 in the absence of acid1 as found above1 ,s#b #a4b;,e#ae4 ,on the other hand1 the addition of alkali to hydrogen sulphide1 by neutralizing and suppressing the hydrogen-ion1 and by forming the salts ,me,s,h and ,me#b,s1 will very greatly increase the concentrations of the hydrosulphide-ion and of the sulphide-ion4 ,since the constant for the secondary ionization of hydrogen sulphide shows that ,,hs is an exceedingly weak acid1 its salts1 ,me#b,s1 are very largely hydrolyzed1 the constant for water being somewhat greater#djj than its own4 ,according to ,knox1 in a #j4a molar solution of ,na#b,s about #ii of the sulphide is hydrolyzed3 ,na#b,s ,h#b,o ,na,s,h ,na,o,h4 ,in spite of this almost complete hydrolysis1 sufficient sodium sulphide remains in a solution of this p#bjb substance1 to yield a concentration of the sulphide-ion that is far greater than that obtained from a solution of hydrogen sulphide4 ,in a #j4a molar solution of sodium sulphide the concentration of the sulphide-ion is1 approximately1 ,s#b;alk4 #j4i;,e#c1 as compared with ,s#b #a4b;,e#ae in a saturated solution of hydrogen sulphide 7#be1 #gfj mm471 and with #a4c;,e#ba in the same solution in the presence of #j4a molar hydrochloric acid4 ,ammonium sulphide 7,,nh#d7b,s is the salt of an extremely weak acid with a much weaker base than sodium hydroxide1 and it is correspondingly more completely decomposed by water4 ,in a #j4a molar solution of the sulphide 7,,nh#d7b,s1 we find the approximate concentration#dja of the sulphide-ion ,s#b;am4 #a4h;,e#f1 as compared with #j4i;,e#c in a similar solution of ,na#b,s4 ,but the concentration of sulphide-ion is still enormously greater than its concentrations in hydrogen sulphide in the absence and in the presence of acids 7see above74 ,the following table#djb contains a summary of the concentrations of sulphide-ion in the various solutions discussed1 as well as its concentration in the presence of #j4b molar hydrochloric acid4 ,in the separation of the copper and arsenic groups from the zinc and aluminium groups1 a concentration of hydrogen-ion corresponding to the presence of #j4ae to #j4be molar hydrochloric acid is satisfactory for an accurate separation for ordinary purposes4 ,solution4 ,s#b #j4a molar ,na#b,s3 #j4i;,e#c #j4a molar ,na,s,h3 #j4h;,e#e #j4a molar 7,,nh#d7b,s3 #a4h;,e#f #j4a molar 7,,nh#d7,,sh3 #a4d;,e#h #j4a molar ,h#b,s1 sat4 aq4 sol41 #be3 #a4b;,e#ae #j4a molar ,h#b,s1 #j4a molar ,h,cl3#djc #a4c;,e#ba #j4a molar ,h#b,s1 #j4b molar ,h,cl3 #c4e;,e#bb p#bjc ,precipitation of ,sulphides by ,hydrogen ,sulphide4--,although the hydrosulphide-ion most likely takes part in the precipitation of sulphides1 the main effect appears to be due to the sulphide-ion4#djd ,the sulphides seem to be both more stable and less soluble1 than the hydrosulphides4 ,it is very likely that hydrosulphides1 mixed with the sulphides1 are precipitated to a certain extent1 but they are unstable1 lose hydrogen sulphide and go over into sulphides much more readily than hydroxides1 as a rule1 change into oxides4#dje ,the final condition of equilibrium1 if one waited1 in a given case1 until equilibrium was established1 would depend1 under these conditions1 rather on the concentration of the sulphide-ion than on that of the hydrosulphide-ion1 although the latter is present in much greater concentrations than the former4 ,for the sake of simplifying the discussion of the theory of the separation of metal ions by precipitation with hydrogen sulphide1 the discussion will be limited to the consideration of the sulphide-ion as the active precipitating agent4 ,as stated1 this seems to be in accordance with the known facts4 ,the absolute values of the solubilities of the various sulphides1 which are involved in the discussion1 are known1 with any degree of accuracy1 only in a few cases4 ,the aim of the discussion will be1 therefore1 to develop1 rather1 the relations in the values involved1 which may be readily determined4 ,wherever absolute quantities can be given1 they also will be referred to4 ,theory of the ,separation of ,sulphides by ,precipitation with ,hydrogen ,sulphide4 ,i4 ,precipitation of ,ferrous ,sulphide4--,if we prepare a solution of ferrous sulphate1 containing #bg4h grams of the salt1 ,fe,s,o#d1 #g ,h#b,o1 in one liter 7#j4a molar71 we may call ,fe#b the concentration of the ferrous-ion in the solution4 ,if such a solution is saturated with hydrogen sulphide1 under atmospheric pressure1 7exp471 ferrous sulphide is not precipitated4 ,we would decide1 on the basis of the principle of the solubility-product1 that the reason no precipitate of ferrous sulphide is formed is1 that the product of the ion concentrations is smaller than the p#bjd solubility-product constant characteristic of the sulphide 7p4 #aea72 ,fe#b ,s#b ,k,fe,s1 in which ,s#b is the concentration of sulphide-ion in the solution thus saturated with hydrogen sulphide4 ,if an alkali1 sodium or ammonium hydroxide1 is added to the solution1 a heavy precipitate of ferrous sulphide is immediately formed 7exp474 ,the salts of hydrogen sulphide1 like all common salts1 as we have just seen1 are very much more highly ionized than is hydrogen sulphide itself1 and the addition of the alkali has the effect of increasing enormously#djf the concentration of sulphide-ion1 say to x,s#b 7p4 #bjb74 ,under these conditions1 the product of the ion concentrations has evidently grown larger than the constant3 ,fe#b x,s#b ,k,fe,s4 ,,ii4 ,precipitation of ,zinc ,sulphide4--,now1 if a solution of zinc sulphate is prepared so as to contain #bh4g grams of ,zn,s,o#d1 #g ,h#b,o1 per liter1 which would make it of the same molar concentration as the ferrous sulphate solution1 we may1 in view of the fact that analogous salts ionize approximately to the same extent in solutions of the same concentration1 consider the concentration1 ,zn#b1 of zinc-ion to be practically the same as the concentration1 ,fe#b1 of the ferrous-ion in the ferrous sulphate solution4 ,we may put ,zn#b ,fe#b4 ,if the solution of zinc sulphate is saturated with hydrogen sulphide1 under the same conditions as were used with the ferrous salt solution 7exp471 or if we add the zinc sulphate solution to the mixture of ferrous sulphate and hydrogen sulphide 7exp471 we immediately obtain heavy white precipitates of zinc sulphide4 ,we would decide1 therefore1 on the basis of the principle of the solubility-product1 that in this case ,zn#b ,s#b ,k,zn,s4 ,since we have used hydrogen sulphide under practically the same conditions1 we may consider that ,s#b1 in this experiment1#djg is the same as in the p#bje test with ferrous sulphate1 and1 by the conditions of the experiment1 we have also made ,zn#b ,fe#b4 ,the two factors of the product are1 therefore1 the same1 for the first moment1 and we may put ,fe#b ,s#b ,zn#b ,s#b ,p4 ,since ,p is smaller than ,k,fe,s and larger than ,k,zn,s1 it is clear that the solubility-product constant for zinc sulphide must be smaller than that for ferrous sulphide4 ,the solubility-product constants1 for similar salts1 are a measure of their solubilities in water4 ,we may obtain their values by determining the solubilities of salts in pure water1 whenever the solubility is not affected by other chemical changes4 ,in the present instance1 the quantitative measurements1 that have been made in this way1 are open to question1 owing to the considerable hydrolysis which sulphides1 as salts of a very weak acid1 undergo in solutions of such extreme dilution4#djh ,until such relations have been taken into account quantitatively1 it is better to limit ourselves for the present to the more accessible question of relative solubility4 ,it is a comparatively easy matter to determine the relative solubility of zinc and ferrous sulphides4 ,if equal quantities of the equivalent solutions are mixed and a precipitant1 ammonium sulphide1 which would precipitate either sulphide1 if its salt were present alone1 is carefully and gradually added to the mixture1 it will precipitate first the less soluble one 7see p4 #afc72 and that one alone can be present permanently 7i4e4 in equilibrium7 in contact with the solution containing the two salts4 ,as a matter of fact1#dji p#bjf we find that zinc sulphide is precipitated first1 under conditions permitting the precipitation of ferrous sulphide if no zinc sulphate were present1 and the precipitate of zinc sulphide remains unchanged in the presence of a mixture of the composition indicated 7exp474 ,it is clear1 therefore1 that the prediction1 based on the conclusion drawn from the application of the principle of the solubility-product1 is verified by experiment4 ,now1 closer examination of the solution of zinc sulphate1 from which zinc sulphide has been precipitated by the action of hydrogen sulphide1 shows1 after the hydrogen sulphide has precipitated as much sulphide as it can and the solution has been passed through a filter1 that a very considerable proportion of zinc salt is still present in the filtrate1 and we must ask why hydrogen sulphide fails to precipitate the zinc completely4 ,the concentration of the zinc-ion has grown somewhat smaller1 but that is not the cause of the nonprecipitation of zinc sulphide under the new conditions1 since hydrogen sulphide will precipitate the sulphide1 if it is passed into a solution of zinc sulphate which contains even a smaller concentration of zinc-ion than the filtrate1 in which it fails to give any further precipitate4 ,if the filtrate is examined1 it is found to be strongly acid1 since sulphuric acid has been liberated by the action of hydrogen sulphide on zinc sulphate3 ,zn,s,o#d ,h#b,s ,zn,s ,h#b,,so#d4 ,sulphuric acid is a strong acid1 which is very highly ionized1 much more so than the exceedingly weak acid hydrogen sulphide1 and consequently1 as the precipitation of zinc sulphide proceeds1 the concentration of hydrogen-ion in the solution rapidly grows larger and larger4 ,but1 the greater the concentration of the hydrogen-ion1 the smaller is that of the sulphide-ion1 since the product ,h#b ,s#b is a constant equation 7,,iv71 p4 #bja for a solution kept saturated with hydrogen sulphide4 ,the sulphide-ion is reduced in concentration very much more rapidly than is the zinc-ion4#daj ,as ,s#b is a factor in the p#bjg solubility-product of zinc sulphide1 it is clear that the value of this product must grow rapidly smaller during the precipitation of zinc sulphide from the solution1 and that it may well1 eventually1 grow too small to surpass the value of the solubility-product constant ,k,zn,s4 ,precipitation of zinc sulphide will then cease4 ,obviously1 the suppression of the sulphide-ion may be accomplished by the addition of hydrochloric1 sulphuric or any other strong acid to the zinc sulphate solution in the first place1 and then hydrogen sulphide should fail to precipitate any zinc sulphide at all4 ,in fact1 if to #ej c4c4 of the #j4a molar zinc sulphate solution #b c4c4 of hexamolar hydrochloric acid is added1#daa hydrogen sulphide does not precipitate even a trace of zinc sulphide 7exp474 ,we have found1 then1 that #j4a molar zinc sulphate solution1 acidified with a small excess of hydrochloric acid1 fails to produce a precipitate of zinc sulphide1 when it is saturated with hydrogen sulphide4 ,we must conclude that1 under these circumstances1 the product of the ion concentrations is smaller than the solubility-product constant for zinc sulphide3 7,zn#b ,s#b _/ x7 ,k,zn,s1 the new concentration of the sulphide-ion being represented by the symbol ,s#b _/ x4 ,it would follow1 from these considerations1 that the action of hydrochloric or sulphuric acid1 in preventing the precipitation of zinc sulphide1 depends on their producing a sufficiently high concentration of the hydrogen-ion1 to keep the concentration of the sulphide-ion1 in a mixture of zinc sulphate and hydrogen sulphide1 below the point where the solution could become supersaturated with zinc sulphide4 p#bjh ,for exactly similar reasons1 none of the sulphides of the zinc group is precipitated by hydrogen sulphide in 7sufficiently7 acid solutions4 ,it is evident1 further1 that1 if a solution of zinc acetate 7without the addition of any acid7 is substituted for the zinc sulphate solution and is treated with hydrogen sulphide1 an entirely different result1 quantitatively considered1 must be obtained4 ,by the action of hydrogen sulphide on the acetate1 acetic acid is liberated1 according to ,zn7,,ch#c;,,co#b7b ,h#b,s ,zn,s #b ,,ch#c;,,cooh4 ,as a weak acid1 acetic acid produces much less hydrogen-ion than is formed in equivalent solutions of sulphuric acid4 ,consequently1 a much slighter suppression of the sulphide-ion and a much more complete precipitation of zinc sulphide from the acetate1 than from the sulphate solution1 must result4 ,such is the case4 ,zinc sulphide is1 indeed1 precipitated quantitatively by hydrogen sulphide from the acetate solution4 ,this behavior of zinc acetate#dab--;and zinc salts of other weak acids show1 of course1 the same behavior--represents one of the pitfalls1 into which the unwary analytical chemist is liable to fall1 when he uses hydrogen sulphide4 ,the separation of groups by hydrogen sulphide depends1 as stated1 on the fact1 that1 in the presence of a certain concentration of hydrogen-ion1 hydrogen sulphide will not precipitate zinc sulphide and the remaining sulphides of the zinc group4 ,to secure this concentration of hydrogen-ion1 some hydrochloric acid is added to solutions1 from which hydrogen sulphide is expected to precipitate none but sulphides of the copper and arsenic groups--and1 as a rule1 the purpose is accomplished1 as desired4 ,it is evident1 however1 that if a solution contains an acetate1 say sodium acetate1 or the salt of any other weak acid1 e4g4 a borate or a phosphate1 the addition of hydrochloric acid will result1 at least at first1 in the liberation of the weaker acid and will not produce the excess of hydrogen-ion1 required for the analysis4 ,zinc sulphide1 and possibly nickel and cobalt sulphides1#dab may1 under such conditions1 be precipitated with the sulphides of the groups mentioned4 ,unless provision is made1 therefore1 to insure a certain excess of hydrogen-ion 7p4 #bac71 or unless we are on our guard and look for zinc1 nickel and cobalt in p#bji the analysis of the precipitate formed by hydrogen sulphide1#dac serious errors obviously could result4 ,to add an inordinately large excess of hydrochloric acid to mixtures1 in order to avoid this pitfall1 will1 as we shall presently see1 only throw us more certainly into still another error1 to which we are exposed in the use of this important reagent1 hydrogen sulphide4 ,,iii4 ,precipitation of ,cadmium ,sulphide4--,now1 if a #j4a molar solution of cadmium sulphate 7#bb4f grams of the salt1#dad ,cd,s,o#d1 ,h#b,o1 per liter7 is prepared1 equivalent1 in concentration1 to the solutions of ferrous and zinc sulphates used previously1 we may consider that the concentration of cadmium-ion is1 approximately1 the same as the concentrations of the ferrous-ion and zinc-ion in the solutions of their sulphates4 ,if the solution of cadmium sulphate is added to the acidified solution of zinc sulphate1 which was saturated with hydrogen sulphide but from which no zinc sulphide could be precipitated 7exp41 p4 #bjg71 a heavy precipitate of cadmium sulphide is at once obtained 7exp474 ,or1 if #b c4c4 of hexamolar hydrochloric acid is added to #ej c4c4 of the cadmium sulphate solution and the mixture is saturated with hydrogen sulphide1#dae cadmium sulphide is precipitated readily 7exp47 and1 in fact1 quantitatively4 ,we would decide1 on the basis of the principle of the solubility-product1 that1 in this mixture1 precipitation results because 7,cd#b ,s#b _/ x7 ,k,cd,s4 ,by the conditions of the experiment we started with a concentration of the cadmium-ion1 ,cd#b1 equal to the concentration1 ,zn#b1 of the zinc-ion in the zinc sulphate solution1 and with the same concentration1#dae ,s#b _/ x1 of sulphide-ion as was used when hydrogen sulphide failed to precipitate zinc sulphide4 ,the corresponding factors of the products of the ion concentrations are equal1 at the beginning of the two experiments1 and we may put 7,cd#b ,s#b _/ x7 7,zn#b ,s#b _/ x7 ,p4 ,we recall the fact1 that we have already concluded1 on the basis of the principle of the solubility-product1 that 7,zn#b ,s#b _/ x71 or ,p1 is smaller than ,k,zn,s 7p4 #bjg71 and that 7,cd#b ,s#b _/ x71 or ,p1 is greater than ,k,cd,s4 ,p being smaller than ,k,zn,s and larger than ,k,cd,s1 it is clear that p#baj ,k,cd,s is smaller than ,k,zn,s and that cadmium sulphide must be the less soluble of the two sulphides4 ,as a matter of fact1 if ammonium sulphide is carefully added to a mixture of equal quantities of the two salt solutions1 cadmium sulphide is precipitated first1 and when practically all of the cadmium is precipitated1 a final precipitate of white zinc sulphide is obtained 7exp42 see note1 p4 #bje74 ,or1 if zinc sulphide is first precipitated by the addition of a little ammonium sulphide to #be c4c4 of the #j4a molar zinc sulphate solution1 care being taken to have zinc sulphate in excess1 and if #be c4c4 of the #j4a molar cadmium sulphate solution is then added to the mixture1 the white zinc sulphide immediately gives way to the less soluble yellow cadmium sulphide 7exp42 see p4 #afe74 ,cadmium sulphide is thus proved to be the less soluble of the two sulphides1 a result which confirms the prediction made above with the aid of the principle of the solubility-product1 and we may indeed conclude that the solubility-product constant ,k,cd,s of cadmium sulphide must be smaller than the constant ,k,zn,s of zinc sulphide 7see pp4 #afc-afh1 on fractional precipitation74 ,we are1 therefore1 also justified in deciding that ,cd,s may well be precipitated from acidulated solutions by hydrogen sulphide1 when ,zn,s is not thus precipitated1 simply because ,k,cd,s is sufficiently small 7,cd,s is sufficiently insoluble7 to make the product of the ion concentrations ,cd#b ,s#b _/ x1 in spite of the extremely small value of ,s#b _/ x1 greater than the constant ,k,cd,s1 whereas the same small value of ,s#b _/ x makes it impossible for the product ,zn#b ,s#b _/ x to reach the value of the larger constant ,k,zn,s1 required for the precipitation of ,zn,s4 ,since cadmium sulphide may be precipitated quantitatively under the conditions given1 it is also evident that it may be precipitated even when the concentration of the cadmium-ion also has a rather small value4 ,the relations1 in regard to this point1 will be discussed presently4 ,the ,separation of the ,copper and ,arsenic ,groups from the ,zinc ,group4--,ferrous-ion and zinc-ion may be taken as typical representatives of the ions of the zinc group1 whose sulphides are not precipitated by hydrogen sulphide in the presence of a definite concentration of hydrogen-ion1 cadmium-ion as a representative of the copper1 silver and arsenic groups1 whose sulphides are precipitated under the same conditions4 ,the separation of the groups depends1 therefore1 on the different solubilities of the sulphides of these p#baa groups1 the sulphides of the zinc group being the most soluble4 ,since even these sulphides are precipitated quantitatively by ammonium sulphide and are very difficultly soluble1 the separation is a kind of fractional precipitation of difficultly soluble salts1 in which the fractionation is made possible and convenient by the use of an agent1 hydrogen sulphide1 the concentration of whose active precipitating component1 the sulphide-ion1 ,s#b1 is easily regulated and readily made sufficiently small1 not to precipitate even the difficultly soluble sulphides of the iron group4 ,solubilities vary from salt to salt1 and we have already found that1 in the zinc group1 zinc sulphide is less soluble than the sulphide of a second member of the group1 ferrous sulphide1 and that the difference is revealed in a somewhat different behavior of their salts toward hydrogen sulphide1 when the action is studied in some detail4 ,similar differences must be expected to exist among the sulphides of the groups that hydrogen sulphide precipitates even in the presence of an excess of hydrochloric acid4 ,as these differences are the sources of some of the most common and most serious errors which analysts are liable to commit1 the detailed study of the action of hydrogen sulphide must be continued a little further4 ,the ,effect of a ,large ,excess of ,acid4--,the precipitation of cadmium sulphide depends on the relation of the product of the concentrations of the cadmium-ion and the sulphide-ion to the solubility-product constant for cadmium sulphide 7see the equation1 p4 #bji74 ,now1 it is clear that if a larger and larger excess of hydrogen-ion is introduced by the addition of more concentrated hydrochloric acid to the cadmium sulphate solution1 the concentration of sulphide-ion is correspondingly reduced4#daf ,the point might be reached1 where the sulphide-ion factor becomes so small1 that the product of the ion concentrations remains smaller than the value ,k,cd,s1 required for precipitation of cadmium sulphide4 ,in fact1 if a large excess#dag of hydrochloric acid is added to #ej c4c4 p#bab of the #j4a molar solution of cadmium sulphate1 hydrogen sulphide fails to precipitate any of the sulphide 7exp474 ,but1 if a few cubic centimeters of a #j4a molar solution of cupric sulphate 7#be4j grams of ,cu,s,o#d1 #e ,h#b,o1 per liter7 are added to the solution from which hydrogen sulphide fails to precipitate cadmium sulphide1 cupric sulphide is at once precipitated4 ,and1 if #ae c4c4 of concentrated hydrochloric acid are added to #ej c4c4 of the #j4a molar cupric sulphate solution1 there results a mixture corresponding to the cadmium sulphate solution from which hydrogen sulphide fails to precipitate ,cd,s2 we find that hydrogen sulphide will precipitate the sulphide of copper very readily1 even under these adverse conditions 7exp474 ,cupric sulphide must be even less soluble in water than cadmium sulphide1#dah and there is no difficulty in showing that such is the case4 ,if ammonium sulphide1 or hydrogen sulphide1 is gradually introduced into a mixture of #be c4c4 each of the #j4a molar sulphate solutions1 cupric sulphide is precipitated first1 and1 if the precipitate is collected in fractions1 p#bac pure yellow cadmium sulphide is precipitated last4#dai ,or1 if #be c4c4 of #j4a molar cupric sulphate is added to the mixture in which a precipitate of cadmium sulphide displaced the more soluble zinc sulphide 7p4 #baj71 the yellow sulphide will1 in turn1 give way to the less soluble black sulphide of copper 7exp474 ,we find thus that the precipitation of cadmium sulphide1 by hydrogen sulphide in acid solution1 can be prevented by the presence of an excess of hydrochloric acid1 which does not prevent the precipitation of the less soluble cupric sulphide4#dbj ,the fact1 then1 that1 in an analysis of some unknown mixture1 hydrogen sulphide produces a precipitate in acid solution1 must not be considered as evidence that the conditions are such as to insure the precipitation of all the sulphides of the groups1 which we intend to precipitate4 ,to avoid error1 conditions must be such as to insure the complete precipitation of the more soluble as well as the less soluble sulphides4 ,the sulphides of cadmium and lead1 in particular1 and1 to a lesser degree1 the sulphides of antimony and tin1 are most liable to remain unprecipitated and thus escape detection in systematic analysis4 ,this is a matter of special importance1 also1 in detecting traces of the ions of these metals1 especially of lead1 which is a slow cumulative poison1 even when absorbed in minute amounts1 and which analysts must therefore be able to detect1 even in traces1 with absolute certainty4 ,it is clear1 from a consideration of the product of the ion concentrations1 as affecting the precipitation or nonprecipitation of such a sulphide1 that a much smaller excess of acid will prevent the precipitation of the last traces of lead sulphide1 and1 therefore1 of all of it1 if only traces are present1 than will interfere with the precipitation of the sulphide in bulk4 ,the ,desirable ,concentration of ,acid 7of ,hydrogen-ion7 and an ,indicator for ,correct ,acidification4--,summarizing the conclusions reached in regard to the conditions necessary for a successful separation of the copper and arsenic groups1 by means of hydrogen sulphide1 from the zinc and aluminium groups1 we find p#bad that the concentration of the hydrogen-ion1 in the solution to be treated with hydrogen sulphide1 is the most important factor4 ,too great a concentration1 as has just been shown1 will prevent the precipitation of all1 or part1 of the more soluble sulphides of the former groups1 notably of the sulphides of cadmium and lead1 which is a common error in the laboratory4 ,too small a concentration1 which may result when a salt of a weak acid1 such as an acetate1 borate or phosphate is present1 may lead1 as was shown above1 to the precipitation of part of the zinc group1 notably of zinc and possibly of nickel and cobalt1 with the copper and arsenic groups1 and thus lead to other errors4 ,for the ordinary purposes of analysis1 requiring the precipitation of say one milligram of any ion from #ajj c4c4 solution 7one-tenth per cent1 if one gram of substance is used for analysis71 a concentration of hydrogen-ion of #j4a to #j4c gram-ion per liter forms a good basis for work4#dba ,the presence of this concentration of hydrogen-ion1 irrespective of the possible presence of weak organic or inorganic acids1 may be readily insured by a simple test with an appropriate indicator4 ,methyl-violet#dbb is suitable for such a purpose1 because it is sensitive only to the rather high concentrations of hydrogen-ion required3 #j4a c4c4 or two drops of #j4je to #j4a molar hydrochloric acid1 added to an equal volume of a very dilute solution 7#a 3 #ab1ejj7 of the indicator1 changes its color to a pure blue2 #j4b to #j4be molar acid1 used similarly1 turns the indicator to a blue-green tint1 and #j4cc molar acid produces a yellow or yellow-green hue4 ,the blue-green tint1 with which one becomes easily familiar1 and which can1 indeed1 always be prepared for matching tints1 may be used to recognize speedily1 and with sufficient accuracy1 a concentration of the hydrogen-ion of the strength desired1 irrespective of its source4#dbc ,if an analyst aims to find even smaller quantities of a particular metal ion1 e4g4 traces of lead1 the ordinary method of analysis p#bae may be modified1 the source of error in the precipitation of traces of lead sulphide being kept in mind4#dbd ,besides the complications mentioned1 and provided against in the way discussed1 there is still one more complication in the use of hydrogen sulphide3 this is in the matter of the precipitation of arsenic sulphide from solutions containing arsenic in the pentavalent condition4 ,since the interpretation of this complication and the explanation of the methods for avoiding the errors1 which may arise therefrom1 are necessarily intimately connected with the chemical behavior of arsenic acid1 this subject will be considered in the discussion of the arsenic group 7,chapter ,,xiii74 ,,footnotes3 #cie ,auerbach1 ,z4 phys4 ,chem41 #di1 #bbj 7#aijd74 #cif ,see footnote #a1 p4 #bja4 #cig ,knox 7in ,abegg's laboratory71 ,trans4 ,faraday ,soc41 #d1 #dd 7#aijh74 #cih ,the concentration of the hydrogen-ion is really a little greater than that of the hydrosulphide-ion1 as a result of the ionization of the latter1 but the amount of hydrogen-ion formed in this way 7about #a;,e#ae7 is so minute1 compared with that formed by the primary ionization1 that it is negligible4 #cii ,we can obtain the relation1 directly1 from ,h#b,s #b ,h ,s#b and ,h#b ,s#b _/ ,h#b,s ,k #a4a;,e#bb4 ,for a given pressure of the hydrogen sulphide1 ,h#b,s1 expressing its solubility 7about #j4a molar at #be71 is constant1 and therefore ,h#b ,s#b a constant1 as given in equation 7,,iv74 ,putting ,h#b,s #j4a1 we have ,h#b ,s#b #j4a #a4a;,e#bb #a4a;,e#bc4 #djj ,on account of the great mass of water1 we compare 7see equation1 p4 #agf7 ,h ,,ho #a4b;,e#ad 7at #be7 with ,h ,s#b _/ ,,hs #a4b;,e#ae4 #dja ,the calculation was made by the method used by ,knox 7loc4 cit47 for a molar solution4 ,the degree of ionization of the salt was not considered and the correct ionization constant for ammonium hydroxide was used1 #a4h;,e#e in place of #b4c;,e#e4 ,the latter1 evidently1 was used by ,knox as the result of overlooking a correction1 which ,bredig made in his 7,bredig's7 first calculations of the constant2 cf4 ,bredig1 ,z4 phys4 ,chem41 #ac1 #bic1 footnote4 ,the same erroneous constant is found in ,kohlrausch and ,holborn1 loc4 cit41 p4 #aid4 #djb ,for further values and for the method of calculation1 see ,knox1 loc4 cit4 #djc ,s#b #a4a;,e#bc _/ ,h#b1 according to equation 7,,iv71 p4 #bja4 #djd ,knox's work leads to that conclusion4 #dje ,the precipitation of sulphides1 from a solution containing much more of the hydrosulphide-ion than of the sulphide-ion1 is comparable with the precipitation of mercuric oxide1 ,hg,o1 and of silver oxide1 ,ag#b,o1 by sodium or potassium hydroxide4 #djf ,on account of the presence of a small1 unknown amount of sulphuric acid in the original solution1 resulting from the hydrolysis of ferrous sulphate1 the exact value of ,s#b in the first solution cannot be calculated without further examination2 but1 according to the values given in the table on page #bjb1 the value of x1 indicating the growth in the concentration of ,s#b1 is at least #ajab1 if #b equivalents of ,na,o,h1 and #aji1 if #b equivalents of ,,nh#d,,oh are used to convert the #j4a molar hydrogen sulphide into the corresponding sulphide ,me#b,s1 of #j4a molar concentration4 #djg ,s#b is exactly the same in the two products1 when equal volumes of the zinc and ferrous sulphate solutions are mixed and the mixture is saturated with hydrogen sulphide2 zinc sulphide is precipitated4 #djh ,the difference in the values obtained1 when hydrolysis is considered or neglected1 is very considerable4 ,vide ,bodlnder1 on the solubility of calcium carbonate1 ,z4 phys4 ,chem41 #ce1 #bc 7#aijj71 and ,stieglitz1 ,carnegie ,institution ,publications1 ,no4 #ajg1 #bdi 7#aiji74 #dji ,in carrying out this fractional precipitation a very dilute solution of ammonium sulphide is used1 so as to prevent the mechanical enclosure of black ferrous sulphide1 which would discolor the white sulphide4 ,the ammonium sulphide solution should be saturated with hydrogen sulphide1 to prevent the precipitation of green ferrous-ferric oxide by an excess of free ammonia4 ,it is best to prepare a set of the precipitates and to preserve them in well-stoppered vessels1 and not to try to take the time and care necessary to effect a perfect fractionation as a lecture experiment4 ,the presence of the ferrous sulphate1 in the supernatant liquid above the first precipitate of zinc sulphide1 may be readily demonstrated by pouring off some of the solution and adding an excess of ammonium sulphide to it4 ,of course1 it is also perfectly legitimate1 and easier1 to precipitate first zinc sulphide from a pure zinc sulphate solution and then to add ferrous sulphate solution to the mixture and to preserve the mixture4 ,if the zinc sulphide were not the less soluble1 it would be rapidly converted into the black ferrous sulphide4 7,see p4 #afe1 and see below1 pp4 #baj1 #bac1 where similar transformations are carried out as lecture experiments47 #daj ,when #aj of the zinc in a #j4a molar solution has been precipitated1 #j4ja molar sulphuric acid has been formed4 ,for the sake of a rough approximation1 the acid may be considered completely ionized and then ,h #j4jb1 which is #bjj times the value of ,h in a saturated ,h#b,s solution 7p4 #bjj72 if the presence of a little sulphuric acid in the original zinc sulphate solution1 resulting from a slight hydrolysis of the salt1 is ignored1 the concentration of the sulphide-ion is decreased roughly 7#bjj7b or forty thousandfold1 while the concentration of zinc-ion falls #aj4 ,the corrections1 that have been indicated1 would change the quantities involved1 but they would not modify the character of the result4 #daa ,this proportion of acid1 making the concentration of the hydrogen-ion1 approximately1 ,h #j4b1 is used1 not because it represents the minimum concentration of the hydrogen-ion1 which will prevent the precipitation of zinc sulphide in #j4a molar zinc sulphate solution1 but because it represents the practical conditions under which the precipitation of zinc sulphide is avoided1 when the copper and arsenic groups are precipitated in qualitative analysis 7see p4 #bac74 #dab ,nickel and cobalt sulphides are also precipitated by hydrogen sulphide in the presence of free acetic acid1 if sodium or potassium acetate is added1 to suppress the hydrogen-ion of the acetic acid 7p4 #aab74 #dac ,they would be found in the copper group4 #dad ,the sulphate1 of this composition1 is obtained by drying the crystallized sulphate in an air bath at #ajj-aje4 #dae ,cf4 the corresponding experiment with zinc sulphate1 p4 #bjg4 #daf ,s#b k _/ ,h#b4 ,see equation 7,,iv71 p4 #bja4 #dag ,any immediate precipitation of cadmium sulphide will be prevented by the addition of #aj c4c4 of concentrated acid 7sp4 gr4 #a4ai7 to #ej c4c4 of the #j4a molar solution1 and #ae c4c4 will completely prevent any precipitation of the sulphide4 ,of course1 a smaller excess would prevent the precipitation of small quantities of the sulphide 7e4g4 a half milligram of cadmium71 which should easily be found in #ej c4c4 7see p4 #bad74 #dah ,the value of the solubility-product constant for cupric sulphide1 at #be1 was determined by ,knox 7loc4 cit473 ,cu#b ,s#b #a4b;,e#db1 corresponding to a concentration of #a4a;,e#ba of cupric-ion4 ,mercuric sulphide was found even less soluble3 ,hg#b ,s#b #b4h;,e#ed1 and its behavior agrees with such a relation 7,lab4 ,manual1 p4 #ej1 #b74 ,the solubility-product constant for lead sulphide1 which resembles cadmium sulphide in the fact that a large excess of acid prevents its precipitation1 was found to be ,pb#b ,s#b #b4f;,e#ae1 the constant being about #ajbg times as large as the constant for cupric sulphide4 ,this value for the solubility-product constant for lead sulphide must either be considerably larger than the true value or lead must be easily precipitated as a hydrosulphide1 ,pb7,,sh7#b1 since solutions in which the product of the ion concentrations1 ,pb#b ,s#b1 is very much smaller than the constant given1 readily precipitate lead sulphide4 ,thus ,noyes and ,bray ,j4 ,am4 ,chem4 ,soc41 #bi1 #acg 7#aijg7 report it possible to precipitate #a to #b milligrams of lead-ion in #ajj c4c4 of solution 7say ,pb#b #a;,e#d7 with hydrogen sulphide in the presence of #d c4c4 of hydrochloric acid 7sp4 gr4 #a4ab71 for which1 approximately1 ,h #j4be4 ,then 7equation 7,,iv71 p4 #bja7 ,s#b 7#a4a;,e#bc7 _/ 7#j4be7b #a4h;,e#bb1 and ,pb#b ,s#b #a;,e#d #a4h;,e#bb #a4h;,e#bf1 which is a much lower value than that given by ,knox1 and which still is not claimed to represent the limit of insolubility4 ,experiments1 made in this laboratory1 confirm this result and show further1 that lead-ion in a concentration of #a;,e#e is precipitated in the presence of #j4be molar hydrochloric acid 7,h #j4bb74 ,then ,s#b #b4c;,e#bb and ,pb#b ,s#b #b4c;,e#bb #aje #b;,e#bg1 which does not yet express the limit of insolubility4 #dai ,the fractions are not prepared in the lecture1 but the first fraction is kept suspended in part of the solution of the two sulphates and may be kept so for years4 ,the last fraction is kept in a separate container4 #dbj ,a large excess of acid is liable to interfere with the precipitation of the last traces of cupric sulphide and is avoided in exact work4 #dba ,noyes and ,bray use1 approximately1 ,h #j4be ,j4 ,am4 ,chem4 ,soc41 #bi1 #acg 7#aijg74 ,tests in this laboratory showed that #a milligram of cadmium-ion1 or of lead-ion1 in #ajj c4c41 is readily precipitated by hydrogen sulphide in the presence of #j4be molar hydrochloric acid1 7,h #j4bb74 #dbb ,kahlbaum's ,krystallviolett1 7,,ch#c7b,,nc#f;,h#db;,c 3 ,c#f;,h#d,n7,,ch#c7b;,cl1 is referred to4 #dbc ,an indelible ink pencil 7violet7 may1 in most cases1 be used in place of the solution4 ,the details for the application of the indicator are given in the instructions for laboratory practice1 ,lab4 ,manual1 pp4 #ca1 #ajb1 #ajc4 #dbd ,see ,blyth1 ,poisons1 etc41 p4 #fjh 7#ahie71 in regard to the detection of traces of lead4 p#baf ,,chapter ,,xii ,,the ,,copper ,,and ,,silver ,,groups 7,continued74--,,the ,,theory ,,of ,,complex ,,ions ,we will now turn to the consideration of a series of reactions involving the behavior of so-called complex ions1 which are very frequently met with in the various analytical groups and which offer valuable methods of separation and identification of ions4 ,the behavior of silver nitrate solution towards ammonia forms a convenient point of attack in taking up the general subject4 ,action of ,ammonia on ,silver ,nitrate4--,addition of ammonium hydroxide solution to silver nitrate 7exp47 results in the formation of a brown precipitate of silver oxide 7and silver hydroxide74 ,we may consider the supernatant liquid to be saturated with silver hydroxide 7this is in equilibrium with silver oxide71 and for the saturated solution we may put ,ag ,,ho ,k,ag,o,h4 ,if more ammonium hydroxide is added to the mixture1 the precipitate dissolves readily4 ,the excess of ammonium hydroxide must increase the concentration of hydroxide-ion and1 if no other action occurred1 we should1 according to the principle of the solubility-product1 expect that the precipitate would thereby be slightly increased 7p4 #ade71 rather than that it should be dissolved so readily4 ,since solution results even when the value of the one factor1 ,,ho1 of the product is increased1 we must suspect that the value of the other factor1 the concentration ,ag of silver-ion1 is in some way made much smaller by the addition of the excess of ammonium hydroxide4 ,recalling the fact that aluminium hydroxide is soluble in excess of sodium hydroxide1 as the result of its amphoteric character1 a solution of sodium aluminate ,na,al,o#b being obtained1 we might suspect that silver hydroxide also has amphoteric properties1 i4e4 that it might be capable of ionizing into argentate ions1 ,ag,o1 and hydrogen ions1 ,ag,o,h ,ag,o ,h4 ,if such be the case1 the nonionized silver hydroxide is in equilibrium1 not only with the solid phase1 p#bag but also with two sets of ions1 ,ag ,,ho ,ag,o,h ,ag,o,h ,ag,o ,h ,ag,o,h ,ag,o,h 1 and we must have two solubility-product constants1 one corresponding to the basic ionization 7see above7 and the other corresponding to the acid ionization1 and ,ag,o ,h ,k,ag,o,h4 ,if silver hydroxide have acid properties1 the addition of an alkali must suppress the hydrogen-ion and the hydroxide will go into solution as an argentate1 ,me,ag,o4 ,we find1 however1 that sodium or potassium hydroxide1 which would form an argentate very much more readily than ammonium hydroxide1 has no solvent action on silver hydroxide 7exp472 on the contrary1 quantitative experiments show that the alkali makes the hydroxide still less soluble than in pure water--as demanded by the solubility-product for the basic ionization4 ,it is thus evident1 that the solvent action of ammonium hydroxide is not due to its basic functions4 ,we would suspect that we have here an action1 in which ammonia is the active component1 the product of a form of dissociation of ammonium hydroxide1 of which the fixed alkalies are incapable4 ,the ,complex ,silver-,ammonium#dbe-;,ion4--,for a solution of ammonia1 in water1 we have the reversible reactions3 p#bah ,,ho ,h ,,nh#c ,,nh#d ,,ho ,,nh#d,,oh1 and we note that a molecule of ammonia appears to combine first with a hydrogen ion1 to form an ammonium ion1 and this then forms ammonium hydroxide with the hydroxide ion4 ,this suggests that ammonia may have the capacity to combine with positive ions other than hydrogen ion1 and with metal hydroxides other than water4 ,for an analogous reaction of ammonia with silver ion and with silver hydroxide1 we would have3 ,,nh#c ,ag ,,ho 7,,nh#c;,ag7 ,,ho 7,,nh#c;,ag7,,oh4 ,for the condition of equilibrium between ammonia1 the silver-ion and the silver-ammonium-ion1 we would have#dbf3 ,,nh#c ,ag _/ ,,nh#c;,ag ,k4 ,experimental investigations of the quantitative relations1 obtaining in ammoniacal solutions containing silver compounds1 show that no constant value is obtained for the ratio1 as just developed4 ,but the experimental data show equally conclusively1#dbg that a constant is obtained1 when the concentration of the ammonia is raised to the second power1 in the mathematical statement4 ,the significance of this change in the mathematical relation1 it will be recalled 7p4 #id71 is that two molecules of ammonia must combine with one silver ion to form an ion 7,,nh#c7b;,ag1 whereas in the formation of the ammonium ion1 ,,nh#d1 we have a single molecule of ammonia combining with one hydrogen ion4 ,we have then #b ,,nh#c ,ag ,,ho 7,,nh#c7b;,ag ,,ho 7,,nh#c7b;,ag,,oh4 ,we would thus have a silver-ammonium ion1 7,,nh#c7b;,ag1 and its hydroxide1 silver-ammonium hydroxide1 corresponding to the p#bai ammonium ion and its hydroxide1 ammonium hydroxide4 ,the properties of ammoniacal solutions of silver oxide are in entire agreement with this conception4 ,the hydroxide is a stronger base than barium hydroxide4#dbh ,it forms salts1 7,,nh#c7b;,ag,x1 in which silver appears as part of a so-called positive complex ion4 ,the hydroxide1 like ammonium hydroxide1 is unstable and is only known in solution and in the presence of free ammonia1 exactly as is the case for ammonium hydroxide4 ,the mathematical equation expressing the equilibrium conditions for the complex ion1 ,,nh#cb ,ag _/ 7,,nh#c7b;,ag ,k,instability1 gives a definite measure of the stability of this complex ion4 ,it is clear1 that the larger the constant1 the more unstable the complex ion would be1 and so the constant is called the ,instability ,constant#dbi of the complex silver-ammonium-ion4 ,bodlnder found the value of the constant to be #f4h;,e#h at #be4dcj ,according to the composition of the complex ion1 two molecules of ammonia should be required for every molecule of silver nitrate1 to produce a solution containing the nitrate of the complex ion3 ,ag ,,no#c #b ,,nh#c 7,,nh#c7b;,ag ,,no#c4 ,as a matter of fact1 #bj c4c4 of a molar solution of ammonium hydroxide 7 #bjj c4c4 of a #j4a molar solution7 must be added to #ajj c4c4 of a #j4a molar solution of silver nitrate1 to convert the silver nitrate into the salt of the complex silver-ammonium-ion4 ,if the ammonium hydroxide solution is allowed to flow slowly1 from a pipette1 into the silver nitrate solution1 we find that the last trace of the precipitated silver hydroxide redissolves just as the last drop or two of the #bj c4c4 is added to the mixture 7exp474 ,working more exactly1 ,reychler#dca found that the addition of ammonia to a silver nitrate solution1 in the proportion of two molecules of the former to one of the nitrate1 does not change the freezing-point of the solution1 and therefore p#bbj does not increase the total number of molecules in the solution4 ,this result agrees with the conception that two molecules of ammonia combine with one silver ion to form a complex ion4 ,application in ,analysis4--,turning now to the consideration of the bearing of these relations on the detection of silver-ion in analysis1 we may conclude1 in the first place1 from the value of the constant as given1 that only a small proportion of the total silver in such ammoniacal solutions is present in the form of silver-ion2 but1 in the second place1 there is1 at least1 a portion of the silver present in the form of its ion--it is not entirely suppressed2 and1 in the third place1 it is clear1 from the form of the equilibrium equation1 that any excess of ammonia must very rapidly reduce the concentration of silver-ion in such solutions4 ,the bearing of these relations1 which1 it will be noted1 concern concentrations of silver-ion1 can best be seen by working with solutions of definite concentrations4 ,if the solution we have just prepared is diluted with water to #bjj c4c41 a #j4je molar solution of 7,,nh#c7b;,ag,,no#c is formed4 ,in such a solution1 the concentration1 ,ag1 of the silver-ion is only #j4jjji1dcb whereas in #j4je molar silver nitrate solution it is #j4jdce4 ,it is clear that the reactions of the silver-ion will not be observed as readily in such an ammoniacal solution as in a solution of silver nitrate1 which contains the same concentration of total silver4 ,that such is the case1 may be readily demonstrated as follows3 the addition of #a c4c4 of molar sodium bromate to #aj c4c4 of #j4je molar silver nitrate immediately forms a heavy precipitate of the moderately difficultly soluble bromate1 ,ag,br,o#c1 while the same addition to #aj c4c4 of the #j4je molar silver-ammonium nitrate solution produces no precipitate whatever 7exp474 p#bba ,a liter of water dissolves #j4jbe mole 7#f grams7 of silver bromate#dcc at #ah4 ,if the same degree of ionization be assumed for it as for a #j4jbe molar solution of the analogous salt1 silver nitrate1 ,ag,n,o#c1 #ij of the silver bromate in the saturated solution is ionized4 ,the solubility-product constant then is ,ag ,br,o#c 7#j4jbe #j4i7b #j4jjje4 ,when #a c4c4 of molar sodium bromate is added to #aj c4c4 of #j4je molar silver nitrate1 each salt is ionized #hj in the mixture1 and ,ag #j4je #j4h #aj _/ #aa #j4jcg and ,br,o#c 7#a #a _/ #aa7 #j4h #j4jgb4 ,then the product of the ion concentrations1 ,ag ,br,o#c #j4jcg #j4jgb #j4jjbg1 is considerably larger than the constant #j4jjje and precipitation follows4 ,but1 when #a c4c4 of molar sodium bromate is added to #aj c4c4 of a #j4je molar silver-ammonium nitrate solution1 the concentration of silver-ion#dcd is #j4jjjhe and the product of the ion concentrations1 ,ag ,br,o#c #j4jjjhe #j4jgb #f;,e#e1 is smaller than the constant2 the solution will not be saturated with silver bromate and no precipitate is formed4 ,on the other hand1 if #a c4c4 of a #j4a molar solution of sodium chloride is added to #aj c4c4 of #j4je molar silver-ammonium nitrate solution1 a very decided precipitate of silver chloride is formed 7exp474 ,the difference in the action of the sodium bromate and the chloride lies in the fact that silver chloride is #bejj times as insoluble as is silver bromate1 and the chloride may be precipitated from solutions containing a very much smaller concentration of the silver-ion than is required for the precipitation of silver bromate4 ,the quantitative relations for the chloride are as follows3 a liter of water dissolves #j4jjb gram1 or #a4d;,e#e mole1 of silver chloride at #be1dce and the solubility-product constant at #be is ,ag ,cl 7#a4d;,e#e7b #b;,e#aj4 ,now1 if #a c4c4 of #j4a molar sodium chloride is added to #aj c4c4 of #j4je molar silver-ammonium nitrate1 we have1#dcf for the first moment1 ,ag #h4i;,e#d and p#bbb ,cl #j4jjh1 and ,ag ,cl #h4i;,e#d #j4jjh #g;,e#f1 which is much larger than the solubility-product constant1 and precipitation must take place4 ,the precipitate will be quite a heavy one3 as silver-ion is removed from solution1 the complex ion must decompose and furnish a new supply of silver-ion1 and precipitation must continue until the excess of ammonia1 which is liberated by the decomposition of the complex ion 7,ag7,,nh#c7b ,cl ,ag,cl #b ,,nh#c71 suppresses the silver-ion sufficiently to satisfy1 with the diminished concentration of chloride-ion1 the solubility-product constant of silver chloride4 ,it is clear that1 while the reactions of silver-ion are not obtained as readily in the ammoniacal solution as in an equivalent solution of silver nitrate 7bromate experiment71 nevertheless more sensitive tests show that a small portion of the silver still is present as silver-ion in the ammoniacal solution 7chloride experiment74 ,this brings us to our third point1 the influence of an excess of ammonia on the concentration of silver-ion and on its reactions4 ,it is evident1 from the form of the equilibrium equation 7p4 #bai71 that any excess of ammonia must very rapidly reduce the concentration of silver-ion4 ,we may ask what excess will be required to prevent the precipitation of silver chloride in the experiment just tried4 ,the question may be answered as follows3 ,the concentration of chloride-ion1 when #a c4c4 of #j4a molar sodium chloride is added to #aj c4c4 of #j4je molar ,ag7,,nh#c7b,,no#c1 no precipitate being formed1 will be #j4a 7#a _/ #aa7 #j4hg1 the solution being diluted #a to #aa and the percentage of ionization of a salt ,me,x being approximately #hg in #j4je to #j4jf molar concentration4 ,for a solution containing this concentration of chloride-ion1 the concentration ,ag of silver-ion1 which may just be present without leading to the precipitation of silver chloride 7i4e4 for the saturated solution7 is1 according to the principle of the solubility-product1 ,ag ,k,s4,p4 _/ ,cl 7#b;,e#aj7 _/ 7#j4a #j4hg #a _/ #aa74 ,further1 in the presence of an excess of ammonia1 practically all of the silver is present in the complex form1 and1 ,ag7,,nh#c7b #j4je #j4hg #aj _/ #aa the #j4je molar solution being diluted #aj parts to #aa and the salt being #hg ionized4 ,if we call x the concentration of free ammonia required to reduce the concentration of silver-ion to the small value indicated1 we may put ,,nh#cb ,ag _/ ,ag7,,nh#c7b x#b #b;,e#aj _/ 7#j4a #j4hg #a _/ #aa7 _/ 7#j4je #j4hg #aj _/ #aa7 #f4h;,e#h4 ,solving for x1 we obtain x ,,nh#c #j4cc4 ,the concentration of free ammonia1 necessary to prevent precipitation of silver chloride in this system1 is then p#bbc #j4cc1 instead of #j4jjah1 present in the original solution4 ,now1 #aa c4c4 of #j4cc molar ammonia is equal to #aa #j4cc _/ #f1 or #j4fa c4c4 hexamolar ammonia4#dcg ,calculations1 based on the solubility-product constant of silver chloride and on the instability constant of silver-ammonium-ion1 lead1 thus1 to the conclusion that an excess of #j4fa c4c4 of hexamolar ammonia is required1 in #aj c4c4 of #j4je molar ,ag7,,nh#c7b,,no#c1 to prevent the precipitation of silver chloride by #a c4c4 of #j4a molar sodium chloride4 ,conversely1 this excess of ammonia will be required to redissolve the precipitate of silver chloride1 formed when #a c4c4 of #j4a molar sodium chloride solution is added to #aj c4c4 of #j4je molar ,ag7,,nh#c7b,,no#c4 ,the following experiment shows that such is the case4 ,,exp4 #a c4c4 of #j4a molar sodium chloride is added to #aj c4c4 of #j4je molar silver-ammonium nitrate1 prepared as described on p4 #bbj2 hexamolar ammonia is slowly added to the mixture from a #a c4c4 pipette1 graduated in twentieths of a cubic centimeter4 ,the precipitate will be seen to be just about completely dissolved when #j4f to #j4fe c4c4 of the ammonia solution has been used4 ,we find1 in this way1 that the equilibrium equation for the instability constant of the complex silver-ammonium-ion1 together with the principle of the solubility-product1 allows a quantitative interpretation of the problem of the behavior of ammoniacal silver solutions1 as far as the detection of silver by the precipitation of its salts is concerned4 ,if a still larger excess of ammonia is used 7exp471 even the addition of a #aj solution of sodium chloride fails to precipitate the chloride1 and1 vice versa1 ammonia in excess will readily redissolve a heavy precipitate of silver chloride 7exp474 ,advantage is taken of this fact in the separation and identification of silver-ion 7,laboratory ,manual1 q4 v474 ,it is interesting to note that the addition of potassium bromide1 iodide or sulphide to the ammoniacal solution1 in which sodium chloride fails to precipitate any silver chloride1 will still precipitate silver bromide1 iodide or sulphide readily 7exp474 ,judged by the line of argument used above1 in contrasting the behavior of silver bromate and silver chloride1 these silver salts p#bbd must be still less soluble than the chloride4 ,experiment proves1 that such is1 indeed1 the case4#dch ,silver iodide is so insoluble1 that ammonia#dci may be used to separate it1 with a considerable degree of accuracy1 from silver chloride1 and this separation forms the basis of a method to detect chloride-ion in the presence of an iodide4 ,if a solution with a limited concentration of ammonia is used1 the method may be extended also to the separation of chlorides from bromides 7see ,chap4 ,,xvi74#ddj ,complex ,metal-,ammonium ,ions of ,copper1 ,cadmium1 etc4--,quite a number of metal ions are capable of forming more or less stable complex ions with ammonia4 ,for analytical purposes1 the most interesting of such complex ions1 aside from the silver-ammonium-ion1 are those formed by cupric1 cadmium1 zinc and nickel ions1 the most important of which represent bivalent complex ions of the composition#dda ,me7,,nh#c7db4 ,the following instability constants have been determined3#ddb ,at #ba1 ,cd#b ,,nh#cd _/ ,cd7,,nh#c7db #a;,e#g ,zn#b ,,nh#cd _/ ,zn7,,nh#c7db #b4f;,e#aj4 ,cupri-ammonium-ion is far more intensely blue than cupric-ion and its color is used as one of the tests to identify copper in its salts4 ,nickel-ammonium-ion is also blue1 a much paler blue1 and its color must not be mistaken as indicating the presence of a dilute solution of cupric-ammonium-ion4 ,the same kind of relations obtain for these complex ions as for silver-ammonium-ion4 ,for instance1 a salt like cupric phosphate1 which is readily precipitated from cupric sulphate solutions1 is not precipitated from the ammoniacal solutions containing an excess of ammonia 7exp471 while the very much less soluble#ddc cupric sulphide is readily precipitated even from the ammoniacal solutions 7exp474 ,it may p#bbe easily be shown1 in the usual way1#ddd that the sulphide of copper is very much less soluble than its phosphate 7exp474 ,the ,complex ,cyanide ,ions4--,metal ions are capable of forming complex ions1 of importance in analytical work1 with a number of components other than ammonia4 ,among the most important of these are the complex ions formed with cyanide-ion4 ,the theory of the complex cyanide ions is entirely analogous to that of the complex metal-ammonium ions1 but there is a difference in stability that makes their special consideration desirable1 both for practical and for theoretical purposes4 ,the complex ions of silver-ion and cyanide-ion will be discussed first4 ,the ,argenticyanide-,ion4--,when potassium cyanide is added to a solution of silver nitrate1 a very insoluble precipitate of silver cyanide is obtained1 but an excess of potassium cyanide readily redissolves the precipitate 7exp474 ,since solution is effected in spite of the presence of an excess of the precipitating cyanide-ion1 one is led to suspect that the other ion1 the silver-ion1 which is needed to form the precipitate1 is suppressed by entering into some kind of complex with the excess of cyanide4 ,as a matter of fact1 the solution contains a salt1 potassium argenticyanide ,k,ag7,,cn7#b1 in which the silver forms a part of a negative argenticyanide-ion 7,ag7,,cn7#b74dde ,if a current of electricity is passed through such a solution1 the silver 7all but traces71 together with the cyanide groups1 moves towards the positive electrode4#ddf ,the complex has been formed1 then1 by the combination of a positive silver-ion with two negative cyanide ions1#ddg which produce a univalent negative argenticyanide-ion1 ,ag7,,cn7#b4 ,recalling the fact that the complex silver-ammonium-ion is not perfectly stable1 one might suspect that the complex cyanide-ion1 in turn1 is not absolutely stable1 and that the action1 by which it is formed1 is balanced1 when equilibrium is reached1 by a reverse action of decomposition4 ,we would have1 then1 p#bbf ,k ,ag #b 7,,cn7 ,k ,ag7,,cn7#b or1 more simply1 ,ag #b7;,,cn7 ,ag7,,cn7#b4 ,for the condition of equilibrium between the complex and its components1 the relation ,ag ,,cn#b _/ ,ag7,,cn7#b ,k,instability would hold4 ,bodlaender#ddh determined the value of this constant by measuring the concentrations of the three components under varying conditions4 ,the value found is #a;,e#ba4 ,the value of the instability constant for ,ag7,,nh#c7b1 of analogous composition1 is #f4h;,e#h1 a very much larger value than the constant of the ,ag7,,cn7#b complex4 ,the latter is1 therefore1 by far the more stable4 ,it must1 consequently1 be much more difficult to obtain reactions1 such as precipitations1 of silver-ion in cyanide than in ammoniacal solutions4 ,in fact1 it is impossible to precipitate silver chloride by the addition of sodium chloride to ,k,ag7,,cn7#b solution 7exp474#ddi ,silver sulphide was found to be a much less p#bbg soluble salt than the chloride 7p4 #bbd71 and ammonium or sodium sulphide solution1 when added to the cyanide solution1 readily precipitates silver sulphide 7exp474 7,the sulphide is capable of existence in the solid phase1 therefore1 under these conditions47 ,in view of the extremely small concentrations of silver-ion in the cyanide solution1 we have here a striking illustration of the extreme insolubility of the sulphide4 ,according to the equilibrium equation given above1 the larger the excess of cyanide-ion in the solution1 the smaller must be the concentration of silver-ion which is capable of existence in its presence4 ,in agreement with this conclusion1 we find that the addition of an excess of potassium cyanide readily redissolves the precipitated silver sulphide 7exp474#dej ,in other words1 even the minute concentration of silver-ion1 that must be present in the supernatant liquid above a precipitate of silver sulphide 7,ag#b ,s#b ,k,sol4 ,prod41 for a saturated liquid71 cannot be permanently present with an excess of potassium cyanide4 ,consequently1 the solid phase is incapable of existence in the system4 ,the equilibrium equations give us1 thus1 a comprehensive basis for the interpretation of the behavior of cyanide solutions containing silver4 ,first1 in accordance with the small value of the constant1 we find it very much more difficult to obtain precipitates of silver salts in cyanide1 than1 say1 in ammoniacal solutions2 secondly1 in accordance with the fact that a very small1 but definite1 concentration of the silver-ion may still persist in the p#bbh system1 we find it possible1 in the absence of an excess of cyanide1 to precipitate such an extremely insoluble silver salt as silver sulphide represents2 and finally1 in accordance with the form and constant of our equation1 we find it possible1 by using an excess of potassium cyanide1 to suppress the silver-ion to the point where even this extremely insoluble salt can no longer exist4#dea ,cuprocyanide and ,cadmicyanide ,ions4--,very many of the metal ions are capable of forming complexes with cyanide-ion1 of greater or smaller degrees of stability1 and1 as is the case for the complex ions formed by metal ions with ammonia1 a metal ion is frequently able to form more than one complex with cyanide-ion4#deb ,a number of these complex cyanide ions are of particular interest in qualitative analysis4 ,for instance1 we make use of the difference in the stability of the cuprocyanide and the cadmicyanide ions as offering us the most convenient method of recognizing cadmium in the presence of copper4 ,excepting for the sulphide and the oxide1 cadmium does not form salts and compounds of characteristic colors1 and1 except in color1 the salts resemble the corresponding copper salts very much in their physical and chemical behavior4 ,copper and cadmium consequently show the same group reactions in systematic analysis4 ,the more intense colors of the copper compounds--the black sulphide1 the intensely blue cupric-ammonium-ion--mask the cadmium reactions4 ,but cupric-ion may be converted1 by potassium cyanide1 into a complex ion of extreme stability1 from the solutions of which hydrogen sulphide and alkali sulphides fail to precipitate any sulphide of copper1 while cadmium sulphide may be precipitated from the solutions of the much less stable complex cadmicyanide-ion4 ,when potassium cyanide is added to the deep blue ammoniacal solution of cupric-ammonium sulphate ,cu7,,nh#c7d,,so#d1 the cupric-ion is reduced#dec p#bbi to cuprous-ion1 and the latter is converted1 by an excess of cyanide1 into the extremely stable complex ion ,cu7,,cn7#cb and its salt1 potassium cuprocyanide ,k#b;,cu7,,cn7#c4 ,the instability constant of the complex ion is3 ,cu ,,cn#c _/ ,cu7,,cn7#cb #j4e;,e#bg1 and the concentration of cuprous-ion1 in a #j4a molar solution1 is approximately#ded #c4g;,e#h4 ,without an excess of cyanide1 traces of cuprous sulphide may still be precipitated1 but a few drops excess will prevent the precipitation entirely4#dee ,with an excess of potassium cyanide1 cadmium forms the salt ,k#b;,cd7,,cn7#d1 yielding the ion ,cd7,,cn7#db4 ,the instability constant#def of the complex ion is ,cd#b ,,cn#d _/ ,cd7,,cn7#db #a4d;,e#ag4 ,the concentration of cadmium-ion1 in a #j4a molar solution of the salt1 is then approximately#deg #h;,e#e4 ,if potassium cyanide is added to an ammoniacal solution1 containing both cadmium and copper1 until the color of the solution is just discharged1 and if two or three drops excess of the cyanide is then used1 the addition of ammonium sulphide will precipitate pure cadmium sulphide 7exp471 while ammonium sulphide1 added to a portion of the original ammoniacal solution1 will precipitate a dark mixture of cupric and cadmium sulphide 7exp471 in which the yellow color of cadmium sulphide is masked by the black precipitate of cupric sulphide4 ,cobalticyanide and ,nickelocyanide ,ions4--,in much the same way1 in the identification of nickel in the presence of cobalt1 advantage may be taken of the fact that cobalt forms an extremely stable cobalticyanide#deh ion1 ,co7,,cn7#fc1 which does not permit of the precipitation of cobaltic hydroxide1 whereas nickel does not form such an ion1 but only forms a not very stable nickelocyanide ion1 ,ni7,,cn7#db1 which is readily decomposed by bromine and alkali1 nickelic hydroxide being precipitated4 p#bcj ,the following are the chief actions involved in the precipitation of the latter3#dei ,ni7,,cn7#db ,ni#b #d ,,cn #b ,ni#b ,br#b #b ,ni#c #b ,br ,ni#c #c ,,ho ,ni7,,oh7#c ,applications and ,precautions in ,analysis4--,the complex cyanide ions thus give us a convenient means of interfering with the precipitation of certain metal ions1 and of enabling us1 thereby1 to detect other1 closely related1 ions in their presence4 ,at the same time1 we must be careful to identify the ions1 which we wish to suppress1 before converting them into these extremely stable complexes4 ,potassium cuprocyanide and potassium cobalticyanide solutions would not give any of the ordinary tests for ions of copper and cobalt1 and to find the latter in such solutions1 by these tests1 we would have to take the trouble of destroying the complexes4 ,should the destruction of such complexes become necessary 7e4g4 when complex cyanide ions are present in the original substance under examination71 evaporation with sulphuric acid1 with due precautions against inhaling poisonous hydrocyanic acid fumes1 fusion with alkali carbonates1 and perhaps most conveniently1 electrolysis with sufficiently high potentials1#dfj are the methods most frequently employed for the purpose4 ,it will be recalled that we have used the method of fusion with potassium carbonate to find iron in potassium ferrocyanide 7p4 #hi74 ,ferrocyanide and ,ferricyanide ,ions4--,the ferro- and ferricyanide ions may also be treated as complex ions4 ,for instance1 for the ferricyanide-ion1 we would expect a condition of equilibrium to exist between the complex ion and the simple ions according to3 ,fe7,,cn7#fc ,fe#c #f ,,cn and ,fe#c ,,cn#f _/ ,fe7,,cn7#fc ,k4 p#bca ,if the fact is recalled that the extremely sensitive tests for the ferric-ion fail to reveal the least trace of it in a potassium ferricyanide solution1 one must conclude that the ferricyanide-ion must be extremely stable4 ,the conception of the ferricyanide-ion as a complex ion1 subject to the above equilibrium conditions1 suggests that if a considerable excess of hydrogen-ion is added to its solutions1 the concentration of ferric-ion must be increased3 since hydrocyanic acid is an extremely weak acid 7p4 #ajd71 the ratio ,h ,,cn _/ ,,hcn having the value #g _/ #ajaj1 the addition of some concentrated hydrochloric acid must decidedly suppress the cyanide-ion in a ferricyanide solution and thus lead to an increase in the concentration of the ferric-ion4 ,under these conditions1 direct evidence of the presence of the ferric-ion1 and of the fact that the complex ion is a component in a reversible reaction1 may1 indeed1 be obtained1 as well as further evidence of the extreme stability of the complex4 ,the presence of traces of ferric-ion may be detected1 namely1 in the acid solution by the thiocyanate test1 applied in its most sensitive form1 in which any ferrithiocyanate produced is taken up in ether4 ,,exp4 ,potassium ferricyanide1 treated with a thiocyanate and ether1 does not show the least trace of color2 when some concentrated hydrochloric acid is added to the mixture1 a perfectly plain1 although noticeably faint1 pink tint is imparted to the ether solution4 ,mercuric cyanide1 as we have seen 7p4 #aae71 is exceptional in its exceedingly small capacity for ionization4 ,sherrill#dfa has found that the dissociation constant for ,hg#b ,,cn#d _/ ,hg7,,cn7#db has the extremely small value #j4d;,e#da4 ,consequently1 mercuric-ion must be even more effective than hydrogen-ion 7strong acids71 in suppressing the cyanide-ion and liberating the ferrous- or ferric-ion1 in solutions of ferrocyanides or ferricyanides4 ,in fact1 when a solution of potassium ferrocyanide is warmed1 for a moment1 with some mercuric oxide1 the ferrocyanide complex is to some extent decomposed2 the liberated ferrous-ion is oxidized1 by the excess of mercuric oxide1#dfb to ferric-ion1 and the presence of the latter1 in quantity1 is shown by the abundant precipitation of ferric ferrocyanide or ,prussian blue1 when the mixture is acidified with hydrochloric acid 7exp474 p#bcb ,the ,aurocyanide-,ion4--,gold forms a particularly stable complex ion with cyanide-ion4 ,the constant#dfc for the ratio ,au ,,cn#b _/ ,au7,,cn7#b has the value #ajbh4 ,this makes potassium cyanide an excellent solvent for insoluble gold compounds1 such as gold sulphide1 and the cyanide process for the extraction of gold ores makes use of this property4 ,the ,reacting ,components in ,solutions of the ,complex ,cyanide ,ions4--,the extraordinary values1 obtained for the constants expressing the condition of equilibrium between cyanide ions and some of the simple metal ions1 such as gold and silver ions1 and their complex ions1 have led to inquiries concerning a question of fundamental interest in the theory of complex ions and in the theory of ionization itself4 ,in a #j4je molar solution of ,k,ag7,,cn7#b1 containing an excess of #j4a mole of ,,cn1 per liter1 the concentration of silver-ion is only #e;,e#ba4 ,and yet1 the addition of potassium hydrosulphide 7sufficient to make ,,ksh #j4a molar7 will precipitate silver sulphide practically instantaneously from the solution4#dfd ,in solutions containing a larger excess of cyanide1 the concentration of the silver-ion is enormously reduced1 and yet1 while we can no longer precipitate silver sulphide from such a solution1 metallic silver may be precipitated by zinc or by the action of an electric potential at the cathode 7,chapter ,,xv74 ,the question may be asked1 whether we must consider that in these actions the minute quantity of free silver ions1 present at any moment1 is alone capable of the reactions indicated1 and that the decomposition of the complex into its components--as one of these1 the silver-ion1 is removed by precipitation--takes place with sufficient speed to account for the rapid actions1 wholly1 as direct actions of the silver ions4 ,the alternative to an affirmative answer to this question is1 that silver sulphide or silver may be precipitated by direct action of the precipitant on the complex ions1 rather than on the silver ions4 ,we may indicate the first course suggested for the action1 as follows3 #b ,ag7,,cn7#b ,s#b #d ,,cn #b ,ag ,s#b ,ag#b,s #d ,,cn4 ,i ,the second1 suggested1 course of the action would be the following3 #b ,ag7,,cn7#b ,s#b ,ag#b,s #d ,,cn4 ,,ii ,this second action would mean that we could obtain reactions of silver ions1 such as the precipitation of silver sulphide1 without the intermediate formation of the free ions themselves4 ,the consequences of the first1 the ordinary1 conception of such actions as direct actions of silver ions1 have been analyzed by ,haber#dfe from the point of view of the velocities of the actions1 by which the complex must be formed from its components and be decomposed into them1 in order to satisfy the facts concerning the precipitations4 p#bcc ,we may consider1 with ,haber1 a liter of a #j4je molar solution of ,k#b;,ag7,,cn7#c1 containing an excess#dff of #j4ie mole potassium cyanide4 ,in such a solution1 the concentration of silver-ion is reduced to #h;,e#bd gram-ion per liter4 ,now1 according to the best determinations of the ultimate dimensions of molecules1 about #ajbd molecules are estimated to be contained in a mole 7gram-molecule71 and #ajbd ions1 therefore1 in a gram-ion 7e4g4 in #ajh grams of silver-ion there would be #ajbd individual silver ions74 ,then a liter of the solution we are considering would contain1 at any moment1 only eight individual silver ions1 which are different ones from moment to moment1 since the reversible reactions ,ag #c ,,cn ,ag7,,cn7#cb1 are going on continually4 ,thus #ajj c4c4 of the solution would not contain even one silver ion all the time1 but the requirements of the equilibrium conditions could be met#dfg by silver ions flashing up and disappearing in such a way1 that the required average concentration in unit time is maintained4 ,there is nothing irrational in such a conception4 ,one may ask1 however1 what must be the velocities1 with which the complex is formed from the components1 and is resolved into them1 in order to satisfy an instability constant#dff #ajbb and still enable us to obtain a practically instantaneous precipitation1 say of silver sulphide1 the action being analyzed on the basis of the ordinary conception that only the silver-ion itself1 and not the complex ion1 is directly active in the formation of the silver sulphide4 ,a condition of equilibrium1 in a reversible action1 implies that the velocities of the two continuous1 opposed reactions are equal 7p4 #id74 ,for the action ,ag #c ,,cn ,ag7,,cn7#cb the velocity of formation of the complex is proportional to a characteristic constant1 ,k,formation1 to the concentration1 ,ag1 of the silver-ion1 and to the third power 7see p4 #id7 of the concentration1 ,,cn1 of the cyanide-ion4 ,the velocity of the opposed reaction of decomposition of the complex is proportional to another characteristic constant1 ,k,decomposition1 and to the concentration1 ,ag7,,cn7#cb1 of the complex ion4 ,for the condition of equilibrium1 the velocities of the opposed reactions are equal1 and we derive the relation3 ,ag ,,cn#c _/ ,ag7,,cn7#cb ,k,decomposition _/ ,k,formation #a _/ #ajbb4 ,the equilibrium constant of the complex ion is1 then1 the ratio of the velocity constants of its decomposition and formation 7see p4 #id74 ,now1 the velocity constant1 ,k,formation1 represents the concentration1 in moles1 of the complex ion ,ag7,,cn7#cb1that is formed in unit time from unit concentrations of its components ,ag and ,,cn1 and it may be considered as the reciprocal of a time constant1 ,t,formation1 the time required to form unit concentration of the complex ion1 while the components are maintained at unit concentration4 ,the analogous reciprocal relation holds for the velocity constant1 ,k,decomposition1 and a time constant1 ,t,decomposition4 ,the equilibrium equation1 therefore1 expresses also the following relations3#dfh p#bcd ,ag ,,cn#c _/ ,ag7,,cn7#cb ,t,formation _/ ,t,decomposition #a _/ #ajbb4 ,in words1 the time required for the spontaneous decomposition of one mole of the complex is #ajbb times as long as the time required to form one mole of the complex1 from uniformly unit concentrations of the components4 ,if the concentration of silver-ion is reduced to #a _/ #ajbb and the concentrations of the cyanide-ion and the complex ion are maintained at #a1 the formation of the complex takes place #ajbb times as slowly as when ,ag #a1 and a condition of equilibrium is produced1 the time required to decompose and to form the same amount of the complex being now equal4 ,this relation of time constants may be used to obtain some idea of the consequences of assuming certain limiting values for one or the other1 the ratio being maintained at the value #a _/ #ajbb4 ,if the time constant ,t,formation for the formation of the complex be taken as one ten-thousandth of a second1#dfi then1 according to ,haber1 a molar solution of potassium argenticyanide would not be able to form in thousands of years sufficient silver ions to be discovered by any direct test1 a result which is not compatible with the precipitation of silver sulphide and of metallic silver in a few minutes1 since silver ions could not be supplied rapidly enough4 ,it is evident1 thus1 that the ratio #a _/ #ajbb must indicate an exceedingly small value for ,t,formation1 if only silver ions form silver sulphide and silver4 ,if we assume that the complex is decomposed so fast as to supply new silver ions rapidly enough1 to allow us to consider the precipitation of silver and silver sulphide as direct actions of the silver ions1 then we may1 conservatively1 consider ,t,decomposition to be about #a _/ #ajj second4 ,then ,t,formation would be only #a _/ #ajbd second4 ,considering the limiting results for the dimensions of atoms 7and ions7 and taking account of the fact that the formation of the complex involves electrical changes1 that is1 in modern terms1 changes in position of electrons1#dgj ,haber finds1 that to satisfy the above value for the time constant1 such changes must involve a motion of electrical charges at a speed about a million times as great as the velocity of light4 ,such a velocity is1 unquestionably1 incompatible with our knowledge of the velocities of light and of electrical charges4 ,we must draw the conclusion that the complex argenticyanide-ion probably cannot decompose fast enough into its ions1 to enable the latter to be the only components which make it possible to precipitate silver sulphide or metallic silver from its solutions#dga 7see above1 p4 #bcb74 ,that would make it necessary to assume direct action p#bce 7as given in equation ,,ii1 p4 #bcb7 between the complex and the precipitating agent1 to some extent1 at least1 the extent being dependent on the concentrations involved in a given case4 ,if further investigations should confirm such a view1 we would probably find that both the actions under consideration 7equations ,i and ,,ii1 p4 #bcb7 must proceed simultaneously4 ,the second one would have the advantage of enormously greater concentrations of the reacting components1 e4g4 of the complex ion2 the first one would1 probably1 be found to have the advantage of an enormously greater velocity constant4 ,the actual velocities of the two reactions have never been measured#dgb and no final explanation of the relations can be offered4 ,the problem is a very important one1 involving the whole question of the mode of ionic action 7cf4 ,chap4 ,v1 especially p4 #hc74 ,aside from the theoretical value of the problem that has been raised1 the question of immediate moment to us1 from the point of view of analytical chemistry1 is the question whether such conclusions would invalidate1 in any way1 the use we have made of the theory of complex ions1 in elucidating the question of the precipitation and nonprecipitation of salts of simple ions from solutions of their complex ions4 ,the existence of a precipitate in contact with a solution is a question of a condition of equilibrium2 the question raised1 as the result of ,haber's calculations1 deals simply with the problem of the path1 the mechanism by which equilibrium is reached1 but the answer to it does not affect the conditions1 on which the maintenance of equilibrium depends4 ,all the conclusions1 drawn in our discussions of precipitation from solutions of complex ions1 are concerned with final conditions for equilibrium1 i4e4 with the conditions under which a precipitate can exist1 and not with the mechanism of its formation4 ,the conclusions reached are valid1 therefore1 irrespective of what the decision may ultimately be in the question1 whether the simple ions alone are acted upon1 when their salts are precipitated1 or whether the complex ions are also immediately concerned in the action4 ,the precipitation of silver chloride from an ammoniacal solution#dgc may serve to illustrate this point4 ,in the first place1 the precipitation of silver chloride from an ammoniacal solution1 say by sodium chloride1 may be considered to be the result of the direct interaction of chloride ions with the small quantity of silver ions present1 the complex serving only to renew the supply of silver ions1 as the latter are removed from solution1 by the precipitation4 ,the course of the action would be expressed by the equations ,ag7,,nh#c7b;,cl ,ag7,,nh#c7b ,cl #b ,,nh#c ,ag ,cl ,ag,cl #b ,,nh#c4 7#a7 ,ag,cl ,ag,cl ,when the precipitation is ended and equilibrium established1 a trace of silver chloride is in solution1 in contact with the precipitate1 and1 according p#bcf to the principle of the solubility-product1 we must have ,ag ,cl ,k,ag,cl4 ,bodlnder's experiments1#dgd on the solubility of silver chloride in ammonia1 prove that this relation is in perfect agreement with the facts4 ,for the silver-ammonium-ion1 the free ammonia and the silver-ion present in the solution1 we must have the relation ,ag ,,nh#cb _/ ,ag7,,nh#c7b ,k,instab4 ,const44 ,this relation1 according to the experimental evidence1 is also found to hold4 ,now1 we might1 on the other hand1 assume that the primary or main action1 leading to the precipitation of silver chloride1 is the interaction of the chloride ions with the complex ions1 rather than with silver ions4 ,silver-ammonium chloride1 ,ag7,,nh#c7b;,cl1 might first be formed1 for instance1 and then decompose directly into silver chloride and ammonia4 ,this is the simplest assumption we can make for this kind of action and is sufficiently illustrative of any kind of direct action between the chloride ions and the complex ions4 ,the path of the action would then be expressed by the equations ,ag7,,nh#c7b ,cl ,ag7,,nh#c7b;,cl #b ,,nh#c ,ag,cl #b ,,nh#c ,ag ,cl4 7#b7 ,ag,cl ,ag,cl ,it is clear1 from a comparison of this series of equations with equations 7#a71 that they represent the same reversible reactions in a somewhat different order4 ,since equilibrium conditions for any reversible reaction 7e4g4 for ,a ,b ,c ,d7 are independent of the order in which the components 7e4g4 ,a1 ,b1 ,c1 ,d7 are brought into the system 7p4 #id71 the difference of order1 indicated by equations 7#a7 and 7#b71 cannot affect the final condition of equilibrium in the system under discussion4 ,for instance1 since we again have silver chloride in contact with its saturated solution1 we again must have ,ag ,cl ,k,ag,cl1 and the experimental confirmation of this relation 7and similarly of the relation ,ag ,,nh#cb _/ ,ag7,,nh#c7b ,k7 agrees as well with this second path of the action as with the first4 ,conversely1 since the path1 by which the equilibrium is reached1 does not affect the condition of equilibrium1 it is perfectly legitimate to draw conclusions from equilibrium constants1 without assuming to know anything at all about the path by which the condition is reached4#dge ,for analytical work1 the vital point is the ultimate condition of equilibrium1 which determines whether a precipitate may exist and be formed in a given system or not4 ,the instability constants of the complex ions and the solubility-product constants of precipitates are the constant factors involved in the ultimate conditions for equilibrium1 and they do not depend on the path by which equilibrium is reached4 ,consequently1 we find that the application of p#bcg the theory of complex ions to analytical problems of precipitation has been in no wise invalidated by the problems presented by ,haber4 ,the theory forms now1 as before1 in fact1 the best quantitative basis for the expression of the experimental results4 ,the stability constants1 and the concentrations of the components used1 determine the limiting concentrations in which a given metal ion is capable of continued existence1 and determine1 therefore1 the question whether an ionogen1 of a given solubility1 is capable of existence as a solid phase in a given system4 ,the ,structure of ,complex ,ions4--,the ability of ammonia to form complex ions with simple metal ions is commonly ascribed to the unsaturated condition of ammonia 7see p4 #fe74 ,it is interesting to recall the fact1 that the marked power of the cyanide-ion to form complexes of extraordinary stability1 is also associated with a similarly unsaturated condition of the cyanide-ion 7p4 #ff74 ,according to the results of ,nef's researches1#dgf we have1 in hydrocyanic acid and the cyanides1 unsaturated or bivalent carbon2 potassium cyanide1 for instance1 has the structure ,k--,n,c4 ,the two free valences of the carbon atom may1 according to the electrical theory of valence1 be again considered to consist of one negative and one positive charge4 ,the possibility of the formation of complexes is then self-evident1 and we can readily see1 how silver cyanide1 ,ag--,n,c1 should absorb cyanide-ion1#dgg ,c,n1 and form a complex 7,ag--,n,c,c,n7 or ,ag7,,cn7#b1 whose potassium salt would be potassium argenticyanide1 ,k,ag7,,cn7#b4 ,for the potassium salt ,k#b;,ag7,,cn7#c1 of the second complex ion#dgh ,ag7,,cn7#cb of silver and cyanogen1 the most likely structure is ,ag--,n,c--,c,n--,k4 _/ ,c,n--,k ,the other complex cyanide ions1 ferrocyanide1 ferricyanide1 cobalticyanide1 etc41 are considered to have structures entirely similar to those given to the argenticyanide ions4#dgi ,complex ,halide1 ,sulphide1 ,oxide and ,oxonium ,ions4--,in conclusion1 there are other elements besides nitrogen 7in ammonia and its derivatives7 and carbon 7in cyanides71 which form complex ions with simple ions2 notably the halogens form such complexes4 ,chloroplatinic acid1 ,h#b,pt,cl#f1 and its salts 7,lab4 ,manual1 q4 v471 fluorosilicic acid1 ,h#b,si,f#f1 potassium-mercuric iodide1 p#bch ,k,hg,i#c and ,k#b ,hg,i#d1dhj which forms a most sensitive reagent for the detection of traces of ammonia1#dha are instances of complexes of the halogens that are of importance in analysis4 ,it is worthy of note that the most likely structure#dhb for these compounds1 e4g4 ,cl#b,pt7,cl,cl--,h7#b1 bears a very striking analogy to the structures frequently assigned to the cyanide and ammonia complex ions4 ,oxygen and sulphur form complex ions1 of great stability1 with many elements1 and we shall presently have occasion to discuss in detail some of the complex ions formed by sulphur4 ,all of the oxygen acids may be treated as containing complex ions of oxygen and some other element1 and their instability constants#dhc are factors in determining their chemical behavior4 ,for instance1 such is the case1 most likely1 for their behavior as oxidizing and reducing agents 7see ,chapter ,,xvi74 ,the unsaturated condition of oxygen in water1 7,h#b,o71 makes possible1 also1 the formation of complex ions1 7,h#b,o7x,me1 etc41 called oxonium ions and comparable with metal-ammonium ions4 ,they form a most inviting field for rigorous investigation4 ,it is altogether probable that the hydrogen-ion is intimately related1 in aqueous acid solutions1 to the complex oxonium-ion1 7,h#b,o7x,h1 comparable with the ammonium-ion1 7,,nh#c;,h71 and1 possibly1 the greater part of the hydrogen-ion1 in aqueous solutions1 exists in this form of combination4#dhd ,complex ,ions of ,organic ,oxygen ,derivatives4--,a further group of complex ions1 derived from organic derivatives of oxygen1 are of particular importance in analytical work4 ,many organic compounds1 such as sugars1 glycerine1 tartrates1 citrates1 interfere1 more or less1 with the precipitation of metal hydroxides and certain of their salts4 ,for instance1 the addition of cane sugar or of rochelle salt 7sodium potassium tartrate7 to a solution of p#bci cupric sulphate prevents the subsequent precipitation of cupric hydroxide by alkali 7exp474 ,in place of a precipitate of the hydroxide1 a clear1 intensely blue1 solution is formed4 ,in an analogous way1 the same substances and similar compounds interfere with the precipitation of the hydroxides of aluminium and chromium1 and since aluminium and chromium should be precipitated as hydroxides in systematic analysis 7,chap4 ,x71 the presence of such organic compounds must be most carefully considered1 to avoid error4#dhe ,the precipitation of moderately difficultly soluble salts1 such as phosphates1 is also rendered1 appreciably1 more difficult4 ,only extremely insoluble salts1 such as the sulphides of the arsenic1 copper and zinc groups1 are precipitated1 from solutions of organic substances of the character indicated1 without any appreciable interference4#dhf ,these relations clearly recall the characteristic behavior of ammoniacal and cyanide solutions1 in which complex ions are formed1 and the interference of the organic compounds with precipitation is of a similar nature--complex ions are formed by metal ions with these organic compounds1 and the complexes are1 in many instances1 sufficiently stable to reduce the concentrations of the metal ions to the point1 where only very difficultly soluble salts can be precipitated4 ,the relations may be illustrated by the discussion of the complex formed by the cupric-ion with tartrates4 ,the structure of sodium tartrate is expressed by ,na,o#b;,c--,,ch7,,oh7--,,ch7,,oh7--,,co #b,na4 ,the underscored hydroxide groups ,,oh are known in organic chemistry as alcohol groups4#dhg ,now1 alcohols resemble water in very many properties and1 among others1 in the capacity to form metal derivatives or alcoholates1 in which the hydrogen 7ion7 of the hydroxide group is replaced by metal ions4 ,the alcoholates correspond1 thus1 to the metal hydroxides1 which are the analogous p#bdj derivatives of water4 ,exactly as there is a vast difference in the readiness with which the various metal hydroxides1 or bases1 ionize1 many of them being only slightly ionizable 7the weakest bases71 so certain alcoholates are much less readily ionizable than others4 ,the alkali alcoholates are most readily ionized4 ,when sodium tartrate is mixed with an excess of sodium hydroxide1 some of the readily ionizable sodium salt of the alcohol groups of the sodium tartrate is formed and we have3 7,c,h,o,na7#b7;,,co#b7b #b ,na 7,,cho7#b7;,,co#b7b #d ,na4 ,when cupric sulphate is added to this mixture1 a slightly ionizable complex cupri-tartrate-ion is formed by the union of the cupric-ion with the alcoholate-tartrate-ion3 7,,cho7#b7;,,co#b7b ,cu#b 7,,cho7#b;,cu7,,co#b7b4 ,the complex ion is not perfectly stable and so the action is a reversible one1 as indicated in the equation4 ,the greater portion of the copper1 however1 is present as part of the complex negative ion of cupric-tartaric acid and its salts4 ,this may be demonstrated by subjecting the solution to electrolysis in a ,u-tube 7p4 #de74 ,it is readily seen 7exp47 that a deep blue ion1 obviously containing copper1 migrates to the positive pole4#dhh ,the concentration of cupric-ion is so small that its hydroxide and its phosphate are not precipitated from the solution by the addition1 respectively1 of alkali or of a soluble phosphate 7exp474 ,cupric sulphide1 however1 is so insoluble that it may be precipitated completely from the solution by the addition of a sulphide 7exp471 the concentration of cupric-ion being much smaller in the saturated solution of the sulphide than in the solution of sodium cupri-tartrate4 ,citrates1 sugars1 glycerine1 contain alcoholic groups of the same nature as found in the tartrates1 and they are capable of forming similar complexes1 or little ionizable alcoholates1 with metal ions4 ,certain organic acids1 which contain no alcohol groups1#dhi are p#bda also capable of forming fairly stable complexes with metal ions3 thus1 acetates form a complex with lead-ion1 that is sufficiently stable to render lead sulphate1 which is difficultly soluble in water1 readily soluble in ammonium acetate solution#dij 7exp474 ,soluble oxalates readily combine with ferric1 ferrous1 cupric and other oxalates and interfere1 more or less1 with the detection of the metal ions1 as the result of complex formations4 ,all of these complexes are decomposed rather readily by the addition of strong acids1 whose hydrogen-ion breaks up the complex ions1 by suppressing the anions#dia of the much weaker organic acids and alcohols4 ,consequently1 these organic compounds do not interfere with tests which may be carried out in strongly acid solution4 ,for instance1 the addition of potassium ferrocyanide to a solution of ammonium ferrioxalate 7,,nh#d7c;,fe7,c#b,o#d7c1 to which an excess of ammonium oxalate has been added1 gives only a slight indication of the presence of ferric-ion 7a greenish blue solution is obtained72 when hydrochloric acid1 in excess1 is added to the mixture1 ,prussian blue1 ferric ferrocyanide1 is immediately precipitated in quantity 7exp474 ,,footnotes3 #dbe ,the naming of the complex ions1 which ammonia forms with metal ions1 has not yet been satisfactorily settled4 ,english writers frequently speak of ammonio-argentic ion and ammonio-argentic nitrate4 ,german writers speak of ,silber-ammoniak ion 7,abegg1 ,handb4 der anorg4 ,chem41 ,,ii1 #gbh71 which would read silver-ammonia ion in ,english terms4 ,the terminology silver-ammonium ion1 used in this book1 is based on the idea1 that all these complex ions are essentially of the same nature as the well-known ammonium-ion1 ,,nh#d1 the positive charge being1 almost certainly1 carried by nitrogen in these complex ions1 as it is in ammonium-ion4 ,the latter is a complex ion of ammonia with hydrogen-ion4 ,the name ammonio-argentic ion does not bring out this close relationship and puts the emphasis on the silver1 which is probably little concerned in the reactions of the complex as such4 ,the names silver-ammonia ion and silver-ammonia nitrate sound badly and do not emphasize the relation to ammonium1 potassium1 sodium and similar positive ions and their salts4 ,the term ammonium is1 for the reasons given1 used here in a generic sense for all complex ions of ammonia with simple metal ions 7such as ,h1 ,ag1 ,cu#b1 ,zn#b etc471 and the number of ammonia molecules1 entering into the composition of a complex ion1 is not indicated in the names4 ,a similar nomenclature has long been in vogue1 and has worked well1 for the complex ions of metal ions with the cyanide-ion 7see below74 ,we speak of ferrocyanide1 ,fe7,,cn7#fd1 argenticyanide1 ,ag7,,cn7#b and ,ag#b7;,,cn7#cb1 etc41 without indicating the number of cyanide groups1 ,,cn1 in the complex1 and we use the same generic ending cyanide as is used to designate the simple cyanide ion1 e4g4 to designate the ion formed from potassium cyanide1 ,,kcn ,k ,,cn4 #dbf ,the hydroxide-ion appears with the same coefficient1 #a1 on both sides of the equilibrium equation and need not be included in the mathematical statement2 it would appear as a factor in both terms of the ratio given and would cancel out4 #dbg ,bodlnder and ,fittig1 ,z4 phys4 ,chem41 #ci1 #fjb 7#aijc74 #dbh ,bonsdorff1 ,ber4 d4 chem4 ,ges41 #cf1 #bcbd 7#aijc74 #dbi ,it is also frequently called the dissociation constant of the complex ion1 indicating the tendency of the complex ion to dissociate into its components4 #dcj ,two independent experimental methods were used and gave concordant results--one having as its basis the solubility of silver salts 7chloride1 bromide71 the other the electrolytic potentials of silver against ammoniacal silver solutions 7see ,chap4 ,,xv74 #dca ,bull4 de la ,soc4 ,chim4 de ,paris1 7#c71 #ac1 #chf 7#ahie74 #dcb ,we may consider the salt to be ionized to about the same extent as ammonium or potassium nitrate in #j4je molar solutions1 or1 approximately1 #hg4 ,if we call x the concentration of silver-ion1 formed by the decomposition of the silver-ammonium-ion1 then #b x is the concentration of the free ammonia1 and 7#j4je #j4hg x7 is the concentration of the complex ion4 ,since x is a small number in comparison with #j4jdce1 we may write1 with sufficient accuracy for our purposes1 ,,nh#cb ,ag _/ 7,,nh#c7b;,ag 7#b x7#b x _/ #j4jdce #f4h;,e#h4 ,then1 x ,ag #j4jjji4 #dcc ,kohlrausch and ,holborn1 loc4 cit41 p4 #bjb4 #dcd ,the dilution of the silver-ammonium nitrate 7#aj c4c4 to #aa c4c47 and the decrease in ionization due to the added salt reduce the concentration of silver-ion from #j4jjji to #j4jjjhe4 ,ag7,,nh#c7b 7#j4je #aj _/ #aa7 #j4h #j4jcfd and #d x#c #f4h;,e#h #j4jcfd 7see footnote1 p4 #bbj74 ,then x ,ag #j4jjjhe4 #dce ,thiel 7cf4 ,bodlnder and ,fittig1 loc4 cit474 ,the solubility given in the table at the end of the laboratory manual refers to #ah4 ,the constant for the complex ion was determined at #be4 #dcf ,the combined concentration of the salts is #j4jee and their degree of ionization may be taken as #hg1 the same as the degree of ionization of #j4je to #j4jf molar ,,kno#c4 ,then ,cl 7#j4a #a _/ #aa7 #j4hg #j4jjh4 ,ag7,,nh#c7b 7#j4je #aj _/ #aa7 #j4hg #j4jd and x ,ag #j4jjjhi 7see the method of calculation in the footnote1 p4 #bbj74 #dcg ,the strong solution of ammonia is used in order to avoid unnecessary dilution1 and in the experiment1 described below1 the dilution of the liquids by the added ammonia is considered negligible4 #dch ,the following solubilities have been determined at #be3 ,ag ,cl #b;,e#aj2 ,ag #a4d;,e#e4 ,ag ,i #a;,e#ae2 ,ag #a;,e#h4 ,ag#b ,s#b #d;,e#ej2 ,ag #d4c;,e#ag4 #dci #ajj c4c4 molar ammonia dissolves at #be only #j4f milligram of silver iodide 7,bodlnder1 loc4 cit41 p4 #fjf74 #ddj ,fresenius1 ,qualitative ,analysis1 p4 #cgh4 #dda ,in regard to ,cu7,,nh#c7db see ,locke and ,forssall1 ,am4 ,chem4 ,j41 #ca1 #bfh1 #big 7#aijd71 and ,dawson1 ,j4 ,chem4 ,soc4 7,london71 #hi1 #afgd 7#aijf74 #ddb ,euler1 ,ber4 d4 chem4 ,ges41 #cf1 #cdjc 7#aijc74 #ddc ,see footnote1 p4 #bab4 #ddd ,see pp4 #afe1 #baj and #bac4 #dde ,the acid ,h,ag7,,cn7#b1 corresponding to the salt1 is crystallizable and is a strong acid4 ,it is largely decomposed1 by water1 into silver cyanide and hydrocyanic acid4 #ddf ,see the experiments described on pp4 #de and #hi4 #ddg ,in solutions containing an excess of potassium cyanide greater than #j4je molar1 the salt ,k#b;,ag7,,cn7#c is formed4 ,the dissociation or instability constant for the complex ion ,ag7,,cn7#cb is #a;,e#bb4 #ddh ,z4 anorg4 ,chem41 #ci1 #bbb 7#aijd74 #ddi ,the solubility-product constant for silver chloride at #be is #b;,e#aj4 ,if the concentration of chloride-ion be made #a4j by the addition of potassium chloride to a #j4je molar solution of ,k,ag7,,cn7#b1 then the concentration of silver-ion1 necessary for the precipitation of the chloride1 would be ,k,s4,p4 _/ ,cl #b;,e#aj gram-ion4 ,neglecting the fact that the complex salt is not completely ionized and putting ,ag7,,cn7#b #j4je1 and calling x the concentration of the cyanide-ion just necessary to prevent the precipitation of the chloride1 we have3 ,ag ,,cn#b _/ ,ag7,,cn7#b #b;,e#aj x#b _/ #j4je #ajba4 ,we find x #e;,e#g mole1 or approximately #j4jc milligram potassium cyanide 7cyanide-ion7 per liter4 ,this minute quantity of free cyanide1 if not originally present in the solution used1 would be formed by the liberation of potassium cyanide from the complex 7according to ,k,ag7,,cn7#b ,k,cl ,ag,cl #b ,,kcn7 as soon as #b4e;,e#g mole1 or #j4jcf milligram1 of silver chloride per liter have been formed1 a quantity too small to be perceptible4 ,when potassium cyanide is added to a silver nitrate solution1 the precipitate formed is found to be silver argenticyanide1 ,ag,ag7,,cn7#b1 the silver salt of the extremely stable complex1 rather than the simple salt1 silver cyanide1 ,ag,c,n cf4 ,bodlnder1 ,z4 anorg4 ,chem41 #ci1 #bbc 7#aijd74 ,ag,ag7,,cn7#b is even less soluble than silver chloride1 the solubility-product constant for ,ag ,ag7,,cn7#b being #b4be;,e#ab4 ,an excess of only #b;,e#f mole1 or about #j4ae milligram1 of potassium cyanide 7cyanide-ion7 per liter is sufficient to prevent the precipitation of silver cyanide 7silver argenticyanide7 from a #j4a molar solution of ,k,ag7,,cn7#b1 and1 conversely1 at least this minute excess of potassium cyanide is used in the preparation of a clear #j4a molar solution of ,k,ag7,,cn7#b1 by the addition of potassium cyanide to silver nitrate1 until the silver cyanide1 first precipitated1 is just redissolved 7,bodlnder1 loc4 cit474 ,this excess1 as just explained1 is more than sufficient to prevent the precipitation of silver chloride from the cyanide solution1 even by a large excess of potassium or sodium chloride4 ,unless one takes into account1 in the manner indicated1 this marked influence of a minute excess of cyanide-ion in decidedly reducing the concentration of silver-ion in these solutions1 one could be led1 wrongly1 to infer from the value of the instability constant of the complex ion and that of the solubility-product constant of silver chloride1 that silver chloride should still be precipitated by the addition of sodium chloride to a solution of ,k,ag7,,cn7#b4 #dej ,for this reason potassium cyanide is an excellent cleansing agent for stained silverware 7sulphide stains71 and1 since it is an intense poison1 cleaning powders should be examined for it4 #dea ,for the quantitative relations see ,lucas1 ,z4 anorg4 ,chem41 #da1 #aib 7#aijd74 #deb ,see ,bodlaender1 ,z4 phys4 ,chem41 #ci1 #eig 7#aijb72 ,ber4 d4 chem4 ,ges41 #cf1 #cicc 7#aijc74 #dec ,potassium cyanide is a powerful reducing agent 7see p4 #hi7 and is readily oxidized to potassium cyanate4 ,the action1 presumably1 takes the following course 7see ,chapters ,,xiv and ,,xv73 #b ,cu#b #d ,,ho ,,knc #b ,cu #d ,,ho ,,knc#b #b ,cu #b ,,ho ,,knco ,h#b,o4 #ded ,put ,cu x1 and ,,cn #c x1 and1 neglecting the degree of ionization1 ,cu7,,cn7#cb #j4a1 x being so small that it need not be subtracted from #j4a4 ,then x 7#c x7#c #j4a #j4e;,e#bg1 and x #c4g;,e#h4 #dee ,treadwell and ,girsewald1 ,z4 anorg4 ,chem41 #ch1 #ib 7#aijd74 #def ,euler1 ,ber4 d4 chem4 ,ges41 #cf1 #cdjd 7#aijc74 #deg ,putting ,cd#b y1 we have y 7#d y7#d #j4a;,e#ag1 and y #h;,e#e4 ,in view of the values of the constants1 a small excess of potassium cyanide will have a much smaller suppressing effect on the cadmium-ion than on the cuprous-ion4 ,for the excess ,,cn #j4ja1 ,cu #e;,e#bc1 ,cd#b #ajaj as compared with ,cu #d;,e#h in a #j4a molar solution of the salt ,k#c;,cu7,,cn7#c1 and with ,cd#b #h;,e#e in a #j4a molar solution of ,k#b;,cd7,,cn7#d4 #deh ,bromine water is a convenient agent for oxidizing cobaltous to cobaltic ions 7see ,chapter ,,xv74 #dei ,the heavy arrows ,see ,transcriber's ,note indicate the main course the reversible actions take1 under the influence of the reagents used4 ,since the oxidation of nickel-ion by bromine is accomplished only after the bromine has oxidized any excess of cyanide used--potassium cyanide is a powerful reducing agent 7p4 #hi7--the addition of cyanide1 beyond a very small excess1 must be avoided 7see laboratory instructions74 #dfj ,e4g4 for the precipitation of silver1 copper1 nickel1 cobalt and certain other metals from cyanide solutions2 cf4 ,edgar ,f4 ,smith1 ,electro-,analysis 7#aijg74 #dfa ,z4 phys4 ,chem41 #dc1 #gje 7#aijc74 ,vide also ,haber1 ,z4 ,elektrochem41 #aa1 #hdg 7#aije74 #dfb #b ,fe#b ,hg#b #b ,fe#c ,hg 4 ,if the treatment with mercuric oxide is carried to completion the final products of the reaction are ferric hydroxide1 mercuric cyanide1 mercury and potassium hydroxide 7,rose1 ,z4 anal4 ,chem41 #a1 #cjj 7#ahfb773 #b ,k#d;,fe7,,cn7#f #g ,hg,o #g ,h#b,o #c ,hg,hg7,,cn7#d #h ,,koh #b ,fe7,,oh7#c ,hg #dfc ,bodlaender1 loc4 cit4 #dfd ,the solubility-product constant of silver sulphide at #be is #j4e;,e#ea2 for ,s#b #j4h;,e#e 7p4 #bjb71 we would have in the present case ,ag#b ,s#b #b;,e#df1 which is greater than the constant4 ,vide quantitative data by ,lucas1 loc4 cit4 #dfe ,z4 f4 ,elektrochem41 #aj1 #dcc and #ggc 7#aijd74 #dff ,see footnote #d1 p4 #bbe4 #dfg ,ostwald1 ,allgem4 ,chemie1 ,vol4 ,,ii1 part #a1 p4 #hha 7#ahic74 #dfh ,haber1 loc4 cit4 #dfi ,then ,t,decomposition #ajd #ajbb #ajah seconds1 and1 since there are #c4ae;,e#g seconds in a year1 ,t,decomposition #c;,e#aj years4 #dgj ,see p4 #db4 #dga ,since there are still smaller instability constants than that of the argenticyanide-ion 7e4g4 for the gold-cyanide-ion the constant is #a _/ #ajbh71 there is a large margin of safety for the plausibility of ,haber's argument4 ,for full details1 his articles 7loc4 cit471 and the discussion 7by ,abegg1 ,bodlaender1 ,danneel1 ibid47 aroused by them should be consulted4 #dgb ,see ,le ,blanc and ,schick1 ,z4 phys4 ,chem41 #df1 #bac 7#aijc71 on measurements of the speed of ionic actions4 ,the values obtained agree1 in general1 with ,haber's contention4 #dgc ,the concentrations of silver-ion are large1 in comparison with those in cyanide solution1 and the action is1 most likely1 essentially an ionic one2 but the argument applies with equal force to cyanide systems4 #dgd ,loc4 cit4 #dge ,an equilibrium constant1 as we have seen1 is a ratio of velocity constants of balanced reactions 7pp4 #id1 #bcc7 and involves therefore at least two unknown velocity constants4 ,by determining the actual rate of change with known concentrations of reacting components1 i4e4 by determining the velocity constants themselves1 rather than their ratio1 a definite conclusion as to the mechanism or path of a given reaction can often be reached 7see p4 #hj74 #dgf ,proceedings ,amer4 ,academy1 #ahib4 #dgg ,in the absence of any added cyanide1 it combines with itself4 ,silver cyanide1 according to ,bodlnder's results1 is1 in saturated solutions1 chiefly 7,ag,c,n7#b or ,ag,ag7,,cn7#b1 i4e4 ,ag--,n,c,c,n--,ag4 #dgh ,see p4 #bbe1 footnote #d4 #dgi ,werner has developed quite a different theory of the structure of complex ions4 7,cf4 ,nernst1 ,theoretical ,chemistry1 p4 #cgd 7#aijd747 #dhj ,sherrill1 ,z4 phys4 ,chem41 #dc1 #gba 7#aijc74 #dha ,in ,nessler's reagent1 ,fresenius' ,qualitative ,analysis1 p4 #ada4 #dhb ,cf4 ,remsen1 ,am4 ,chem4 ,j41 #aa1 #bia 7#ahii72 #ad1 #ha 7#ahib7 7,stud474 #dhc ,for instance1 for arsenious acid we have #c ,h ,as,o#cc ,h#c;,as,o#c ,as#c #c ,,ho and1 therefore1 ,as#c ,,ho#c _/ 7,as,o#cc ,,ho#c7 k#a4 ,since ,h k,,hoh _/ ,,ho 7p4 #agf71 we have further1 ,as#c ,,ho#f _/ ,as,o#cc k#b4 ,and since we may derive the relation ,,ho#b k#c ,o#b1 by considering the primary and the secondary ionization of water 7see pp4 #bdf1 #bgh71 we have1 finally1 ,as#c ,o#bc _/ ,as,o#cc ,k4 ,the constants for the primary and the secondary ionization of water are included in the value of ,k4 #dhd ,fitzgerald and ,lapworth1 ,j4 ,chem4 ,soc4 7,london71 #ic1 #bafc 7#aijh72 ,lapworth1 ibid41 #bahg4 ,vide also ,franklin on the characteristics of the ,,nh#d ion in liquid ammonia1 ,am4 ,chem4 ,j41 #bc1 #cje 7#aijj74 #dhe ,see the laboratory instructions1 in regard to the precautions used1 to avoid errors from this source4 #dhf ,on the other hand1 colloidal organic substances1 such as casein1 glue or albumen1 interfere with the precipitation of even the most insoluble sulphides1 by producing colloidal suspensions of the latter 7see ,chap4 ,,vii2 cf4 ,mller1 ,allgemeine ,chemie der ,kolloide1 p4 #ef 7#aijg774 #dhg ,in alcohols the hydroxide group is held by a carbon atom1 whose remaining valences are satisfied by hydrogen or carbon atoms1 as in ordinary or ethyl alcohol1 ,h#c;,c--,,ch#b7,,oh74 #dhh ,kster1 ,z4 ,elektrochem41 #d1 #aag 7#ahig74 #dhi ,the most common organic acids contain the acid group --,,co7,,oh71 as in acetic acid1 ,,ch#c;,,co7,,oh74 ,the hydroxide group ,,oh of the alcohols1 e4g4 in ,,ch#c;,,ch#b7,,oh71 is still found in these organic acids1 but its tendency to form hydrogen-ion is very much increased by the replacement of two hydrogen atoms of the alcohols by the oxygen atom1 as found in the acids4 ,to a certain degree1 the properties of the alcohol hydroxide are maintained in the properties shown by the acid hydroxide group4 ,thus1 the organic acids1 on the whole1 are still rather weak acids1 and their salts1 in many instances1 are appreciably less ionizable than the salts of strong inorganic acids4 ,the organic acids1 further1 may combine1 to a certain extent1 with water and thus form hydrates 7e4g4 ,,ch#c;,,cooh ,h#b,o ,,ch#c;,c7,,oh7#c7 containing a number of hydroxide groups3 the second and third hydroxide groups must have a very much smaller tendency to form hydrogen ions and ionizable salts1 than has the first hydroxide group 7p4 #ajb71 and the former1 thus show1 more nearly1 the behavior of alcoholic hydroxide groups4 ,finally1 organic acids also show a tendency to combine with themselves1 forming complex acids 7e4g41 7,,ch#c;,,cooh7#b or ,,ch#c;,c7,,oh7#b,,oocch#c71 from which complex salts may be derived1 which may be little ionizable4 ,the power of the organic acids to form complex ions--which they share with many inorganic acids--is most likely intimately connected with the relations described4 #dij ,lead acetate1 itself1 is less ionized than most salts and this property contributes to the solubility of lead sulphate in acetate solutions4 7,cf4 ,noyes and ,bray1 loc4 cit47 #dia ,on p4 #bca1 the same effect is discussed1 in detail1 in connection with the ferricyanide-ion4 p#bdb ,,chapter ,,xiii ,,the ,,arsenic ,,group4 ,,sulpho-,,acids ,,and ,,sulpho-,,salts ,the analytical groups1 which we have heretofore discussed1 contain elements1 whose oxides are preminently base-forming4 ,the methods of separation of these groups1 from each other1 involve1 primarily1 physical#dib differences between the groups--in the matter of the relative insolubility of analogous salts4 ,thus1 barium1 strontium and calcium carbonates are precipitated1 and separated from the alkalies1 by means of ammonium carbonate1 not because the alkalies do not form carbonates when their salts1 in solution1 are treated with ammonium carbonate1 but wholly because barium1 strontium and calcium carbonates are very difficultly1 the alkali carbonates easily1 soluble in water4 ,the hydroxides of the aluminium group and the sulphides of the zinc group are less soluble than the hydroxides and sulphides of the alkaline earths and alkalies4 ,the sulphides of the copper and the arsenic groups1 again1 are still less soluble than the sulphides of the zinc group1 and thus the former may be precipitated by hydrogen sulphide1 even when its precipitating power is reduced by the suppression of its sulphide 7and hydrosulphide7 ions by the addition of a strong acid4 ,on the other hand1 the separation of the arsenic group 7arsenic1 antimony1 tin1 gold and platinum7 from the copper group1 with which it is precipitated by hydrogen sulphide from acid solutions1 depends1 essentially1 on a chemical difference between the groups4 ,the oxides1 especially the higher oxides1 of the arsenic group1 are preminently acid-forming2 the higher oxides form such acids as arsenic acid1 ,h#c;,as,o#d1 antimonic acid1 ,h#c,sb,o#d1 stannic acid1 ,h#b,sn,o#c1 platinic acid1 ,h#b,pt,o#c1 and auric acid1 ,h,au,o#b4 ,these p#bdc hydroxides are1 however1 all more or less weakly basic in character as well4 ,the hydroxides of the lower oxides of the metals are1 as one must expect1 much more strongly basic1 but most of them--arsenious1 antimonous and stannous hydroxides--still show sufficient acid character to be distinctly amphoteric in behavior4 ,but1 with the exception of arsenious acid1 the basic ionization of the hydroxides of the lower oxides is more pronounced than their acid ionization4 ,the basic ionization of the hydroxides of their lower and higher oxides brings these elements into the plan of analysis for the metal or positive ions in systematic analysis4 ,in the presence of hydrochloric acid they form chlorides1 which yield positive ions in sufficient quantity#dic to allow their extremely insoluble sulphides to be precipitated by hydrogen sulphide in acid solution1 together with the1 likewise1 very insoluble sulphides of the copper group4 ,the acid-forming properties of the oxides of the arsenic group are maintained in their sulphides4 ,again1 this is especially evident in the higher sulphides4 ,the element sulphur is substituted for the closely related element oxygen without any profound change in the chemical behavior of the compounds4 ,advantage is taken of this acid-forming power to separate the sulphides of the arsenic group from the sulphides of the copper group1 which either are not acid-forming at all1 or exhibit this property only to a very slight degree4#did ,sulpho-,salts4--,the similarity in the behavior of oxygen and sulphur derivatives1 in this respect1 is general and is not restricted to the metal sulphides we are discussing4 ,for instance1 the acid-forming power of carbon dioxide is shown also by carbon disulphide1 the corresponding sulphur derivative of carbon4 ,just as the former combines with potassium hydroxide to form a carbonate1 so carbon disulphide dissolves in solutions of potassium hydrosulphide and potassium sulphide to form potassium sulpho-carbonate3 ,,co#b #b ,,koh ,k#b;,,co#c ,h#b,o4 7#a7 ,,cs#b #b ,,ksh ,k#b;,,cs#c ,h#b,s4 7#b7 ,,cs#b ,k#b,s ,k#b;,,cs#c4 7#c7 p#bdd ,the higher sulphides of the arsenic group1 and arsenious and antimonious sulphides among the lower ones1 combine with the alkali sulphides to form soluble alkali salts of sulpho-acids1 in the same way as carbon bisulphide does4 ,in the case of arsenious sulphide1 for instance1 we have the action ,as#b,s#c 7,,nh#d7b,s #b ,,nh#d;,as,s#b4 7#d7 ,the salt1 ammonium sulpharsenite1 is ionized as follows3 ,,nh#d;,as,s#b ,,nh#d ,as,s#b4 ,sulpho-,acids4--,the free sulpho-acids are liberated1 from their salts1 by any stronger acid1 such as hydrochloric acid2 the acids are extremely unstable and revert rapidly to the sulphides1 from which their salts were originally obtained4 ,we have1 for instance1 #b ,h,as,s#b ,as#b ,s#c ,h#b,s 4 ,this instability of the sulpho-acids is entirely analogous to the instability of the metal hydrosulphides 7p4 #bjc7 and to the instability of certain oxygen acids1 notably of carbonic acid4 ,sulpho-carbonic acid1 ,h#b;,,cs#c1 is the best-known free acid of this type4 ,it may be precipitated1 undecomposed1 as an oil1 and its gradual decomposition into hydrogen sulphide and carbon disulphide may be observed4 ,sulpho-,bases4--,since one meets1 in this group1 sulpho-acids and sulpho-salts1 corresponding to the oxygen acids and their salts1 one is naturally led to inquire1#die whether the third great class of oxygen compounds is not found duplicated among sulphur compounds1 whether sulpho-bases1 as well as sulpho-acids and salts1 are known4 ,one would look for such bases1 with the most pronounced basic character1 among the compounds obtained by the substitution of sulphur for oxygen in the strongest oxygen bases4 ,to a certain extent potassium and sodium hydrosulphides and sulphides show1 in fact1 properties1 which are akin to those fundamentally characteristic of ordinary bases4 ,they combine with acid sulphides to form sulpho-salts1 as the oxygen bases combine with acid oxides4 ,to a very considerable extent they neutralize all but the very weakest acids2 hydrogen sulphide1 itself a very weak acid1 is driven out of its salts by all stronger acids1 and the latter are almost completely neutralized4 ,for instance1 we have3 p#bde ,,koh ,h,cl ,k,cl ,h#b,o1 and ,,ksh ,h,cl ,k,cl ,h#b,s and ,k#b,s #b ,h,cl #b ,k,cl ,h#b,s4 ,the concentration of the hydrogen-ion is reduced most decidedly in each of these reactions4 ,,exp4--,a solution of potassium hydrosulphide is saturated with hydrogen sulphide1 in order to prevent hydrolysis and the formation of potassium hydroxide#dif 7p4 #ahj71 as far as possible1 and the solution is added to an acid 7hydrochloric7 solution of methyl orange2#dig the acid color is changed to orange1 as a result of the almost complete neutralization of the acid4 ,the potassium hydrosulphide 7the hydrosulphide-ion ,,hs7 neutralizes the hydrogen-ion 7of hydrochloric acid71 that converts methyl orange into its pink salt1 and hydrogen sulphide is formed1 which is too weak an acid to affect the color of the indicator 7p4 #gi74 ,the objection that potassium sulphide and hydrosulphide are salts1 the salts of hydrogen sulphide1 might be raised against the conception of their possessing a certain measure of basic functions2 but the common oxygen base1 potassium hydroxide1 is also a salt1 the salt of a still weaker acid1 water4 ,indeed1 the characteristic properties of ordinary bases are due essentially to the fact1 that they are the more or less readily ionizable salts of an extremely weak acid1 water1 and these properties may well be duplicated by salts of other weak acids1 duplicated in a very much weaker way1 in proportion as the acids are stronger than water4 ,the difference is1 then1 really one of degree and not of kind4#dih ,owing to the fact that hydrogen sulphide is a much stronger acid than water1 the action of potassium hydrosulphide on an acid sulphide1 like carbon disulphide 7equation 7#b71 p4 #bdc71 is reversed to a correspondingly greater degree than the action of potassium hydroxide on carbon dioxide#dii 7equation 7#a71 p4 #bdc74 ,the dissociation constant for the secondary ionization of hydrogen sulphide 7,,hs ,h ,s#b7 is very much smaller than the constant for the primary ionization 7,,hs is a much weaker acid than ,,hsh71 and so we find that a sulphide like ,k#b,s exhibits very much stronger basic functions than do the hydrosulphides1 as1 for instance1 in forming salts with acid-forming sulphides p#bdf 7equation 7#c71 p4 #bdc7 and in neutralizing acids4 ,there can be no question that1 if we could have an aqueous solution of potassium oxide1 ,k#b,o1 it would show1 similarly1 the characteristic actions of strong bases even more powerfully than the hydroxide1 ,,koh2 for instance1 in acting on acid-forming oxides 7equation 7#a71 p4 #bdc71 in neutralizing acids1 in saponifying esters 7p4 #ha71 and so forth4 ,it is1 in fact1 on account of this property1 that potassium oxide is decomposed by water4 ,it is a salt involving the secondary ionization of water1 7,,ho ,h ,o#b71 which has a much smaller dissociation constant even than the primary ionization 7,h#b,o ,h ,,ho74 ,the oxide1 ,k#b,o1 is decomposed by neutralizing hydrogen ions formed by the primary ionization of water4 ,we have #b ,k ,o#b ,h ,,ho #b ,k #b ,,ho1 which is entirely analogous1 in principle1 to ,k ,,ho ,h ,cl ,k ,cl ,,hoh4 ,sulphoxy-,salts4--,the close relations between the oxygen and the sulphur series are seen also in the fact that an oxygen base may be combined with an acid sulphide1 and vice versa2 arsenious sulphide1 for instance1 dissolves even in the solution of so weak a base as ammonium hydroxide 7exp474 ,the salts produced by this crossing are usually hybrid salts1 partly sulpho-1 partly oxygen-salts4 ,there is1 for instance1 a series of arseniates1#ejj ,me#c;,as,o#d1 ,me#c;,as,s,o#c1 ,me#c;,as,s#b,o#b1 ,me#c;,as,s#c,o and ,me#c;,as,s#d4 ,in analytical work the pure types are ordinarily utilized1 rather than the mixed types4 ,complex ,sulphide ,ions4--,the ions of the sulpho-acids1 like the ions of oxygen-acids 7p4 #bch71 may also be treated as complex ions--of the positive metal ions and the sulphide-ion1 ,s#b4 ,ammonium sulphide combines with stannic sulphide1 forming ammonium sulphostannate3 ,sn,s#b 7,,nh#d7b,s 7,,nh#d7b,sn,s#c4 ,if the action is considered to be the result of interactions of the ions of stannic and ammonium sulphides1 we can resolve the equation into the following one3 ,sn#d #b ,s#b #b ,,nh#d ,s#b #b ,,nh#d ,sn,s#cb4 ,the ammonium-ion1 appearing with the same coefficient on both sides of the last equation1 evidently takes no direct part in the action and we have more simply3 ,sn#d #c ,s#b ,sn,s#cb4 ,for the condition of equilibrium between the complex and its components we have3#ejaejb ,sn#d ,s#bc _/ ,sn,s#cb ,k4 p#bdg ,sulphurization of ,sulphides4--,since the solubility of the arsenic group of sulphides in ammonium sulphide solution--the reagent commonly used in analysis--depends on the formation of soluble sulpho-salts1 due consideration must be taken of the fact that some of the lower sulphides--notably stannous1 aurous and platinous sulphides--do not possess acid-forming properties in any marked degree2 even antimonous sulphide is soluble only in a considerable excess of ammonium sulphide4 ,in order1 then1 to insure a more complete separation of the arsenic from the copper group1 precautions are taken to sulphurize the lower sulphides to higher1 stronger acid-forming1 sulphides1 in the course of the separation4 ,for this purpose so-called yellow ammonium sulphide1 containing persulphides of ammonium1 7,,nh#d7b,s#b1 etc41 is used in place of a solution of ammonium sulphide and ammonium hydrosulphide4 ,stannous sulphide1 for instance1 is dissolved by the reagent as ammonium sulphostannate3 ,sn,s 7,,nh#d7b,s#b 7,,nh#d7b,sn,s#c4 ,behavior of ,arsenic ,acid toward ,hydrogen ,sulphide4--,in conclusion1 special consideration must still be given to the behavior of arsenic acid1 ,h#c;,as,o#d4 ,as its name indicates1 it is an acid1 and1 in fact1 a rather strong acid1 of the order of strength#ejc of phosphoric acid1 ,h#c,,po#d1 which it resembles in composition and in many of its properties4 ,as a strong acid1 arsenic acid1 when it is ionized1 yields chiefly negative arseniate ions1 ,h#b;,as,o#d1 ,h,as,o#db and ,as,o#dc4 ,any basic properties1 which it may and1 most likely1 does possess1 must be extremely weak4 ,it is1 therefore1 not surprising to find that unusual difficulties are experienced in precipitating arsenic sulphide1 by hydrogen sulphide1 from arseniate p#bdh solutions1 in as much as hydrogen sulphide is an agent for the precipitation of the sulphides of cations4 ,arsenious acid1 the hydroxide of the lower oxide1 on the other hand1 is a much weaker acid and shows more pronounced basic 7amphoteric7 properties1 and arsenic trisulphide is precipitated1 without difficulty1 from solutions of arsenious acid in hydrochloric acid4 ,we have3 #b ,as#c #c ,s#b ,as#b,s#c 4 ,when arsenic acid is reduced to arsenious acid by sulphurous acid1 by iodides 7see ,chap4 ,,xvi7 or by hydrogen sulphide 7see below71 no further difficulty in precipitating a sulphide 7,as#b,s#c7 is experienced4 ,when a solution of arsenic acid1 containing the usual small amount of hydrochloric acid 7#j4c molar71 is treated with hydrogen sulphide at ordinary temperatures1 the following three reactions take place1 but exceedingly slowly3 #b ,h#c;,as,o#d #e ,h#b,s ,as#b,s#e #h ,h#b,o 7#a7ejd ,h#c;,as,o#d ,h#b,s ,h#c;,as,o#c ,s ,h#b,o 7#b7eje #b ,h#c;,as,o#c #f ,h,cl #c ,h#b,s #b ,as,cl#c #c ,h#b,o #c ,h#b,s ,as#b,s#c #f ,h,cl #c ,h#b,o 7#c7 ,even in the presence of a considerable amount of arsenic acid1 precipitation1 either of the trisulphide or of the pentasulphide1 may not occur for some time1 and1 unless one takes account of that fact1 the dangerous element1 arsenic1 would easily be overlooked4 ,heat accelerates both the precipitation of the pentasulphide and the reduction of arsenic acid and the subsequent precipitation of arsenic trisulphide4#ejf ,the interesting observation has also been made that1 in the presence of an unusually large excess of hydrochloric acid and of a rapid stream of hydrogen sulphide1 the precipitation of the pentasulphide 7equation 7#a77 is favored and accelerated4#ejg ,for instance1 if #ajj c4c4 of concentrated hydrochloric acid 7sp4 gr4 #a4b7 are added to #ej c4c4 of a #j4a molar solution of potassium arseniate and a rapid stream of hydrogen sulphide is passed through the mixture at the ordinary temperature1 a copious precipitate is formed within a minute 7exp474 ,the precipitate formed under these conditions p#bdi is the pentasulphide4#ejh ,on the other hand1 a mixture of #e c4c4 of hexanormal hydrochloric acid and #ej c4c4 of #j4a molar potassium arseniate fails1 for a long time1 to give a precipitate when treated in the same way 7exp474 ,the acceleration of the precipitation of the pentasulphide by the presence of a large excess of hydrochloric acid forms a problem of peculiar interest and importance1 and no complete explanation of it has yet been offered4#eji ,the following considerations lead to one explanation1 that has been suggested4 ,arsenic acid1 by virtue of its close relations to antimonic1 stannic and arsenious acids1 may be assumed to have extremely weak basic1 as well as pronounced acid1 properties4 ,for its ionization1 we would have #c ,h ,as,o#dc ,h#c;,as,o#d 7 ,h#b,o7 ,as7,,oh7#e ,as#e #e ,,ho4 ,further1 the precipitation of ,as#b,s#e may be assumed to result1 ultimately1#eaj from the action of the sulphide-ion ,s#b on the positive ion ,as#e 7#b ,as#e #e ,s#b ,as#b,s#e 74 ,the favorable action of the hydrochloric acid might1 consequently1 be thought to result from the fact1 that it facilitates the ionization of arsenic acid as a base and the formation of a salt#eaa ,as,cl#e4 ,it could thus greatly increase the concentration of the ion ,as#e and facilitate its combination with the sulphide-ion4 ,treatment of a solution of arsenic acid with a concentrated acid1 yielding a large concentration of hydrogen-ion1 would carry the series of actions1 represented in the above ionization equation for arsenic acid1 decidedly toward the right--suppressing the arseniate-ion ,as,o#dc and increasing the concentration of the arsenic-ion ,as#e4 ,since we cannot apply the equilibrium laws 7or the principle of the solubility-product7 to solutions as concentrated as the one under discussion1 a quantitative theoretical treatment of the subject cannot be given4 ,the following may be suggested3 ,the action of the acid would be favorable to the precipitation of ,as#b,s#e by suppressing the arseniate-ion ,as,o#dc and thus increasing the concentration of the hydroxide ,as7,,oh7#e1 available for ionization as a base and for the production of the ion ,as#e4 ,but the further favorable effect of the hydrochloric acid1 in converting the hydroxide into a salt ,as,cl#e and increasing thereby the concentration of ,as#e1 would be very largely offset by the action of the acid in suppressing the p#bej sulphide-ion 7,s#b k _/ ,h#b2 see p4 #bja74 ,for systems to which the equilibrium laws could be applied1 the concentration of ,as#e 7except for the suppression of the ion ,as,o#dc7 would grow1 approximately1 with the fifth power#eab of the concentration of the hydrogen-ion1 and the concentration of the sulphide-ion would decrease1 approximately1 proportionally to the square of the concentration of the hydrogen-ion4 ,further1 the precipitation of ,as#b,s#e1 in a system to which the principle of the solubility-product were applicable1 would depend on the relation of the product ,as#eb ,s#be to the solubility-product constant2 it is evident that the value for ,as#eb would increase proportionally to the tenth power of ,h and the value of ,s#b decrease proportionally to the tenth power of the same factor ,h4 ,the two effects would consequently offset each other under such conditions4 ,however1 the equilibrium laws cannot legitimately be applied to such concentrated solutions and the relation has been developed only to indicate opposing factors1 which must be taken into account4 ,an experimental study of the problem would be extremely interesting4#eac ,since it involves the question of the minute basic ionization of a moderately strong acid 7,h#c;,as,o#d71 which may be open to measurement 7see ,chap4 ,,xvi71 the problem is one of particular interest and importance4 ,the analytical precautions1 taken to insure the precipitation1 by hydrogen sulphide1 of arsenic sulphide1 when arsenic is present in quinquivalent form1 are based on the observations described2 in quantitative analysis1 for the sake of securing a precipitate of uniform composition1 the aim is to precipitate the pure pentasulphide and a considerable excess of hydrochloric acid is used4 ,in qualitative analysis1 where the composition of the precipitate is a matter of indifference and a large excess of acid would seriously interfere with the precipitation of certain sulphides 7e4g4 ,cd,s1 see p4 #baa71 a smaller excess of acid is used and the precipitation of arsenic sulphide is insured by prolonged treatment of a solution with hydrogen sulphide at a high temperature4 ,,footnotes3 #dib ,the weak basic properties of the hydroxides of the aluminium group1 as compared with those of the zinc group1 a chemical difference1 and the resulting great instability of the carbonates of the former group1 are used in the separation of the aluminium from the zinc group1 by barium carbonate2 but the physical element of extreme insolubility of the trivalent hydroxides enters also as an important factor 7see footnote #c1 p4 #aid74 #dic ,see p4 #bdg1 in regard to the behavior of arsenic acid in this respect4 #did ,see p4 #bdf1 footnote #c1 in regard to the action of sodium sulphide on mercuric and bismuth sulphide4 #die ,vide ,nilson1 ,j4 prakt4 ,ch41 #ad1 #aej 7#ahgf74 #dif ,such a solution does not react alkaline to phenolphthalen4 #dig ,hydrogen sulphide rapidly destroys the indicator and the experiment is best carried out by preparing #ej c4c4 of a saturated aqueous solution of hydrogen sulphide1 containing #a or #b c4c4 of normal hydrochloric acid1 and by adding a considerable excess of methyl orange to the solution immediately before the addition of potassium hydrosulphide solution1 which has been prepared as described in the text4 #dih ,see the discussion on p4 #agg4 ,see also the discussion by ,remsen on acidic and basic halides1 ,am4 ,chem4 ,j41 #aa1 #cjj 7#ahhi7 ,stud4 #dii ,in both cases acid salts1 ,,khco#c and ,,khcs#c1 are also formed4 #ejj ,mc,cay1 ,z4 anorg4 ,chem41 #bi1 #cf 7#aija74 #eja ,on p4 #bch the analogous equation for the condition of equilibrium of the anion of an oxygen acid with its components was developed4 ,applying the result to the ion ,sn,o#cb of stannic acid1 ,h#b,sn,o#c1 we have3 ,sn#d ,o#bc _/ ,sn,o#cb ,k4 ,it is evident1 from the form of the equation1 that for the stronger oxygen acids1 which are most stable as acids and ionize as bases at most in traces1 the value of the constant must be extremely small4 #ejb ,mercuric sulphide is somewhat soluble in potassium and sodium sulphides1 forming the salts ,me#b;,hg,s#b1 and the complex ion ,hg,s#bb4 ,a liter of #j4a molar ,na#b,s dissolves1 at #be1 #a4i grams 7#j4jjhb mole7 of ,hg,s ,knox1 ,trans4 ,faraday ,society1 #d1 #cf 7#aijh74 ,while the oxide 7hydroxide7 shows no perceptible tendency toward acid ionization1 mercuric salts1 it will be recalled1 show in many cases an abnormally small tendency to form the mercuric-ion 7see p4 #aae71 and the latter also shows a particularly great tendency towards forming very stable complex ions of all kinds 7e4g4 ,hg,i#db1 in ,k#b;,hg,i#d1 ,hg,cl#db in ,k#b;,hg,cl#d1 ,hg7,,cn7#db1 etc474 ,knox found for ,hg#b ,s#bb _/ ,hg,s#bb k1 the approximate value of k to be #a _/ #ajec4 ,bismuth sulphide is also very sparingly soluble in sodium or potassium sulphide1 but not in ammonium sulphide4 ,solid salts1 ,k,bi,s#b and ,na,bi,s#b are known ,knox1 ,j4 ,chem4 ,soc4 7,london71 #ie1 #agfj 7#aiji74 #ejc ,see the table1 p4 #ajd4 #ejd ,see the discussion of the reaction1 given below4 #eje ,see ,chap4 ,,xvi1 for the interpretation of the reduction as an ionic reaction4 #ejf ,bunsen1 ,ann4 7,liebig71 #aib1 #cje 7#ahgh74 ,brauner and ,tomicek1 ,j4 ,chem4 ,soc4 7,london71 #ec1 #ade 7#ahhh74 ,usher and ,travers1 ibid41 #hg1 #acgj 7#aije74 #ejg ,neher1 ,z4 anal4 ,chem41 #cb1 #de 7#ahic74 #ejh ,neher1 loc4 cit4 #eji ,the theory of the relations favoring the precipitation expressed in equation 7#a7 as against the reduction expressed in equation 7#b71 forms a second interesting problem4 #eaj ,intermediate derivatives1 such as ,h#c;,as,s,o#c 7p4 #bdf71 could be the result of the ionization of ,as7,,oh7#e1 or of ,as,cl#e1 in stages 7see p4 #ajf74 ,neher1 loc4 cit41 ,mc,cay1 loc4 cit4 #eaa ,neher 7loc4 cit47 suggested that the favorable action of the large excess of hydrochloric acid might well be due to the formation of ,as,cl#e4 ,mc,cay1 ,j4 ,am4 ,chem4 ,soc41 #bd1 #ffa 7#aijb71 discusses the ionization of arsenic acid as a base1 in connection with the precipitation of ,as#b,s#e4 #eab ,as7,,oh7#e is considered to be an extremely weak base and ,as,cl#e to be an ionizable salt4 #eac ,to a certain extent1 the effect of the acid may be to coagulate and precipitate the colloidal sulphide4 ,possibly1 also1 the concentrated acid renders inactive a considerable portion of the water present 7forming oxonium salts ,,oh#c;,cl1 etc41 see p4 #bch71 which tends1 by hydrolysis1 to reverse the formation of the chloride ,as7,,oh7#e #e ,h,cl ,as,cl#e #e ,h#b,o4 ,possibly1 the formation of the pentasulphide is not wholly an ionic reaction1 its precipitation being always a more or less slow process1 and there may be intermediate products whose formation could be accelerated by the presence of acids 7see ,bredig and ,walton1 ,z4 ,elektrochem41 #i1 #aad 7#aijc7 for the study of a simple inorganic action involving such catalytic effects of acids74 p#bea ,,chapter ,,xiv ,,oxidation ,,and ,,reduction ,,reactions4 ,i ,oxidation and reduction reactions are frequently met with in analysis1 and we shall turn now to the consideration of such reactions1 from the point of view of the modern theory of solution and the laws of equilibrium4 ,leaving until later the discussion of the most important and most common oxidizing agents1 such as oxygen1 nitric acid1 permanganate1 etc41 we shall1 in order to develop the subject most simply1 confine ourselves1 for the moment1 to the qualitative study of some oxidations and reductions met with early in the study of analytical reactions4 ,one such reaction is the reduction of ferric salts by hydrogen sulphide1 and the simultaneous oxidation of the latter to sulphur 7exp474 ,the reaction may be expressed by the equation #b ,fe,cl#c ,h#b,s #b ,fe,cl#b #b ,h,cl ,s 4 ,if the action is considered to be the result of the interaction of the ionized ferric chloride and hydrogen sulphide1 it would be represented by the equation #b ,fe#c #f ,cl #b ,h ,s#b #b ,fe#b #f ,cl #b ,h ,s 4 ,it is then clear that the reacting components1 according to such a conception1 are the ferric and the sulphide ions1 whose electrical charges mutually discharge each other4 ,considering only those components whose charges are changed1 we have #b ,fe#c ,s#b #b ,fe#b ,s 4 ,the reduction of a ferric to a ferrous salt would then be accomplished by the discharge of one of the three positive charges on the ferric ions2 the oxidation of hydrogen sulphide to sulphur would be accomplished by the complete discharge of the sulphide ions4 ,ferric salts are reduced1 much in the same way1 by iodides 7exp471 iodine being liberated3 #b ,fe#c #b ,i #b ,fe#b ,i#b4 ,reduction then appears to involve a loss of positive charges by ions1 oxidation a loss of negative charges4 p#beb ,conversely1 we frequently have occasion to oxidize ferrous salts to the ferric condition1 and among the most convenient reagents for the purpose are chlorine and bromine water 7exp474 ,for instance1 we have #b ,fe,cl#b ,cl#b #b ,fe,cl#c1 or1 considering the action from the point of view of the theory of ionization1#ead #b ,fe#b ,cl#b #b ,fe#c #b ,cl4 ,in this case the oxidation of the ferrous to the ferric ion consists in the assumption of an additional positive charge2 reduction of chlorine to the chloride-ion consists in the assumption of negative charges by the chlorine atoms4 ,definitions of ,oxidation and ,reduction in ,electric ,terms4--,the definitions must then be amplified and oxidation be considered to involve ultimately the assumption of positive1 or the loss of negative1 electrical charges by ions or atoms1 reduction to involve ultimately the assumption of negative1 or the loss of positive1 charges4 ,according to the electron theory of electricity a unit negative charge is an electron1 the unit positive charge1 probably1 the charge left on an atom when it has lost an electron2 and1 thus1 oxidation may simply be defined1 according to the electric theory of oxidation and reduction1 as consisting1 fundamentally1 in the loss of electrons by atoms or ions1 reduction as consisting in a gain of electrons4 ,for instance1 when hydrogen sulphide reduces a ferric salt1 #b ,fe#c ,s#b #b ,fe#b ,s1 the sulphide ions transfer their electrons to the ferric ions4 ,oxidations and ,reductions by ,electric ,currents4--,all of the oxidation and reduction reactions which have been discussed may1 in fact1 be effected by the use of an electric current in the place of chemical agents4 ,ferrous salts1 for instance1 are oxidized1 at the positive pole1 by the current to ferric salts3#eae ,fe#b ,fe#c1 or ,fe#b ,fe#c4 ,ferric salts are reduced1 at the negative pole1 to ferrous salts3 ,fe#c ,fe#b1 or ,fe#c ,fe#b4 p#bec ,,exp4--,a solution of ferrous chloride1 freshly prepared from iron wire1 or a freshly prepared solution of ferrous-ammonium sulphate1 is placed in a very small beaker2 a solution of ferric chloride1 acidulated with hydrochloric acid to prevent subsequent complete reduction of the ferric-ion to iron1 is brought into a similar beaker4 ,a small amount 7#e c4c47 of each solution is tested1 the former with potassium thiocyanate and the latter with ferricyanide solution1 to show the absence of perceptible quantities of ferric and ferrous ions in them1 respectively4 ,platinum electrodes1 consisting best of cylinders of platinum gauze1 are introduced into the solutions1 the solutions are connected by means of a salt bridge 7a ,u-tube filled with a solution of sodium chloride and closed at both ends by plugs of filter paper71 and a current of #j4b ampere is passed through the system1 the positive current entering the solution containing the ferrous salt4 ,after the current has been allowed to pass for a minute or two1 #e c4c4 is withdrawn1 by a pipette1 from the meshes of the positive electrode and tested with thiocyanate1 and #e c4c41 withdrawn in the same way from the negative electrode1 is tested with potassium ferricyanide4 ,production of ,electric ,currents by ,means of ,oxidation and ,reduction ,reactions4--,not only may all the oxidations and reductions which we have discussed be accomplished with the aid of the electric current1 but vice versa1 an electric current may readily be produced by a proper arrangement of the components of any one of these reactions4 ,care need only be taken to have the simultaneous loss and gain of electrons1 characteristic of all oxidation and reduction reactions1 occur in separate localities1 which must be connected1 however1 in such a way as to make the transfer of electrons1 a flow of electricity1 possible4 ,,exp4 ,for instance1 some ferric chloride and sodium chloride solution may be put into a small beaker1 some sodium chloride solution into a second beaker of the same size1 and the two solutions connected1 first by means of a salt-bridge1 and then by means of two platinum electrodes dipping into the solutions and connected with the terminals of a sensitive voltmeter4#eaf ,if p#bed all of the connections are made1 the introduction of the salt-bridge being left to the last1 a momentary slight motion of the needle is observed1 when the bridge is introduced4 ,the needle then falls back to the zero point 7see p4 #bgf74 ,if now some hydrogen sulphide water is poured into the beaker containing sodium chloride1 a decided1 and continuing1 deflection of the needle of the voltmeter is immediately observed1 showing the passage of an electric current1 and it is in the direction anticipated by the consideration of the reaction equation3 #b ,fe#c ,s#b #b ,fe#b ,s 4 ,the positive current passes into the voltmeter from the ferric chloride solution1 where ferric ions are giving up their charges2 the negative current enters the voltmeter from the solution containing the hydrogen sulphide1 where sulphide ions are being discharged4 ,the salt-bridge is necessary to complete the electrical circuit and prevent any local accumulation of positive or negative electricity 7polarization74 ,for instance1 as the ferric ions are discharged1 an excess of chloride ions would remain in the beaker1 rendering the solution negative and preventing the flow of electricity from the electrode1 if negative ions did not move off1 through the salt-bridge1 into the beaker containing hydrogen sulphide and1 simultaneously1 positive ions migrate into the beaker containing the ferric salt4 ,similarly1 the accumulation of positive electricity in the hydrogen sulphide solution1 on account of the hydrogen ions left free by the discharge of sulphide ions1 is prevented by the flow of positive ions 7sodium and hydrogen7 through the ,u-tube into the beaker containing the ferric chloride and the flow of negative 7chloride7 ions into the hydrogen sulphide solution4 ,thus a current of electricity passes through the whole circuit4 ,it is thus possible to reduce ferric chloride in one vessel by hydrogen sulphide poured into another vessel1#eag and an electric current may be obtained from the simultaneous discharge of the sulphide and ferric ions in the action4 ,effects of ,ion ,concentrations on the ,current4--,hydrogen sulphide1 it will be recalled1 is an extremely weak acid 7p4 #aii71 only a very small proportion is ionized and1 consequently1 the concentration of the discharging 7reducing7 sulphide-ion must be minute in this solution4 ,its salts1 however1 are highly ionized1 and by the addition of an alkali to the solution containing the hydrogen sulphide1 the concentration of the discharging ion would be very greatly increased and the current should therefore be intensified most decidedly--provided the hydrogen sulphide really reduces by means of its negative ion and not by the action of the nonionized acid4 ,as a matter of fact1 the anticipated decided increase in the intensity of the current is observed1 when alkali is added to the mixture containing the hydrogen sulphide 7exp474 ,similarly1 p#bee we have assumed that the oxidizing agent is the highly charged ferric-ion1 not the nonionized ferric salt4 ,now iron forms rather stable complex ions#eah with the fluoride-ion1 for instance1 ,fe,f#fc1 which yield ferric ions very much less readily than do ferric salts4 ,hence the addition of a fluoride--potassium or ammonium fluoride--should1 according to this view1 reduce the oxidizing power of the iron solution by suppressing the ferric-ion and converting it into the complex ,fe,f#fc4 ,in fact1 the addition of potassium fluoride immediately reduces the intensity of the current 7exp471 and1 simultaneously1 the deep yellow-brown color of the ferric salt solution gives way to the very pale yellow tint of the complex ion and its salt4#eai ,further ,illustrations4--,if ferrous sulphate solution is put into one beaker and sodium chloride solution into another1 connections being made similar to those used in the previous experiment1 then a vigorous current is instantly produced 7exp471 when some bromine or chlorine water is added to the sodium chloride solution1 the positive current flowing into the voltmeter from the beaker containing the bromine 7chlorine72 the bromine atoms 7chlorine atoms7 combine with electrons lost by the ferrous ions and are reduced to bromide ions 7chloride ions7 7see p4 #beb74 ,it would appear possible1 in fact1 to obtain an electrical current from any oxidation-reduction reaction1 if the oxidizing and reducing agents can be1 experimentally1 properly arranged for this purpose4 ,summary4--,we find thus that there is a most intimate connection between oxidation and reduction phenomena and electrical charges on atoms or ions4 ,in the first place1 an electrical current may be used as an oxidizing and reducing agent2 indeed1 a current cannot be passed through any solution without simultaneous oxidation and reduction at the positive and negative poles1 respectively4 ,and1 conversely1 an electric current may1 in turn1 be produced by a proper combination of the reagents in oxidation and reduction reactions4 ,need of the ,study of the ,quantitative ,relations4--,the interpretation of such actions from the point of view of the theory p#bef of ionization offers1 then1 no particular difficulties4 ,but1 as far as we have developed the theory1 that is1 essentially from its qualitative side1 difficulty would be encountered in understanding why certain other reactions1 involving a similar simultaneous discharge of positive and negative electricity by ions1 which might be expected to take place1 do not seem to take place4 ,thus1 solutions of ferric sulphate do not appear to be reduced appreciably by the hydroxide and oxide ions of the water present4 ,although the possibility of such a reduction exists through the simultaneous discharge of the positive electricity of the ferric ions and the negative charge on the oxide ions 7or hydroxide ions7 of water 7#d ,fe#c ,o#b #d ,fe#b ,o#b or #d ,fe#c #d ,,ho #d ,fe#b ,o#b #b ,h#b,o71 comparable with the reduction of ferric ions by sulphide ions1 such a reduction does not take place appreciably4#ebj ,and1 similarly1 whereas the iodide-ion1 as we have seen1 reduces the ferric-ion very readily1 the analogous chloride-ion does not appear to do so4 ,sodium chloride may be added to ferric sulphate solution and potassium ferricyanide fails to show that any ferrous salt is produced 7exp474 ,the mere possibility of a transfer of charges1 or electrons1 is therefore apparently#eba not sufficient to induce an oxidation and reduction reaction--much in the same way as1 for instance1 the mere presence1 simultaneously1 of the barium-ion and the carbonate-ion1 in itself1 does not necessarily lead to the precipitation of barium carbonate 7p4 #ij71 although the latter is difficultly soluble4 ,in order to understand the problem of precipitation or nonprecipitation of salts1 it was found necessary to examine the question from its quantitative side 7p4 #ia71 and1 similarly1 the solution of the difficulty concerning the occurrence or nonoccurrence of oxidation and reduction reactions1 where the possibility of a transfer of electrons is given1 will be found in a study of the problem from its quantitative side4 ,oxidation and ,reduction ,reactions as ,reversible ,reactions4--,in order to reduce the development of the quantitative p#beg relations to the simplest possible terms1 we may turn to still simpler oxidation and reduction reactions than those studied thus far4 ,if a rod of zinc is placed in a solution of copper sulphate1 copper is deposited and zinc sulphate is formed4 ,if we consider the action to be an ionic one1 we have3 ,cu#b ,,so#db ,zn ,zn#b ,,so#db ,cu 1 or1 since the sulphate-ion is not directly concerned in the action1 we have more simply3 ,cu#b ,zn ,cu ,zn#b4 ,cupric-ion has been reduced1 therefore1 to metallic copper1 the metallic zinc oxidized to zinc-ion1 each zinc atom transferring two electrons to a cupric ion4 ,closer analysis of the action shows that this interpretation of the action1 from the electrical point of view1 is not at all in conflict with the older definitions and conceptions of oxidation and reduction3 copper is deprived of the oxygen with which it is combined in nonionized copper sulphate1 ,o ,cu ,,so#b1 and by evaporation of the solution1 ,o ,o zinc sulphate1 ,zn ,,so#b1 ,o containing the zinc combined with oxygen1 is obtained4 ,we shall presently find1 however1 that it is just in the quantitative formulation of the relations1 that the interpretation of the action from the point of view of the theory of ionization has proved its superiority over the older view4 ,if a strip of copper is placed in a solution of mercuric nitrate1 copper1 in turn1 is dissolved1 being oxidized to the form of cupric-ion1 and mercury is deposited3 ,cu ,hg#b ,cu#b ,hg 4 ,we find1 then1 that cupric-ion has a tendency to give up its charges1 to be reduced to the metallic condition2 metallic copper1 in turn1 has a tendency to revert to the ionic condition1 to be oxidized and to form cupric-ion4 ,we may consider the two opposed tendencies1 shown in these relations1 as representing a reversible reaction3 ,cu ,cu#b4 ,,exp4 ,if an electric current is passed through a copper sulphate solution1 copper is deposited on the negative 7platinum7 electrode2 if the current is reversed1 the copper vanishes quite as rapidly at what is now the positive pole4 p#beh ,condition of ,equilibrium4--,for such a reversible reaction we might expect1 if we may apply the law of equilibrium to it1 that the ratio of the concentrations of copper and of the cupric-ion would be a constant for the condition of equilibrium at a given temperature4#ebb ,we would then have3 ,cu#b _/ ,cu k4 ,since the concentration ,cu of a pure1 dense#ebc piece of copper may be considered a constant at a given temperature1 it would follow1 that the first term in our relation would also have a constant definite value for the condition of equilibrium between the metal and its ion4 ,consequently1 for the condition of equilibrium we would have3 ,cu#b ,k,cu#b4 ,metallic copper would then be in equilibrium1 at a given temperature1 with solutions containing cupric-ion only if the latter has a perfectly definite1 constant concentration4 ,nernst#ebd discovered this and similar relations1 as a result of a more rigorous analysis of the energy changes involved in the ionization and precipitation of metals1 and proved the validity of the relations4 ,the value of the constant1#ebe which1 according to ,nernst's p#bei suggestion is called the electrolytic solution-tension constant1 is #h;,e#bb for copper#ebf2 that is1 copper is directly in equilibrium with a solution containing cupric-ion only if the concentration of the latter is #h;,e#bb gram-ion per liter4 ,we see1 then1 that copper would be directly in equilibrium with solutions of cupric salts only if they contain this exceedingly minute concentration of cupric ions4 ,when such is the case1 the ionization of the metal and the formation of the metal1 by the deposit of discharging ions1 may be considered to proceed with the same velocity 7p4 #id74 ,but1 if the metal is dipped into a solution of greater concentration of cupric ions than that represented by the constant1 say into a solution of #j4a molar copper sulphate1 the velocity of deposition of the metal would be proportionally increased 7p4 #ib71 while the velocity of ionization and solution of the metal would remain unchanged4 ,we would consequently have the ions discharging and forming metal more rapidly than they are formed4 ,a condition of change1 not of equilibrium1 exists4 ,if we p#bfj consider the changes that must occur1 we see that the ions1 discharging on the metal1 would charge it with positive electricity1 and the positive charge would1 in turn1 repel from the metal the positive cupric ions remaining in the solution4 ,equilibrium would be expected to result when the charge on the plate becomes heavy enough to repel from the film1 immediately surrounding it1 all the cupric ions excepting those representing a concentration of #h;,e#bb1 as required by the value of the equilibrium constant4 ,the positive charge on the plate would attract and hold negative sulphate ions1 freed by the discharge of cupric ions1 in a kind of double layer1 the surface of the metal holding positive charges and the film of liquid in contact with it holding an excess of negative ions4 ,an electric potential would thus be established between the positive metal and the negative solution1 bathing it4#ebg ,it is evident that the more concentrated the solution of cupric ions1 the heavier the charge must be that will be required to repel the cupric ions sufficiently to establish equilibrium4#ebh ,if copper is placed in a solution in which the concentration of the cupric ions is smaller than the constant #h;,e#bb1 the velocity of ionization will be greater than the velocity of the deposition of the metal4 ,the ions formed1 having assumed positive charges1 will leave a negative charge on the metal1 and1 as a result of the electrical attraction1 a double layer1 surrounding the metal1 will again be formed1 the positive ions clinging to the negative metal4 ,equilibrium will be reached when the concentration of the cupric ions originally present1 increased by the new ions formed in this double layer1 will have reached1 in the film bathing the plate1 the concentration demanded by the equilibrium constant4 ,an electrical potential will be established as before1 the metal being negative1 the solution1 in this case1 positive4 ,by developing the quantitative relations between osmotic forces and the electrical potential1 ,nernst#c was able to show that1 at room temperature#ebi 7#ag-ah71 the following logarithmic relation p#bfa holds for the potential difference between a metal#ecj and a solution of its ion1 which bathes it3 ,me1 ,me-salt 7#j4jege _/ v7 log7,c _/ ,k74 ,in this equation ,me1 ,me-salt is the electrical potential1 in volts1 existing between the metal ,me and the solution of its salt1 ,me-salt2 v is the number of electrical charges transferred from the metal to its ion1 and vice versa1 in the action ,me ,meion2 in the present case1 it is identical with the valence of the metal ion1 which the metal forms4 ,c is the concentration of this ion in any given case1 and ,k is the concentration represented by the solution-tension constant1 i4e4 by the equilibrium constant4 ,the logarithm is the common one4 ,in place of the concentrations1 ,k and ,c1 the corresponding osmotic pressures of the metal ion 7,p and p1 as used by ,nernst7 may be used in the equation1 and for solutions in which osmotic pressure and concentration are not strictly proportional1 the osmotic pressure should be used by preference 7see footnote #d1 p4 #beh74 ,the sign#eca given to p#bfb ,me1 ,me-salt1 in any given case1 shows the sign of the electric charge on the first component named in the subscript1 which is the metal1 in the present instance4 ,for the relation between copper and cupric-ion we would have3 ,cu1 ,cu-salt 7#j4jege_/b7 log7,c _/ ,k74 ,when the concentration of cupric-ion is equal to the constant1 ,c ,k1 the logarithm has the value #j and the potential difference is #j4 ,when the concentration of cupric-ion is smaller than the constant1 ,c ,k1 the potential ,cu1 ,cu-salt is negative1 i4e4 the metal receives a negative charge4 ,this negative charge is the greater1 the smaller ,c is4 ,when ,c ,k1 ,cu1 ,cu-salt is positive1 the copper plate receives a positive charge1 and this positive charge is the greater1 the larger the value of ,c is4 ,applications4--,it should be clear1 from these considerations1 that an electric current will result1 if copper plates are introduced into solutions containing different concentrations of cupric-ion and the solutions and electrodes are connected in such a way as to allow the flow of a current4 ,if we call ,cu the copper plate dipping into a solution containing cupric-ion at a concentration ,c1 and ,cu the plate in a solution containing ,cu#b ,c1 we have#ecb3 p#bfc ,cu1 ,cu ,cu1 ,cu,x ,cu1 ,cu,x 7#j4jege _/ #b7 log7,c _/ ,k7 log7,c _/ ,k7 and#ecc ,cu1 ,cu 7#j4jege _/ #b7 log7,c _/ ,c74 ,it is also clear1 from this equation1 that the greater the difference in concentration of the cupric-ion in the two solutions1 the greater should be the potential difference produced4 ,the following series of experiments illustrates these relations and confirms the conclusions reached4 p#bfd ,if two electrodes of pure copper are introduced into solutions of cupric sulphate of equal concentration1#ecd no current is produced1 when the solutions are connected by a salt bridge and the electrodes with a voltmeter 7exp42 the chemometer described on p4 #bec is used74 ,if one of the beakers is partially emptied1 only a few drops of the solution being left in it1 and is then filled with a solution of sodium sulphate1 we notice that the voltmeter immediately indicates the establishing of a potential difference--a current is produced4 ,from the experimental arrangement and from the manner of the deflection of the needle of the chemometer1 we note1 too1 that the plate dipping into the more concentrated solution of the cupric-ion is the positive pole1 and hence the cupric ions are discharged on it2 this solution is therefore growing less concentrated in regard to cupric-ion4 ,in the other vessel1 copper is dissolving and the concentration of cupric-ion is increasing4 ,both changes tend toward equalizing the concentrations in the two solutions and thus toward establishing equilibrium4 ,the diffusion of ions1 from and to the plates1 is a very slow process 7p4 #h71 and since the potential produced depends on the momentary concentrations of the liquid films immediately next to the plates1 the potential difference1 first observed1 is seen to disappear rapidly4 ,more decided and lasting potential differences are obtained by introducing reagents1 which keep the concentration of the cupric-ion1 automatically1 at very low values in the one solution1 and which thus make us less dependent on the slow diffusion of the ions around the plates4 ,we may add1 for instance1 sodium hydroxide to a solution of copper sulphate to precipitate cupric hydroxide2 cupric hydroxide being a difficultly soluble compound1 its saturated solution contains only a very small concentration of p#bfe cupric-ion4 ,if we connect1 again1 copper plates in two equally concentrated solutions of copper sulphate1 and add a little more than the equivalent amount of sodium hydroxide to the solution holding the plate connected with the negative post of the voltmeter1 cupric hydroxide is thereby precipitated1 and we note that a decided difference of potential is established and maintained 7exp474 ,an excess of a concentrated solution of sodium hydroxide should1 according to the principle of the solubility-product1 reduce the concentration of cupric-ion still more1 and the potential is1 in fact1 thereby increased 7exp474 ,cupric sulphide is much less soluble than cupric hydroxide1 and if we add sodium sulphide 7a little more than one equivalent7 to the mixture containing the hydroxide1 we find that the hydroxide is converted into the less soluble1 black sulphide1 leaving a still smaller concentration of cupric-ion in this solution1 and the potential is again increased 7exp474 ,we found that the complex ions of copper with the cyanide-ion are so extremely stable as to allow of the existence of a concentration of cupric-ion so minute1 that copper sulphide cannot be precipitated from cyanide solutions 7p4 #bbh74 ,if sufficient potassium cyanide is added to the mixture containing the suspension of cupric sulphide1 the sulphide dissolves readily1#ece and the largest potential difference1 yet noted1 is produced4#ecf ,we find thus that the behavior of the metal1 in contact with these different solutions1 agrees with the demands of the theory4 ,the ,equilibrium ,relations between ,two ,metals and ,their ,ions4--,the tendency of a metal to ionize and of its ion to be reduced has been aptly likened to the tendency of a liquid to form its vapor and of the vapor to condense to its liquid 7the name solution tension expresses the analogy to vapor tension74 ,as different liquids have vastly different tendencies to vaporize at a given temperature1 so different metals1 different elements1 have vastly different tendencies to ionize4 ,we shall consider1 briefly1 this tendency also in the case of zinc4 ,in aqueous solutions1 the concentration of zinc-ion with which the metal would be in equilibrium1 as found by calculation from the potential difference between zinc and zinc sulphate solutions p#bff of realizable concentrations of zinc-ion1 is #ajag1 a value#ecg enormously larger than #ajba1 the value of the corresponding constant for copper4 ,a zinc rod1 in contact with a solution of a zinc salt1 like zinc sulphate1 will acquire a negative charge1 as the metal must ionize much more rapidly than the ion will be discharged1 since even a saturated solution would contain only a relatively small concentration of the ion4 ,copper1 as we have seen1 placed in a copper sulphate solution of moderate concentration1 is charged with positive electricity1 the concentration of cupric-ion being very much larger than that required for the condition of equilibrium between the metal and its ion4 ,when zinc1 immersed in a zinc sulphate solution1 and copper1 immersed in a copper sulphate solution1 are connected through a metal circuit1 e4g4 that of a voltmeter1 and the solutions are connected by a salt-bridge 7exp471 a current is established1 the positive current flowing from the copper through the metal circuit to the zinc1 metallic copper being deposited and zinc going into solution4 ,the combination represents the well-known ,daniell cell4 ,we note that in each solution the change in concentration of the ion is towards the solution-tension constant1 towards a condition of equilibrium4 ,we may inquire1 a little more closely1 what would be the condition for equilibrium for such a system4 ,if we imagine a copper plate dipping into a solution containing a concentration of #ajba of cupric-ion 7the solution-tension constant71 the metal will be directly in equilibrium with the solution and will not acquire any electrical charge4 ,if we imagine a zinc rod immersed1 in the same way1 in a solution containing a concentration of zinc-ion of #ajag 7this is not practically feasible71 the metal and its ion would also be in equilibrium with each other and the metal would not assume any charge4 ,it is evident that1 if the zinc and copper and the solutions of their salts were connected1 no current would be established1 p#bfg zinc would not be oxidized to zinc-ion1 and cupric-ion would not be reduced4 ,in this condition of equilibrium1 then1 the ratio of the concentrations of the respective ions in the solutions bathing the metals would be1 also1 the ratio of the solution-tension constants4 ,this is a general relation for these two metals--the individual concentrations of the ions need not have the value of the solution-tension constants1 but equilibrium will be established whenever the ratio of the concentrations of the cupric-ion and the zinc-ion has the same value as the ratio of the solution-tension constants4#ech ,the condition for equilibrium1 in mathematical form1 is then ,zn#b _/ ,cu#b ,k,zn _/ ,k,cu ,keq42 and ,k,zn _/ ,k,cu #ajag _/ #a;,e#ba #ajch ,keq4 ,the nearer the ratio is to the equilibrium constant1 the smaller the potential will be1 until1 when the constant is reached1 it becomes #j4 ,we cannot increase the concentration of zinc-ion indefinitely in order to reach the condition of equilibrium1 but we may reduce the concentration of cupric-ion practically at will1 as we have seen 7p4 #bfe71 and we may thus approach the constant4 ,in fact1 if we add to the copper sulphate solution of the copper-zinc element1 described above1 a solution of sodium hydroxide1 and thus leave1 in the solution1 only the small concentration of cupric-ion belonging to the difficultly soluble cupric hydroxide1 the potential of the copper-zinc element is decidedly reduced 7exp474 ,if sodium sulphide is added to the cupric hydroxide1 to convert the hydroxide into the less soluble sulphide1 which yields a smaller concentration of cupric-ion1 the potential is again reduced most decidedly 7exp474 ,it has now so small a value that we may readily anticipate that1 if the cupric-ion is suppressed so thoroughly1 by the addition of potassium cyanide1 that even the sulphide cannot persist1 the value of the ratio ,zn#b 3 ,cu#b may grow even larger than the p#bfh equilibrium constant #ajch1 and we would have a system in which chemical change in the opposite direction must result from the tendency to establish equilibrium4 ,in fact1 if potassium cyanide is added to the mixture surrounding the copper plate1 in sufficient quantity to dissolve the sulphide1 we find that a current is established in the opposite direction#eci--zinc is now precipitated at the expense of the solution of metallic copper2 that means1 that the zinc-ion is being reduced by metallic copper1 which in turn is oxidized to cupric-ion 7exp474 ,we may apply the conclusions1 reached1 to the action of metallic zinc when it is introduced into the solution of a cupric salt4 ,the oxidation of zinc to the zinc-ion and the reduction of the cupric-ion to copper must be reversible reactions1 ,zn ,cu#b ,zn#b ,cu 1 which will come to a condition of equilibrium1 according to the laws of equilibrium1 when ,zn#b 3 ,cu#b ,k #ajch4 ,the value of this ratio shows that the cupric-ion will be practically completely reduced1 and precipitated as copper1 by a sufficient quantity of zinc1 the trace of cupric-ion1 required to maintain the equilibrium ratio1 being too minute to be detected4 ,by the study of this oxidation and reduction reaction with the aid of potential differences1 as just described1 the validity of the relation is subject to demonstration1 and the value of the equilibrium constant is brought into definite relation to the solution-tension constants of the metals4 ,each element has its own characteristic solution-tension constant 7see the table at the end of ,chapter ,,xv71 and the relation just established for the reduction of cupric-ion1 at the expense of the oxidation of metallic zinc1 may be applied to any pair of metals and their ions4#edj ,general ,principles ,concerning ,equilibrium in ,reversible ,oxidation and ,reduction ,reactions4--,we may now extend the conclusions1 reached in the study of these particularly simple oxidations and reductions1 to oxidation and reduction reactions in general4 ,we must expect that1 when such an action is reversible and subject to the laws of equilibrium1 its course will1 as in all p#bfi previous applications of the equilibrium laws1 depend1 at a given temperature1 in the first place1 on the values of constants4 ,the 7solution-tension7 constants1 involved in this class of actions1 measure what we may call the affinity of atoms and ions for electric charges1 or electrons4 ,in the second place1 the course of the action will depend1 in each case1 on the concentrations of the ions1 concentrations which are1 to a considerable extent1 variable at will1 as we go from case to case4 ,in the third place1 all such reversible reactions will come ultimately to a condition of equilibrium1 in which neither action is absolutely completed1 and the course of the action1 in any given system not in equilibrium1 will always proceed toward this condition of equilibrium4 ,the oxidation and reduction reactions1 such as ,zn ,cu#b ,cu ,zn#b1 to which we have heretofore limited the discussion of the quantitative relations1 are particularly simple actions1 involving only two variables 7in this case ,cu#b and ,zn#b74 ,but the knowledge of the general principles of the quantitative relations will now enable us to answer questions1 in connection with more complicated cases1 which the qualitative relations alone did not put us into the position of answering 7see p4 #bef74 ,applications2 ,reduction of ,ferric ,salts and ,oxidation of ,ferrous ,salts4--,it will not be difficult to arrive now at definite conceptions as to why certain reactions of oxidation and reduction do not seem to take place1 although they are1 qualitatively1 entirely analogous to reactions which take place readily4 ,the study of one of the questions previously raised 7see p4 #bef71 namely as to why ferric ions apparently are not reducible by chloride ions1 while they are easily reduced by iodide ions1 will be sufficient to illustrate the application of the principles4 ,in considering the question of the possible reduction of ferric to ferrous ions1 at the expense of the oxidation of chloride ions to chlorine1 we must bear in mind the fact that the reduction of the ferric ions is a reversible process1 ,fe#c ,fe#b1 and that the oxidation of chloride ions to chlorine is also a reversible process1 #b ,cl ,cl#b4 ,we will deal first1 in some detail1 with the action ,fe#c ,fe#b4 ,for this reversible action we have an equilibrium constant#eda ,fe#b 3 ,fe#c ,k,ferro1 ,ferri #ajag1 which must be p#bgj taken into account in all oxidation and reduction reactions involving these ions4#edb ,in a system containing the two ions1 the tendency towards reduction of ferric-ion and the tendency toward oxidation of ferro-ion would be directly in equilibrium 7i4e4 without the intervention of other opposed forces1 such as an electric potential1 produced by an opposing cell or produced by an opposing action#edc of other components in the solution7 only when the concentration of ferro-ion is #ajag times as great as the concentration of ferric-ion4 ,if we connect a #j4a-molar solution of ferric chloride with a #j4a-molar solution of ferrous chloride1 by means of a salt bridge and a pair of platinum electrodes dipping into the solutions and connected with the voltmeter 7see p4 #bec71 a current is produced1 the positive current entering the voltmeter from the electrode placed in the ferric chloride solution 7exp474 ,it is evident that1 in the effort to establish equilibrium1 ferric ions in the ferric chloride solution are reduced at the expense of the oxidation of ferrous ions in the ferrous chloride solution4 ,if we consider only the ratio of the concentration of the ferro-ion to that of the ferric-ion in each of the salt solutions and leave out of consideration1 for the moment1 other1 secondary1 electrical forces1#edd it is clear that the ratio p#bga ,fe#ba 3 ,fe#ca in the ferrous salt solution1 considered by itself1 is far closer to the point of equilibrium#ede than the ratio ,fe#bb 3 ,fe#cb in the ferric chloride solution1 in which the concentration of ferric-ion is enormously greater than that of ferro-ion1 while the equilibrium constant demands that the ferro-ion should be in great excess4 ,the strongest tendency to change must be toward a reduction of the concentration of the ferric-ion in the solution of ferric chloride1 which is in agreement with the observed direction of the current4 ,equilibrium1 it may be added1 will be reached when the ratio of the concentration of ferro-ion to that of ferric-ion is the same in both solutions4#edf ,the addition of potassium fluoride to the ferric chloride solution converts the ferric-ion into the rather stable complex ferrifluoride-ion ,fe,f#fc1 whose potassium salt ,k#c;,fe,f#f is formed4 ,the p#bgb concentration of ferric-ion being decidedly reduced1 the system must be nearer to the condition of equilibrium1 the potential must fall 7exp474 ,it is again evident 7p4 #bee7 that the oxidizing agent is clearly the ferric-ion1 and not the total quantity of the ferric salt in the solution4 ,intensity of ,reactions4--,vice versa1 any oxidizing agent1 which has the power to oxidize ferro-ion to ferric-ion1 does so the more readily and vigorously1 the more completely any ferric-ion1 present or formed1 is suppressed4 ,if ferrous sulphate is added to a solution of silver nitrate1 a slow#edg reduction of the silver-ion1 and oxidation of the ferro-ion1 takes place according to ,fe#b ,ag ,fe#c ,ag 4 ,now1 if a little potassium fluoride is added to the mixture1 so as to suppress the ferric-ion1 which is always present1 by contamination1 in the original ferrous sulphate solution1 and which is formed in the action by the silver nitrate1 the oxidation of the ferrous salt and the precipitation of metallic silver is very much accelerated1#edh and a heavy black precipitate of silver is formed instantly 7exp474 ,the experiment is an illustration of the rle of potential in oxidation-reduction reactions1 the potential and the reducing power of ferro-ion being decidedly diminished by the presence of its oxidation product1 the ferric-ion4#edi ,it is also a further illustration of the rle the ions play in these actions1 the total amount of ferric salts not being changed by the introduction of the fluoride1 which simply suppresses ferric ions4 ,reduction of ,ferric ,salts by ,iodides4--,in the study of the oxidation of the ferro-ion and the reduction of the ferric-ion1 we p#bgc have thus far considered only the reversible tendencies of the two ions to change into each other1 tendencies which would be directly balanced1 in a given solution1 without the intervention of other forces1 when the ratio of the concentrations of the ions is that of the equilibrium constant1 #ajag4 ,in reactions involving the oxidation of a ferrous salt1 we have to deal1 however1 in exactly the same way1 with the reversible tendency of the oxidizing substance to act as oxidizing agent1 and1 similarly1 in every reduction of a ferric salt1 we have to deal also with the reversible tendency of the reducing agent to act as such4 ,in order to reach some definite conceptions as to the influences of these conflicting tendencies1 we shall consider1 next1 the reduction of ferric salts by iodides1 and then contrast this reduction with the action of chlorides on ferric salts1 and we shall thus complete the study of this action 7see p4 #bfi74 ,for the reduction of ferric salts by iodides 7p4 #bea71 we have to consider the reversible tendency of iodide-ion to form iodine and to be formed from iodine3 #b ,i ,i#b4 ,the constant#eej ,k,i1 ,iodine for the equilibrium ratio ,i#b _/ ,i#b is #e4f;,e#bi at #be4 p#bgd ,the reduction of ferric salts by iodides is a reversible reaction3 #b ,fe#c #b ,i #b ,fe#b ,i#b1 and the ultimate condition of equilibrium will depend on the values of the constants1 ,k,ferro1 ,ferri and ,k,i1 ,iodine1 and on the concentrations of the components used4 ,for the condition of equilibrium we have ,fe#cb ,i#b _/ 7,fe#bb ,i#b7 ,keq1 and for this constant the relation#eea ,keq ,k,i1 ,iodine _/ 7,k,ferro1 ,ferri7#b #e4f;,e#bi _/ 7#ajag7b #e4f _/ #aje p#bge can be established4 ,it is evident1 from the value of the constant1 that the chief tendency of the reversible reaction will be toward the reduction of the ferric ions and the liberation of iodine1 which is in accord with experience 7exp41 p4 #bea74 ,it is interesting to note1 again1 that the reduction of the ferric salt depends on the reduction of the ferric-ion3 the ferric-ion may be suppressed1 with the aid of potassium fluoride 7see p4 #bee71 and the addition of potassium iodide to a mixture of ferric chloride and potassium fluoride leads to the formation of traces1 only1 of free iodine 7exp474 ,action of ,chlorides on ,ferric ,salts4--,now1 when a chloride is used in place of an iodide1 we have to do with an ion1 ,cl1 which has an enormous affinity for its charge1 as compared with that of iodide-ion4 ,the equilibrium relation for the reversible reaction #b ,cl ,cl#b has the form ,cl#b 3 ,cl#b ,k,cl1 ,chlorine1 and the value#eeb of the constant is #b;,e#fj4 ,for the reaction of chloride-ion on ferric-ion we would have1 as in the case of the action of iodide-ion1 #b ,fe#c #b ,cl #b ,fe#b ,cl#b and ,fe#cb ,cl#b _/ 7,fe#bb ,cl#b7 ,keq4 ,for this equilibrium constant we have the relation1 as determined above 7p4 #bgd71 ,keq ,k,cl1 ,chlorine _/ 7,k,ferro1 ,ferri7#b 7#b;,e#fj7 _/ 7#ajag7b #b;,e#bf4 p#bgf ,it is evident1 from the value of the equilibrium constant1 that the action of chloride-ion on ferric-ion must result quantitatively so differently from the action of the analogous iodide-ion 7p4 #bge71 that the net qualitative results are entirely dissimilar4 ,whereas in the case of the iodide1 liberation of iodine and reduction of the ferric-ion are bound to be the chief and obvious actions1 in the case of the chloride-ion1 on the other hand1 the equilibrium constant demands that there should be no appreciable reduction of the ferric-ion or liberation of chlorine--which is in accordance with our experience 7exp41 p4 #bef74 ,it is noteworthy1 however1 that the equilibrium relations demand that at least traces of chlorine be liberated1 and traces of ferrous salt be formed1 since neither ,fe nor ,cl#b may have the value #j4 ,if we add some sodium chloride to a solution of sodium sulphate1 connected electrically1 in the usual way1 with a solution of ferric sulphate1 a very slight momentary current is produced 7exp474 ,the liberation of the first traces of chlorine and of ferro-ion on the electrodes is necessary1 and also sufficient1 to satisfy the conditions for equilibrium as expressed by the constant1 until diffusion from the electrodes removes these traces4 ,summary4--,we find1 thus1 that the general principle of the quantitative relations governing oxidation and reduction gives us the means of interpreting the differences in results in 7qualitatively7 similar combinations1 which1 qualitatively1 might lead to an oxidation-reduction reaction1 and which1 in certain cases1 do produce such reactions 7ferric-ion with iodide-ion71 and in other cases do not 7ferric-ion with chloride-ion74 ,,footnotes3 #ead ,the oxidation by chlorine may also be represented on the basis of the conception that the chlorine molecule contains a positive and a negative chlorine atom1 ,cl,cl4 7,vide ,w4 ,a4 ,noyes1 ,j4 ,am4 ,chem4 ,soc41 #bc1 #dfj 7#aija72 ,stieglitz1 ibid41 #bc1 #gif 7#aija72 ,walden1 ,z4 phys4 ,chem41 #dc1 #che 7#aijc72 ,j4 ,j4 ,thomson1 ,corpuscular ,theory of ,matter1 p4 #acj 7#aijg774 ,we may consider the action to take place as follows3 #b ,fe#b ,cl #b ,fe#c ,cl4 #eae is used to indicate an electron4 #eaf ,the whole device is an adaptation of ,ostwald's ,chemometer see ,z4 phys4 ,chem41 #ae1 #cii 7#ahid74 ,it has been found best to convert a ,weston voltmeter into a lecture table apparatus by lengthening its index to #aj inches1 with the aid of a very light1 hollow aluminium wire carrying an index and playing over a scale #aj inches wide1 drawn on glass and divided into #aej divisions4 ,the scale is illuminated by means of five small one-candle-power lamps4 ,the whole is encased in a simple wooden frame4 ,the voltmeter shows a range of #j4g volt1 but1 on account of its low resistance 7#gh ohms71 it is used only for qualitative purposes and does not register the true potentials1 quantitatively4 7,such adaptations of ,weston voltmeters may be purchased from the ,weston ,electrical ,instrument ,co41 or a similar instrument obtained from ,hartmann and ,braun1 ,frankfurt a_/,m1 ,germany47 #eag ,chemical ,action at a ,distance1 ,ostwald1 ,z4 phys4 ,chem41 #i1 #edj 7#ahib74 #eah ,peters1 ,z4 phys4 ,chem41 #bf1 #bbi 7#ahih74 #eai ,see below1 in regard to the quantitative relations for reactions of this nature4 #ebj ,,exp4 ,ferric sulphate solution is tested with a ferricyanide4 #eba ,rigorous quantitative examination of the relations shows 7p4 #bge7 that these reductions and oxidations do take place1 but equilibrium is reached when they have proceeded to so slight an extent1 that1 qualitatively1 they are not always obvious or discernible4 #ebb ,a change in the nature of the solvent changes the value of the equilibrium constant1 just as it changes the ionization constant of electrolytes4 ,see p4 #fa and see remarks by ,sackur1 ,z4 ,elektrochem41 #aa1 #chg 7#aije74 #ebc ,for exceedingly thin films of copper we cannot make this assumption1 and for such films the conclusions1 that follow1 are1 in fact1 found not to hold4 7,overbeck4 ,vide ,le ,blanc1 ,electrochemistry1 p4 #beb 7#ahif774 #ebd ,z4 phys4 ,chem41 #d1 #abi 7#ahhi74 #ebe ,the values of this and similar equilibrium constants are derived by means of ,nernst's formula 7see below7 for the potential difference between an element and solutions of its ions4 ,the derivation involves the assumption that this formula expresses correctly the relation between the potential change and the concentration change at all concentrations4 ,this assumption appears to be justified by all experimental indications thus far observed4 ,the constants are of importance1 primarily1 for the calculations which can be made with their aid 7see below71 and may1 conservatively1 be considered to be essentially calculation factors 7,rechengrssen1 according to ,haber4 ,see pp4 #bcb-g1 ,chapter ,,xii74 ,the constants may be expressed1 as in the text1 in terms of 7molar7 concentrations of the ions1 or in terms of the osmotic pressures of the ions1 a molar solution at #j producing an osmotic pressure of #bb4d atmospheres4 ,where osmotic pressure and concentration are not strictly proportional 7e4g4 for concentrated solutions71 the osmotic pressure1 rather than the concentration1 is the determining factor and1 when known1 is used in exact calculations4 ,the plan1 pursued in the text1 is adopted in order to express these constants in the terms used for all the other equilibrium constants4 ,it should be recalled 7e4g4 p4 #cj7 that in calculations1 in general1 where pressure and concentration are not strictly proportional1 the pressure is the determining factor4 ,a third method of expressing the solution-tension relations consists in giving the potential differences1 which exist between elements and solutions of their ions1 in which the ions have unit 7molar7 concentration4 ,these potential differences are functions of the solution-tension constants1 as will be discussed below1 and the constants1 in terms of concentrations or osmotic pressures1 may be easily calculated1 from the potential differences1 with the aid of this function 7see below1 and see the table at the end of ,chapter ,,xv74 #ebf ,according to ,wilsmore's tabulation 7,z4 phys4 ,chem41 #cf1 #ib 7#aija771 the potential difference ,cu1 ,cu#b of copper against a #j4e molar solution of cupric sulphate1 in which ,cu#b #j4aa1 is #j4ehd volt4 ,inserting these values for ,cu#b and ,cu1 ,cu#b in the equation ,cu1 ,cu#b 7#j4jege _/ #b7 log7,cu#b _/ ,k7 7see below7 and solving the equation for ,k1 we find ,k #h;,e#bb4 ,for ,cu#b #j4bd1 ,cu1 ,cu#b is #j4eid volt and ,k #h;,e#bb4 ,in regard to the convention determining the signs used 7in the present case ,cu1 ,cu#b is positive71 see the footnote below1 p4 #bfb1 and in regard to the definition of zero potential1 to which the potential differences used in this book refer1 see the table and summary at the end of ,chapter ,,xv4 #ebg ,nernst1 loc4 cit41 p4 #aea4 #ebh ,in other words1 the greater the concentration of cupric-ion1 the greater its osmotic pressure must be1 and the repelling electric force1 required to overcome the pressure of the cupric-ion1 would be correspondingly greater4 #ebi ,cf4 ,nernst1 ,theoretical ,chemistry 7#aijd71 pp4 #gbj-gbc1 in regard to the derivation and the general form of his formula4 #ecj ,for elements that form negative ions1 e4g4 for chlorine1 bromine1 oxygen1 etc41 the equation reads 7see pp4 #bgc1 #bge and the table at the end of ,chapter ,,xv73 ,elem41 ,electrolyte 7#j4jege _/ v7 log7,c _/ ,k74 ,note the changed sign of the expression on the right4 ,the difference in sign expresses the fact that1 when negative ions discharge on an electrode1 they render it negative1 and when they are formed by an electrode1 they leave the latter positive2 for positive ions1 it will be recalled1 the conditions are just the reverse 7see above74 ,where a soluble element 7e4g4 chlorine7 or a solution of a metal 7e4g4 sodium amalgam7 is used as an electrode1 its concentration1 in general1 is not constant1 as in the case of a pure1 solid metal like copper 7p4 #beh74 ,in such cases1 the quantity in the denominator of the ratio in the logarithm cannot be expressed by a constant ,k1 but is expressed by ,k ,c,element1 ,c,element being used to indicate the concentration of the element in the experiment in question4 #eca ,the convention1 adopted in the text1 for the use of the positive and negative signs in expressing potentials1 is that proposed by ,luther 7cf4 ,le ,blanc's ,lehrbuch der ,elektrochemie 7third edition71 p4 #bab74 ,the sign always denotes the character of the charge on the first component written in the subscript to 4 ,thus1 for a copper plate in contact with a solution of cupric sulphate1 when ,c ,k1 the logarithm1 log7,c _/ ,k71 has a positive value and ,cu1 ,cu,s,o#d is positive1 which means that the metal will be positive1 the electrolyte negative4 ,for instance1 for ,cu#b #a1 ,cu1 ,cu,s,o#d is found to be #j4fjf 7see the table at the end of ,chapter ,,xv74 ,cu1 ,cu,s,o#d ,cu,s,o#d1 ,cu4 ,by this use of the signs one is never in doubt as to their meaning4 ,unfortunately1 widely different definitions of the signs have been used 7cf4 ,le ,blanc1 ,electrochemistry 7#ahif71 pp4 #bji1 #bai1 and ,lehfeldt1 ,electro-,chemistry 7#aijd71 p4 #aei74 ,care must be taken1 in using the data of original papers1 to be informed as to the definition used4 ,in accordance with the convention as to signs1 adopted in this book1 the ratio of concentrations 7,c _/ ,k71 used in the logarithm of ,nernst's formula1 is the reciprocal of the ratio usually given4 ,the change has been made in order that the algebraic signs of the values obtained from the application of the formula should be the same as those observed in the experimental arrangements1 as demanded by the convention4 #ecb ,when two electrodes are combined to form an electric cell or couple1 the potential difference of the couple is always the 7algebraic7 difference of the two individual electrode potentials1 and hence these are subtracted from each other 7algebraically74 ,the electrode of the first term of the difference 7the minuend7 is named first in the subscript of the potential of the couple2 then the sign of the difference represents the character of the charge on that electrode1 in agreement with the convention 7see footnote #b1 p4 #bfa74 ,in illustration3 two copper electrodes may be taken1 each of which1 considered by itself1 carries a positive charge1 because the concentrations of the cupric-ion in the solutions bathing them are both greater than ,k2 when they are combined1 each of the two electrodes will tend to send a positive current1 in opposite directions1 into the metal connecting them4 ,but the potential of the electrode with the heavier charge 7the one dipping into the solution containing the greater concentration of cupric-ion7 will overcome the potential of the other electrode1 and the current will flow1 through the connecting metal1 with a potential that represents the difference between the two values4 ,if the electrode of the more concentrated solution is named first in the subscript of the potential of the couple1 its individual electrode-potential appears as the first term of the difference 7the minuend7 and is reduced by the value of the electrode-potential of the second electrode2 as this is numerically smaller than the value of the minuend1 the difference will be positive1 showing that the electrode in the stronger solution1 named first in the subscript of the potential difference of the couple1 carries a positive charge4 ,further1 if the second electrode dips into a solution1 in which the concentration of the cupric-ion is smaller than ,k1 the logarithmic expression for its electrode-potential will be found to give a negative value2 and the 7algebraic7 subtraction of this negative quantity from the electrode-potential of the first electrode will give a larger potential difference1 for the couple1 than that possessed by the first electrode alone--all of which agrees with the experimental results1 when such combinations are made4 ,where negative elements are concerned1 the same convention holds1 but the logarithmic expression for the potential of such an electrode carries a negative sign 7see footnote #a1 p4 #bfa71 which must be inserted1 algebraically1 when the expression is used as a term in the difference under discussion4 #ecc ,if ,c ,c1 the logarithm will be positive and ,cu1 ,cu will have a positive value1 which means that the copper plate1 ,cu1 which is named first in the subscript to 1 will be charged positively1 when the system works4 ,if ,c ,c1 the logarithm will be negative1 which means that the first plate1 ,cu1 mentioned in the subscript1 will receive a negative charge1 when the system works4 ,the sign is therefore intended1 by the convention adopted 7p4 #bfa71 to express any result for the working system1 irrespective of the charge on the individual plates before they are combined4 ,for instance1 for ,c #a and ,c #ajaj1 both plates are positive1 before they are connected with each other1 since in each case ,c ,k1 and ,cu1 ,cu,x 7#j4jege _/ #b7 log7,c _/ ,k7 a positive value4 ,when the plates are combined1 we find from ,cu1 ,cu 7#j4jege _/ #b7 log7,c _/ ,c7 that the first plate1 dipping in the more concentrated solution of cupric-ion1 is positive1 which is confirmed by experiment4 #ecd 7#a _/ #aj7-molar cupric sulphate1 #ajj c4c41 containing some sodium sulphate or nitrate1 to reduce the resistance1 is a convenient concentration4 #ece ,the copper plate is best freed from adhering sulphide by means of a strong cyanide solution1 and re-introduced into the solution4 #ecf ,kster1 ,z4 ,elecktrochem41 #d1 #aaj and #ejc 7#ahig74 #ecg ,in a solution of zinc sulphate in which ,zn#b #j4aad1 the potential ,zn1 ,zn,s,o#d #j4ead 7the minus sign indicates that the metal named first in the subscript has a negative charge74 ,inserting the values for ,zn#b and ,zn1 ,zn,s,o#d in the general equation given on p4 #bfa1 and solving for ,k1 we find ,k #ajag4 ,for ,zn#b #j4jbb and ,zn1 ,zn,s,o#d #j4ece1 we find ,k #ajaf4h4 7,cf4 ,wilsmore's tables1 loc4 cit47 #ech ,equilibrium will be established whenever the potential of the system is equal to #j4 ,the potential of the system may be calculated according to the equation 7see footnote #a1 p4 #bfb7 ,cu1 ,zn ,cu1 ,cu,s,o#d ,zn1 ,zn,s,o#d 7#j4jege _/ #b7 7log7,cu#b _/ ,k,cu7 log7,zn#b _/ ,k,zn774 ,the potential ,cu1 ,zn is #j whenever ,cu#b _/ ,k,cu ,zn#b _/ ,k,zn1 i4e4 when ,zn#b _/ ,cu#b ,k,zn _/ ,k,cu4 ,for ions of different valence1 such as silver and cupric ions1 the equilibrium equation assumes a somewhat less simple form4 ,for ,cu #b ,ag #b ,ag ,cu#b1 we have ,ag#b _/ ,cu#b 7,k,ag7#b _/ ,k,cu4 #eci ,vide ,ostwald's ,lehrbuch der allgemeinen ,chemie1 #b;d ,ed41 ,vol4 ,,ii1 p4 #hgd1 for the historical data on this action4 ,vide ,kster's experiments1 ,z4 ,elektrochem41 #d1 #ejc 7#ahig74 #edj ,see the footnote1 p4 #bfg1 in regard to the form the equilibrium ratio assumes when metals producing ions of different valence are used4 #eda ,the value of the constant is calculated from the data given by ,peters1 ,z4 phys4 ,chem41 #bf1 #aic 7#ahih74 #edb ,the fact that this equilibrium relation has been proved to hold for the action ,fe#b ,fe#c and that it must be taken into account in all oxidation-reduction reactions involving these ions1 in no wise excludes the possibility that other equilibrium relations can also exist between ferrous and ferric compounds4 ,for instance1 ferrous hydroxide ,fe7,,oh7#b may well have a characteristic tendency of its own to assume a further positive charge 7lose an electron7 according to ,fe7,,oh7#b ,fe7,,oh7#b1 the potential of which action may1 under given conditions1 be a main determining factor in the course of an action1 e4g4 in alkaline mixtures4 ,it is not impossible1 even1 that we also must consider negative ions ,fe,o#bb and their tendency to be oxidized4 ,evidence would suggest that ferrous hydroxide1 or its negative ion ,fe,o#bb1 may have1 indeed1 a very great tendency to be oxidized1 possibly much greater than the tendency of ,fe#b to form ,fe#c4 7,cf4 ,manchot1 ,z4 anorg4 ,chem41 #bg1 #dai 7#aija71 and ,mc,coy and ,bunzel1 ,j4 ,am4 ,chem4 ,soc41 #ca1 #cgj 7#aiji774 ,closer investigations of these relations1 from a quantitative viewpoint1 would probably determine this question and bring exceedingly important relations to light4 #edc ,e4g4 by the potential of the action ,cl#b #b ,cl4 #edd ,the potential of a solution of the iron salts is given by #j4jeh log7#ajag ,fe#c _/ ,fe#b74 ,in a solution of a ferric salt1 if ,fe#b #j1 the potential would obviously be 1 which could not present a condition of equilibrium4 ,equilibrium is established in such a solution1 as will be shown further on in the text1 by the liberation of chlorine and the formation of ferro-salt1 according to #b ,fe#c #b ,cl #b ,fe#b ,cl#b1 until the potential1 resulting from the tendency of chlorine to form chloride-ion1 just balances the tendency of the ferric-ion to form ferro-ion4 ,but when a ferric chloride solution is used as the source of supply of positive electricity1 as in the experiment described in the text1 both the ferric-ion and the chlorine tend to charge the platinum electrode with positive electricity and to revert to a condition of equilibrium in reference to their individual constants4 ,the relations are much like those between a cupric salt solution and a copper plate3 if ,cu#b ,k,cu#b1 equilibrium will be established1 as we have seen1 by the positive charging of the plate in sufficient degree to oppose the tendency of the cupric-ion to discharge 7see p4 #bei74 ,but when the solution and plate are used as the source of supply for an electric current 7p4 #bfd71 both the positive charge on the plate1 and the tendency of the cupric-ion to discharge and acquire the concentration ,cu#b ,k,cu#b1 will supply the positive current4 ,in calculations we ignore the positive charge already deposited on the plate and deal only with the concentration of ,cu#b4 ,the chlorine1 liberated in a solution of ferric chloride1 plays practically the same rle as does the copper plate in a cupric salt solution1 and it can be ignored in the discussion of the combination described in the text4 ,in a ferrous salt solution1 in a similar manner1 some ferric-ion must always be formed by liberation of hydrogen 7see p4 #bhb71 until equilibrium is reached according to #b ,fe#b #b ,h #b ,fe#c ,h#b4 ,hydrogen plays here the same rle as chlorine does in the ferric chloride solution4 #ede ,the condition for equilibrium is ,fe#b 3 ,fe#c #ajag1 in a solution considered for itself4 #edf ,this ratio need not be #ajag1 since we have two solutions combined with each other and the total potential will be expressed by3 #a #b #j4jeh 7log7#ajag ,fe#ca _/ ,fe#ba7 log7#ajag ,fe#cb _/ ,fe#bb77 #j4jeh log7,fe#ca ,fe#bb _/ 7,fe#ba ,fe#cb774 ,equilibrium is reached when the total potential is #j4 ,then ,fe#ca ,fe#bb _/ 7,fe#ba ,fe#cb7 #a and ,fe#ba _/ ,fe#ca ,fe#bb _/ ,fe#cb4 #edg ,in order to have very decided differences in the speeds of the action in the absence and presence of fluoride1 it is best to use an old ferrous sulphate1 or ferrous ammonium sulphate1 solution which contains considerable ferric salt4 #edh ,vide ,peters1 loc4 cit41 p4 #bcf4 #edi ,ostwald ,lehrbuch d4 allgem4 ,chem41 #b;d ,ed41 ,,ii1 #hhc 7#ahic71 first emphasized the fact that potential differences are a measure of oxidizing and reducing powers4 #eej ,the constant is calculated from the data of ,kster and ,crotogino on the potential of solutions of iodine in potassium iodide ,z4 anorg4 ,chem41 #bc1 #hh 7#aijj74 ,owing to the formation of complex ions ,i#c1 for which due allowance has not been made in the calculation1 and owing to some uncertainty as to the vague definition of the concentration of iodine used1 the estimation of the constant can only be considered a rough one4 ,the value given expresses the order of the equilibrium ratio sufficiently well for our present purposes4 ,in a recent paper1 ,bray and ,mac,kay ,j4 ,am4 ,chem4 ,soc41 #cb1 #iad 7#aiaj7 have determined the constant for the formation of the complex ion according to ,i#c ,i#b ,i1 which might be used to correct the data of ,kster and ,crotogino2 but in view of other uncertainties and inaccuracies1 the correction has not been considered advisable4 ,several related methods may be used to calculate the equilibrium constant for ,i#b 3 ,i#b ,k from the data of ,kster and ,crotogino4 ,perhaps the simplest method is the following3 ,a solution of iodine 7,i #a _/ #cb normal1 and therefore ,i#b #a _/ #fd molar7 in #a_/h molar potassium iodide1 in which1 the degree of ionization being taken into account1 ,i #j4aji1 was observed to show a potential ,i#b1 ,i #j4hfj 7the convention as to signs1 discussed on p4 #bfa1 is used here and the potential1 observed against a so-called calomel electrode1 is reduced to the so-called absolute potential2 cf4 ,le ,blanc1 ,lehrbuch der ,elektrochemie1 p4 #bad74 ,now1 there must be a certain concentration of iodide-ion1 which we will call ,c1 with which iodine of the above concentration would be directly in equilibrium and would give no potential at all 7cf4 pp4 #bfa and #beh in regard to copper74 ,with a change in the concentration of the iodide-ion1 a potential would be produced according to ,i#b1 ,i #j4jege log7,c _/ ,i74 ,this relation is of exactly the same nature as that developed for the potential of copper plates1 immersed in solutions of cupric-ion of different concentrations 7but see footnote #a1 p4 #bfa1 concerning the sign of the new relation74 ,in the present case1 we are dealing with univalent ions1 ,i1 in place of bivalent ions ,cu#b1 and the factor #j4jege is used instead of #j4jege _/ #b 7see p4 #bfa74 ,if we insert the observed values1 ,i #j4aji and #j4hfj1 of the experiment described above1 into the equation ,i#b1 ,i #j4jege log7,c _/ ,i7 and solve the equation for ,c1 we find ,c #ajad4 ,that means1 #a _/ #fd molar iodine would be directly in equilibrium with a concentration of iodide-ion #ajad 7if this value is inserted for ,i in the logarithmic equation1 the potential is found to be #j74 ,for the condition of equilibrium for ,i#b #b ,i1 according to ,i#b 3 ,i#b ,k1 we have then 7#ajad7b 3 7#a _/ #fd7 ,k #f4d;,e#bi4 ,similarly1 for ,i #j4aji and ,i#b #a _/ #eab the potential #j4hca is observed1 and the equilibrium constant is found to be #e4a;,e#bi4 ,when ,i #j4aji and ,i#b #a _/ #abh1 the potential is #j4hej and the constant is calculated to be #e4c;,e#bi4 ,the mean value for ,k is #e4f;,e#bi4 ,in these calculations1 the formation of ions ,i#c1 affecting the values for ,i and ,i#b1 has not been considered1 and there is some doubt whether the concentrations of iodine1 given by ,kster and ,crotogino1 do not represent ,i#b rather than ,i1 as assumed in the calculations4 ,if the former be the case1 the mean value of the above experiments would be #b4h;,e#bi4 ,the value1 used in the text1 is considered sufficiently accurate for the purposes of this book4 #eea ,this relation of the equilibrium constant and the solution-tension constants may be deduced in a manner similar to that for the analogous equilibrium constant for the oxidation of zinc by the cupric-ion1 as given in footnote #a1 on page #bfg4 ,the exact value of the equilibrium constant is uncertain1 since ,k,i1 ,iodine has not yet been determined with a sufficient degree of accuracy2 but the value1 used1 gives the order of the constant sufficiently well for our purposes1 especially when it is considered in connection with the constant given below for the same relation1 when the chloride-ion is substituted for the iodide-ion4 #eeb ,this is the value of the constant as calculated from the data given by ,wilsmore 7,z4 phys4 ,chem41 #cf1 #ia 7#aijj77 for the solution-tension of chlorine under atmospheric pressure at #ah4 ,the calculation may be made exactly as in the case of the similar constant for iodine 7p4 #bgc74 ,there must be a concentration of chloride-ion1 which we will call ,c1 with which chlorine1 of one atmosphere pressure at #ah1 would be directly in equilibrium4 ,the potential of chlorine1 against any other concentration of chloride-ion1 would be ,cl#b1 ,cl #j4jege log7,c _/ ,cl74 ,for ,cl #a1 is #a4fid 7see the table at the end of ,chapter ,,xv71 and inserting these values in our equation and solving it for ,c1 we find ,c #b4hh;,e#bi4 ,that means1 that chlorine1 at #ah and of atmospheric pressure1 would be in equilibrium with chloride-ion of the concentration given4 ,since chlorine1 at this temperature and pressure1 has a concentration of #a _/ #bc4i moles 7at #ah1 one mole is contained in #bc4i liters1 instead of in #bb4d liters1 at ,o71 we have for the condition of equilibrium3 ,cl#b 3 ,cl#b 7#b4hh;,e#bi7b 3 7#a _/ #bc4i7 #b;,e#fj4 ,cl#b represents1 thus1 in the calculation of this constant1 the concentration of chlorine gas 7see ,chapter ,,xv concerning gas electrodes7 and not the concentration of the dissolved chlorine2 the latter1 however1 is proportional to the gas concentration 7,chapter ,,vii74 p#bgg ,,chapter ,,xv ,,oxidation ,,and ,,reduction4 ,,ii4 ,,oxidation ,,by ,,oxygen1 ,,permanganates1 ,,etc42 ,,oxidation ,,of ,,organic ,,compounds ,we will turn now to the consideration of the question1 how the principles of the theory of electric oxidation and reduction may be applied to the most important oxidizing agent1 oxygen1 and to such vigorous and common oxidizing agents as permanganates1 dichromates1 nitric acid1 and similar substances4 ,oxidation of ,hydrogen by ,oxygen4--,the oxidation of hydrogen by oxygen may be first considered1 as representing a typical and1 in some respects1 the most important case of oxidation by oxygen4 ,hydrogen1 like copper1 zinc1 and other elements1 has a certain tendency to form its ion1 ,h1 and the latter1 in turn1 has a tendency to be reduced to hydrogen4 ,we may put ,h#b #b ,h and the condition for equilibrium1 at a given temperature1 will be ,h#b _/ ,h#b ,k,h1 ,hydrogen4 ,in this equation ,h#b represents the concentration of the hydrogen in contact with the electrode 7see below7 and with the solution1 and ,h represents the concentration of hydrogen-ion in the solution bathing the electrode4 ,the ionization of hydrogen1 at a given temperature1 depends1 according to this equation1 on two variables1 the concentration1 or pressure1 of the gas and the concentration1 or osmotic pressure1 of the hydrogen-ion in a given solution4 ,if platinum gauze1 coated with platinum black1 is charged with hydrogen1 then1 the greater the pressure of the gas1 the more soluble the hydrogen will be in the platinum 7p4 #aba74 ,such a charged gauze may be used as a hydrogen electrode 7,fig4 #ac1 p4 #bha71 the concentration of the hydrogen in which is proportional to the concentration1 or pressure1 of the hydrogen gas surrounding it2 the platinum will allow of the ready transmission of electric charges from and to the hydrogen dissolved in it4 p#bgh ,the value of the constant#eec ,k,h1 ,hydrogen ,h#b _/ ,h#b1 at #ah1 is found to be #e4ee;,e#i1 and hydrogen1 at #ah1 under atmospheric pressure1 is directly in equilibrium with hydrogen-ion of the concentration ,h #a4eb;,e#e4 ,if such an electrode1 in contact with hydrogen of atmospheric pressure1 is dipped into the solution of some neutral salt1 say sodium chloride1 in which the concentration of the hydrogen-ion1 formed by the ionization of water1 at #ah1 is #j4i;,e#g1 which is less than #a4e;,e#e1 the hydrogen in the electrode must tend to ionize more rapidly than it is formed from the ion1 and the electrode must receive a negative charge1 exactly as in the case of zinc1 placed in a zinc sulphate solution4 ,for oxygen similar relations may be developed4#eed ,we have3 ,o#b #b ,o#b and ,o#bb _/ ,o#b ,k#a4 7#a7 ,if we use the relation of the oxide-ion1 ,o#b1 to the more stable hydroxide-ion1 ,,ho1 we also have3#eee p#bgi ,,ho#d _/ ,o#b ,k#b ,k,,ho1 ,oxygen 7#b7 ,the value of the constant ,k,,ho1 ,oxygen is #h4b;,e#di at #ah1 and oxygen of atmospheric pressure at this temperature should be in equilibrium with solutions containing hydroxide-ion at a concentration#eef of #a4cf;,e#ab4 ,an electrode of platinum gauze1 charged with oxygen under atmospheric pressure1 when dipped into the solution of a neutral salt1 acquires a very strong positive charge1 the minute concentration of hydroxide-ion1 #j4i;,e#g1 being very much smaller than the value required by the constant1 and the oxygen ionizing very much more rapidly1 in consequence1 than it is formed by the discharge of hydroxide ions 7see p4 #bei74 p#bhj ,when we combine the hydrogen and the oxygen electrodes1 dipping into a solution of sodium chloride1 we find a current is1 in fact1 established 7the apparatus discussed on p4 #bha is used71 and it flows in the direction anticipated from the above development1 the positive current entering the voltmeter from the oxygen electrode4#eeg ,the potential of the hydrogen electrode1 for a constant pressure of hydrogen1 is dependent on the concentration of hydrogen-ion in the solution surrounding the electrode1 exactly as the potential of a copper plate1 against a solution of cupric-ion1 depends on the concentration1 or osmotic pressure1 of cupric-ion in the solution in which the plate is immersed4 ,the concentration of hydrogen-ion1 in the present instance1 is very small 7#j4i;,e#g1 at #ah71 the solution being practically neutral2 but the addition of an alkali must reduce its concentration far below even this value1 since for water the product of the concentrations of hydrogen-ion and hydroxide-ion is a constant 7p4 #agf7 and the increase in the concentration of hydroxide-ion1 produced by the addition of alkali1 must decrease the concentration of the hydrogen-ion proportionally4 ,we would expect1 then1 that the potential of the hydrogen electrode must increase1 when we add alkali to the solution surrounding it1 the hydrogen now ionizing against a much smaller concentration of its ion4 ,such is in fact the case 7exp471 and the increase is found to be subject to a logarithmic function for the relation between potential and the concentration of the ion1 similar to that found to hold for copper and its ion4#eeh ,in the same way1 the potential of the oxygen electrode must depend on the concentration#eei of the hydroxide-ion in the solution bathing it4 ,the addition of a strong acid1 like sulphuric acid1 to this solution1 by suppressing the hydroxide-ion1 small as its concentration is1 should increase the potential of the p#bha electrode and the total potential of the cell4 ,this1 in fact1 is the case 7exp472 the cell working under these conditions shows us the largest potential yet observed4#efj ,illustration3 ,,fig4 #ad4 ,the arrangement of the apparatus and the course of the current are shown in ,fig4 #ad4 ,the glass tube of the hydrogen electrode is connected with a hydrogen generator1 the tube of the oxygen electrode with a cylinder or gasometer filled with oxygen4 ,the hydrogen electrode is connected with the negative post of the voltmeter1 the oxygen electrode with the positive post4 ,since the hydrogen ionizes1 under the conditions used1 more rapidly than it is formed from the small concentration of the hydrogen ions surrounding the hydrogen electrode1 hydrogen ions pass from the electrode into solution ,a1 leaving a negative charge on the electrode2 there is a migration of sodium ions through the salt bridge 7see p4 #bed7 to solution ,b1 and the hydrogen ions formed combine with hydroxide ions and produce water4 ,in a similar way1 oxygen passes into solution ,b in the form of hydroxide ions and these combine with hydrogen ions of the sulphuric acid1 forming water2 ,,so#db ions migrate from the solution ,b through the salt bridge toward solution ,a and thus prevent polarization 7p4 #bed74 ,while water is an actual product of the action of the cell1 working under these conditions1 the essential feature of the oxidation of hydrogen is its ionization--,h#b #b ,h2 it would be in the same condition of oxidation if the hydrogen ions combined with any negative ions other than ,,ho1 or if they remained ions 7as they would1 if sodium chloride surrounded the hydrogen electrode74 ,similarly1 the essential feature of the reduction of oxygen is its ionization in the form of ,,ho ions2 in the present p#bhb instance1 these actually combine with hydrogen ions and form water1 but the reduction of oxygen would also be accomplished1 if the hydroxide ions remained ionized 7as they would1 if sodium chloride bathed the oxygen electrode74 ,the formation of water is the result of a union of ions1 following the oxidation-reduction reaction1 which may be expressed in the following condensed form3 #b ,h#b #d ,h #b ,,hoh ,o#b #d ,,ho #d ,,ho #d ,h#b,o ,summary4--,we thus find that the oxidation of hydrogen by oxygen may be used to develop an electric current1 exactly in the same way as the other oxidation and reduction reactions1 which we have discussed1 are found available for the same purpose4 ,and at a given temperature1 the oxidation is subject to the influence of analogous factors1--the solution-tension constants1 the concentrations of the corresponding ions in the solutions surrounding the electrodes1 and the concentrations of the gases4 ,interpretation of ,oxidation-,reduction ,reactions in ,terms of the ,oxygen-,hydrogen ,gas ,cell4--,it is possible to interpret all classes of reversible oxidations and reductions1 carried out in aqueous solutions1 in terms of this so-called oxygen-hydrogen gas cell1 if the assumption is made that each oxidizing agent1 such as nitric acid1 permanganate1 dichromate1 etc41 has a tendency to liberate1 either from its own molecules or by its action on water1 oxygen of a definite concentration or pressure1 and that each reducing agent1 in turn1 has a tendency to liberate hydrogen1 from water1 of a definite pressure or concentration4 ,the potential of the oxygen-hydrogen cell is dependent on the concentrations of the gases with which the electrodes are in contact3#efa therefore1 each oxidation and reducing agent1 yielding its own characteristic concentration of oxygen or hydrogen1 respectively1 would have a characteristic constant1 corresponding to the solution-tension constants of the elements and measuring its oxidizing or reducing power4 ,this interpretation of oxidation-reduction reactions has received extended attention and recognition4 ,the study1 just made1 of the oxidation of hydrogen by oxygen1 sufficiently suggests the treatment of oxidation and reduction from this viewpoint4 ,interpretation of ,oxidation-,reduction ,reactions in ,terms of ,direct ,transfers of ,electric ,charges4--,in the study of the p#bhc oxidation of zinc by cupric-ion1 ,zn ,cu#b ,cu ,zn#b1 of the oxidation of iodides and sulphides by ferric salts1 #b ,fe#c #b ,i #b ,fe#b ,i#b1 and #b ,fe#c ,s#b #b ,fe#b ,s1 and of similar actions1 it has been possible to represent the oxidation-reduction actions as the result of direct transfers of electric charges between atoms and their ions4#efb ,in the following discussions1 the attempt will be made to interpret1 in the same terms1 the oxidizing power of the most important remaining oxidizing agents1 which include such compounds as nitric1 permanganic1 chromic1 arsenic and similar oxygen acids4 ,the interpretation will avoid the assumption of the liberation of oxygen and hydrogen1 under hypothetical1#efc and1 sometimes1 enormous pressures1 as intermediate products in the actions4 ,arsenic ,acid as an ,oxidizing ,agent4--,arsenic acid is occasionally used as an oxidizing agent 7e4g4 in the aniline-dye industry71 and1 although it is not a very powerful one1 its study is of theoretical interest4 ,if to a solution of potassium arseniate some potassium iodide is added1 practically no iodine is liberated 7exp474 ,if dilute hydrochloric acid1 in excess1 is added to this mixture1 iodine is slowly liberated 7exp474 ,but the addition of concentrated hydrochloric acid causes iodine to be liberated at once in very large amounts 7exp474 ,we may ask in what way the p#bhd addition of the concentrated acid causes such a decided difference in the ease and speed with which arsenic acid oxidizes the iodide-ion to free iodine and is reduced1 in turn1 to arsenious acid and its derivatives4#efd ,we may recall the fact that a solution of potassium arseniate1 to which dilute hydrochloric acid has been added1 will remain clear for some time when the mixture is saturated with hydrogen sulphide 7exp474 ,if a considerable excess of concentrated hydrochloric acid is added to this mixture1 hydrogen sulphide immediately forms a dense precipitate 7exp47 of arsenic pentasulphide--presumably through the union of quinquivalent arsenic-ion with the sulphide-ion3 #b ,as#e #e ,s#b ,as#b,s#e 7see p4 #bdg74 ,this behavior suggested that arsenic acid1 although a moderately strong acid1 might nevertheless be somewhat amphoteric1 might have slight basic properties1 as well as its ordinary acid functions4 ,the relation is expressed in the equations3#efe #c ,h ,as,o#dc 7,,ho7#c;,as,o 7,,ho7#c;,as,o ,,hoh ,as7,,oh7#e ,as#e #e ,,ho4 ,since oxidations by arsenic acid involve its reduction to arsenious acid1 containing trivalent1#eff in place of quinquivalent arsenic1 one might well suspect1 that the oxidizing component is the quinquivalent arsenic-ion1 ,as#e1 the discharge of two of whose positive charges would cause oxidation 7e4g4 of iodide-ion71 exactly as the discharge of positive charges at the positive pole of an electric current causes oxidation 7p4 #beb73 ,as#e #b ,i ,as#c ,i#b4 p#bhe ,in a solution of potassium arseniate1 we would have only the faintest trace of the ion ,as#e1 since the addition of an alkali to the system1 expressed in the above equations1 would carry the reversible reactions towards the left4 ,the addition of dilute hydrochloric acid to the system must carry the reactions towards the right and increase the concentration of ,as#e2 the addition of concentrated acid must increase the concentration of ,as#e very much more4 ,even if the concentration of ,as#e remained minute1 the oxidizing power would be increased proportionally to the ratio of the concentrations in the first and the last solutions4 ,a millionfold increase in concentration1 even when we are dealing with very small numbers1 would imply a millionfold increase in the activity of the solution4 ,if1 then1 the oxidizing component of arsenic acid is the quinquivalent ion1 ,as#e1 which would tend to discharge two of its positive 7oxidizing7 charges1 arsenic acid should be a much more powerful oxidizing agent in strong acid solution than in alkaline or neutral solutions4 ,we thus arrive at the conclusion that the addition of hydrochloric acid to a mixture of arseniate and iodide may be effective1 in bringing about the reduction of the arseniate and the oxidation of the iodide1 primarily because of its action on arsenic acid1 perhaps by facilitating its ionization as a base1 and that it is not effective through any action on the iodide1 for instance by producing free hydroiodic acid1 as is often assumed4 ,this conclusion may easily be tested with the aid of the chemometer 7see p4 #bec73 potassium arseniate against potassium iodide gives only the faintest possible current1 barely perceptible with the aid of a very sensitive voltmeter4#efg ,the addition of hydrochloric acid to the beaker containing the potassium iodide does not increase the potential 7it rather decreases it somewhat71 whereas the addition of the concentrated acid to the potassium arseniate solution produces a most decided increase in the potential#efh 7exp474 ,it is evident1 therefore1 that the addition of the acid is primarily and directly intended to increase the oxidizing power of the arsenic acid1 rather than to increase the reducing power of the iodide4 p#bhf ,the more common methods of expressing oxidation-reduction reactions of this type are illustrated in the following equations3 ,na#c;,as,o#d #b ,,hi ,na#c;,as,o#c ,h#b,o ,i#b 7#a7efi and ,as,o#dc #b ,h #b ,i ,as,o#cc ,h#b,o ,i#b4 7#b7 ,both of these forms of expression give the net results of the action correctly4 ,neither attempts to interpret the interesting and important fact that the reduction of arsenic acid is facilitated by the presence of acids 7of hydrogen-ion74 ,it is1 at least1 also permissible to consider ,as#e ions to be present and to express the oxidation-reduction reaction with the aid of this conception1#egj as has been done in the previous discussion4 ,in the final analysis1 this method seems to have the advantage of showing directly the changes of the valences#ega 7electric charges7 of the atoms involved in the oxidation-reduction1 and it also expresses1 clearly and definitely1 the relation of the hydrogen-ion to the action4#ega ,the following case furnishes an illustration as to how the new point of view works out from the standpoint of a quantitative study of an oxidation-reduction reaction of this type#egb3 uranyl salts1 such as the sulphate ,,uo#b,,so#d1 are oxidizing reagents1 which are readily reduced1 particularly in acid solutions1 to uranous salts 7e4g4 to the sulphate1 ,u7,,so#d7b74 ,the potential of a mixture of uranyl and uranous salts is found#egc to depend on the action expressed in the equation ,,uo#bb #d ,h #b ,u#d #b ,h#b,o4 ,for the condition of equilibrium 7zero potential71 it follows that ,,uo#bb ,h#d _/ ,u#d ,kequil4 7#c7 ,the value of this constant1 at #ah1 is found1 by calculation1#egd to be approximately #a _/ #ajbd4 ,now1 the uranyl-ion ,,uo#bb may be assumed to have the power of ionizing1 with the aid of water1 to a very slight degree into ions ,u#f and ,,ho1 according to ,,uo#bb #b ,h#b,o ,u7,,oh7#db ,u#f #d ,,ho4 7#d7 ,for the ionization of an extremely weak base of this character1 we have1 further1 ,u#f ,,ho-#d _/ ,,uo#bb kbase4 ,and1 since ,,ho ,k,,hoh _/ ,h1 we also find1 by substitution and by solving for ,u#f1 ,u#f ,,uo#bb ,h#d kbase _/ 7,k,,hoh7#d4 7#e7 p#bhg ,in other words1 we may substitute ,u#f and a constant factor ,k,,hoh#d _/ kbase for ,,uo#bb ,h#d in the first term 7numerator7 of the oxidation-reduction equation 7#c71 derived from ,luther's quantitative work4 ,we thus obtain3 ,u#f _/ ,u#d ,kequil4 kbase _/ ,k,,hoh#d ,k1 7#f7 which must agree just as well with the quantitative data1#ege as does the original equilibrium equation 7#c74 ,it follows1 that we may write the chemical equation1 for the action in acid solutions1 simply ,u#f ,u#d1 exactly as we have ,fe#c ,fe#b 7p4 #bfi74 ,u#f cannot be measured1 as yet1 but in the analogous case of ,fe#c ,fe#b1 where both terms of the equilibrium equation are accessible to direct measurement1 the experimental evidence distinctly favors#egf the views expressed4#egg ,permanganic ,acid1 ,chromic ,acids1 etc41 as ,oxidizing ,agents4--,we may extend the same views to the oxidizing power of such important agents as permanganic1 dichromic1 and nitric acids4 ,in each case we may assume that the oxidizing component is a highly charged positive ion1 e4g4 in the case of ,k,mn,o#d a septavalent manganese-ion1 ,mn#g1 whose oxidizing power will depend on its tendency to discharge part of its heavy positive electrical charge and whose efficiency1 in accordance with the law of equilibrium1 will also be proportional to the concentration1 in which the highly charged ion is present4 ,permanganate is used as a favorite oxidizing agent in the laboratory1 for instance1 in the oxidation of ferrous to ferric salts in quantitative analysis2 the action proceeds quantitatively and rapidly in acid solution1 and the end of the action is recognized by the fact that the intense pink color of the permanganate is not destroyed 7exp474 p#bhh ,if we bring permanganate1 against potassium iodide1 into the beakers of the chemometer 7p4 #bec71 we find that it is a much more vigorous oxidizing agent than is arsenic acid1 and again we find that the addition of acid 7sulphuric7 to the permanganate solution enormously increases the potential 7exp47 and therefore its oxidizing power4 ,the addition of an acid would1 obviously1 enormously increase the concentration of a positive septavalent ion1 if permanganic acid is assumed to be1 to a slight extent1 base forming and therefore amphoteric3 ,h ,mn,o#d 7,,ho7,mn,o#c 7,,ho7,mn,o#c #c ,,hoh ,mn7,,oh7#g ,mn#g #g ,,oh4 ,similar experiments may be made with ferrous sulphate against permanganate4 ,the oxidation of ferro-ion1 or of iodide-ion1 may be represented1 most simply1 by the equations3 #b ,mn#g #aj ,fe#b #b ,mn#b #aj ,fe#c and #b ,mn#g #aj ,i #b ,mn#b #e ,i#b4 ,each heptavalent manganese ion is derived from a salt1 such as ,mn,x#g or ,mn#b,y#g1 and1 consequently1 when two manganese ions ,mn#g are reduced1 ten univalent negative ions ,x1 or five bivalent ions ,y1 are liberated and become available for salt formation with the ferric ions1 produced1 or with the hydrogen ions 7from hydroiodic acid7 set free by the oxidation of the iodide ions to iodine4 ,thus1 the oxidation of ferrous sulphate by permanganate1 in the presence of sulphuric acid1 may be represented1 in greater detail1 by the equations3 #b ,k,mn,o#d ,h#b,,so#d ,k#b,,so#d #b ,h,mn,o#d 7#a7 #b ,h,mn,o#d #g ,h#b,,so#d ,mn#b7,,so#d7g #h ,h#b,o 7#b7 ,mn#b7,,so#d7g #b ,mn#g #g ,,so#db 7#c7 #b ,mn#g #g ,,so#db #aj ,fe#b #aj ,,so#db #b ,mn#b #a ,o,fe#c #ag ,,so#db 7#d7 #b ,mn,s,o#d #e ,fe#b7,,so#d7c 7#e7 ,analogous results are obtained with potassium chromate or dichromate against potassium iodide1 ferrous sulphate1 hydrogen sulphide1 and other reducing agents4 ,nitric ,acid4--,it is characteristic of nitric acid that1 ionized as an acid1 it is not a powerful oxidizing agent2 that is1 the nitrate-ion1 ,,no#c1 is not the oxidizing component4 ,for instance1 a nitrate1 such as potassium nitrate1 in aqueous solution1 does not appreciably oxidize ferro-ion or iodide-ion 7exp474 ,concentrated nitric acid1 or a mixture of a large excess of concentrated p#bhi sulphuric acid with a nitrate1 are far more effective in oxidizing the substances mentioned1 as shown by experiments with the chemometer and with the mixtures described4 ,it is significant that1 in concentrated nitric acid1 and in the presence of concentrated sulphuric acid1 the basic ionization of nitric acid ,h ,,no#c 7,,ho7,,no#b 7,,ho7,,no#b #b ,,hoh ,n7,,oh7#e ,n#e #e ,,ho would be facilitated by the high concentration of hydrogen-ion4 ,summary4--,in every instance1 then1 we find that it is possible to produce an electric current by using one of these common1 powerful oxidizing agents in aqueous solution1 just as it is possible with oxygen and with the simpler agents discussed earlier4 ,whatever the theory of the formation of the current1 whether we are dealing1 in the last cases considered1 with acids which have the capacity to ionize minimally as bases1 forming highly charged positive ions1 whose discharge involves an oxidation of the substance receiving the discharged electricity1 or whether we accept the view that oxygen is liberated by them in exceedingly concentrated form and tends to form in aqueous solutions the hydroxide-ion1 ,,ho1 unquestionably the closest possible relation has been established between oxidation-reduction reactions and electrical relations1 as formulated on the basis of the theory of ionization4 ,in all cases1 at a constant temperature1 as demanded by the law of mass action1 the net result of an action will depend on constant factors1 measuring the tendencies of atoms to assume or lose electric charges 7electrons71 and on variable factors1 the concentrations of the reacting components4 ,oxidation of ,organic ,compounds4--,in conclusion1 it may be asked whether the oxidation of organic compounds may also be brought into relation with electrical charges and interpreted on the basis of the theory which has been presented4 ,for this purpose we may study the oxidation of one of the simplest of organic compounds1 formaldehyde ,,ch#b,o1 which forms the active component in solutions of formalin4 ,formaldehyde is also intimately related to some of the most important food products1 the carbohydrates1 whose oxidation is utilized in the animal economy4 ,it is formed#egh in the green leaves of plants by the p#bij reduction of carbon dioxide1 absorbed from the atmosphere1 with the aid of the energy of the sun's light3 ,,co#b ,h#b,o ,,ch#b,o ,o#b4 ,it is readily condensed1 forming glucose 7#f ,,ch#b,o ,c#f;,h#ab,o#f71 cane sugar ,c#ab;,h#bb,o#aa1 and still more complex carbohydrates1 such as starch4 ,formaldehyde1 like other aldehydes1 is readily oxidized4 ,a favorite reagent1 used in oxidizing it1 is an ammoniacal solution of silver nitrate 7exp471 the separation of silver from such a solution being a characteristic reaction of aldehydes4 ,the reagent is rendered still more sensitive by the addition of sodium or potassium hydroxide4#egi ,we may ask how we would interpret1 from the point of view of the electric theory of oxidation and reduction1 the oxidation of formaldehyde and the reduction of silver nitrate to silver1 under these conditions4 ,according to the theory1 the oxidizing agent in silver nitrate is the silver-ion1 the discharge of which gives positive electricity1 which the oxidized substance1 the formaldehyde1 must absorb4 ,but in a silver nitrate solution there is a far larger concentration of the silver-ion than in an ammoniacal solution 7p4 #bbj71 containing the same total concentration of silver4 ,the complex silver-ammonium-ion ,ag7,,nh#c7b1 it may be recalled1 is a rather stable one1#ehj and1 consequently1 the addition of ammonia to silver nitrate should decidedly weaken its oxidizing power4 ,still1 the practical use of ammonia1 especially in combination with sodium hydroxide1 is found to be most effective4 ,we are led to suspect that1 in spite of the untoward effect of ammonia on the oxidizing power of the silver compound1 an alkaline solution is desirable for the sake of the effect of the alkali on formaldehyde1 the reducing substance involved4 ,to follow up this conclusion1 we must next consider1 in some detail1 the nature of formaldehyde2 we shall presently find that the conclusion1 which we have just reached1 as to the probably favorable effect of alkali on the reducing power of formaldehyde1 will be verified by experiments1 which the consideration of formaldehyde will suggest4 ,the oxidation of formaldehyde may most clearly be formulated on the basis of views1 developed by ,nef1 on the formation of methylene#eha derivatives1 containing bivalent carbon atoms4 ,a solution p#bia of formalin contains formaldehyde in a variety of forms1 in a very complex condition of equilibrium4 ,of these compounds1 the aldehyde1 ,,ch#b,o1 probably exists in two forms1 which have the same composition and molecular weight1 but which differ in the arrangement of the atoms in the molecules 7in the structure of the molecules72 we probably have ,,ch#b,o ,,ch7,,oh71 the former of which 7,,ch#b,o7 is1 most likely1 by far the more stable and the chief one of these two substances1 present under ordinary conditions4 ,the second compound ,,ch7,,oh7 may be present in traces only4 ,one difference1 we note1 lies in the position of one of the hydrogen atoms in the respective molecules2 the second form contains a hydroxide group 7,,oh71 which gives it the properties of an acid and renders it capable of forming salts ,,ch7,o,me7 with bases4 ,but the molecule of this second form also would contain a carbon atom1 only two of whose valences are satisfied 7by ,h and ,,oh71 two of the ordinary four valences of a carbon atom being thus left free or unsaturated4 ,we may indicate the two free carbon valences in the formula ,,ch7,,oh74 ,such an unsaturated1 bivalent carbon atom ,c would be particularly sensitive to oxidation4#ehb ,besides these two forms1 a formalin solution also contains a polymerized form1 probably 7,,ch#b,o7#b1 which in dilute solution1 or under the influence of heat1 slowly breaks down into formaldehyde1 7,,ch#b,o7#b #b ,,ch#b,o4 ,the addition of alkali to the mixture probably leads to the formation of the salt ,,ch7,o,me71 thus disturbing all the conditions of equilibrium and leading to the transformation of a very much larger part of the aldehyde into a compound containing the characteristic unsaturated 7bivalent7 carbon1 than was originally present4 ,the aldehyde will thus become more susceptible to oxidation as a result of the enormous increase in the concentration of the oxidizable component4 ,we may assume this to be either the salt1 ,,ch7,o,me71 or its negative ion1 ,,ch7,o71 or both1 or some analogous derivative4 ,further1 the two free valences of a bivalent carbon atom may be considered to consist of a positive and a negative charge of electricity1 either actual or potential1#ehc and the oxidation will consist p#bib primarily in the absorption of two positive charges1 from the oxidizing agent1 to convert the negative charge on the carbon atom1 say in ,,ch7,o,na71 into a positive charge4#ehd ,if the oxidizing agent is alkaline silver nitrate solution1 we may formulate the successive actions as follows3 7,na,o7,,hc #b ,ag 7,na,o7,,hc#b #b ,ag 4 ,the two positive silver ions correspond to two negative ions1 e4g4 hydroxide ions ,,ho1 which are set free by the discharge of the silver ions1 and which1 in turn1 will combine with the oxidized carbon atom holding the two positive charges3 7,na,o7,,hc#b #b ,,ho 7,na,o7,,hc7,,oh7#b 7,na,o7,,hc3,o ,h#b,o4 ,the salt formed1 ,,hco#b,na1 is sodium formate1 which is the first isolated product of the oxidation of formaldehyde4 ,it would appear1 from this point of view1 that the alkaline nature of the silver nitrate mixture is advantageous primarily because a base is required by the formaldehyde1 the reducing agent1 to convert it into some readily oxidizable form4 ,and the proved efficiency of the alkaline mixture 7see above7 makes it appear probable that the advantage gained by this result more than offsets the loss in oxidizing power1 suffered by the silver nitrate following the suppression of its real oxidizing component1 the silver-ion1 when1 in the presence of ammonia1 the latter is converted largely into the ion1 ,ag7,,nh#c7b4 ,ammonia1 in turn1 is employed in the oxidizing mixture1 essentially with the object of preventing the precipitation of the silver-ion1 as silver oxide1 by the hydroxide-ion of an alkaline mixture4 ,these conclusions1 as well as1 in particular1 the main conception that in the oxidation of formaldehyde there is an actual transfer of electrical charges1 may be fully confirmed with the aid of the chemometer4#ehe ,,exp4 ,a small beaker1 containing a platinum electrode1 which is connected with the positive post of the voltmeter1 is half filled with a solution of silver and sodium nitrates4 ,a similar small beaker1 containing a platinum electrode leading to the negative post of the voltmeter1 is charged with a solution of sodium nitrate 7to render the solution a good conductor7 and with some formalin4 ,the solutions in the two beakers are connected by means of a salt-bridge containing sodium nitrate4 p#bic ,only a very slight current is produced under these conditions2 the potential between silver nitrate and formaldehyde is found to be extremely small4 ,if1 now1 sodium hydroxide is added to the formalin mixture1 an enormous increase in potential is observed1 proving1 unmistakably1 that the addition of the alkali to the formalin solution enormously increases the concentration of the reacting1 oxidizable component4#ehf ,when some ammonia is added to the silver nitrate mixture1 we find1 as anticipated1 that the oxidizing power of the silver solution is greatly reduced1 the silver-ion being converted into the complex ion1 ,ag7,,nh#c7b2 but the potential is still very much greater than the potential between silver nitrate and formalin without any alkali--which shows that the advantage of using alkali with the formaldehyde greatly outweighs the disadvantage of using ammonia with the silver nitrate4 ,an electric current may also be readily obtained by combining alkaline formaldehyde with other oxidizing agents--for instance with an oxygen electrode 7p4 #bgi74 ,we find 7exp47 that the oxidation proceeds with remarkable ease under these conditions4 ,permanganate1 dichromate1 etc41 may be substituted for oxygen1 with the same general result4 ,summary4--,it is clear1 then1 that the oxidation of an organic substance may readily be interpreted as consisting1 ultimately1 in a transfer of electrical charges1 of exactly the same nature1 as is found in the other oxidation reactions which we have considered1 p#bid and that the conditions for producing a maximum current1 as investigated with the aid of the chemometer1 give us1 again1 important guidance in following the course of the reactions4 ,it is needless to say that the oxidation of other organic compounds1 such as glucose1 alcohol1 etc41 may be profitably studied from the same point of view4 ,it also follows1 from the conclusions reached1 that1 under proper experimental conditions1 electricity1 in the form of a current1 must be capable of effecting the oxidation1 or the reduction1 of organic as well as inorganic compounds 7p4 #beb74 ,extended investigations have1 indeed1 shown that electric currents belong to the most important and efficient agents for this purpose1 because the oxidation1 or the reduction1 of the organic compound becomes susceptible to the most exact control through the regulation of the potentials used4#ehg ,tables and ,summaries4--,in the first table the equilibrium 7solution-tension7 constants of a number of metals and non-metallic elements are given4 ,the table is followed by brief explanations of its meaning and a summary of some of its more important applications4 ,,table,a ,,of ,,equilibrium 7,,solution-,,tension7 ,,constants 7,,in ,,molar ,,terms7 ,,and ,,of ,,potential ,,differences ,,between ,,elements ,,and ,,their ,,ions ,,in ,,unimolar ,,aqueous ,,solutions4 ,element1 ,ion4 ,e4,p4,el41,ion4 ,k,ion4 ,k1 ,k,b 7#b4ib7 #f;,e#ej ,na1 ,na,c #b4dd #b4e;,e#db ,ba1 ,ba#b 7#b4ed7 #b4a;,e#hh ,sr1 ,sr#b 7#b4di7 #d4j;,e#hf ,ca1 ,ca#b 7#b4bh7 #b4j;,e#gi ,mg1 ,mg#b 7#b4bf7 #d4a;,e#gh ,al1 ,al#c;,d #j4iii 8 #a4c;,e#eb ,mn1 ,mn#b #j4gih #e4g;,e#bg ,zn1 ,zn#b #j4dic #a4d;,e#ag ,cd1 ,cd#b #j4adc #i4e;,e#d ,fe1 ,fe#b;,e #j4abb 8 #a4h;,e#d ,co1 ,co#b;,f #j4jach 8 #j4ccad ,ni1 ,ni#b;,g #j4ajh 8 #a4h;,e#d ,sn1 ,sn#b #j4jhe #a4a;,e#c ,pb1 ,pb#b #j4abi #c4c;,e#e ,h#b1 ,h,h #j4bgg #a4eb;,e#e ,cu1 ,cu#b #j4fjf #h4c;,e#bb ,as1 ,as #j4egj #b4g;,e#cj ,bi1 ,bi#c #j4ffh #a4d;,e#ce ,sb1 ,sb#c #j4gdc #a4g;,e#ci ,hg1 ,hg #a4jbg #a4ch;,e#ah ,ag1 ,ag #a4jdh #f;,e#ai ,pt1 ,pt#d #a4adj #e;,e#hj ,au1 ,au#c #a4cef #a4h;,e#ga ,f#c1 ,f,h 7#b4bd7 #i4j;,e#hh ,cl#b1 ,cl,h #a4fid #c4af;,e#bi ,br#b1 ,br #a4bgj #a4bc;,e#bb ,i#b1 ,i #j4gig 8 #g4bf;,e#ac ,o#b1 ,,ho,i #j4fih #a4cf;,e#ab ,,table ,,notes3 ,a4 ,the table is based on ,wilsmore's compilation of solution-tension potentials1 ,z4 phys4 ,chem41 #cf1 #ia 7#aija74 ,b4 ,values in parentheses have been estimated by indirect measurements4 ,c4 ,g4 ,n4 ,lewis1 ,j4 ,am4 ,chem4 ,soc41 #cb1 #adfg 7#aiaj74 ,d4 ,values marked with8 are uncertain4 ,e4 ,calculated from the data of ,richards and ,behr 7,z4 phys4 ,chem41 #eh1 #cja 7#aijg771 who found the potential of iron against #j4e molar ,fe,s,o#d to be #j4ae volt4 ,the degree of ionization of #j4e molar ,fe,s,o#d is taken as #bb4 #be4h 7,kohlrausch and ,holborn1 loc4 cit41 p4 #aeb7 and is taken as #aag1 as for ,zn,s,o#d 7ibid41 p4 #bjj74 ,on account of the doubtful value for the degree of ionization1 the values in the table are marked81 but the value found by ,richards and ,behr appears to be quite accurate4 ,f4 ,calculated from the data of ,schildbach 7,z4 fr ,elektroch41 #af1 #ifg 7#aiaj774 ,the same uncertainty as to the degree of ionization exists as that discussed in the previous footnote4 ,g4 ,calculated from the data of ,e4 ,p4 ,schoch 7,am4 ,chem4 ,j41 #da1 #bjh 7#aiji774 ,the same uncertainty as to the degree of ionization exists as that discussed in footnote #e1 p4 #bid4 ,h4 ,the values for gaseous elements refer to the gases under one atmosphere pressure4 ,i4 ,the potential of oxygen at #ah1 #gfj mm41 against an alkaline solution in which ,,ho #a4 ,k,ion refers to the concentration of ,,ho1 with which oxygen under atmospheric pressure would be directly in equilibrium1 at #ah4 ,the potential differences1 given in the table1 are based on the assumption that the absolute zero of potential is at such a point1 that the so-called standard normal calomel electrode has a value of #j4ef volt relative to this zero 7cf4 ,ostwald1 ,z4 phys4 ,chem41 #cf1 #ig 7#aija774 ,the exact determination of this value is a very difficult matter4 ,recently ,palmaer 7ibid41 #ei1 #abi 7#aijg771 located the absolute zero at a point #j4jd volt more positive than the above1 making the absolute potential of the normal calomel electrode1 approximately1 #j4eb volt4 ,to refer potentials1 given in this book1 to this new zero1 one would subtract #j4jd volt from all positive potentials and add #j4jd to the numbers representing negative potentials 7e4g4 ,e4 ,p4,zn1,zn#b would become #j4efi in place of #j4ebi volt74 ,since the equilibrium 7solution-tension7 constants are calculated from the potential differences referred to the absolute zero 7p4 #bei71 any change in the zero involves corresponding changes in the values of the equilibrium constants1 as calculated for this book4 ,however1 it should be noted that all potential differences would be corrected by the same constant quantity 7#j4jd volt for ,palmaer's zero73 all the equilibrium constants for univalent metallic ions would be increased proportionally to a constant factor c 7c is very nearly equal to #e1 for ,palmaer's zero71 the equilibrium constants for bivalent metallic ions would be increased proportionally to c#b1 etc4 ,the equilibrium ratio for two metals and their ions would in no wise be changed by these alterations3 e4g4 for the equilibrium between zinc and copper and p#bif their ions 7p4 #bfg71 ,kequil4 ,k,zn#b _/ ,k,cu#b2 the factor c#b would be introduced into both terms of the ratio and would not affect the value of the latter4 ,for the condition of equilibrium between silver and copper and their ions 7p4 #bfg7 ,kequil4 ,k,ag#b _/ ,k,cu#b1 and since 7c7#b c#b1 this equilibrium ratio would also not be affected4 ,for elements1 which produce negative ions1 the corresponding correction factors would be #a _/ c1 #a _/ c#b1 etc41 and the equilibrium relations between two such elements and their ions likewise would remain unchanged4 ,since these equilibrium relations are the significant ones in this work1 and since our conclusions have been based on them1 it is clear that a change in the absolute zero would not affect the conclusions reached4 ,on account of the uncertainty attaching to the determination of the absolute zero of potential1 it is preferred1 in practice1 to report the experimentally determined potentials as measured against a constant1 well-defined electrode 7such as the calomel electrode or a hydrogen electrode7 and thus to eliminate the variation1 which a change in the determination of the zero potential would make necessary4 ,however1 for an elementary discussion of oxidation-reduction reactions1 from the same viewpoint as is used in considering all other reversible chemical actions1 the idea of the absolute potential has certain advantages1 making a uniform treatment possible4 #a4 ,meaning of ,k,ion4 ,under ,k,ion is given1 for each element1 the concentration of its ion1 with which the element would be directly in equilibrium at the ordinary temperature 7see p4 #beh74 ,the constants for gaseous elements represent the constants of the gases under atmospheric pressure4 #b4 ,the ,condition for ,equilibrium between ,two ,elements and ,their ,ions4 ,the condition of equilibrium in a system of two elements and their ions may be found with the aid of the constants ,k,ion1 as follows3 ,for ,zn ,cu#b ,zn#b ,cu we have for the condition of equilibrium 7see p4 #bfg7 ,zn#b _/ ,cu#b ,k and ,k ,k,zn#b _/ ,k,cu#b #a4d;,e#ag _/ #h4c;,e#bb #a4g;,e#ch4 ,zinc-ion must be present in enormous excess in the condition of equilibrium and zinc will precipitate copper from solutions of cupric salts until this relation is established4 ,the suppression of the cupric-ion--by precipitation in the form of insoluble salts or by conversion into very stable complex ions--makes ,cu#b exceedingly small and makes it increasingly difficult for zinc to precipitate copper1 and1 under certain conditions1 the ordinary course of the action may be reversed 7p4 #bfh74 ,for ,cu #b ,ag ,cu#b #b ,ag 1 we have 7p4 #bfg7 ,cu#b _/ ,ag#b ,k and ,k ,k,cu#b _/ ,k,ag#b #h4c;,e#bb _/ 7#f;,e#ai7b #b4c;,e#ae4 #c4 ,potential ,differences ,calculated with the ,aid of ,k,ion4 ,for metallic elements1 which send out positive ions1 in contact with an aqueous solution containing the ion in concentration ,c1 the potential difference is 7see p4 #bfa7 ,me1 ,ionv 7#j4jege _/ v7 log7,c _/ ,k,ion7 volts1 p#big and for elements which form negative ions 7see footnote #a1 p4 #bfa71 ,elem41 ,ionv 7#j4jege _/ v7 log7,c _/ ,k,ion7 volts4 ,in these equations v represents the valence of the ion4 ,it is clear that for the condition of equilibrium1 in which ,c ,k,ion1 the potential is #j4 ,further1 for the potential difference between copper and a cupric salt solution in which ,cu#b #a1 we would have ,cu1 ,cu#b 7#j4jege _/ #b7 log7#a _/ #h4c;,e#bb7 #ba4jh #j4jege _/ #b #j4fjf volts4 #d4 ,meaning of ,e4,p4,element1 ,ion4 ,under ,e4,p4,element1 ,ion the table gives the potential difference in volts1 calculated for the element named and an aqueous solution of its ion in unit concentration 7one gram-ion per liter74 ,for instance1 for zinc and ,zn#b #a 7#fe4d grams zinc-ion per liter71 we have a potential ,e4,p4,zn1 ,zn#b #j4dic4 ,the signs used1 in accordance with the convention adopted 7p4 #bfa71 indicate the character of the charge on the element electrode 7which is named first in the subscript to ,e4,p474 ,for instance1 zinc in a solution in which ,zn#b #a would acquire a negative charge 7p4 #bff71 the potential difference ,e4,p4,zn1 ,zn#b being #j4dic according to the table2 silver1 immersed in a solution in which ,ag #a1 would acquire a positive charge1 the potential difference ,e4,p4,ag1 ,ag #a4jdh4 ,the potentials given for the gaseous elements represent the potentials of the gases under #gfj mm4 pressure4 #e4 ,potential ,differences ,calculated with the ,aid of ,e4,p4,element1 ,ion4 ,the potential corresponding to any concentration ,c of a metal ion may be found from the equation#a ,el41 ,ionv ,e4,p4,el41 ,ion 7#j4jege _/ v7 log,c volts1 and the potential for any concentration ,c of the ions of elements forming negative ions is found#ehh according to ,el41 ,ionv ,e4,p4,el41 ,ion 7#j4jege _/ v7 log,c volts4 #f4 ,the ,condition for ,equilibrium between ,two ,metals and ,their ,ions1 ,calculated with the ,aid of ,e4,p4,element1 ,ion4 ,the condition for equilibrium in a system of two metals and their ions is determined by the fact that the potential of the system must be #j when equilibrium is established4 ,we have1 for instance for the two metals zinc and copper and their ions1 ,zn#b and ,cu#b1 for ,zn ,cu#b ,cu ,zn#b the condition for equilibrium that ,cu1 ,cu#b ,zn1 ,zn#b #j4 ,according to the equation given in #e1 we have1 then1 for the condition of equilibrium1 ,e4,p4,cu1 ,cu#b 7#j4jege _/ #b7 log,cu#b ,e4,p4,zn1 ,zn#b 7#j4jege _/ #b7 log,zn#b #j4 p#bih ,then 7#j4jege _/ #b7 log7,zn#b _/ ,cu#b7 ,e4,p4,cu1,cu#b ,e4,p4,zn1,zn#b #j4fjf 7#j4dic7 #a4jii4 ,from the last relation we find log7,zn#b _/ ,cu#b7 #ch4bbfa1 and therefore1 for the condition of equilibrium1 ,zn#b _/ ,cu#b #a4g;,e#ch4 #g4 ,equilibrium ,constants for ,elements with ,variable ,concentration4 ,the concentration of a pure metal at a given temperature may be considered a constant1 except in the case of extremely thin films of the metal 7p4 #beh74 ,the concentration of hydrogen1 and of the non-metallic elements given in the table1 is variable1 and ,k,ion has a definite value only when the concentration of the element is defined 7see the preceding table1 footnotes #c1 #d1 p4 #bie74 ,for certain estimations the equilibrium constants1 which show the relation between the two variables1 namely the concentration of the element and that of its ion1 are very helpful 7see pp4 #bgd and #bge74 ,in the following table some of the more important equilibrium constants of this nature are given4 ,,table ,,of ,,equilibrium ,,constants4 ,element4 ,kequil44 ,hydrogen3 ,h#b 3 ,h#b #e4f;,e#i ,oxygen3 ,,ho#d 3 ,o#b #h4b;,e#di ,chlorine3 ,cl#b 3 ,cl#b #b;,e#fj ,iodine,a3 ,i#b 3 ,i#b #e4f;,e#bi ,,table ,,note3 ,a4 ,the value of the constant1 as given1 is only an approximate estimation 7p4 #bgc74 ,the significance of the constants is indicated by the ratios given in the table4 ,the relation of these constants to those given in the first table may be seen from the following illustration4 ,for hydrogen we have ,h#b #b ,h4 ,the first table tells us that hydrogen1 at #ah under atmospheric pressure1 is in equilibrium with its ion when the concentration of hydrogen-ion is #a4eb;,e#e 7under ,k,ion74 ,now1 a mole of hydrogen at #ah occupies #bb4d #bia _/ #bgc #bc4i liters under atmospheric pressure1 and its concentration 7per liter7 is therefore #a _/ #bc4i mole4 ,then equilibrium exists1 when ,h#b #a _/ #bc4i and ,h #a4eb;,e#e and ,kequil4 ,h#b 3 ,h#b 7#a4eb;,e#e7b #bc4i #e4f;,e#i4 ,,footnotes3 #eec ,these constants are calculated from data given in ,wilsmore's tables 7loc4 cit47 on the solution tension of hydrogen4 ,hydrogen1 at #ah under one atmosphere pressure1 produces a potential of ,h#b1 ,h #j4bgg 7see p4 #bfa1 in regard to the sign7 against a solution containing hydrogen-ion in a concentration ,h #a 7see the table at the end of this chapter74 ,now1 there must be some concentration of hydrogen-ion1 which we will call ,c1 with which hydrogen at #ah and #gfj mm4 pressure is directly in equilibrium1 with the potential #j4 ,for any concentration of hydrogen-ion ,h1 other than ,c1 a potential is produced according to ,h#b1 ,h #j4jege log7,h _/ ,c74 ,if we insert into this equation the values ,h #a and the potential #j4bgg1 and if we solve the equation for ,c1 we find ,c #a4eb;,e#e4 ,that is the concentration of ,h1 with which hydrogen of one atmosphere pressure at #ah is directly in equilibrium4 ,since under these conditions of temperature and pressure ,h#b #a _/ #bc4i mole1 we have for the condition of equilibrium ,h#b _/ ,h#b ,k 3 7#a4eb;,e#e7b 3 7#a _/ #bc4i7 #e4ee;,e#i ,k4 #eed ,experimentally the relations for an oxygen electrode are much more complicated than for a hydrogen electrode1 as a result1 apparently1 of the oxidation of the metal 7e4g4 platinum71 with the aid of which the electrode is prepared4 ,for a critical review and summary of the more recent results on this point1 vide ,schoch1 ,j4 phys4 ,chem41 #ad1 #ffe 7#aiaj74 ,for the purposes of this book it will be sufficient to limit our discussion to the behavior of an ideal oxygen electrode4 #eee ,the bivalent oxygen ions1 ,o#b1 combine with hydrogen ions 7formed1 for instance1 by the ionization of water7 and form the more stable hydroxide ions 7p4 #bdf73 ,o#b ,h ,,ho #b ,,ho1 or simply1 ,o#b ,h ,,ho4 ,then1 ,o#b ,h _/ ,,ho k and ,o#b k ,,ho _/ ,h4 ,but since we have ,h ,,ho ,k,,hoh for the ionization of water 7p4 #agf71 we also have3 ,h ,k,,hoh _/ ,,ho and ,o#b 7k _/ ,k,,hoh7 ,,ho#b4 ,by substituting this value for the concentration ,o#b of the oxide-ion in equation 7#a71 equation 7#b7 is obtained4 ,the constant ,k#b includes then the constants k and ,k,,hoh4 #eef ,the constants are calculated from the estimated potential of the oxygen-hydrogen cell1 #a4bca volt1 at #ah4 7,vide ,g4 ,n4 ,lewis1 ,z4 phys4 ,chem41 #ee1 #dfe 7#aijf72 ,nernst and ,wartenberg1 ibid41 #ef1 #ecd 7#aijf72 ,brnsted1 ibid41 #fe1 #ia 7#aijh72 and a summary and discussion by ,schoch1 loc4 cit47 ,at #ah oxygen1 under one atmosphere pressure1 gives an estimated potential ,o#b1 ,,ho #a4ejh against an acid solution1 in which the concentration of the hydrogen-ion ,h #a 7see the table at the end of this chapter74 ,since at #ah ,h ,,ho #j4ha;,e#ad1 the value for ,,ho in this acid solution is #j4ha;,e#ad4 ,now1 for oxygen1 at #ah and #gfj mm41 there must be some concentration of hydroxide-ion1 which we will call ,c1 at which the tendency of the oxygen to ionize is exactly balanced by the tendency of the hydroxide-ion to form oxygen--at this point the potential is #j4 ,for any concentration ,,ho of the hydroxide-ion1 other than ,c1 a potential will exist ,o#b1 ,,ho #j4jege log7,c _/ ,,ho74 ,since for ,,ho #j4ha;,e#ad1 we have a potential ,o#b1 ,,ho #a4ejh1 these values can be introduced into the equation and the latter solved for ,c4 ,we find thus ,c #a4cf;,e#ab1 and oxygen1 at #ah and #gfj mm4 pressure1 would be directly in equilibrium with a solution in which ,,ho #a4cf;,e#ab4 ,at #ah and #gfj mm4 pressure a liter of oxygen contains #a _/ #bc4i mole1 and thus we have for the condition of equilibrium ,,ho#d 3 ,o#b ,k 3 7#a4cf;,e#ab7d 3 7#a _/ #bc4i7 #h4b;,e#di ,k4 #eeg ,the most convenient form of electrode for this purpose consists 7see ,fig4 #ad7 of a cylinder 7about one inch long7 of platinum gauze1 which is fused to a glass tube and connected with a wire leading through the tube to some mercury1 held in a small branch tube1 fused into the main tube near its upper end4 ,the gas is easily conducted to the platinum gauze electrode through such a tube4 ,the cylinder of platinum gauze may be made by joining the ends of rolled gauze with pieces of molten glass4 ,it is coated with platinum black4 #eeh ,cf4 footnote #a1 p4 #bgh4 #eei ,cf4 footnote #a1 p4 #bgi4 #efj ,see ,ostwald1 ,z4 phys4 ,chem41 #aa1 #eba 7#ahic71 ,arrhenius1 ibid41 #aa1 #hje 7#ahic71 and ,nernst1 ibid41 #ad1 #aee 7#ahic71 for a detailed discussion of oxygen-hydrogen gas cells4 ,for more recent work1 vide ,g4 ,n4 ,lewis1 ,j4 ,am4 ,chem4 ,soc41 #bh1 #aeh 7#aije71 where references to other recent investigations are given4 #efa ,cf4 footnote #a1 p4 #bfa1 and pp4 #bgg-bgi4 #efb ,see pp4 #db1 #beb1 for the expression of the changes as transfers of electrons4 #efc ,fredenhagen1 ,z4 anorg4 ,chem41 #bi1 #dbd 7#aijb71 has brought interesting experimental evidence of the charging of an electrode with gaseous oxygen1 when ferric-ion is the oxidizing agent in aqueous solutions4 ,whether the oxygen1 which is liberated by the action of the ferric-ion on water1 #d ,fe#c #d ,,ho #d ,fe#b ,o#b #b ,h#b,o1 is always the intermediate product and the direct oxidizing agent in aqueous solution1 can hardly be considered decided by the experiment--it may well be the product of a parallel action1 which must take place to a certain extent1 according to the laws of equilibrium1 in a system containing both ,fe#c and ,,ho ions4 ,the result hardly proves that oxygen must be the intermediate product in the main action1 when ferric ions act as the oxidizing agent4 ,we may consider1 for instance1 a solution containing an iodide and a ferric salt3 iodide ions have a far smaller affinity for their negative charges 7electrons7 than hydroxide ions have1 and1 consequently1 will transfer their negative charges 7electrons7 more readily to the ferric ions than the hydroxide ions would4 ,the action1 if oxygen were first liberated1 would lead to the same ultimate result1 but the observation made by ,fredenhagen would not prove that the main action would not nevertheless go by the shorter direct path rather than through an intermediate formation of oxygen4 #efd ,according to the theory1 that arsenic acid is an oxidizing agent because it gives up oxygen of a definite pressure1 this pressure would be the more effective1 the more completely the opposing hydroxide-ion is suppressed by added acid 7p4 #bhj2 see also p4 #bgb1 on the action of ferro-ion on silver-ion in the presence and in the absence of fluorides74 #efe ,only the simplest form of basic ionization of arsenic acid is considered4 ,intermediate ionization into ,as7,,oh7#d1 ,as7,,oh7#cb1 etc4 7see p4 #bdi71 is1 of course1 to be assumed in any complete investigation of the subject4 #eff ,arsenious acid ,as7,,oh7#c1 or ,h,as,o#b1 as well as its anions ,as,o#cc and ,as,o#b1 may have their own characteristic tendencies to assume positive charges and be oxidized to arsenic acid and its derivatives 7see footnote #a1 p4 #bgj74 ,in alkaline solutions these tendencies1 and the potentials corresponding to them1 might well be more important factors in determining the course of an action1 than the tendency of ,as#c to form ,as#e4 ,the discussion in the text1 which deals primarily with acid solutions1 does not exclude such relations4 #efg ,a millivoltmeter is used for this experiment4 #efh ,see footnote #a1 p4 #bhd1 in regard to the interpretation of this experiment on the basis of the theory of liberation of oxygen by arsenic acid4 #efi ,cf4 ,smith's ,general ,inorganic ,chemistry1 p4 #gab4 #egj ,the essential feature of this point of view was first published by ,abegg1 ,z4 anorg4 ,chem41 #ci1 #ccj 7#aijd71 and ,z4 phys4 ,chem41 #dc1 #che 7#aijc72 vide also ,stieglitz1 ,am4 ,chem4 ,j41 #ci1 #ea 7footnote7 7#aijh71 and ,qualitative ,analysis ,notes1 ,university of ,chicago 7#aije74 ,abegg's view has recently received support from ,j4 ,j4 ,thomson in his ,corpuscular ,theory of ,matter1 p4 #aah4 #ega ,h does not change its valence 7charge7 in the action1 and yet it appears as an essential component in both styles of the current equations for the oxidation-reduction reaction4 #egb ,a somewhat similar development of these relations1 for arsenic acid1 has been found in ,abegg's ,anorg4 ,chem41 ,,iii1 #c1 p4 #eeb 7#aijg74 #egc ,luther and ,michie1 ,z4 fr ,elektroch41 #ad1 #hbf 7#aijh74 #egd ,the calculation is based on the results obtained by ,luther and ,michie4 #ege ,the proportion of ,,uo#bb converted into ,u#f would be so minute1 that in an experimental determination of the concentration ,,uo#bb1 the concentration ,u#f would no doubt be a negligible quantity4 #egf ,peters1 ,z4 phys4 ,chem41 #bf1 #aic 7#ahih74 #egg ,in other instances1 the action of the hydrogen-ion in facilitating and accelerating chemical actions 7often called its catalytic effect7 has been explained1 in a similar fashion1 as being based on salt formation1 followed by the ionization of the salts formed1 the active components being the ions 7vide1 for instance1 ,bredig1 ,z4 fr ,elektroch41 #i1 #aah and #aj1 #ehf 7#aijd7 and ,stieglitz1 ,report of the ,congress of ,arts and ,sciences1 ,st4 ,louis1 #d1 #bgf 7#aijd7 and ,am4 ,chem4 ,j41 #ci1 #bi1 #dae 7#aijh7 and later articles74 ,in many of these cases1 the ion concentrations of the reacting components have not yet been accessible to direct measurements1 but the viewpoint has been sustained by quantitative studies of analogous reactions1 which were selected for study1 because the factors involved could be measured 7cf4 ,stieglitz1 loc4 cit474 #egh ,usher and ,priestley1 ,proc4 ,roy4 ,soc41 ,b1 #gg1 #cfi 7#aije72 #gh1 #cah 7#aijh74 #egi ,tollens1 ,ber4 d4 chem4 ,ges41 #ae1 #afce 7#ahhb74 #ehj ,ag ,,nh#cb _/ ,ag7,,nh#c7b #a _/ #ajg4 #eha ,methylene ,,ch#b1 itself1 has never been isolated1 but derivatives of it are known1 such as the cyanides1 ,c7,,nh71 ,c7,,nk7 7see pp4 #ff1 #bcg74 #ehb ,potassium cyanide1 ,c7,,nk71 is a powerful reducing agent 7see p4 #hi74 #ehc ,pp4 #fe1 #ff4 #ehd ,if a negative charge is an electron1 a positive charge the absence of an electron in an atom1 the bivalent carbon atom loses two electrons1 when it is oxidized4 #ehe ,see ,stieglitz1 ,science1 #bg1 #ggd 7#aijh74 #ehf ,the oxidation occurs essentially in the same manner as described 7p1 #bib7 for the action of formaldehyde on ammoniacal silver solution1 when they are brought together in a single vessel4 ,in the present case1 where the action is used to produce an electric current1 there is a migration of negative ions into the formalin solution through the salt-bridge 7p4 #bed74 ,for every two silver ions discharged on the electrode in the silver nitrate solution1 two hydroxide ions are liberated in the formaldehyde solution1 as a result of this migration1 and they combine with the oxidized carbon atom4 ,the oxidation may be expressed1 then1 simply as follows3 7,na,o7,,hc #b #b ,,ho 7,na,o7,,hc#b #b ,,ho 7,na,o7,,hc3,o ,h#b,o4 ,by comparison with the equations given on p4 #bib1 it is evident1 that the only difference lies in the fact that the positive charges1 in the present case1 are carried to the formaldehyde salt through metal wires and a metal electrode1 while previously they were discharged directly by silver ions on the formaldehyde salt4 #ehg ,cf4 ,nernst1 ,theoretical ,chemistry 7#aijd71 p4 #gci1 and the applications mentioned there4 #ehh ,le ,blanc1 ,elektrochemie1 p4 #bae2 v is the valence of the ion4 p#bii ,,chapter ,,xvi ,,systematic ,,analysis ,,for ,,acid ,,ions ,the systematic analysis for acid ions is made on a plan differing in an important particular from the systematic analysis for metal ions4 ,the latter1 as has been seen1 are divided into groups1 which1 by precipitation or solution of characteristic salts1 are successively separated from subsequent groups1 before the isolated groups are analyzed4 ,that is1 in general1 a group of metal ions is examined in the absence of the ions of all other groups4 ,acid ions are also divided into groups1 but1 as a rule1 the groups are not separated from each other for analysis4 ,the reason for this difference in procedure is found1 chiefly1 in the fact that foreign acid ions interfere#ehi to a smaller degree with the specific tests for the ions of a group1 than is the case in the analysis for metal ions4 ,grouping of ,acid ,ions4--,while there is general agreement1 among the most important systems of analysis1 in the grouping of metal ions1 there is notable variation in the way in which acids are grouped by different authors4 ,we shall confine ourselves here to the consideration of two different modes of general procedure and not discuss differences in minor details4 ,if acids were present only in the form of the free acids or of their alkali salts1 the division into groups could naturally and profitably be made to include groups1 which are identified by reactions carried out in neutral or alkaline solution1 as well as by such as are made in acid solutions4 ,now1 cations other than the alkali ions are liable to interfere with tests designed for alkaline or neutral solutions4 ,for instance1 a group of acid ions1 in which the phosphate-ion is included1 is characterized by the fact that the acids form barium salts1 which are soluble in acid but not in neutral or alkaline solutions4 ,the absence or presence of such a group may be recognized1 if no cations other than the alkali metal ions are present1 by the addition of barium chloride to the solution and by careful neutralization of any free acid1 by ammonium p#cjj hydroxide4 ,barium phosphate and the barium salts of the other acids of the group will be precipitated1 if their ions are present4 ,it is clear1 however1 that a number of metal ions must interfere with the test4 ,for instance1 a solution of aluminium nitrate or of ferric chloride1 treated with barium chloride1 and with ammonium hydroxide to neutralize the acid present in the solution as a result of the hydrolysis of the salt1 would give a precipitate of aluminium hydroxide or of ferric hydroxide1 and not of barium salts4 ,the formation of a precipitate under these conditions evidently will not constitute any basis whatever for reaching a conclusion as to the presence or absence of acid ions1 such as can form precipitates of barium salts under the same circumstances4 ,systematic ,analysis for ,acid ,ions1 ,based on the ,removal of ,metal ,ions other than the ,alkali ,metal ,ions4--,on account of this kind of interference1 by cations other than those of the alkali group1 with a number of group and specific tests for anions1 that may be made in neutral or alkaline solutions1 provision is made1 in most systems of analysis1 for the removal of such ions by proper treatment of the substance under examination with sodium carbonate4 ,interfering metal ions are thereby converted into carbonates or hydroxides which are insoluble in water1 while the acids form sodium salts which pass into solution in water4 ,occasionally1 recourse is also taken to hydrogen sulphide to remove ions of the arsenic and copper groups4 ,the treatment with sodium carbonate1 while advantageous in certain cases1 is not uniformly successful#eij3 it is also frequently complicated by the presence of amphoteric bases or of organic substances1 and frequently demands treatments and tests beyond those made with the solution thus prepared4 ,furthermore1 if a group is found to be present1 say a group of acid ions forming barium or calcium salts insoluble in water1 but soluble in acids1#eia all the acids of the group1 which have not been found to be present or absent in the analysis for metal ions1#eib must be specifically p#cja tested for1 although they may all be absent and the only representative of the group present may be an ion previously found in the analysis for metal ions4#eic ,then1 too1 when the group is found to be absent by the group test1 more sensitive tests for some of the acid ions of the group must still be made to insure their complete absence4#eid ,while much may be said in favor of the systematic analysis for acid ions1 based on the preparation of a solution containing only the alkali salts of the anions1 and while one should be familiar with the plan and be able to have recourse to it at will1 yet the drawbacks mentioned suggest another basis for the analysis4 ,systematic ,analysis for ,acid ,ions in ,acid ,solution4--,if the systematic analysis for acid ions is carried out entirely in acid solutions1 interference of cations with tests for anions is rarely met with and in those rare cases may be easily provided against4 ,such a method of systematic analysis in acid solution is frequently more direct and more convenient than a method based on the removal of cations other than the alkali metal ions4 ,almost all of the most characteristic tests for anions1 as it is1 are carried out in acid solutions1 and only a very few good tests1 which must be made in neutral or alkaline solution1 are sacrificed by placing the emphasis on those carried out in acid solutions4 ,the method1 on the whole1 has proved a time-saving and convenient one1 without loss in the trustworthiness of the results4 ,desirability of ,experience with ,both ,methods4--,it is desirable to have experience with both methods1 and to learn by such experience1 when to have recourse to the one or the other method4 ,suggestions as to the choice of method are given in the ,laboratory ,manual1 p4 #aai4 ,the ,groups of ,acid ,ions4--,the arrangement of the acid ions into groups1 for analysis in acid solution1 does not differ in any essential respect from the arrangement based on the use of solutions of sodium salts of the acid ions--only one group test1 which must be made in neutral solutions1 is omitted when the acid solution is used1 and the individual members of this group are tested p#cjb for1 specifically4 ,as that is also very frequently necessary when solutions of sodium salts are used1 no notable sacrifice in convenience is made4 ,since the grouping for both methods of analysis may be made the same1 the following grouping of acid ions has been adopted4 ,only the group characteristics are given2 the members of the groups are described in detail in the ,laboratory ,manual 7,part ,,iii74 ,i4 ,ions of ,amphoteric ,acids and of ,related ,acids4 ,this group includes those acids whose amphoteric character1 or whose ready reduction by hydrogen or ammonium sulphide1 leads to their being found1 or indicated1 in the systematic analysis for metal ions4 ,,ii4 ,the ,carbonate ,group4 ,this group includes those acids whose physical properties 7insolubility71 or the physical properties of decomposition products of which 7carbon dioxide is a decomposition product of carbonic acid71 usually lead to their discovery in the course of the preparation of solutions or of the analysis for cations4 ,,iii4 ,the ,sulphate ,group4 ,the barium salts of this group of acid ions are insoluble in acid solution4 ,barium nitrate1 added to a solution acidified with nitric acid1 is the group reagent4 ,,iv4 ,the ,chloride ,group4 ,the anions of this group form silver salts1 which are insoluble in nitric acid4 ,silver nitrate1 added to a solution acidified with nitric acid1 is the group reagent4 ,v4 ,the ,phosphate ,group4 ,a test for this group1 as a whole1 can be made only if cations other than the alkali metal ions are absent3 the barium salts of the acid ions of the group are insoluble in neutral1 but soluble in strongly acid1 solutions4 ,barium nitrate1 used with a neutral solution1 is the group reagent in the absence of metal ions other than the alkali metal ions4 ,in the presence of other cations1 the three members of the group1 which are not found in some other group1#eie namely3 phosphate1 borate and fluoride ions1 are tested for specifically1 and the group test omitted4 ,phosphate-ion is tested for in nitric acid solution1 in the same solution as is used for the tests for groups ,,iii and ,,iv4 p#cjc ,,vi4 ,the ,nitrate ,group4 ,the salts of the acids of this group are readily soluble in water and specific tests for the acid ions are made2 there is no group test4 ,,vii4 ,the ,group of ,organic ,acids4 ,this group need only be considered when a test for organic matter reveals its presence4 ,applications of ,physico-,chemical ,principles and ,theories4--,the physico-chemical principles and theories1 which have been developed in the previous chapters1 naturally apply also to the reactions by which acid ions are identified4 ,in many cases such characteristic reactions are identical with reactions studied in connection with the metal ions4 ,for instance1 the precipitation of silver chloride1 used to identify the silver-ion 7reagent1 chloride-ion71 may be used1 with certain precautions1 to identify chloride-ion as well 7reagent1 silver-ion74 ,in the following1 only a few typical and interesting applications of the principles and theories to acid ions will be given2 numerous other applications will suggest themselves in connection with the laboratory work on the acids4 ,fractional ,precipitation of ,salts with a ,common ,ion4 ,for saturated solutions of silver chloride1 bromide and iodide1 we have1 according to the principle of the solubility-product#eif3 ,ag#a ,cl#a ,k,ag,cl #a;,e#aj2 ,ag#b ,br#b ,k,ag,br #d;,e#ac2 ,ag#c ,i#c ,k,ag,i #c;,e#af4 ,for a solution saturated simultaneously with the three silver salts1 the value of the concentration of the silver-ion is the same in the three solubility-products 7see p4 #afd74 ,consequently1 for such a solution1 with which the three solid salts are in equilibrium1 the ratios of the concentrations of the anions must be3 ,cl 3 ,br 3 ,i ,k,ag,cl 3 ,k,ag,br 3 ,k,ag,i #c #aje 3 #acjj 3 #a4 ,that is1 if silver nitrate is added to a mixture of iodides1 bromides and chlorides1 silver iodide must be precipitated first1 until the concentration of bromide-ion1 in solution1 is #acjj times as great as the concentration of the iodide-ion left in solution4 ,then bromide and traces of iodide of silver will be precipitated1 until the concentration of chloride-ion is #cjj1jjj times as great as the concentration of iodide-ion and some #bej times as great as the concentration of the bromide-ion4 ,in other words1 if silver nitrate is added gradually to such a mixture1 iodide-ion and bromide-ion will be almost completely removed from solution before a precipitate of silver chloride can be in equilibrium with the solution4 ,this gives us a convenient and rapid method of detecting chlorides1 if present1 p#cjd in more than small quantities1 with iodides and bromides4 ,silver nitrate1 a few drops at a time1 is added to the solution and the mixture vigorously shaken after each addition4 ,as long as a yellow 7,ag,i7 or yellowish 7,ag,br7 silver salt is precipitated on the addition of silver nitrate to the supernatant liquid 7the precipitate settles quickly71 silver nitrate is added as before2 when the color becomes quite pale1 the solution is filtered and silver nitrate added a drop at a time2 if a pure white precipitate results finally1 chloride-ion is present in the mixture 7exp474 ,complex ,ions4 ,instances of the rle of complex ions in the analysis for acid ions are numerous4 ,one of the most interesting illustrations is the application of the equilibrium conditions for the complex silver-ammonium-ion 7p4 #bbd7 to the separation of silver chloride1 bromide and iodide4 ,a rather more convenient and more sensitive method#eig for detecting the three halide ions in the presence of each other than the method just considered1 may be discussed from this point of view4 ,the condition of equilibrium between silver-ion1 ammonia and silver-ammonium-ion is expressed in the relation3 ,ag ,,nh#cb _/ ,ag7,,nh#c7b ,k #a _/ #ajg4 ,the concentration of silver-ion1 which may exist in an ammoniacal solution1 evidently must decrease rapidly with increasing concentrations of the free ammonia4 ,now1 let us imagine only sufficient free ammonia1 in solution1 added to a mixture of silver chloride1 bromide and iodide1 to keep the concentration of silver-ion1 which can exist in the solution1 say at ,ag #f;,e#i1 which is just #a _/ #ajjth of the concentration of silver-ion in a saturated aqueous solution of silver bromide4 ,such a solution of ammonia1 in contact with the three silver salts mentioned1 will dissolve silver chloride1 if sufficient is present1 until ,cl ,k,ag,cl _/ #f;,e#i #j4jag molar4 ,at the same time1 silver bromide would be dissolved until ,br ,k,ag,br _/ #f;,e#i #j4jjj1jf molar4 ,in other words1 silver chloride could be dissolved in some quantity1 while silver bromide is dissolved only in traces 7the ratio of ,cl 3 ,br is again about #bej 3 #a74 ,when such an ammoniacal extract is acidified with nitric acid1 almost pure 7white7 silver chloride would be precipitated and only traces of bromide would be lost4 ,after the extraction of the chloride1 an increased concentration of ammonia would lead1 similarly1 to a solution in which silver bromide would dissolve readily and only traces of the iodide be lost1 and thus a separation of bromide and iodide may be effected4 ,in ,hagar's method1 the concentration of ammonia1 required to dissolve silver chloride with but traces of bromide1 is attained by the use of a solution of ammonium sesqui-carbonate1#eih in which free ammonia is present only in small concentration1 as a result of the hydrolysis of the salt4 ,after the p#cje extraction of the chloride by this solution1 the bromide is extracted with a #e solution of ammonia4 ,complex ,ions of ,acid ,ions with ,other ,acids4--,in the study of complex ions we found that positive ions 7silver1 cupric1 etc47 may form complex positive ions with ammonia#eii or complex negative ions with acid ions 7e4g4 with cyanide-ion74 ,in the study of the acid ions we also meet instances of complexes formed by the union of two acids to form a new complex acid4 ,ammonium phosphomolybdate1 an important salt that is extremely useful in detecting the presence of phosphate-ion1 is the most interesting instance of the salt of such an acid1 which is met in elementary qualitative analysis4#fjj ,ammonium phosphomolybdate1 7,,nh#d7c,,po#d1 #ab ,mo,o#c1 is the salt of a complex phosphomolybdic acid1 formed from phosphoric acid1 ,o3,p7,,oh7#c1 and molybdic acid1 ,o#b,mo7,,oh7#b1 by a loss of water1 much as potassium dichromate is formed from potassium acid chromate ,,ko7,cr,o#b7,,oh ,,ho7,cr,o#b7,,ok ,,ko7,cr,o#b7,o7,cr,o#b7,,ok4 ,the only difference between the two actions lies in the fact that1 in the case of the dichromate1 anhydride formation occurs between two molecules of a single acid2 in the case of the phosphomolybdate1 anhydride formation takes place between molecules of different acids1 and a much larger number of molecules is involved4 ,if we suppose the combination between the two acids to proceed symmetrically1#fja we may consider the following to be the action3 ,o3,p7,,oh7#c #c ,,ho7,mo,o#b7,,oh ,,ho7,mo,o#b7,,oh ,,ho7,mo,o#b7,,oh ,,ho7,mo,o#b7,,oh ,o3,p,o7,mo,o#b7,o7,mo,o#b7,o7,mo,o#b7,o 7,mo,o#b7,,oh#c #ab ,h#b,o4 ,intermediate complex acids1 containing less molybdic acid1 are no doubt formed first 7the action is a relatively slow one71 and the action proceeds until the formation of an insoluble salt leads to the final precipitation of all of the phosphate in this form4 ,the precipitate shows the characteristic behavior of an acid anhydride--alkalies dissolve it readily and form phosphate and molybdate--e4g4 ammonium hydroxide forms ,,nh#db;,,hpo#d and 7,,nh#d7b,mo,o#d 7exp474 ,dichromates1 in a similar way1 are converted by alkalies into chromates1 an action which may readily be followed by the change in color 7exp474 ,oxidation and ,reduction4--,while fractional precipitation of silver iodide1 bromide and chloride1 and fractional solution of the silver salts in ammonia are convenient methods for detecting the three halide ions in the presence of one another1 the most accurate and most convenient methods for this purpose depend on the different sensitiveness which iodide1 bromide and chloride ions exhibit towards oxidizing agents4 ,of the three halogens1 iodine shows the smallest tendency to form its ion 7see the table1 p4 #bid71 chlorine the greatest4 ,vice versa1 of the three halide ions1 iodide-ion is most readily1 chloride-ion least readily1 oxidized4 ,treatment with a mild oxidizing agent1 such as ferric-ion p#cjf 7see ,chap4 ,,xiv and ,laboratory ,manual under iodide-ion71 suffices to oxidize iodide-ion to iodine3 #b ,fe#c #b ,i #b ,fe#b ,i#b4 ,bromide-ion and chloride-ion are left practically unaffected by this agent 7see ,chap4 ,,xiv74 ,a somewhat stronger oxidizing agent1 chromic acid 7or its ion ,cr#f1 see ,chap4 ,,xv71 oxidizes bromide-ion and leaves chloride-ion practically unaffected3 #b ,cr#f #f ,br #b ,cr#c #c ,br#b4 ,this method of fractional oxidation forms one of the most convenient and sensitive methods for detecting the three halide ions in the presence of one another4#fjb ,we shall discuss here only one other oxidation-reduction reaction1 taken in connection with the laboratory work--the oxidation of hydroiodic acid by exposure to the air and the resistance to oxidation shown by an iodide1 such as potassium iodide1 under the same conditions4 ,the following method of proximate analysis of the chief relations involved may also be used to interpret the contrast in the behavior of hydroiodic acid and that of hydrobromic or hydrochloric acid 7,laboratory ,manual1 q4 v474 ,in all of these cases the actual relations are rendered more complex in consequence of secondary reactions1 than is indicated in the text that follows3 it is intended only to outline the most effective of the factors involved and to illuminate the qualitative results observed4 ,oxidation of ,hydroiodic ,acid by ,air4--,the oxidation of hydroiodic acid1 or of potassium iodide1 by the oxygen of the air may be considered 7,chapters ,,xiv and ,,xv7 to involve primarily the action #d ,i ,o#b #b ,,hoh #b ,i#b #d ,,ho4 7#a7 ,the condition for equilibrium will be ,i#d ,o#b _/ 7,i#bb ,,ho#d7 ,kequil4 7#b7fjc ,a system in which ,i is directly in equilibrium with ,i#b 7for which ,i#ab 3 ,i#ba ,k,i1 ,iodine #e4f;,e#bi1 at room temperature 7p4 #bih77 and in which1 at the same time1 ,,ho is directly in equilibrium with ,o#b 7for which at room temperature ,,ho#ad 3 ,o#ba ,k,,ho1 ,oxygen #h4b;,e#di 7p4 #bih77 would also represent a condition of equilibrium for the four components4 ,we find thus ,kequil4 ,k,i1 ,iodine#b _/ ,k,,ho1 ,oxygen 7#e4f;,e#bi7b _/ 7#h4b;,e#di7 #d;,e#i4 7#c7 ,with the aid of this constant and of equation 7#b7 we can obtain1 at least1 an approximate interpretation of the results of the exposure of hydroiodic acid and of potassium iodide to the influence of atmospheric oxygen4#fjd ,we may p#cjg calculate1 first1 what concentration of free iodine would be required to prevent oxidation of hydroiodic acid1 in molar solution1 by the oxygen of the air1 i4e4 to establish equilibrium4 ,we will call x that concentration of ,i#b4 ,as hydroiodic acid is a very strong acid1 ionized to the extent of about #hj in molar solution1 we may1 with sufficient accuracy for our purpose1 consider it completely ionized and put ,i #a and ,h #a4 ,since at #be ,h ,,ho #a4b;,e#ad 7p4 #ajd71 we may put ,,ho #ajad4 ,the concentration of oxygen in the air1 at room temperature1 may be considered to be approximately ,o#b 7#a_/e7 7#a _/ #bc4i74 ,inserting all these given values in equation 7#b71 we have ,i#d ,o#b _/ 7,i#bb ,,ho#d7 #a 7#a_/e7 7#a _/ #bc4i7 _/ 7x#b 7#ajad7d7 #d #aji4 7#d7 ,solving for x1 we find x #ajbb ,i#b4 ,that is1 free iodine of this enormous concentration would be required to prevent oxidation of hydroiodic acid in molar solution by the oxygen of the air at room temperatures4 ,it is obvious that hydroiodic acid must be extremely sensitive to oxidation by exposure to air4 ,one might estimate1 in a similar way1 the extent to which hydroiodic acid1 of a given concentration1 would be oxidized by air before equilibrium would be reached4 ,the process would involve simultaneous changes in three factors--iodide-ion is destroyed1 iodine is formed and hydroxide-ion increases1 as the result of the neutralization of hydrogen-ion by the hydroxide-ion formed in the action 7see above74 ,the solution of the equilibrium equation is too involved for the elementary purposes of this discussion3 it leads to the same qualitative conclusion as was just reached4 ,oxidation of ,potassium ,iodide by ,air4 ,we may now ask what the relations would be1 if we used a molar solution of potassium iodide in place of the free acid4 ,i and ,o#b would have the same value as before4 ,the solution being originally neutral1 ,,ho would at first have the value 7#a4b;,e#ad7 #a4a;,e#g4 ,but when potassium iodide is exposed to the air1 if iodine is liberated1 the solution becomes alkaline#fje 7,,ho is formed according to equation 7#a77 and the concentration of ,,ho consequently grows continuously greater4 ,we will1 therefore1 formulate the problem as follows3 how much iodine#fjf must be liberated1 by oxidation of iodide-ion1 in molar potassium iodide solution in order to establish equilibrium8 ,for every two molecules of iodine liberated1 four ,,ho ions are formed 7equation 7#a774 ,if we call y the concentration of iodine at the point of equilibrium1 then #b y is the concentration of ,,ho at that point1 formed by the oxidation process4 ,inserting the given values#fjg in equation 7#b71 we have ,i#d ,o#b _/ 7,i#bb ,,ho#d7 #a 7#a_/e7 7#a _/ #bc4i7 _/ 7y#b 7#b y7#d7 #d;,e#i4 p#cjh ,solving for y1 we find y #j4jjg4 ,that is1 in molar solution1 about #a4d of the iodide#fjh would be oxidized 7carbonic acid and other acids being excluded72 in #e c4c4 7see ,lab4 ,manual1 p4 #gc7 #i milligrams of iodine#fji would be liberated to reach a condition of equilibrium4#faj ,it is thus clear that the conditions for equilibrium between a solution of an iodide and air would be satisfied1 in the case of an alkali iodide1 by the liberation of a mere trace of iodine1 whereas1 as was previously shown1 in the case of hydrogen iodide1 a very large proportion of iodine must be liberated before equilibrium could obtain4 ,a careful comparison of the two developments shows that the difference in result#faj is plainly due to the higher oxidizing power1 the higher potential of oxygen 7p4 #bhj71 in acid solutions1 containing only a minute concentration of hydroxide-ion1 as compared with its efficiency in neutral or slightly alkaline solution4 ,,footnotes3 #ehi ,in the few cases when there is interference1 it is provided against4 #eij ,cf4 ,fresenius1 ,qualitative ,analysis1 p4 #ebj4 #eia ,the group includes phosphate1 borate1 fluoride1 oxalate1 silicate1 arsenite1 arseniate1 chromate and tartrate ions4 #eib ,the ions of the amphoteric acids1 arsenic and arsenious acids1 and chromate-ion1 which is reduced by hydrogen sulphide to chromium-ion1 are found in the systematic analysis for metal ions4 #eic ,the ions of the amphoteric acids1 arsenic and arsenious acids1 and chromate-ion1 which is reduced by hydrogen sulphide to chromium-ion1 are found in the systematic analysis for metal ions4 #eid ,see ,fresenius1 loc4 cit41 p4 #eaa1 footnote1 and p4 #ebj4 #eie ,other acid ions which would show the group test--precipitation of a barium salt in a neutral solution--are determined in other groups1 as follows3 arsenite1 arseniate and chromate ions in the group of amphoteric acids1 etc4 7,i72 carbonate and silicate ions in the carbonate group 7,,ii72 and oxalate and tartrate ions in the group of organic acids 7,,vii74 #eif ,the constants refer to #ah4 ,the subindices are used to distinguish the 7unequal7 concentrations of the silver-ion and of the halide ions in the different solutions referred to in the text4 #eig ,hagar's method4 ,see ,fresenius1 loc4 cit41 pp4 #cef and #cgh4 #eih ,see ,fresenius1 loc4 cit41 pp4 #cef and #cgh1 for the preparation of the solution and for details of the method1 and see ,smith1 ,general ,inorganic ,chemistry1 p4 #eff1 as to the nature of the sesqui-carbonate4 #eii ,they also form complex ions with substances related to ammonia1 such as the organic amines4 #fjj ,ammonium arsenomolybdate is an analogous salt 7see ,laboratory ,manual1 ,part ,,iii74 ,a similar complex acid1 phosphotungstic acid1 is used in alkaloidal analysis4 #fja ,the exact structure of the complex acid is not known4 #fjb ,in the ,laboratory ,manual a second1 similar method is also given4 #fjc ,it is considered that water has a constant concentration in a dilute solution and that for its active components ,h ,,ho is a constant 7p4 #agf74 #fjd ,in the calculation which follows1 which is meant merely for a rough survey1 no account is taken of the formation of complex ions ,i#c1 or of the tendency of hydroiodic acid to decompose spontaneously into iodine and hydrogen3 #b ,h #b ,i ,h#b ,i#b1 a reaction which could also be studied profitably with the aid of the equilibrium constants for ,i#b #b ,i and for ,h#b #b ,h4 ,the value of the iodide constant is also uncertain 7see p4 #bgc74 #fje #d ,k #d ,i ,o#b #b ,,hoh #b ,i#b #d ,k #d ,,ho4 #fjf ,the formation of complex ions ,i#c and other secondary reactions 7formation of hypoiodite1 iodate1 etc47 are ignored4 #fjg y has so small a value that we may consider ,i practically unchanged4 #fjh #j4jjg ,i#b #j4jad ,i4 #fji ,a mole of ,i#b #b #abg #bed grams2 7#j4jjg #bed #e7 _/ #ajjj #j4jji gram4 #faj ,the tendency of iodine to form hypoiodous acid1 iodates1 etc41 is not taken into consideration here and involves another relation4 ,,index ,numbers marked 77 refer to subjects illustrated by experiments1 heavy numbers refer to tables4 ,acetic acid1 #ih1 #aja1 #aaa-aad ,acid ions1 systematic analysis for1 #bii et seq4 groups of1 #cja ,acids1 #ha1 #hb1 #ajj1 #ajd ,acid salts1 #ajc ,alkali group1 #aeh1 #aei ,alkaline earth group1 #aeh1 #afb ,aluminate-ion1 #agb ,aluminium group1 #aeh1 #ahh et seq41 #aie ,aluminium hydroxide1 #aga et seq41 #aif ,aluminium-ion1 #aeh1 #agb1 #ahh et seq4 ,ammonia1 complex ions of1 #baf et seq41 #bbd ionization of1 #hg ,ammonium hydroxide1 conductivity of1 #gg dissociation of1 #afj ionization of1 #gh1 #aad strength as base1 #gh1 #gi1 #afh ,ammonium-ion1 #afa ,ammonium salts1 dissociation of1 #cd1 #aei effect on ammonium hydroxide1 #afh ,amphoteric acids1 group of1 #cjb ,amphoteric hydroxides1 #aga et seq41 #ahg1 #ahh1 #aif ,antimony1 ions of1 #agd ,argenticyanide-ion1 #bbe ,arrhenius's theory of ionization1 see ,ionization ,arsenic acid1 #bdg1 #bej1 #bhc ,arsenic group1 #aeh1 #baj1 #bdb et seq4 ,arsenic1 ions of1 #aeh1 #agd1 #bdb et seq4 ,arsenic pentasulphide1 #bdg ,arsenious sulphide1 colloidal1 #abe ,association1 #ai1 #fd ,aurocyanide-ion1 #bcb ,avogadro's hypothesis1 #cc1 #cd ,avogadro-van 't ,hoff ,hypothesis1 #ae1 #cg ,azolitmin1 #gi ,barium carbonate1 as reagent1 #aic ,barium-ion1 #afb ,bases1 #gi1 #ha1 #aje1 #ajf ,basic salts1 #ajf1 #aid ,bismuth-ion1 #aeh ,boiling-point1 #ag1 #cf1 #ch ,borates1 hydrolysis of1 #ij ,bromine1 #beb ,cadmium-ion1 #aeh complex ions of1 #bbd1 #bbh sulphide1 #bji et seq4 ,calcium-ion1 #afb ,carbonate group1 #cjb ,carbonic acid1 #ij1 #ajj ,chemical activity of ions1 #gb1 #gh1 #hg1 #bcb of acids1 #ha1 #hb1 #aje of bases1 #gi1 #ha of molecules1 #gd1 #hc1 #bcb of salts1 #gd1 #ajg1 #aaf ,chemical equilibrium1 #ij et seq41 #if and direction of action1 #aab and path of action1 #bce and physical equilibrium1 #aci et seq4 of electrolytes1 #ih1 #aaa-aae ,chemical equilibrium1 law of1 #ia1 #id and ionization of strong electrolytes1 #ajh factors of1 #ie et seq4 limitations to1 #ie ,chemometer1 #bec ,chloride group1 #cjb ,chloride-ion1 oxidation of1 #bge1 #bgf ,chlorine1 #df1 #beb1 #bge ,chromium-ion1 #aeh1 #ahh et seq4 ,chromic acid1 #bhg ,cobalt-ion1 #aeh1 #aib ,cobalticyanide-ion1 #bbi ,cobalt sulphide1 #aib ,colloidal condition1 #abe et seq4 definition of1 #acj relations to analysis1 #aca1 #acf solution theory of1 #abh suspension theory of1 #abi ,colloids1 electric charges on1 #aca precipitation of1 #acc protective action of1 #acf1 #acg ,complex ions1 #hh1 #baf et seq4 applications in analysis1 #bbj1 #bcj of acid ions1 #cje of ammonia1 #baf et seq4 of cyanide-ion1 #bbe et seq4 of halide ions1 #bcg of oxide-ion1 #bch of sulphide-ion1 #bch1 #bdf organic1 #bch ,concentration1 definition of1 #ia ,conductivity1 #dd1 #df1 #dg1 #di1 #ea1 #ef partial1 see ,mobilities ,copper1 equilibrium with cupric-ion1 #beh1 #bfd oxidation of1 #beg et seq4 solution-tension of1 #bei ,copper group1 #aeh1 #aii et seq41 #baj1 #baf et seq4 ,cupric-ion1 complex ions of1 #bbd equilibrium with copper1 #beh1 #bfd reduction of1 #beg sulphide1 #bab ,cuprous-ion1 complex ions of1 #bbh ,cyanide-ion1 complex ions of1 #hh1 #bbe et seq41 #bcb ,dialysis1 #abh ,dielectric constants1 #fb1 #fc ,diffusion1 of gases1 #bi of ions1 #ei of solutes1 #i ,dissociation of complex ions1 #bai electrolytic1 see ,ionization gaseous1 #cd1 #cf1 #if ,dry salts1 #gd ,electrolysis1 #df1 #eh ,electrolytes1 see ,ionogens ,electron theory1 #db ,equilibrium1 see also ,chemical equilibrium and ,physical equilibrium constants1 #ie1 #ih1 #bcc1 #bcf1 #bih oxidation and reduction1 #beh1 #bfe et seq41 #bfg1 #bgc et seq4 ,faraday's law1 #eh ,ferric hydroxide1 #abg1 #agj ,ferric-ion1 #hh1 #bea1 #beb1 #bfi ,ferricyanide-ion1 #hh1 #bcj ,ferrocyanide-ion1 #hh1 #bcj ,ferrous-ion1 #hh1 #bea1 #beb1 #bfi ,formaldehyde1 #bhi et seq4 ,fractional oxidation1 #cje1 #cjf ,fractional precipitation1 #afc1 #afe1 #cjc ,fractional solution1 #cjd ,freezing-point1 #ag1 #cf1 #ch ,fused salts1 #ge ,gold1 #aeh1 #bdb et seq4 colloidal1 #abf see also ,aurocyanide-ion ,groups of metal ions1 #aeg ,groups of acid ions1 #cja ,heat1 #ge1 #gf ,heterogeneous equilibrium1 see ,physical equilibrium ,hydrogen1 oxidation of1 #bgg1 #bgh1 #bhj ,hydrogen chloride1 #cd1 #cg1 #db1 #gb1 #gc1 #hd ,hydrogen-ion1 action on indicators1 #gi1 #aje chemical activity1 #gb-gd1 #ha1 #hb1 #bgh et seq4 concentration for precipitation by ,h#b,s1 #bac mobility1 #ed1 #ef ,hydrogen sulphide1 ionization of1 #aii1 #bde oxidation of1 #bea1 #bed precipitation by1 #ij1 #aii et seq41 #bjc ,hydrol1 #age ,hydrolysis of salts1 #abg1 #agh et seq41 #aij ,hydroxide-ion1 action on indicators1 #gh1 #gi chemical activity1 #gi1 #ha1 #afh mobility1 #ed1 #ef ,indicators1 #gi1 #afe1 #bad ,instability constants1 #bai1 #bbd1 #bbf ,iodide-ion1 #hh1 #bgb1 #cje ,iodine1 #bgc1 #cje ,ionization and chemical activity1 #fi1 #gb1 #gi1 #ij et seq41 #aaf1 #bcb and conductivity1 #dd1 #gg1 #aae and dielectric constants1 #fb-fd and electron theory1 #db and ,faraday's law1 #eh and osmotic pressure1 #fg and solvents1 #fa constants1 #ih1 #ajj1 #ajd1 #ajf1 #ajh degree of1 #ej exceptional1 of certain salts1 #aae in stages1 #ajj1 #ajb of acids1 #fi1 #ih1 #ajj1 #ajd1 #ajh of bases1 #fi1 #aje1 #ajf1 #ajh of colloids1 #acb of salts1 #fi1 #gd1 #ge1 #ajg1 #ajh1 #aae theory of ,arrhenius1 #dj1 #da1 #ea theory of ,clausius1 #ea ,ionogens1 #fi ,ion-product1 see ,solubility-product ,ions1 #db charges on1 #da1 #eh combination with solvents1 #db1 #fe composition of1 #fi1 #hi migration of1 #de1 #ec1 #ed mobilities of1 #ef ,kinetic theory1 of gases1 #bf and osmotic pressure1 #bf ,lead-ion1 #aeh sulphide1 #bab1 #bac ,light1 #gf ,litmus1 #gi ,magnesium hydroxide1 #afh ,magnesium-ion1 #afb ,manganous-ion1 #aeh ,mass action1 law of1 #ic1 #if ,mercuric chloride1 #eg1 #aae ,mercuric cyanide1 #aae1 #aaf1 #bca ,mercuric-ion1 #aeh1 #beg ,mercurous-ion1 #aeh ,mercury1 #beg ,methyl orange1 #gi ,methyl violet1 #bac ,mobilities of ions1 #ec1 #ef ,molecular weights1 #cc1 #cf1 #cg ,nernst's formula1 #bfa et seq41 #bif et seq4 ,nickel-ion1 #aeh cyanide-ion1 #bbi sulphide1 #aib ,nitrate group1 #cjb ,nitric acid1 #bhh ,organic acids1 group of1 #cjb ,organic substances1 complex ions of1 #bch oxidation of1 #bhi et seq4 ,osmosis1 #aj1 #bb1 #bd ,osmotic pressure1 #h et seq4 and ionization1 #dj1 #fg definition of1 #aj indirect determination of1 #af laws of1 #ab-bj measurement of1 #aj theories of1 #cb ,oxalates1 complex ions of1 #bda ,oxidation1 #bea et seq41 #bhb et seq4 by electric current1 #beb definition of1 #bea of organic compounds1 #bhi production of current by1 #bec relation to theory of ionization1 #bea et seq4 ,oxidation-reduction1 reversibility of1 #bef1 #bfh et seq4 interpretations of1 #bea1 #bhb1 #bhf ,oxygen1 oxidation by1 #bgg1 #bgh1 #bhj1 #cje ,oxygen-hydrogen cell1 #bhj ,permanganic acid1 #bhg ,perpetuum mobile1 #ab ,phases1 #aah ,phenolphthalen1 #gi ,phosphate group1 #cjb ,phosphomolybdates1 #cje ,phosphoric acid1 #ajb1 #acd ,physical equilibrium1 #aah et seq4 and chemical equilibrium1 #aci et seq4 applications of law of1 #abj law of1 #aah ,platinum1 #aeh1 #bdb et seq4 ,potassium hydroxide1 #ggha1 #ajf ,potassium-ion1 #aeh1 #afa ,potential differences1 #bfa et seq4 and concentrations1 #bfa1 #bfc and osmotic pressures1 #bfa sign of1 #bfa ,precipitates1 see also ,precipitation solution of1 #aea washing of1 #adh ,precipitation1 #abb1 #ade et seq4 and ionization1 #gd1 #ij1 #aeb1 #bbj et seq4 fractional1 #afc1 #afe influence of a common ion1 #add1 #adf1 #adg influence of electrolytes1 #add1 #aej of electrolytes1 #ade ,primary ionization1 #aja1 #ajb ,purple of ,cassius1 #abf1 #acd ,reduction1 see also ,oxidation by electric current1 #beb definition of1 #beb interpretations of1 #bea1 #bhb1 #bhf production of current by1 #bec ,salt-effect1 #hb1 #aji1 #aaj ,secondary ionization1 #aja1 #ajb1 #bdf ,silver1 colloidal1 #abg ,silver-ammonium-ion1 #bag et seq4 ,silver bromide1 #bbd1 #cjc ,silver chloride1 colloidal1 #ach precipitation of1 #aej solubility of1 #bba ,silver chromate1 #ada1 #afe ,silver group1 #aeg1 #aii et seq41 #baf et seq4 ,silver iodide1 #bbd1 #cjc ,silver-ion1 #aeh as oxidizing agent1 #bij complex ions of1 #baf1 #bbe ,sodium hydroxide1 #ha1 #ajf1 #agc ,sodium-ion1 #aeh1 #afa ,solubility1 #aba1 #abc1 #adf1 #adg1 #aec1 #aee ,solubility-product principle1 #ada et seq4 applications of1 #ade1 #adg1 #adi1 #aea derivation of1 #aci et seq4 ,solution1 theories of1 #h1 #cb ,solution of electrolytes1 #aea ,solutions1 concentrated1 #ae1 #cb1 #adb dilute1 see ,osmotic pressure non-aqueous1 #fb1 #gc1 #hd supersaturated1 #aba ,solution-tension1 electrolytic1 #beh et seq4 constants1 #bei1 #bff1 #bid1 #bie ,solvents and ionization1 #fa1 #fd and solubility of electrolytes1 #aed1 #aee ,strength of acids1 #ajd ,strength of bases1 #gh1 #ajf ,strontium-ion1 #aeh1 #afb ,sulphate group1 #cjb ,sulphide-ion1 complex ions of1 #bch1 #bdf concentration of1 #bjb oxidation of1 #bea1 #bed ,sulphides1 precipitation of1 #aii1 #bjc et seq4 solubilities of1 #bjc et seq41 #bab ,sulpho-acids1 #bdd et seq4 ,sulpho-bases1 #bdd et seq4 ,sulpho-salts1 #bdc et seq4 ,sulphuric acid1 ionization of1 #ajc ,supersaturation1 #aba ,systematic analysis1 of metal ions1 #aeg et seq4 of acid ions1 #bii et seq4 ,tartaric acid1 complex ions of1 #bch ,tin1 ions of1 #aeh1 #agd1 #bdb et seq4 ,unsaturated compounds1 #fd ,uranyl salts1 #bhf ,valence1 #ei and precipitating power of ions1 #ace ,van 't ,hoff's hypothesis1 see ,avogadro ,van 't ,hoff's theory of solution1 #ab et seq4 apparent exceptions to1 #ah ,vapor tension1 #ag1 #cf1 #ch ,velocity of action1 #ib ,water1 see also ,hydrolysis composition of1 #age dielectric constant of1 #fc formation by electrolytic oxidation1 #bhj1 #bhb ionization by1 #cg1 #da1 #dg1 #fa1 #gc1 #gd ionization of1 #ec1 #ajd1 #ajf1 #agf et seq4 oxonium ions of1 #bch secondary ionization of1 #bdf1 #bgh ,zinc1 #beg1 #bff ,zinc group1 #aeh1 #ahh et seq41 #baj ,zinc-ion1 #bff ,zinc sulphide1 #bjd et seq4 ,,transcriber',s ,,note4 ,original printed spelling and grammar is generally retained4 ,footnotes were renumbered and relocated to the ends of chapters4 ,notes to tables were left in their original locations4 ,some mathematical and chemical formulas and equations were modified in format or rearranged4 ,text originally printed in italics is herein marked thus4 ,originally bold text is herein like this4 ,original small caps is herein all capitals4 ,this book uses many uncommon ,unicode characters1 and careful selection of the ebook reader software and font used to view it is necessary4 ,some of the uncommon characters not already mentioned are3 ,u#bbif 2 ,u#bbie 2 ,u#bba;,e 2 ,u#bba;,b 2 ,u#bbab 1 ,minus ,sign2 ,u#ba;,c#d 2 ,u#baib 2 ,u#begb 2 and ,u#bega 4 ,the use of a monospaced font is important for the data tables1 and for some chemical formulas4 ,on the other hand1 the ,thin ,space ,u#bjji is used aesthetically in most of the chemical and mathematical equations1 and an exact monospaced font will not display ,thin ,space correctly4 ,adobe's ,source ,code ,pro is an unusual monospace font that does display ,thin ,space1 the chemical formulas1 and the data tables correctly4 ,deja,vu ,sans ,mono is another good choice1 but it does not display ,thin ,space correctly4 ,the notation ,dx signifies ,d subscript x4 ,the notation ,dy signifies ,d superscript y4 ,in unambiguous cases where the superscripted text is a single digit exponent 7#j-i71 this is simplified to ,dy4 ,the archaic form of scientific notation exemplified by #j4jdac1 is herein simplified either to decimal form--#j4jjjjac in this example--or to modern scientific ,e notation1 #a4c;,e#e4 ,in this1 ,e means times ten raised to the power of4 ,furthermore1 ,e notation has also been substituted herein for most numbers originally printed like this3 a #aj;b4 ,the name van't ,hoff was changed to van 't ,hoff throughout2 likewise ,van't to ,van 't4 ,the hyphen is used inconsistently throughout the book1 in words such as hydrogen-ion versus hydrogen ion or non-ionized versus nonionizied4 ,these have been retained4 ,the word difficulty was sometimes employed as an adverb2 herein it is converted to difficultly in this usage4 ,page #de3 ,changed permangante to permanganate4 ,page #ha3 ,removed the unmatched right parenthesis from the difference in ionization between potassium hydroxide and ammonium hydroxide744 ,page #ajd3 ,in the table1 ,hydrogen sulphide was changed to ,h#b,s to meet maximum line-length constraints for this ebook4 ,furthermore1 the table notes were reordered and renumbered to match the sequence of note anchors in the table4 ,the anchor in the table title originally linked to a footnote instead of a table note2 this footnote was converted to a table note 7the first one74 ,page #ajf3 ,the label for the sixth note to the table ,the ,ionization ,constants of ,bases was changed from #c to ,f4 ,page #aag3 ,the chemical reaction schema1 originally comprising two balanced equations and two unbalanced equations using vertical arrows has been rearranged into four balanced equations1 with horizontal arrows4 ,such rearrangements have been silently performed elsewhere4 ,on page #bag1 a schema of three equilibrium equations was separated into three equations1 and also removed from its embedded location within its paragraph line4 ,page #aag3 ,the printed symbol that might be described as normal leftward arrow over rightward dark arrow 7or heavy arrow7 has been represented herein with a more readily available character --the ,unicode character with hexadecimal number #bidb 7,u#bidb71 rightward arrow over short leftward arrow4 ,the same character is used herein for the printed symbol which might be described as downward dark arrow left beside upward short arrow right--the equations having been rearranged into a horizontal format--and also for rightward dark arrow over leftward arrow4 ,a different character ,u#bidc represents normal rightward arrow over heavy leftward arrow4 ,page #abe3 ,in the reaction of arsenious oxide with hydrogen sulphide1 changed ,h#c,s to ,h#b,s4 ,page #adf3 ,in the table heading1 ,,ch#c;,,coo- was changed to acetate to save space4 ,the same thing was done in the table on page #adf4 ,page #aeg ,mendelejeff changed to ,mendeleff4 ,page #ahh1 second footnote 7#chj73 ,the printed structure for glycocoll a4k4a4 glycine was shown roughly as follows3 ,h#c,n4,,ch#b;,,coo with a line drawn between the ,n and the right-hand ,o4 ,this has been herein modernized to ,h#c,n4,,ch#b4;,,coo1 showing explicitly the zwitterion structure 7the second full stop added to emphasize that ,,coo is a unit74 ,the html and mobile versions reproduce the original structure4 ,page #aig3 ,changed ,al,o#c y to ,al,o#cc y4 ,page #bbf etc43 ,both forms ,bodlaender and ,bodlnder are retained4 ,page #bci3 ,the letters originally underscored are herein marked with ,u#bjag1 ,double ,low ,line1 e4g4 ,,oh4 ,page #bdf3 ,changed saponifying esters 7p4 #hja7 to saponifying esters 7p4 #ha74 ,page #beb3 ,substituted for a symbol that might be described as circled epsilon4 ,page #bhc3 ,in the equation showing the oxidation of zinc by cupric ion1 the upward arrow originally shown beside the symbol for copper metal is changed to downward arrow4 ,page #caj3 ,the reference for mobility of ,hydroxide-ion was changed from #aef to #ef4