file which includes the original illustrations4 ,see #cddeg-;h4htm or #cddeg-;h4zip3 7https3_/_/www4gutenberg4org_/cache_/epu b_/#cddeg_/pg#cddeg-;images4html7 or 7https3_/_/www4gutenberg4org_/files_/#cd deg_/cddeg-;h4zip7 ,transcriber's note3 ,page numbers enclosed by curly braces 7example3 #be7 have been incorporated to facilitate the use of the ,table of ,contents4 ,in chemical formulas an underscore is used to indicate that the following number enclosed by curly braces is a subscript4 ,for example1 the formula of water is indicated by ,h#b,o4 ,a carat character followed by a number enclosed by curly braces indicate an exponent4 ,for example1 ten raised to the minus #gth power is indicated by #aj-g4 ,a few typographical errors have been corrected and are listed at the end of the text4 ,,the ,,phase ,,rule ,,and ,,its ,,applications by ,,alex4 ,,findlay1 ,m4,a41 ,,ph4,d41 ,d4,,sc4 99 99 99 99 99 ,,text-,,books ,,of ,,physical ,,chemistry4 ,,edited ,,by ,,sir ,,william ,,ramsay1 ,k4,c4,b41 ,f4,r4,s41 ,d4,,sc4 99 99 99 99 99 ,,stoichiometry4 ,by ,,sydney ,,young1 ,d4,sc41 ,f4,r4,s41 ,professor of ,chemistry in the ,university of ,dublin2 together with an ,,introduction ,,to ,,the ,,study ,,of ,,physical ,,chemistry by ,sir ,,william ,,ramsay1 ,k4,c4,b41 ,f4,r4,s41 ,editor of the ,series4 ,crown #hvo4 #gs4 #f;d4 ,,an ,,introduction ,,to ,,the ,,study ,,of ,,physical ,,chemistry4 ,being a ,general ,introduction to the ,series by ,sir ,,william ,,ramsay1 ,k4,c4,b41 ,f4,r4,s41 ,d4,sc4 ,crown #hvo4 #as4 net4 ,,chemical ,,statics ,,and ,,dynamics1 including ,,the ,,theories ,,of ,,chemical ,,change1 ,,catalysis ,,and ,,explosions4 ,,by ,j4 ,w4 ,,mellor1 ,d4,sc4 7,n4,z471 ,b4,sc4 7,vict47 ,crown #hvo4 #gs4 #f;d4 ,,the ,,phase ,,rule ,,and ,,its ,,applications4 ,by ,,alex4 ,,findlay1 ,m4,a41 ,ph4,d41 ,d4,sc41 ,lecturer and ,demonstrator in ,chemistry1 ,university of ,birmingham4 ,with #acd ,figures in the ,text4 ,crown #hvo4 #es4 ,,spectroscopy4 ,by ,e4 ,c4 ,c4 ,,baly1 ,f4,i4,c41 ,lecturer on ,spectroscopy and ,assistant ,professor of ,chemistry1 ,university ,college1 ,london4 ,with #afc ,illustrations4 ,crown #hvo4 #ajs4 #f;d4 ,,thermochemistry4 ,by ,,julius ,,thomsen1 ,emeritus ,professor of ,chemistry in the ,university of ,copenhagen4 ,translated by ,,katharine ,a4 ,,burke1 ,b4,sc4 7,lond471 ,assistant in the ,department of ,chemistry1 ,university ,college1 ,london4 ,crown #hvo4 #is4 ,,electro-,,chemistry4 ,,part ,i4--,,general ,,theory4 ,by ,r4 ,a4 ,,lehfeldt1 ,d4,sc41 ,professor of ,physics at the ,east ,london ,technical ,college4 ,including a ,chapter on the ,relation of ,chemical ,constitution to ,conductivity1 by ,t4 ,s4 ,,moore1 ,b4,a41 ,b4,sc41 ,lecturer in the ,university of ,birmingham4 ,crown #hvo4 #es4 ,,part ,,ii4--,,applications ,,to ,,electrolysis1 ,,primary ,,and ,,secondary ,,batteries1 etc4 ,by ,n4 ,t4 ,m4 ,,wilsmore1 ,d4,sc4 ,in the press4 ,,stereochemistry4 ,by ,a4 ,w4 ,,stewart1 ,d4,sc41 ,carnegie ,research ,fellow1 ,lecturer on ,stereochemistry in ,university ,college1 ,london4 ,with #hg ,illustrations4 ,crown #hvo4 #ajs4 #f;d4 ,,relations ,,between ,,chemical ,,constitution ,,and ,,physical ,,properties4 ,by ,,samuel ,,smiles1 ,d4,sc4 ,in preparation4 ,,thermodynamics4 ,by ,f4 ,g4 ,,donnan1 ,m4,a41 ,ph4,d4 ,in preparation4 ,,actinochemistry4 ,by ,c4 ,e4 ,k4 ,,mees1 ,d4,sc41 and ,s4 ,e4 ,,sheppard1 ,d4,sc4 ,in preparation4 ,,practical ,,spectrographic ,,analysis4 ,by ,j4 ,h4 ,,pollok1 ,d4,sc4 ,in preparation4 ,,longmans1 ,,green1 ,,and ,,co4 #ci ,,paternoster ,,row1 ,,london ,,new ,,york1 ,,bombay1 ,,and ,,calcutta 99 99 99 99 99 ,,the ,,phase ,,rule ,,and ,,its ,,applications ,,by ,,alex4 ,,findlay1 ,m4,a41 ,,ph4,d41 ,d4,,sc4 ,lecturer on ,physical ,chemistry1 ,university of ,birmingham ,with ,one ,hundred and ,thirty-,four ,figures in the ,text ,third ,impression ,longmans1 ,green1 and ,co4 #ci ,paternoster ,row1 ,london ,new ,york1 ,bombay1 and ,calcutta #aijh ,all rights reserved ,,dedicated ,,to ,,francis ,,robert ,,japp1 ,,ll4,d41 ,f4,r4,s4 ,,professor ,,of ,,chemistry1 ,,university ,,of ,,aberdeen1 ,,in ,,gratitude ,,for ,,early ,,training ,,and ,,advice vii ,,preface ,,to ,,the ,,second ,,edition4 ,during the two years which have elapsed since the first edition of this book appeared1 the study of chemical equilibria has been prosecuted with considerable activity1 and valuable additions have been made to our knowledge in several departments of this subject4 ,in view of the scope of the present work1 it has been1 of course1 impossible to incorporate all that has been done2 but several new sections have been inserted1 notably those on the study of basic salts2 the interpretation of cooling curves1 and the determination of the composition of solid phases without analysis2 the equilibria between iron1 carbon monoxide1 and carbon dioxide1 which are of importance in connection with the processes occurring in the blast furnace2 and the ,phase ,rule study of the ammonia-soda process4 ,i have also incorporated a short section on the reciprocal salt-pair barium carbonate--potassium sulphate1 which had been written for the ,german edition of this book by the late ,professor ,w4 ,meyerhoffer4 ,the section on the iron-carbon alloys1 which in the first edition was somewhat unsatisfactory1 has been rewritten4 ,a4 ,f4 ,september1 #aijf4 viii ,,preface ,although we are indebted to the late ,professor ,willard ,gibbs for the first enunciation of the ,phase ,rule1 it was not till #ahhg that its practical applicability to the study of ,chemical ,equilibria was made apparent4 ,in that year ,roozeboom disclosed the great generalization1 which for upwards of ten years had remained hidden and unknown save to a very few1 by stripping from it the garb of abstract ,mathematics in which it had been clothed by its first discoverer4 ,the ,phase ,rule was thus made generally accessible2 and its adoption by ,roozeboom as the basis of classification of the different cases of chemical equilibrium then known established its value1 not only as a means of co-ordinating the large number of isolated cases of equilibrium and of giving a deeper insight into the relationships existing between the different systems1 but also as a guide in the investigation of unknown systems4 ,while the revelation of the principle embedded in the ,phase ,rule is primarily due to ,roozeboom1 it should not be forgotten that1 some years previously1 van't ,hoff1 in ignorance of the work of ,willard ,gibbs1 had enunciated his law of the incompatibility of condensed systems1 which in some respects coincides with the ,phase ,rule2 and it is only owing to the more general applicability of the latter that the very ix important generalization of van't ,hoff has been somewhat lost sight of4 ,the exposition of the ,phase ,rule and its applications given in the following pages has been made entirely non-mathematical1 the desire having been to explain as clearly as possible the principles underlying the ,phase ,rule1 and to illustrate their application to the classification and investigation of equilibria1 by means of a number of cases actually studied4 ,while it has been sought to make the treatment sufficiently elementary to be understood by the student just commencing the study of chemical equilibria1 an attempt has been made to advance his knowledge to such a stage as to enable him to study with profit the larger works on the subject1 and to follow with intelligence the course of investigation in this department of ,physical ,chemistry4 ,it is also hoped that the volume may be of use1 not only to the student of ,physical ,chemistry1 or of the other branches of that science1 but also to the student of ,metallurgy and of ,geology1 for whom an acquaintance with at least the principles of the ,phase ,rule is becoming increasingly important4 ,in writing the following account of the ,phase ,rule1 it is scarcely necessary to say that ,i have been greatly indebted to the larger works on ,chemical ,equilibria by ,ostwald 7,lehrbuch71 ,roozeboom 7,die ,heterogenen ,gleichgewichte71 and ,bancroft 7,the ,phase ,rule72 and in the case of the first-named1 to the inspiration also of personal teaching4 ,my indebtedness to these and other authors ,i have indicated in the following pages4 ,in conclusion1 ,i would express my thanks to ,sir ,william ,ramsay1 whose guidance and counsel have been constantly x at my disposal2 and to my colleagues1 ,dr4 ,t4 ,slater ,price and ,dr4 ,a4 ,mc,kenzie1 for their friendly criticism and advice4 ,to ,messrs4 ,j4 ,n4 ,friend1 ,m4,sc41 and ,w4 ,e4 ,s4 ,turner1 ,b4,sc41 ,i am also indebted for their assistance in reading the proof-sheets4 ,a4 ,f4 ,november1 #aijc4 xi ,,contents ,,page ,,chapter ,i ,,introduction #a ,general1 ,i4 ,homogeneous and heterogeneous equilibrium1 #e4 ,real and apparent equilibrium1 #e4 ,,chapter ,,ii ,,the ,,phase ,,rule #g ,phases1 #h4 ,components1 #aj4 ,degree of freedom4 ,variability of a system1 #ad4 ,the ,phase ,rule1 #af4 ,classification of systems according to the ,phase ,rule1 #ag4 ,deduction of the ,phase ,rule1 #ah4 ,,chapter ,,iii ,,typical ,,systems ,,of ,,one ,,component #ba ,a4 ,water4 ,equilibrium between liquid and vapour4 ,vaporization curve1 #ba4 ,upper limit of vaporization curve1 #bc4 ,sublimation curve of ice1 #bd4 ,equilibrium between ice and water4 ,curve of fusion1 #be4 ,equilibrium between ice1 water1 and vapour4 ,the triple point1 #bg4 ,bivariant systems of water1 #bi4 ,supercooled water4 ,metastable state1 #cj4 ,other systems of the substance water1 #cb4 ,b4 ,sulphur1 #cc4 ,polymorphism1 #cc4 ,sulphur1 #cd4 ,triple point--,rhombic and monoclinic sulphur and vapour4 ,transition point1 #cd4 ,condensed systems1 #cf4 ,suspended transformation1 #cg4 ,transition curve--,rhombic and monoclinic sulphur1 #cg4 ,triple point--,monoclinic sulphur1 liquid1 and vapour4 ,melting point of monoclinic sulphur1 #ch4 ,triple point--,rhombic and monoclinic sulphur and liquid1 #ch4 ,triple point--,rhombic sulphur1 liquid1 and vapour4 ,metastable triple point1 #ch4 ,fusion curve of rhombic sulphur1 #ci4 ,bivariant systems1 #ci4 ,c4 ,tin1 #da4 ,transition point1 #da4 xii ,enantiotropy and monotropy1 #dd4 ,d4 ,phosphorus1 #df4 ,enantiotropy combined with monotropy1 #ea4 ,e4 ,liquid ,crystals1 #ea4 ,phenomena observed1 #ea4 ,nature of liquid crystals1 #eb4 ,equilibrium relations in the case of liquid crystals1 #ec4 ,,chapter ,,iv ,,general ,,summary #ee ,triple point1 #ee4 ,theorems of van't ,hoff and of ,le ,chatelier1 #eg4 ,changes at the triple point1 #eh4 ,triple point solid--solid--vapour1 #fb4 ,sublimation and vaporization curves1 #fc4 ,fusion curve--,transition curve1 #ff4 ,suspended transformation4 ,metastable equilibria1 #fi4 ,velocity of transformation1 #gj4 ,law of successive reactions1 #gc4 ,,chapter ,v ,,systems ,,of ,,two ,,components--,,phenomena ,,of ,,dissociation #gf ,different systems of two components1 #gg4 ,,phenomena ,,of ,,dissociation4 ,bivariant systems1 #gi4 ,univariant systems1 #hj4 ,ammonia compounds of metal chlorides1 #hb4 ,salts with water of crystallization1 #he4 ,efflorescence1 #hf4 ,indefiniteness of the vapour pressure of a hydrate1 #hg4 ,suspended transformation1 #hi4 ,range of existence of hydrates1 #ij4 ,constancy of vapour pressure and the formation of compounds1 #ij4 ,measurement of the vapour pressure of hydrates1 #ia4 ,,chapter ,,vi ,,solutions #ib ,definition1 #ib4 ,,solutions ,,of ,,gases ,,in ,,liquids1 #ic4 ,,solutions ,,of ,,liquids ,,in ,,liquids1 #ie4 ,partial or limited miscibility1 #if4 ,phenol and water1 #ig4 ,methylethylketone and water1 #ajj4 ,triethylamine and water1 #aja4 ,general form of concentration-temperature curve1 #aja4 ,pressure-concentration diagram1 #ajb4 ,complete miscibility1 #ajd4 ,pressure-concentration diagram1 #ajd4 ,,chapter ,,vii ,,solutions ,,of ,,solids ,,in ,,liquids1 ,,only ,,one ,,of ,,the ,,components ,,being ,,volatile #ajf ,general1 #ajf4 ,the saturated solution1 #ajh4 ,form of the solubility curve1 #ajh4 ,a4 ,,anhydrous ,,salt ,,and ,,water4 xiii ,the solubility curve1 #aaa4 ,suspended transformation and supersaturation1 #aac4 ,solubility curve at higher temperatures1 #aad4 7#a7 ,complete miscibility of the fused components4 ,ice as solid phase1 #aaf4 ,cryohydrates1 #aag4 ,changes at the quadruple point1 #aai4 ,freezing mixtures1 #abj4 7#b7 ,partial miscibility of the fused components4 ,supersaturation1 #abd4 ,pressure-temperature diagram1 #abf4 ,vapour pressure of solid--solution--vapour1 #abf4 ,other univariant systems1 #abg4 ,bivariant systems1 #abi4 ,deliquescence1 #acj4 ,separation of salt on evaporation1 #acj4 ,general summary1 #aca4 ,,chapter ,,viii ,,solutions ,,of ,,solids ,,in ,,liquids1 ,,only ,,one ,,of ,,the ,,components ,,being ,,volatile #acc ,b4 ,,hydrated ,,salt ,,and ,,water1 7#a7 ,the compounds formed do not have a definite melting point4 ,concentration-temperature diagram1 #acc4 ,sodium sulphate and water1 #acd4 ,suspended transformation1 #acg4 ,dehydration by means of anhydrous sodium sulphate1 #ach4 ,pressure-temperature diagram1 #ach4 7#b7 ,the compounds formed have a definite melting point4 ,solubility curve of calcium chloride hexahydrate1 #ade4 ,pressure-temperature diagram1 #adi4 ,the indifferent point1 #aej4 ,the hydrates of ferric chloride1 #aea4 ,suspended transformation1 #aee4 ,evaporation of solutions at constant temperature1 #aee4 ,inevaporable solutions1 #aeg4 ,illustration1 #aeh4 ,,chapter ,,ix ,,equilibria ,,between ,,two ,,volatile ,,components #afa ,general1 #afa4 ,iodine and chlorine1 #afa4 ,concentration-temperature diagram1 #afb4 ,pressure-temperature diagram1 #afe4 ,bivariant systems1 #afg4 ,sulphur dioxide and water1 #afi4 ,pressure-temperature diagram1 #agj4 ,bivariant systems1 #agc4 ,,chapter ,x ,,solid ,,solutions4 ,,mixed ,,crystals #age ,general1 #age4 ,solution of gases in solids1 #agf4 ,palladium and hydrogen1 #agh4 ,solutions of solids in solids4 ,mixed crystals1 #ahj4 ,formation of mixed crystals of isomorphous substances1 #ahb4 ,i4 ,the two components can form an unbroken series of mixed crystals4 7a7 ,the freezing points of all mixtures lie between the freezing points of the pure components4 ,examples1 #ahc4 ,melting-point curve1 #ahc4 7b7 ,the freezing-point curve passes through a maximum4 ,example1 #ahf4 7c7 ,the freezing-point curve passes through a minimum4 ,example1 #ahh4 ,fractional xiv crystallization of mixed crystals1 #ahh4 ,,ii4 ,the two components do not form a continuous series of mixed crystals4 7a7 ,the freezing-point curve exhibits a transition point1 #aij4 ,example1 #aij4 7b7 ,the freezing-point curve exhibits a eutectic point1 #aia4 ,examples1 #aib4 ,changes in mixed crystals with the temperature1 #aib4 ,,chapter ,,xi ,,equilibrium ,,between ,,dynamic ,,isomerides #aie ,temperature-concentration diagram1 #aif4 ,transformation of the unstable into the stable form1 #bja4 ,examples1 #bjc4 ,benzaldoximes1 #bjc4 ,acetaldehyde and paraldehyde1 #bjd4 ,,chapter ,,xii ,,summary4--,,application ,,of ,,the ,,phase ,,rule ,,to ,,the ,,study ,,of ,,systems ,,of ,,two ,,components #bjg ,summary of the different systems of two components1 #bjh4 7#a7 ,organic compounds1 #bab4 7#b7 ,optically active substances1 #bac4 ,examples1 #baf4 ,transformations1 #bag4 7#c7 ,alloys1 #bbj4 ,iron--carbon alloys1 #bbc4 ,determination of the composition of compounds without analysis1 #bbh4 ,formation of minerals1 #bcb4 ,,chapter ,,xiii ,,systems ,,of ,,three ,,components #bcd ,general1 #bcd4 ,graphic representation1 #bce4 ,,chapter ,,xiv ,,solutions ,,of ,,liquids ,,in ,,liquids #bdj #a4 ,the three components form only one pair of partially miscible liquids1 #bdj4 ,retrograde solubility1 #bde4 ,the influence of temperature1 #bdg4 #b4 ,the three components can form two pairs of partially miscible liquids1 #bdi4 #c4 ,the three components form three pairs of partially miscible liquids1 #bea4 ,,chapter ,,xv ,,presence ,,of ,,solid ,,phases #bec ,a4 ,the ternary eutectic point1 #bec4 ,formation of compounds1 #bee4 ,b4 ,equilibria at higher temperatures4 ,formation of double salts1 #beh4 ,transition point1 #beh4 ,vapour pressure4 xv ,quintuple point1 #bfa4 ,solubility curves at the transition point1 #bfd4 ,decomposition of the double salt by water1 #bfg4 ,transition interval1 #bgj4 ,summary1 #bga4 ,,chapter ,,xvi ,,isothermal ,,curves ,,and ,,the ,,space ,,model #bgb ,non-formation of double salts1 #bgb4 ,formation of double salt1 #bgc4 ,transition interval1 #bgg4 ,isothermal evaporation1 #bgh4 ,crystallization of double salt from solutions containing excess of one component1 #bhj4 ,formation of mixed crystals1 #bha4 ,application to the characterization of racemates1 #bhb4 ,representation in space4 ,space model for carnallite1 #bhd4 ,summary and numerical data1 #bhg4 ,ferric chloride--hydrogen chloride--water1 #bij4 ,ternary systems1 #bia4 ,the isothermal curves1 #bid4 ,basic ,salts1 #bif4 ,bi#b,o#c--,n#b,o#e--;,h#b,o1 #bih4 ,basic mercury salts1 #cja4 ,indirect determination of the composition of the solid phase1 #cjb4 ,,chapter ,,xvii ,,absence ,,of ,,liquid ,,phase #cje ,iron1 carbon monoxide1 carbon dioxide1 #cje4 ,,chapter ,,xviii ,,systems ,,of ,,four ,,components #cab ,reciprocal salt-pairs4 ,choice of components1 #cac4 ,transition point1 #cad4 ,formation of double salts1 #cae4 ,transition interval1 #cae4 ,graphic representation1 #caf4 ,example1 #cag4 ,ammonia-soda process1 #cbj4 ,preparation of barium nitrite1 #cbg4 ,barium carbonate and potassium sulphate1 #cbh4 ,,appendix ,,experimental ,,determination ,,of ,,the ,,transition ,,point #cca ,i4 ,the dilatometric method1 #cca4 ,,ii4 ,measurement of the vapour pressure1 #ccd4 ,,iii4 ,solubility measurements1 #cce4 ,,iv4 ,thermometric method1 #ccg4 ,v4 ,optical method1 #cch4 ,,vi4 ,electrical methods1 #cch4 ,,name ,,index #cda ,,subject ,,index #cde 99 99 99 99 99 #a ,,the ,,phase ,,rule ,,chapter ,i ,,introduction ,general4--,before proceeding to the more systematic treatment of the ,phase ,rule1 it may1 perhaps1 be not amiss to give first a brief forecast of the nature of the subject we are about to study1 in order that we may gain some idea of what the ,phase ,rule is1 of the kind of problem which it enables us to solve1 and of the scope of its application4 ,it has long been known that if water is placed in a closed1 exhausted space1 vapour is given off and a certain pressure is created in the enclosing vessel4 ,thus1 when water is placed in the ,torricellian vacuum of the barometer1 the mercury is depressed1 and the amount of depression increases as the temperature is raised4 ,but1 although the pressure of the vapour increases as the temperature rises1 its value at any given temperature is constant1 no matter whether the amount of water present or the volume of the vapour is great or small2 if the pressure on the vapour is altered while the temperature is maintained constant1 either the water or the vapour will ultimately disappear2 the former by evaporation1 the latter by condensation4 ,at any given temperature within certain limits1 therefore1 water and vapour can exist permanently in contact with one another--or1 as it is said1 be in equilibrium with one another--only when the pressure has a certain definite value4 ,the same law of constancy of vapour pressure at a given #b temperature1 quite irrespective of the volumes of liquid and vapour1#a holds good also in the case of alcohol1 ether1 benzene1 and other pure liquids4 ,it is1 therefore1 not unnatural to ask the question1 ,does it hold good for all liquids8 ,is it valid1 for example1 in the case of solutions8 ,we can find the answer to these questions by studying the behaviour of a solution--say1 a solution of common salt in water--when placed in the ,torricellian vacuum4 ,in this case1 also1 it is observed that the pressure of the vapour increases as the temperature is raised1 but the pressure is no longer independent of the volume2 as the volume increases1 the pressure slowly diminishes4 ,if1 however1 solid salt is present in contact with the solution1 then the pressure again becomes constant at constant temperature1 even when the volume of the vapour is altered4 ,as we see1 therefore1 solutions do not behave in the same way as pure liquids4 ,moreover1 on lowering the temperature of water1 a point is reached at which ice begins to separate out2 and if heat be now added to the system or withdrawn from it1 no change will take place in the temperature or vapour pressure of the latter until either the ice or the water has disappeared4#b ,ice1 water1 and vapour1 therefore1 can be in equilibrium with one another only at one definite temperature and one definite pressure4 ,in the case of a solution of common salt1 however1 we may have ice in contact with the solution at different temperatures and pressures4 ,further1 it is possible to have a solution in equilibrium not only with anhydrous salt 7,na,cl71 but also with the hydrated salt 7,na,cl1 #b;,h#b,o71 as well as with ice1 and the question1 therefore1 arises3 ,is it possible to state in a general manner the conditions under which such different systems can exist in equilibrium2 or to obtain some insight #c into the relations which exist between pure liquids and solutions8 ,as we shall learn1 the ,phase ,rule enables us to give an answer to this question4 ,the preceding examples belong to the class of so-called physical equilibria1 or equilibria depending on changes in the physical state4 ,more than a hundred years ago1 however1 it was shown by ,wenzel and ,berthollet that chemical equilibria can also exist2 that chemical reactions do not always take place completely in one direction as indicated by the usual chemical equation1 but that before the reacting substances are all used up the reaction ceases1 and there is a condition of equilibrium between the reacting substances and the products of reaction4 ,as an example of this1 there may be taken the process of lime-burning1 which depends on the fact that when calcium carbonate is heated1 carbon dioxide is given off and quicklime is produced4 ,if the carbonate is heated in a closed vessel it will be found1 however1 not to undergo entire decomposition4 ,when the pressure of the carbon dioxide reaches a certain value 7which is found to depend on the temperature71 decomposition ceases1 and calcium carbonate exists side by side with calcium oxide and carbon dioxide4 ,moreover1 at any given temperature the pressure is constant and independent of the amount of carbonate or oxide present1 or of the volume of the gas2 nor does the addition of either of the products of dissociation1 carbon dioxide or calcium oxide1 cause any change in the equilibrium4 ,here1 then1 we see that1 although there are three different substances present1 and although the equilibrium is no longer due to physical1 but to chemical change1 it nevertheless obeys the same law as the vapour pressure of a pure volatile liquid1 such as water4 ,it might be supposed1 now1 that this behaviour would be shown by other dissociating substances1 e4g4 ammonium chloride4 ,when this substance is heated it dissociates into ammonia and hydrogen chloride1 and at any given temperature the pressure of these gases is constant1#c and is independent of the amounts of solid and gas present4 ,so far1 therefore1 ammonium chloride behaves like calcium carbonate4 ,if1 however1 one of the #d products of dissociation be added to the system1 it is found that the pressure is no longer constant at a given temperature1 but varies with the amount of gas1 ammonia or hydrogen chloride1 which is added4 ,in the case of certain dissociating substances1 therefore1 addition of one of the products of dissociation alters the equilibrium1 while in other cases it does not4 ,with the help of the ,phase ,rule1 however1 a general interpretation of this difference of behaviour can be given--an interpretation which can be applied not only to the two cases cited1 but to all cases of dissociation4 ,again1 it is well known that sulphur exists in two different crystalline forms1 octahedral and prismatic1 each of which melts at a different temperature4 ,the problem here is1 therefore1 more complicated than in the case of ice1 for there is now a possibility not only of one solid form1 but of two different forms of the same substance existing in contact with liquid4 ,what are the conditions under which these two forms can exist in contact with liquid1 either singly or together1 and under what conditions can the two solid forms exist together without the presence of liquid sulphur8 ,to these questions an answer can also be given with the help of the ,phase ,rule4 ,these cases are1 however1 comparatively simple2 but when we come1 for instance1 to study the conditions under which solutions are formed1 and especially when we inquire into the solubility relations of salts capable of forming1 perhaps1 a series of crystalline hydrates2 and when we seek to determine the conditions under which these different forms can exist in contact with the solution1 the problem becomes more complicated1 and the necessity of some general guide to the elucidation of the behaviour of these different systems becomes more urgent4 ,it is1 now1 to the study of such physical and chemical equilibria as those above-mentioned that the ,phase ,rule finds application2 to the study1 also1 of the conditions regulating1 for example1 the formation of alloys from mixtures of the fused metals1 or of the various salts of the ,stassfurt deposits2 the behaviour of iron and carbon in the formation of steel and the #e separation of different minerals from a fused rock-mass4#d ,with the help of the ,phase ,rule we can group together into classes the large number of different isolated cases of systems in equilibrium2 with its aid we are able to state1 in a general manner at least1 the conditions under which a system can be in equilibrium1 and by its means we can gain some insight into the relations existing between different kinds of systems4 ,homogeneous and ,heterogeneous ,equilibrium4--,before passing to the consideration of this generalization1 it will be well to first make mention of certain restrictions which must be placed on its treatment1 and also of the limitations to which it is subject4 ,if a system is uniform throughout its whole extent1 and possesses in every part identical physical properties and chemical composition1 it is called homogeneous4 ,such is1 for example1 a solution of sodium chloride in water4 ,an equilibrium occurring in such a homogeneous system 7such as the equilibrium occurring in the formation of an ester in alcoholic solution7 is called homogeneous equilibrium4 ,if1 however1 the system consists of parts which have different physical properties1 perhaps also different chemical properties1 and which are marked off and separated from one another by bounding surfaces1 the system is said to be heterogeneous4 ,such a system is formed by ice1 water1 and vapour1 in which the three portions1 each in itself homogeneous1 can be mechanically separated from one another4 ,when equilibrium exists between different1 physically distinct parts1 it is known as heterogeneous equilibrium4 ,it is1 now1 with heterogeneous equilibria1 with the conditions under which a heterogeneous system can exist1 that we shall deal here4 ,further1 we shall not take into account changes of equilibrium due to the action of electrical1 magnetic1 or capillary forces1 or of gravity2 but shall discuss only those which are due to changes of pressure1 temperature1 and volume 7or concentration74 ,real and ,apparent ,equilibrium4--,in discussing equilibria1 also1 a distinction must be drawn between real and #f apparent equilibria4 ,in the former case there is a state of rest which undergoes continuous change with change of the conditions 7e4g4 change of temperature or of pressure71 and for which the chief criterion is that the same condition of equilibrium is reached from whichever side it is approached4 ,thus in the case of a solution1 if the temperature is maintained constant1 the same concentration will be obtained1 no matter whether we start with an unsaturated solution to which we add more solid1 or with a supersaturated solution from which we allow solid to crystallize out2 or1 in the case of water in contact with vapour1 the same vapour pressure will be obtained1 no matter whether we heat the water up to the given temperature or cool it down from a higher temperature4 ,in this case1 water and vapour are in real equilibrium4 ,on the other hand1 water in contact with hydrogen and oxygen at the ordinary temperature is a case only of apparent equilibrium2 on changing the pressure and temperature continuously within certain limits there is no continuous change observed in the relative amounts of the two gases4 ,on heating beyond these limits there is a sudden and not a continuous change1 and the system no longer regains its former condition on being cooled to the ordinary temperature4 ,in all such cases the system may be regarded as undergoing change and as tending towards a state of true or real equilibrium1 but with such slowness that no change is observed4 ,although the case of water in contact with hydrogen and oxygen is an extreme one1 it must be borne in mind that the condition of true equilibrium may not be reached instantaneously or even with measurable velocity1 and in all cases it is necessary to be on one's guard against mistaking apparent 7or false7 for real 7or true7 equilibrium4 ,the importance of this will be fully illustrated in the sequel4 99 99 99 99 99 #g ,,chapter ,,ii ,,the ,,phase ,,rule ,although the fact that chemical reactions do not take place completely in one direction1 but proceed only to a certain point and there make a halt1 was known in the last quarter of the eighteenth century 7,wenzel1 #aggg2 ,berthollet1 #agii72 and although the opening and subsequent decades of the following century brought many further examples of such equilibria to our knowledge1 it was not until the last quarter of the nineteenth century that a theorem1 general in its application and with foundations weakened by no hypothetical assumptions as to the nature or constitution of matter1 was put forward by ,willard ,gibbs2#e a generalization which serves at once as a golden rule by which the condition of equilibrium of a system can be tested1 and as a guide to the similarities and dissimilarities existing in different systems4 ,before that time1 certainly1 attempts had been made to bring the different known cases of equilibria--chemical and physical--under general laws4 ,from the very first1 both ,wenzel#f and ,berthollet#g recognized the influence exercised by the mass of the substances on the equilibrium of the system4 ,it was reserved1 however1 for ,guldberg and ,waage1 by their more general statement and mathematical treatment of the ,law of ,mass ,action1#h to inaugurate the period of quantitative study of equilibria4 ,the law which these investigators enunciated #h served satisfactorily to summarize the conditions of equilibrium in many cases both of homogeneous and1 with the help of certain assumptions and additions1 of heterogeneous equilibrium4 ,by reason1 however1 of the fact that it was developed on the basis of the kinetic and molecular theories1 and involved1 therefore1 certain hypothetical assumptions as to the nature and condition of the substances taking part in the equilibrium1 the law of mass action failed1 as it necessarily must1 when applied to those systems in which neither the number of different molecular aggregates nor the degree of their molecular complexity was known4 ,ten years after the law of mass action was propounded by ,guldberg and ,waage1 ,willard ,gibbs1#i ,professor of ,physics in ,yale ,university1 showed how1 in a perfectly general manner1 free from all hypothetical assumptions as to the molecular condition of the participating substances1 all cases of equilibrium could be surveyed and grouped into classes1 and how similarities in the behaviour of apparently different kinds of systems1 and differences in apparently similar systems1 could be explained4 ,as the basis of his theory of equilibria1 ,gibbs adopted the laws of thermodynamics1#aj a method of treatment which had first been employed by ,horstmann4#aa ,in deducing the law of equilibrium1 ,gibbs regarded a system as possessing only three independently variable factors#ab--temperature1 pressure1 and the concentration of the components of the system--and he enunciated the general theorem now usually known as the ,phase ,rule1 by which he defined the conditions of equilibrium as a relationship between the number of what are called the phases and the components of the system4 ,phases4--,before proceeding farther we shall first consider what exactly is meant by the terms phase and component4 ,we have already seen 7p4 #e7 that a heterogeneous system is made #i up of different portions1 each in itself homogeneous1 but marked off in space and separated from the other portions by bounding surfaces4 ,these homogeneous1 physically distinct and mechanically separable portions are called phases4 ,thus ice1 water1 and vapour1 are three phases of the same chemical substance--water4 ,a phase1 however1 whilst it must be physically and chemically homogeneous1 need not necessarily be chemically simple4 ,thus1 a gaseous mixture or a solution may form a phase2 but a heterogeneous mixture of solid substances constitutes as many phases as there are substances present4 ,thus when calcium carbonate dissociates under the influence of heat1 calcium oxide and carbon dioxide are formed4 ,there are then two solid phases present1 viz4 calcium carbonate and oxide1 and one gas phase1 carbon dioxide4 ,the number of phases which can exist side by side may vary greatly in different systems4 ,in all cases1 however1 there can be but one gas or vapour phase on the account of the fact that all gases are miscible with one another in all proportions4 ,in the case of liquid and solid phases the number is indefinite1 since the above property does not apply to them4 ,the number of phases which can be formed by any given substance or group of substances also differs greatly1 and in general increases with the number of participating substances4 ,even in the case of a single substance1 however1 the number may be considerable2 in the case of sulphur1 for example1 at least eight different solid phases are known 7v4 ,chap4 ,,iii474 ,it is of importance to bear in mind that equilibrium is independent of the amounts of the phases present4#ac ,thus it is a familiar fact that the pressure of a vapour in contact with a #aj liquid 7i4e4 the pressure of the saturated vapour7 is unaffected by the amounts1 whether relative or absolute1 of the liquid and vapour2 also the amount of a substance dissolved by a liquid is independent of the amount of solid in contact with the solution4 ,it is true that deviations from this general law occur when the amount of liquid or the size of the solid particles is reduced beyond a certain point1#ad owing to the influence of surface energy2 but we have already 7p4 #e7 excluded such cases from consideration4 ,components4--,although the conception of phases is one which is readily understood1 somewhat greater difficulty is experienced when we come to consider what is meant by the term component2 for the components of a system are not synonymous with the chemical elements or compounds present1 i4e4 with the constituents of the system1 although both elements and compounds may be components4 ,by the latter term there are meant only those constituents the concentration of which can undergo independent variation in the different phases1 and it is only with these that we are concerned here4#ae ,to understand the meaning of this term we shall consider briefly some cases with which the reader will be familiar1 and at the outset it must be emphasized that the ,phase ,rule is concerned merely with those constituents which take part in the state of real equilibrium 7p4 #e72 for it is only to the final state1 not to the processes by which that state is reached1 that the ,phase ,rule applies4 ,consider now the case of the system water--vapour or ice--water--vapour4 ,the number of constituents taking part in the equilibrium here is only one1 viz4 the chemical substance1 water4 ,hydrogen and oxygen1 the constituents of water1 are not to be regarded as components1 because1 in the first place1 they are #aa not present in the system in a state of real equilibrium 7p4 #f72 in the second place1 they are combined in definite proportions to form water1 and their amounts1 therefore1 cannot be varied independently4 ,a variation in the amount of hydrogen necessitates a definite variation in the amount of oxygen4 ,in the case1 already referred to1 in which hydrogen and oxygen are present along with water at the ordinary temperature1 we are not dealing with a condition of true equilibrium4 ,if1 however1 the temperature is raised to a certain point1 a state of true equilibrium between hydrogen1 oxygen1 and water-vapour will be possible4 ,in this case hydrogen and oxygen will be components1 because now they do take part in the equilibrium2 also1 they need no longer be present in definite proportions1 but excess of one or the other may be added4 ,of course1 if the restriction be arbitrarily made that the free hydrogen and oxygen shall be present always and only in the proportions in which they are combined to form water1 there will be1 as before1 only one component1 water4 ,from this1 then1 we see that a change in the conditions of the experiment 7in the present case a rise of temperature7 may necessitate a change in the number of the components4 ,it is1 however1 only in the case of systems of more than one component that any difficulty will be found2 for only in this case will a choice of components be possible4 ,take1 for instance1 the dissociation of calcium carbonate into calcium oxide and carbon dioxide4 ,at each temperature1 as we have seen1 there is a definite state of equilibrium4 ,when equilibrium has been established1 there are three different substances present--calcium carbonate1 calcium oxide1 and carbon dioxide2 and these are the constituents of the system between which equilibrium exists4 ,now1 although these constituents take part in the equilibrium1 they are not all to be regarded as components1 for they are not mutually independent4 ,on the contrary1 the different phases are related to one another1 and if two of these are taken1 the composition of the third is defined by the equation ,ca,c,o#c ,ca,o ,,co#b #ab ,now1 in deciding the number of components in any given system1 not only must the constituents chosen be capable of independent variation1 but a further restriction is imposed1 and we obtain the following rule3 ,as the components of a system there are to be chosen the smallest number of independently variable constituents by means of which the composition of each phase participating in the state of equilibrium can be expressed in the form of a chemical equation4 ,applying this rule to the case under consideration1 we see that of the three constituents present when the system is in a state of equilibrium1 only two1 as already stated1 are independently variable4 ,it will further be seen that in order to express the composition of each phase present1 two of these constituents are necessary4 ,the system is1 therefore1 one of two components1 or a system of the second order4 ,when1 now1 we proceed to the actual choice of components1 it is evident that any two of the constituents can be selected4 ,thus1 if we choose as components ,ca,c,o#c and ,ca,o1 the composition of each phase can be expressed by the following equations3-- ,ca,c,o#c ,ca,c,o#c #j;,ca,o ,ca,o ,ca,o #j;,ca,c,o#c ,,co#b ,ca,c,o#c - ,ca,o ,as we see1 then1 both zero and negative quantities of the components have been introduced2 and similar expressions would be obtained if ,ca,c,o#c and ,,co#b were chosen as components4 ,the matter can1 however1 be simplified and the use of negative quantities avoided if ,ca,o and ,,co#b are chosen2 and it is1 therefore1 customary to select these as the components4 ,while it is possible in the case of systems of the second order to choose the two components in such a way that the composition of each phase can be expressed by positive quantities of these1 such a choice is not always possible when dealing with systems of a higher order 7containing three or four components74 ,from the example which has just been discussed1 it might #ac appear as if the choice of the components was rather arbitrary4 ,on examining the point1 however1 it will be seen that the arbitrariness affects only the nature1 not the number1 of the components2 a choice could be made with respect to which1 not to how many1 constituents were to be regarded as components4 ,as we shall see presently1 however1 it is only the number1 not the nature of the components that is of importance4 ,after the discussion of the conditions which the substances chosen as components must satisfy1 another method may be given by which the number of components present in a system can be determined4 ,suppose a system consisting of several phases in equilibrium1 and the composition of each phase determined by analysis4 ,if each phase present1 regarded as a whole1 has the same composition1 the system contains only one component1 or is of the first order4 ,if two phases must be mixed in suitable quantities in order that the composition of a third phase may be obtained1 the system is one of two components or of the second order2 and if three phases are necessary to give the composition of a fourth coexisting phase1 the system is one of three components1 or of the third order4#af ,although the examples to be considered in the sequel will afford sufficient illustration of the application of the rules given above1 one case may perhaps be discussed to show the application of the method just given for determining the number of components4 ,consider the system consisting of ,glauber's salt in equilibrium with solution and vapour4 ,if these three phases are analyzed1 the composition of the solid will be expressed by ,na#b,,so#d1 #aj;,h#b,o2 that of the solution by ,na#b,,so#d x,h#b,o1 while the vapour phase will be ,h#b,o4 ,the system evidently cannot be a one-component system1 for the phases have not all the same composition4 ,by varying the amounts of two phases1 however 7e4g4 ,na#b,,so#d1 #aj;,h#b,o and ,h#b,o71 the composition of the third phase--the solution--can be obtained4 ,the system is1 therefore1 one of two components4 ,but sodium sulphate can also exist in the anhydrous form and as the hydrate ,na#b,,so#d1 #g;,h#b,o4 ,in these cases there may #ad be chosen as components ,na#b,,so#d and ,h#b,o1 and ,na#b,,so#d1 #g;,h#b,o and ,h#b,o respectively4 ,in both cases1 therefore1 there are two components4 ,but the two systems 7,na#b,,so#d1 #aj;,h#b,o--,h#b,o1 and ,na#b,,so#d1 #g;,h#b,o--,h#b,o7 can be regarded as special cases of the system ,na#b,,so#d--;,h#b,o1 and these two components will apply to all systems made up of sodium sulphate and water1 no matter whether the solid phase is anhydrous salt or one of the hydrates4 ,in all three cases1 of course1 the number of components is the same2 but by choosing ,na#b,,so#d and ,h#b,o as components1 the possible occurrence of negative quantities of components in expressing the composition of the phases is avoided2 and1 further1 these components apply over a much larger range of experimental conditions4 ,again1 therefore1 we see that1 although the number of the components of a system is definite1 a certain amount of liberty is allowed in the choice of the substances2 and we also see that the choice will be influenced by the conditions of experiment4 ,summing up1 now1 we may say-- 7#a7 ,the components are to be chosen from among the constituents which are present when the system is in a state of true equilibrium1 and which take part in that equilibrium4 7#b7 ,as components are to be chosen the smallest number of such constituents necessary to express the composition of each phase participating in the equilibrium1 zero and negative quantities of the components being permissible4 7#c7 ,in any given system the number of the components is definite1 but may alter with alteration of the conditions of experiment4 ,a certain freedom of choice1 however1 is allowed in the 7qualitative1 not quantitative7 selection of the components1 the choice being influenced by considerations of simplicity1 suitability1 or generality of application4#ag ,degree of ,freedom4 ,variability of a ,system4--,it is well known that in dealing with a certain mass of gas or vapour1 e4g4 water vapour1 if only one of the independently variable factors--temperature1 pressure1 and concentration 7or volume7--is fixed1 the state of the gas or vapour is undefined2 while occupying the same volume 7the concentration1 therefore1 remaining #ae unchanged71 the temperature and the pressure may be altered2 at a given temperature1 a gas can exist under different pressures and occupy different volumes1 and under any given pressure the temperature and volume may vary4 ,if1 however1 two of the factors are arbitrarily fixed1 then the third factor can only have a certain definite value2 at any given values of temperature and pressure a given mass of gas can occupy only a definite volume4 ,suppose1 however1 that the system consists of water in contact with vapour4 ,the condition of the system then becomes perfectly defined on arbitrarily giving one of the variables a certain value4 ,if the temperature is fixed1 the pressure under which water and water vapour can coexist is also determined2 and conversely1 if a definite pressure is chosen1 the temperature is also defined4 ,water and vapour can coexist under a given pressure only at a definite temperature4 ,finally1 let the water and vapour be cooled down until ice begins to separate out4 ,so soon as the third phase1 ice1 appears1 the state of the system as regards temperature and pressure of the vapour is perfectly defined1 and none of the variables can be arbitrarily changed without causing the disappearance of one of the phases1 ice1 water1 or vapour4 ,we see1 therefore1 that in the case of some systems two1 in other cases1 only one of the independent variables 7temperature1 pressure1 concentration7 can be altered without destroying the nature of the system2 while in other systems1 again1 these variables have all fixed and definite values4 ,we shall therefore define the number of degrees of freedom#ah of a system as the number of the variable factors1 temperature1 pressure1 and concentration of the components1 which must be arbitrarily fixed in order that the condition of the system may be perfectly defined4 ,from what has been said1 therefore1 we shall describe a gas or vapour as having two degrees of freedom2 the system water--vapour as having only one2 and the system ice--water--vapour as having no degrees of freedom4 ,we may also speak of the #af variability or variance of a system1 and describe a system as being invariant1 univariant1 bivariant1 multivariant1#ai according as the number of degrees of freedom is nought1 one1 two1 or more than two4 ,a knowledge of its variability is1 therefore1 of essential importance in studying the condition and behaviour of a system1 and it is the great merit of the ,phase ,rule that the state of a system is defined entirely by the relation existing between the number of the components and the phases present1 no account being taken of the molecular complexity of the participating substances1 nor any assumption made with regard to the constitution of matter4 ,it is1 further1 as we see1 quite immaterial whether we are dealing with physical or chemical equilibrium2 in principle1 indeed1 no distinction need be drawn between the two classes1 although it is nevertheless often convenient to make use of the terms1 in spite of a certain amount of indefiniteness which attaches to them--an indefiniteness1 indeed1 which attaches equally to the terms physical and chemical process4#bj ,the ,phase ,rule4--,the ,phase ,rule of ,gibbs1 which defines the condition of equilibrium by the relation between the number of coexisting phases and the components1 may be stated as follows3 ,a system consisting of n components can exist in n #b phases only when the temperature1 pressure1 and concentration have fixed and definite values2 if there are n components in n #a phases1 equilibrium can exist while one of the factors varies1 and if there are only n phases1 two of the varying factors may be arbitrarily fixed4 ,this rule1 the application of which1 it is hoped1 will become clear in the sequel1 may be very concisely and conveniently summarized in the form of the equation-- ,p ,f ,c #b1 or ,f ,c #b - ,p where ,p denotes the number of the phases1 ,f the degrees of freedom1 and ,c the number of components4 ,from the second form of the equation it can be readily seen that the greater the number of the phases1 the fewer are the degrees of freedom4 ,with increase in the number of the phases1 therefore1 the #ag condition of the system becomes more and more defined1 or less and less variable4 ,classification of ,systems according to the ,phase ,rule4--,we have already learned in the introductory chapter that systems which are apparently quite different in character may behave in a very similar manner4 ,thus it was stated that the laws which govern the equilibrium between water and its vapour are quite analogous to those which are obeyed by the dissociation of calcium carbonate into carbon dioxide and calcium oxide2 in each case a certain temperature is associated with a definite pressure1 no matter what the relative or absolute amounts of the respective substances are4 ,and other examples were given of systems which were apparently similar in character1 but which nevertheless behaved in a different manner4 ,the relations between the various systems1 however1 become perfectly clear and intelligible in the light of the ,phase ,rule4 ,in the case first mentioned1 that of water in equilibrium with its vapour1 we have one component--water--present in two phases1 i4e4 in two physically distinct forms1 viz4 liquid and vapour4 ,according to the ,phase ,rule1 therefore1 since ,c #a1 and ,p #b1 the degree of freedom ,f is equal to #a #b - #b #a2 the system possesses one degree of freedom1 as has already been stated4 ,but in the case of the second system mentioned above there are two components1 viz4 calcium oxide and carbon dioxide 7p4 #ab71 and three phases1 viz4 two solid phases1 ,ca,o and ,ca,c,o#c1 and the gaseous phase1 ,,co#b4 ,the number of degrees of freedom of the system1 therefore1 is #b #b - #c #a2 this system1 therefore1 also possesses one degree of freedom4 ,we can now understand why these two systems behave in a similar manner2 both are univariant1 or possess only one degree of freedom4 ,we shall therefore expect a similar behaviour in the case of all univariant systems1 no matter how dissimilar the systems may outwardly appear4 ,similarly1 all bivariant systems will exhibit analogous behaviour2 and generally1 systems possessing the same degree of freedom will show a like behaviour4 ,in accordance with the ,phase ,rule1 therefore1 we may classify the different systems which may be found into invariant1 univariant1 bivariant1 multivariant1 #ah according to the relation which obtains between the number of the components and the number of coexisting phases2 and we shall expect that in each case the members of any particular group will exhibit a uniform behaviour4 ,by this means we are enabled to obtain an insight into the general behaviour of any system1 so soon as we have determined the number of the components and the number of the coexisting phases4 ,the adoption of the ,phase ,rule for the purposes of classification has been of great importance in studying changes in the equilibrium existing between different substances2 for not only does it render possible the grouping together of a large number of isolated phenomena1 but the guidance it affords has led to the discovery of new substances1 has given the clue to the conditions under which these substances can exist1 and has led to the recognition of otherwise unobserved resemblances existing between different systems4 ,deduction of the ,phase ,rule4--,in the preceding pages we have restricted ourselves to the statement of the ,phase ,rule1 without giving any indication of how it has been deduced4 ,at the close of this chapter1 therefore1 the mathematical deduction of the generalization will be given1 but in brief outline only1 the reader being referred to works on ,thermodynamics for a fuller treatment of the subject4#ba ,all forms of energy can be resolved into two factors1 the capacity factor and the intensity factor2 but for the production of equilibrium1 only the intensity factor is of importance4 ,thus1 if two bodies having the same temperature are brought in contact with each other1 they will be in equilibrium as regards heat energy1 no matter what may be the amounts of heat 7capacity factor7 contained in either1 because the intensity factor--the temperature--is the same4 ,but if the temperature of the two bodies is different1 i4e4 if the intensity factor of heat energy is different1 the two bodies will no longer be in equilibrium2 but heat will pass from the hotter to the colder until both have the same temperature4 ,as with heat energy1 so with chemical energy4 ,if we have a substance existing in two different states1 or in two different #ai phases of a system1 equilibrium can occur only when the intensity factor of chemical energy is the same4 ,this intensity factor may be called the chemical potential2 and we can therefore say that a system will be in equilibrium when the chemical potential of each component is the same in all the phases in which the component occurs4 ,thus1 for example1 ice1 water1 and vapour have1 at the triple point1 the same chemical potential4 ,the potential of a component in any phase depends not only on the composition of the phase1 but also on the temperature and the pressure 7or volume74 ,if1 therefore1 we have a system of ,c components existing in ,p phases1 then1 in order to fix the composition of unit mass of each phase1 it is necessary to know the masses of 7,c - #a7 components in each of the phases4 ,as regards the composition1 therefore1 each phase possesses 7,c - #a7 variables4 ,since there are ,p phases1 it follows that1 as regards composition1 the whole system possesses ,p7,c - #a7 variables4 ,besides these there are1 however1 two other variables1 viz4 temperature and pressure1 so that altogether a system of ,c components in ,p phases possesses ,p7,c - #a7 #b variables4 ,in order to define the state of the system completely1 it will be necessary to have as many equations as there are variables4 ,if1 therefore1 there are fewer equations than there are variables1 then1 according to the deficiency in the number of the equations1 one or more of the variables will have an undefined value2 and values must be assigned to these variables before the system is entirely defined4 ,the number of these undefined values gives us the variability or the degree of freedom of the system4 ,the equations by which the system is to be defined are obtained from the relationship between the potential of a component and the composition of the phase1 the temperature and the pressure4 ,further1 as has already been stated1 equilibrium occurs when the potential of each component is the same in the different phases in which it is present4 ,if1 therefore1 we choose as standard one of the phases in which all the components occur1 then in any other phase in equilibrium with #bj it1 the potential of each component must be the same as in the standard phase4 ,for each phase in equilibrium with the standard phase1 therefore1 there will be a definite equation of state for each component in the phase2 so that1 if there are ,p phases1 we obtain for each component 7,p - #a7 equations2 and for ,c components1 therefore1 we obtain ,c7,p - #a7 equations4 ,but we have seen above that there are ,p7,c - #a7 #b variables1 and as we have only ,c7,p - #a7 equations1 there must be ,p7,c - #a7 #b - ,c7,p - #a7 ,c #b - ,p variables undefined4 ,that is to say1 the degree of freedom 7,f7 of a system consisting of ,c components in ,p phases is-- ,f ,c #b - ,p 99 99 99 99 99 #ba ,,chapter ,,iii ,,typical ,,systems ,,of ,,one ,,component ,a4 ,water4 ,for the sake of rendering the ,phase ,rule more readily intelligible1 and at the same time also for the purpose of obtaining examples by which we may illustrate the general behaviour of systems1 we shall in this chapter examine in detail the behaviour of several well-known systems consisting of only one component4 ,the most familiar examples of equilibria in a one-component system are those furnished by the three phases of water1 viz4 ice1 water1 water vapour4 ,the system consists of one component1 because all three phases have the same chemical composition1 represented by the formula ,h#b,o4 ,as the criterion of equilibrium we shall choose a definite pressure1 and shall study the variation of the pressure with the temperature2 and for the purpose of representing the relationships which we obtain we shall employ a temperature-pressure diagram1 in which the temperatures are measured as abscissae and the pressures as ordinates4 ,in such a diagram invariant systems will be represented by points2 univariant systems by lines1 and bivariant systems by areas4 ,equilibrium between ,liquid and ,vapour4 ,vaporization ,curve4--,consider in the first place the conditions for the coexistence of liquid and vapour4 ,according to the ,phase ,rule 7p4 #af71 a system consisting of one component in two phases has one degree of freedom1 or is univariant4 ,we should therefore expect that it will be possible for liquid water to coexist with water vapour at different values of temperature and #bb pressure1 but that if we arbitrarily fix one of the variable factors1 pressure1 temperature1 or volume 7in the case of a given mass of substance71 the state of the system will then be defined4 ,if we fix1 say1 the temperature1 then the pressure will have a definite value2 or if we adopt a certain pressure1 the liquid and vapour can coexist only at a certain definite temperature4 ,each temperature1 therefore1 will correspond to a definite pressure2 and if in our diagram we join by a continuous line all the points indicating the values of the pressure corresponding to the different temperatures1 we shall obtain a curve 7,fig4 #a7 representing the variation of the pressure with the temperature4 ,this is the curve of vapour pressure1 or the vaporization curve of water4 ,illustration3 ,,fig4 #a4 ,now1 the results of experiment are quite in agreement with the requirements of the ,phase ,rule1 and at any given temperature the system water--vapour can exist in equilibrium only under a definite pressure4 ,the vapour pressure of water at different temperatures has been subjected to careful measurement by ,magnus1#bb ,regnault1#bc ,ramsay and ,young1#bd ,juhlin1#be ,thiesen and ,scheel1#bf and others4 ,in the following table the values of the vapour pressure from -#aj;deg to #ajj;deg are those calculated from the measurements of ,regnault1 corrected by the measurements of ,wiebe and ,thiesen and ,scheel2#bg those from #abj;deg to #bgj;deg were determined #bc by ,ramsay and ,young1 while the values of the critical pressure and temperature are those determined by ,battelli4#bh ,,vapour ,,pressure ,,of ,,water4 ---------------------------------------- ------------------------ ,temperature4 ,pressure in cm4 ,temperature4 ,pressure in cm4 mercury4 mercury4 ---------------------------------------- ------------------------ -#aj;deg #j4bac #abj;deg #adh4d #j;deg #j4dehbi #acj;deg #bja4i #bj;deg #a4geb #aej;deg #cef4h #dj;deg #e4eaf #bjj;deg #aafb4e #fj;deg #ad4icb #bej;deg #bigc4d #hj;deg #ce4ed #bgj;deg #daaj4a #ajj;deg #gf4jj #cfd4c;deg #adgij4d 7#aid4f atm47 7critical 7critical pressure74 temperature7 ---------------------------------------- ------------------------ ,the pressure is1 of course1 independent of the relative or absolute volumes of the liquid and vapour2 on increasing the volume at constant temperature1 a certain amount of the liquid will pass into vapour1 and the pressure will regain its former value4 ,if1 however1 the pressure be permanently maintained at a value different from that corresponding to the temperature employed1 then either all the liquid will pass into vapour1 or all the vapour will pass into liquid1 and we shall have either vapour alone or liquid alone4 ,upper ,limit of ,vaporization ,curve4--,on continuing to add heat to water contained in a closed vessel1 the pressure of the vapour will gradually increase4 ,since with increase of pressure the density of the vapour must increase1 and since with rise of temperature the density of the liquid must decrease1 a point will be reached at which the density of liquid and vapour become identical2 the system ceases to be heterogeneous1 and passes into one homogeneous phase4 ,the temperature at which this occurs is called the critical temperature4 ,to this temperature there will1 of course1 correspond a certain definite pressure1 called the critical pressure4 ,the curve representing the #bd equilibrium between liquid and vapour must1 therefore1 end abruptly at the critical point4 ,at temperatures above this point no pressure1 however great1 can cause the formation of the liquid phase2 at temperatures above the critical point the vapour becomes a gas4 ,in the case of water1 the critical temperature is #cfd4c;deg1 and the critical pressure #aid4f atm42 at the point representing these conditions the vapour-pressure curve of water must cease4 ,sublimation ,curve of ,ice4--,vapour is given off not only by liquid water1 but also by solid water1 or ice4 ,that this is so is familiar to every one through the fact that ice or snow1 even at temperatures below the melting point1 gradually disappears in the form of vapour4 ,even at temperatures considerably lower than #j;deg1 the vapour pressure of ice1 although small1 is quite appreciable2 and it is possible1 therefore1 to have ice and vapour coexisting in equilibrium4 ,when we inquire into the conditions under which such a system can exist1 we see again that we are dealing with a univariant system--one component existing in two phases--and that1 therefore1 just as in the case of the system water and vapour1 there will be for each temperature a certain definite pressure of the vapour1 and this pressure will be independent of the relative or absolute amounts of the solid or vapour present1 and will depend solely on the temperature4 ,further1 just as in the case of the vapour pressure of water1 the condition of equilibrium between ice and water vapour will be represented by a line or curve showing the change of pressure with the temperature4 ,such a curve1 representing the conditions of equilibrium between a solid and its vapour1 is called a sublimation curve4 ,at temperatures represented by any point on this curve1 the solid 7ice7 will sublime or pass into vapour without previously fusing4 ,since ice melts at #j;deg 7vide infra71 the sublimation curve must end at that temperature4 ,the following are the values of the vapour pressure of ice between #j;deg and -#ej;deg4#cj #be ,,vapour ,,pressure ,,of ,,ice4 ---------------------------------------- ----------------------- ,temperature4 ,pressure in mm4 ,temperature4 ,pressure in mm4 mercury4 mercury4 ---------------------------------------- -------------------- -#ej;deg #j4jej -#h;deg #b4cgi -#dj;deg #j4aba -#f;deg #b4hba -#cj;deg #j4cab -#d;deg #c4ccd -#bj;deg #j4hjf -#b;deg #c4ibe -#ae;deg #a4bgi #j;deg #d4fjb -#aj;deg #a4iii ---------------------------------------- ------------------------ ,equilibrium between ,ice and ,water4 ,curve of ,fusion4--,there is still another univariant system of the one component water1 the existence of which1 at definite values of temperature and pressure1 the ,phase ,rule allows us to predict4 ,this is the system solid--liquid4 ,ice on being heated to a certain temperature melts and passes into the liquid state2 and since this system solid--liquid is univariant1 there will be for each temperature a certain definite pressure at which ice and water can coexist or be in equilibrium1 independently of the amounts of the two phases present4 ,since now the temperature at which the solid phase is in equilibrium with the liquid phase is known as the melting point or point of fusion of the solid1 the curve representing the temperatures and pressures at which the solid and liquid are in equilibrium will represent the change of the melting point with the pressure4 ,such a curve is called the curve of fusion1 or the melting-point curve4 ,it was not until the middle of the nineteenth century that this connection between the pressure and the melting point1 or the change of the melting point with the pressure1 was observed4 ,the first to recognize the existence of such a relationship was ,james ,thomson1#ca who in #ahdi showed that from theoretical considerations such a relationship must exist1 and predicted that in the case of ice the melting point would be lowered by pressure4 ,this prediction was fully confirmed by his brother1 ,w4 ,thomson#cb 7,lord ,kelvin71 who found that under a pressure #bf of #h4a atm4 the melting point of ice was -#j4jei;deg2 under a pressure of #af4h atm4 the melting point was -#j4abi;deg4 ,the experiments which were first made in this connection were more of a qualitative nature1 but in recent years careful measurements of the influence of pressure on the melting point of ice have been made more especially by ,tammann1#cc and the results obtained by him are given in the following table and represented graphically in ,fig4 #b4 ,,fusion ,,pressure ,,of ,,ice4 ---------------------------------------- ----------------------------- ,pressure in kilogms4 per ,change of melting point for ,temperature4 sq4 cm4#cd an increase of pressure of #a kilogm4 per sq4 cm4 ---------------------------------------- ----------------------------- -#j;deg #a -#b4e;deg #ccf #j4jjgd;deg -#e;deg #fae #j4jjij;deg -#g4e;deg #hij #j4jjia;deg -#aj4j;deg #aaee #j4jjid;deg -#ab4e;deg #adaj #j4jajj;deg -#ae4j;deg #afbe #j4jaaf;deg -#ag4e;deg #ahce #j4jaai;deg -#bj4j;deg #bjdb #j4jaba;deg -#bb4a;deg #bbjj #j4jacc;deg ---------------------------------------- ----------------------------- ,from the numbers in the table and from the figure we see that as the pressure is increased the melting point of ice is lowered2 but we also observe that a very large change of pressure is required in order to produce a very small change in the melting point4 ,the curve1 therefore1 is very steep4 ,increase of pressure by one atmosphere lowers the melting point by only #j4jjgf;deg1#ce or an increase of pressure of #ace atm4 is required to produce a lowering of the melting point of #a;deg4 ,we see further that the fusion curve bends slightly as the pressure is increased1 which signifies that the variation of #bg the melting point with the pressure changes2 at -#ae;deg1 when the pressure is #afbe kilogm4 per sq4 cm41 increase of pressure by #a kilogm4 per sq4 cm4 lowers the melting point by #j4jab;deg4 ,this curvature of the fusion curve we shall later 7,chap4 ,,iv47 see to be an almost universal phenomenon4 ,illustration3 ,,fig4 #b4 ,illustration3 ,,fig4 #c4 ,equilibrium between ,ice1 ,water1 and ,vapour4 ,the ,triple ,point4--,on examining the vapour-pressure curves of ice and water 7,fig4 #c71 we see that at a temperature of about #j;deg and under a pressure of about #d4f mm4 mercury1 the two curves cut4 ,at this point liquid water and solid ice are each in equilibrium with vapour at the same pressure4 ,since this is so1 they must1 of course1 be in equilibrium #bh with one another1 as experiment also shows4 ,at this point1 therefore1 ice1 water1 and vapour can be in equilibrium1 and as there are three phases present1 the point is called a triple point4#cf ,the triple point1 however1 does not lie exactly at #j;deg ,c41 for this temperature is defined as the melting point of ice under atmospheric pressure4 ,at the triple point1 however1 the pressure is equal to the vapour pressure of ice and water1 and this pressure1 as we see from the tables on pp4 #ba and #bc1 is very nearly #d4f mm41 or almost #a atm4 less than in the previous case4 ,now1 we have just seen that a change of pressure of #a atm4 corresponds to a change of the melting point of #j4jjgf;deg2 the melting point of ice1 therefore1 when under the pressure of its own vapour1 will be very nearly #j4jjgf;deg1 and the pressure of the vapour will be very slightly greater than #d4egi mm41 which is the pressure at #j;deg 7p4 #ba74 ,the difference is1 however1 slight1 and may be neglected here4 ,at the temperature1 then1 of #j4jjgf;deg1 and under a pressure of #d4f mm4 of mercury1 ice1 water1 and vapour will be in equilibrium2 the point in our diagram representing this particular temperature and pressure is1 therefore1 the triple point of the system ice--water--vapour4 ,since at the triple point we have three phases of one component1 the system at this point is invariant--it possesses no degrees of freedom4 ,if the temperature is changed1 the system will undergo alteration in such a way that one of the phases will disappear1 and a univariant system will result2 if heat be added1 ice will melt1 and we shall have left water and vapour2 if heat be abstracted1 water will freeze1 and we shall have left ice and vapour2 if1 when the temperature is altered1 the pressure is kept constant1 then we shall ultimately obtain only one phase 7see ,chap4 ,,iv474 ,the triple point is not only the point of intersection of the vaporization and sublimation curves1 but it is also the end-point of the fusion curve4 ,the fusion curve1 as we have seen1 is the curve of equilibrium between ice and water2 and since at the triple point ice and water are each in equilibrium with #bi vapour of the same pressure1 they must1 of course1 also be in equilibrium with one another4 ,illustration3 ,,fig4 #d4 ,bivariant ,systems of ,water4--,if we examine ,fig4 #d1 we see that the curves ,,oa1 ,,ob1 ,,oc1 which represent diagrammatically the conditions under which water and vapour1 ice and vapour1 and water and ice are in equilibrium1 form the boundaries of three fields1 or areas1 ,i41 ,,ii41 ,,iii4 ,these areas1 now1 represent the conditions for the existence of the single phases1 solid1 liquid1 and vapour respectively4 ,at temperatures and pressures represented by any point in the field ,i41 solid only can exist as a stable phase4 ,since we have here one component in only one phase1 the system is bivariant1 and at any given temperature1 therefore1 ice can exist under a series of pressures2 and under any given pressure1 at a series of temperatures1 these pressures and temperatures being limited only by the curves ,,ob1 ,,oc4 ,similarly also with the areas ,,ii4 and ,,iii4 ,we see1 further1 that the different areas are the regions of stability of the phase common to the two curves by which the area is enclosed4#cg ,thus1 the phase common to the two systems #cj represented by ,,bo 7ice and vapour71 and ,,oa 7water and vapour7 is the vapour phase2 and the area ,,boa is therefore the area of the vapour phase4 ,similarly1 ,,boc is the area of the ice phase1 and ,,coa the area of the water phase4 ,supercooled ,water4 ,metastable ,state4--,when heated under the ordinary atmospheric pressure1 ice melts when the temperature reaches #j;deg1 and it has so far not been found possible to raise the temperature of ice above this point without liquefaction taking place4 ,on the other hand1 it has long been known that water can be cooled below zero without solidification occurring4 ,this was first discovered in #agbd by ,fahrenheit1#ch who found that water could be exposed to a temperature of -#i4d;deg without solidifying2 so soon1 however1 as a small particle of ice was brought in contact with the water1 crystallization commenced4 ,superfused or supercooled water--i4e4 water cooled below #j;deg--is unstable only in respect of the solid phase2 so long as the presence of the solid phase is carefully avoided1 the water can be kept for any length of time without solidifying1 and the system supercooled water and vapour behaves in every way like a stable system4 ,a system1 now1 which in itself is stable1 and which becomes instable only in contact with a particular phase1 is said to be metastable1 and the region throughout which this condition exists is called the metastable region4 ,supercooled water1 therefore1 is in a metastable condition4 ,if the supercooling be carried below a certain temperature1 solidification takes place spontaneously without the addition of the solid phase2 the system then ceases to be metastable1 and becomes instable4 ,not only has water been cooled to temperatures considerably below the melting point of ice1 but the vapour pressure of the supercooled water has been measured4 ,it is of interest and importance1 now1 to see what relationship exists between the vapour pressure of ice and that of supercooled water at the same temperature4 ,this relationship is clearly shown by the numbers in the following table1#ci and is represented in ,fig4 #c1 #ca p4 #bg41 and diagrammatically in ,fig4 #d1 the vapour pressures of supercooled water being represented by the curve ,,oa'1 which is the unbroken continuation of ,,ao4 ,,vapour ,,pressure ,,of ,,ice ,,and ,,of ,,supercooled ,,water4 ---------------------------------------- ----------------------------- ,pressure in mm4 mercury4 ---------------------------------------- -------------- ,temperature4 ,water4 ,ice4 ,difference4 ---------------------------------------- ----------------------------- #j;deg #d4fah #d4fjb #j4jafdj -#b;deg #c4iie #c4ibe #j4jgj -#d;deg #c4dej #c4ccd #j4aaf -#h;deg #b4eeh #b4cgi #j4agi -#aj;deg #b4aig #a4iii #j4aih -#ae;deg #a4dib #a4bgi #j4bac -#bj;deg #a4jje #j4hjf #j4aii ---------------------------------------- ----------------------------- ,at all temperatures below #j;deg 7more correctly #j4jjgf;deg71 at which temperature water and ice have the same vapour pressure1 the vapour pressure of supercooled water is greater than that of ice at the same temperature4 ,from the relative positions of the curves ,,ob and ,,oa 7,fig4 #d7 we see that at all temperatures above #j;deg1 the 7metastable7 sublimation curve of ice1 if it could be obtained1 would be higher than the vaporization curve of water4 ,this shows1 therefore1 that at #j;deg a break must occur in the curve of states1 and that in the neighbourhood of this break the curve above that point must ascend less rapidly than the curve below the break4 ,since1 however1 the differences in the vapour pressures of supercooled water and of ice are very small1 the change in the direction of the vapour-pressure curve on passing from ice to water was at first not observed1 and ,regnault regarded the sublimation curve as passing continuously into #cb the vaporization curve4 ,the existence of a break was1 however1 shown by ,james ,thomson#da and by ,kirchhoff#db to be demanded by thermo-dynamical considerations1 and the prediction of theory was afterwards realized experimentally by ,ramsay and ,young in their determinations of the vapour pressure of water and ice1 as well as in the case of other substances4#dc ,from what has just been said1 we can readily understand why ice and water cannot exist in equilibrium below #j;deg4 ,for1 suppose we have ice and water in the same closed space1 but not in contact with one another1 then since the vapour pressure of the supercooled water is higher than that of ice1 the vapour of the former must be supersaturated in contact with the latter2 vapour must1 therefore1 condense on the ice2 and in this way there will be a slow distillation from the water to the ice1 until at last all the water will have disappeared1 and only ice and vapour remain4#dd ,other ,systems of the ,substance ,water4--,we have thus far discussed only those systems which are constituted by the three phases--ice1 water1 and water vapour4 ,it has1 however1 been recently found that at a low temperature and under a high pressure ordinary ice can pass into two other crystalline varieties1 called by ,tammann#de ice ,,ii4 and ice ,,iii41 ordinary ice being ice ,i4 ,according to the ,phase ,rule1 now1 since each of these solid forms constitutes a separate phase 7p4 #i71 it will be possible to have the following 7and more7 systems of water1 in addition to those already studied1 viz4 water1 ice ,i41 ice ,,ii42 water1 ice ,i41 ice ,,iii42 water1 ice ,,ii41 ice ,,iii41 forming invariant systems and existing in equilibrium only at a definite triple point2 further1 water1 ice ,,ii42 water1 ice ,,iii42 ice ,i41 ice ,,ii42 ice ,i41 ice ,,iii42 ice ,,ii41 ice ,,iii41 forming univariant systems1 existing1 therefore1 at definite corresponding values of #cc temperature and pressure2 and lastly1 the bivariant systems1 ice ,,ii4 and ice ,,iii4 ,several of these systems have been investigated by ,tammann4 ,the triple point for water1 ice ,i41 ice ,,iii41 lies at -#bb;deg1 and a pressure of #bbjj kilogms4 per sq4 cm4 7#bacj atm471 as indicated in ,fig4 #b1 p4 #bg4df ,in contrast with the behaviour of ordinary ice1 the temperature of equilibrium in the case of water--ice ,,ii41 and water--ice ,,iii41 is raised by increase of pressure4 ,b4 ,sulphur4 ,polymorphism4--,reference has just been made to the fact that ice can exist not only in the ordinary form1 but in at least two other crystalline varieties4 ,this phenomenon1 the existence of a substance in two or more different crystalline forms1 is called polymorphism4 ,polymorphism was first observed by ,mitscherlich#dg in the case of sodium phosphate1 and later in the case of sulphur4 ,to these two cases others were soon added1 at first of inorganic1 and later of organic substances1 so that polymorphism is now recognized as of very frequent occurrence indeed4#dh ,these various forms of a substance differ not only in crystalline shape1 but also in melting point1 specific gravity1 and other physical properties4 ,in the liquid state1 however1 the differences do not exist4 ,according to our definition of phases 7p4 #i71 each of these polymorphic forms constitutes a separate phase of the particular substance4 ,as is readily apparent1 the number of possible systems formed of one component may be considerably increased when that component is capable of existing in different crystalline forms4 ,we have1 therefore1 to inquire what are the conditions under which different polymorphic forms can coexist1 either alone or in presence of the liquid and vapour phase4 ,for the purpose of illustrating the general behaviour of such systems1 we shall study the systems formed by the different crystalline forms of sulphur1 tin1 and benzophenone4 #cd ,sulphur exists in two well-known crystalline forms--rhombic1 or octahedral1 and monoclinic1 or prismatic sulphur4 ,of these1 the former melts at #aad4e;deg2 the latter at #abj;deg4#di ,further1 at the ordinary temperature1 rhombic sulphur can exist unchanged1 whereas1 on being heated to temperatures somewhat below the melting point1 it passes into the prismatic variety4 ,on the other hand1 at temperatures above #if;deg1 prismatic sulphur can remain unchanged1 whereas at the ordinary temperature it passes slowly into the rhombic form4 ,if1 now1 we examine the case of sulphur with the help of the ,phase ,rule1 we see that the following systems are theoretically possible3-- ,i4 ,bivariant ,systems3 ,one component in one phase4 7a7 ,rhombic sulphur4 7b7 ,monoclinic sulphur4 7c7 ,sulphur vapour4 7d7 ,liquid sulphur4 ,,ii4 ,univariant ,systems3 ,one component in two phases4 7a7 ,rhombic sulphur and vapour4 7b7 ,monoclinic sulphur and vapour4 7c7 ,rhombic sulphur and liquid4 7d7 ,monoclinic sulphur and liquid4 7e7 ,rhombic and monoclinic sulphur4 7f7 ,liquid and vapour4 ,,iii4 ,invariant ,systems3 ,one component in three phases4 7a7 ,rhombic and monoclinic sulphur and vapour4 7b7 ,rhombic sulphur1 liquid and vapour4 7c7 ,monoclinic sulphur1 liquid and vapour4 7d7 ,rhombic and monoclinic sulphur and liquid4 ,illustration3 ,,fig4 #e4 ,triple ,point--,rhombic and ,monoclinic ,sulphur and ,vapour4 ,transition ,point4--,in the case of ice1 water and vapour1 we saw that at the triple point the vapour pressures of ice and water are equal2 below this point1 ice is stable2 above this point1 water is stable4 ,we saw1 further1 that below #j;deg the vapour pressure of the stable system is lower than that of the metastable1 and therefore that at the triple point there is a break in the vapour pressure curve of such a kind that above #ce the triple point the vapour-pressure curve ascends more slowly than below it4 ,now1 although the vapour pressure of solid sulphur has not been determined1 we can nevertheless consider that it does possess a certain1 even if very small1 vapour pressure1#ej and that at the temperature at which the vapour pressures of rhombic and monoclinic sulphur become equal1 we can have these two solid forms existing in equilibrium with the vapour4 ,below that point only one form1 that with the lower vapour pressure1 will be stable2 above that point only the other form will be stable4 ,on passing through the triple point1 therefore1 there will be a change of the one form into the other4 ,this point is represented in our diagram 7,fig4 #e7 by the point ,o1 the two curves ,,ao and ,,ob representing diagrammatically the vapour pressures of rhombic and monoclinic sulphur respectively4 ,if the vapour phase is absent and the system maintained under a constant pressure1 e4g4 #cf atmospheric pressure1 there will also be a definite temperature at which the two solid forms are in equilibrium1 and on passing through which complete and reversible transformation of one form into the other occurs4 ,this temperature1 which refers to equilibrium in absence of the vapour phase1 is known as the transition temperature or inversion temperature4 ,were we dependent on measurements of pressure and temperature1 the determination of the transition point might be a matter of great difficulty4 ,when we consider1 however1 that the other physical properties of the solid phases1 e4g4 the density1 undergo an abrupt change on passing through the transition point1 owing to the transformation of one form into the other1 then any method by which this abrupt change in the physical properties can be detected may be employed for determining the transition point4 ,a considerable number of such methods have been devised1 and a description of the most important of these is given in the ,appendix4 ,in the case of sulphur1 the transition point of rhombic into monoclinic sulphur was found by ,reicher#ea to lie at #ie4e;deg4 ,below this temperature the octahedral1 above it the monoclinic1 is the stable form4 ,condensed ,systems4--,we have already seen that in the change of the melting point of water with the pressure1 a very great increase of the latter was necessary in order to produce a comparatively small change in the temperature of equilibrium4 ,this is a characteristic of all systems from which the vapour phase is absent1 and which are composed only of solid and liquid phases4 ,such systems are called condensed systems1#eb and in determining the temperature of equilibrium of such systems1 practically the same point will be obtained whether the measurements are carried out under atmospheric pressure or under the pressure of the vapour of the solid or liquid phases4 ,the transition point1 therefore1 as determined in open vessels at atmospheric pressure1 will differ only by a very slight amount from the triple point1 or point at which the two solid or liquid phases are in equilibrium under the pressure of their vapour4 #cg ,the determination of the transition point is thereby greatly simplified4 ,suspended ,transformation4--,in many respects the transition point of two solid phases is analogous to the melting point of a solid1 or point at which the solid passes into a liquid4 ,in both cases the change of phase is associated with a definite temperature and pressure in such a way that below the point the one phase1 above the point the other phase1 is stable4 ,the transition point1 however1 differs in so far from a point of fusion1 that while it is possible to supercool a liquid1 no definite case is known where the solid has been heated above the triple point without passing into the liquid state4 ,transformation1 therefore1 is suspended only on one side of the melting point4 ,in the case of two solid phases1 however1 the transition point can be overstepped in both directions1 so that each phase can be obtained in the metastable condition4 ,in the case of supercooled water1 further1 we saw that the introduction of the stable1 solid phase caused the speedy transformation of the metastable to the stable condition of equilibrium2 but in the case of two solid phases the change from the metastable to the stable modification may occur with great slowness1 even in presence of the stable form4 ,this tardiness with which the stable condition of equilibrium is reached greatly increases in many cases the difficulty of accurately determining the transition point4 ,the phenomena of suspended transformation will1 however1 receive a fuller discussion later 7p4 #fh74 ,transition ,curve--,rhombic and ,monoclinic ,sulphur4--,just as we found the melting point of ice to vary with the pressure1 so also do we find that change of pressure causes an alteration in the transition point4 ,in the case of the transition point of rhombic into monoclinic sulphur1 increase of pressure by #a atm4 raises the transition point by #j4jd;deg-#j4je;deg4#ec ,the transition curve1 or curve representing the change of the transition point with pressure1 will therefore slope to the right away from the pressure axis4 ,this is curve ,,oc 7,fig4 #e74 #ch ,triple ,point--,monoclinic ,sulphur1 ,liquid1 and ,vapour4 ,melting ,point of ,monoclinic ,sulphur4--,above #ie4e;deg1 monoclinic sulphur is1 as we have seen1 the stable form4 ,on being heated to #abj;deg1 under atmospheric pressure1 it melts4 ,this temperature is1 therefore1 the point of equilibrium between monoclinic sulphur and liquid sulphur under atmospheric pressure4 ,since we are dealing with a condensed system1 this temperature may be regarded as very nearly that at which the solid and liquid are in equilibrium with their vapour1 i4e4 the triple point1 solid 7monoclinic7--liquid--vapour4 ,this point is represented in the diagram by ,b4 ,triple ,point--,rhombic and ,monoclinic ,sulphur and ,liquid4--,in contrast with that of ice1 the fusion point of monoclinic sulphur is raised by increase of pressure1 and the fusion curve1 therefore1 slopes to the right4 ,the transition curve of rhombic and monoclinic sulphur1 as we have seen1 also slopes to the right1 and more so than the fusion curve of monoclinic sulphur4 ,there will1 therefore1 be a certain pressure and temperature at which the two curves will cut4 ,this point lies at #aea;deg1 and a pressure of #acbj kilogm4 per sq4 cm41 or about #abhh atm4#ed ,it1 therefore1 forms another triple point1 the existence of which had been predicted by ,roozeboom1#ee at which rhombic and monoclinic sulphur are in equilibrium with liquid sulphur4 ,it is represented in our diagram by the point ,c4 ,beyond this point monoclinic sulphur ceases to exist in a stable condition4 ,at temperatures and pressures above this triple point1 rhombic sulphur will be the stable modification1 and this fact is of mineralogical interest1 because it explains the occurrence in nature of well-formed rhombic crystals4 ,under ordinary conditions1 prismatic sulphur separates out on cooling fused sulphur1 but at temperatures above #aea;deg and under pressures greater than #abhh atm41 the rhombic form would be produced4#ef ,triple ,point--,rhombic ,sulphur1 ,liquid1 and ,vapour4 ,metastable ,triple ,point4--,on account of the slowness with #ci which transformation of one form into the other takes place on passing the transition point1 it has been found possible to heat rhombic sulphur up to its melting point 7#aad4e;deg74 ,at this temperature1 not only is rhombic sulphur in a metastable condition1 but the liquid is also metastable1 its vapour pressure being greater than that of solid monoclinic sulphur4 ,this point is represented in our diagram by the point b4 ,from the relative positions of the metastable melting point of rhombic sulphur and the stable melting point of monoclinic sulphur at #abj;deg1 we see that1 of the two forms1 the metastable form has the lower melting point4 ,this1 of course1 is valid only for the relative stability in the neighbourhood of the melting point2 for we have already learned that at lower temperatures rhombic sulphur is the stable1 monoclinic sulphur the metastable 7or unstable7 form4 ,fusion ,curve of ,rhombic ,sulphur4--,like any other melting point1 that of rhombic sulphur will be displaced by increase of pressure2 increase of pressure raises the melting point1 and we can therefore obtain a metastable fusion curve representing the conditions under which rhombic sulphur is in equilibrium with liquid sulphur4 ,this metastable fusion curve must pass through the triple point for rhombic sulphur--monoclinic sulphur--liquid sulphur1 and on passing this point it becomes a stable fusion curve4 ,the continuation of this curve1 therefore1 above #aea;deg forms the stable fusion curve of rhombic sulphur 7curve ,,cd74 ,these curves have been investigated at high pressures by ,tammann1 and the results are represented according to scale in ,fig4 #f1eg a being the curve for monoclinic sulphur and liquid2 b1 that for rhombic sulphur and liquid2 and c1 that for rhombic and monoclinic sulphur4 ,bivariant ,systems4--,just as in the case of the diagram of states of water1 the areas in ,fig4 #e represent the conditions for the stable existence of the single phases3 rhombic sulphur in the area to the left of ,,aocd2 monoclinic sulphur in the area ,,obc2 liquid sulphur in the area ,,ebcd2 sulphur vapour below the curves ,,aobe4 ,as can be seen from the diagram1 #dj the existence of monoclinic sulphur is limited on all sides1 its area being bounded by the curves ,,ob1 ,,oc1 ,,bc4 ,at any point outside this area1 monoclinic sulphur can exist only in a metastable condition4 ,illustration3 ,,fig4 #f4 ,other crystalline forms of sulphur have been obtained1#eh so that the existence of other systems of the one-component sulphur besides those already described is possible4 ,reference will be made to these later 7p4 #ea74 #da ,c4 ,tin4 ,another substance capable of existing in more than one crystalline form1 is the metal tin1 and although the general behaviour1 so far as studied1 is analogous to that of sulphur1 a short account of the two varieties of tin may be given here1 not only on account of their metallurgical interest1 but also on account of the importance which the phenomena possess for the employment of this metal in everyday life4 ,after a winter of extreme severity in ,russia 7#ahfg-ahfh71 the somewhat unpleasant discovery was made that a number of blocks of tin1 which had been stored in the ,customs ,house at ,st4 ,petersburg1 had undergone disintegration and crumbled to a grey powder4#ei ,that tin undergoes change on exposure to extreme cold was known1 however1 before that time1 even as far back as the time of ,aristotle1 who spoke of the tin as melting4#fj ,ludicrous as that term may now appear1 ,aristotle nevertheless unconsciously employed a strikingly accurate analogy1 for the conditions under which ordinary white tin passes into the grey modification are1 in many ways1 quite analogous to those under which a substance passes from the solid to the liquid state4 ,the knowledge of this was1 however1 beyond the wisdom of the ,greek philosopher4 ,for many years there existed considerable confusion both as to the conditions under which the transformation of white tin into its allotropic modification occurs1 and to the reason of the change4 ,under the guidance of the ,phase ,rule1 however1 the confusion which obtained has been cleared away1 and the mysterious behaviour of tin brought into accord with other phenomena of transformation4#fa ,transition ,point4--,just as in the case of sulphur1 so also in the case of tin1 there is a transition point above which the #db one form1 ordinary white tin1 and below which the other form1 grey tin1 is the stable variety4 ,in the case of this metal1 the transition point was found by ,cohen and van ,eyk1 who employed both the dilatometric and the electrical methods 7,appendix7 to be #bj;deg4 ,below this temperature1 grey tin is the stable form4 ,but1 as we have seen in the case of sulphur1 the change of the metastable into the stable solid phase occurs with considerable slowness1 and this behaviour is found also in the case of tin4 ,were it not so1 we should not be able to use this metal for the many purposes to which it is applied in everyday life2 for1 with the exception of a comparatively small number of days in the year1 the temperature of our climate is below #bj;deg1 and white tin is1 therefore1 at the ordinary temperature1 in a metastable condition4 ,the change1 however1 into the stable form at the ordinary temperature1 although slow1 nevertheless takes place1 as is shown by the partial or entire conversion of articles of tin which have lain buried for several hundreds of years4 ,on lowering the temperature1 the velocity with which the transformation of the tin occurs is increased1 and ,cohen and van ,eyk found that the temperature of maximum velocity is about -#ej;deg4 ,contact with the stable form will1 of course1 facilitate the transformation4 ,the change of white tin into grey takes place also with increased velocity in presence of a solution of tin ammonium chloride 7pink salt71 which is able to dissolve small quantities of tin4 ,in presence of such a solution also1 it was found that the temperature at which the velocity of transformation was greatest was raised to #j;deg4 ,at this temperature1 white tin in contact with a solution of tin ammonium chloride1 and the grey modification1 undergoes transformation to an appreciable extent in the course of a few days4 ,fig4 #g is a photograph of a piece of white tin undergoing transformation into the grey variety4#fb ,the bright surface of the tin becomes covered with a number of warty masses1 formed of the less dense grey form1 and the number and size of these continue to grow until the whole of the white tin has passed #dc into a grey powder4 ,on account of the appearance which is here seen1 this transformation of tin has been called by ,cohen the tin plague4 ,illustration3 ,,fig4 #g4 #dd ,enantiotropy and ,monotropy4--,in the case of sulphur and tin1 we have met with two substances existing in polymorphic forms1 and we have also learned that these forms exhibit a definite transition point at which their relative stability is reversed4 ,each form1 therefore1 possesses a definite range of stable existence1 and is capable of undergoing transformation into the other1 at temperatures above or below that of the transition point4 ,another class of dimorphous substances is1 however1 met with as1 for instance1 in the case of the well-known compounds iodine monochloride and benzophenone4 ,each crystalline form has its own melting point1 the dimorphous forms of iodine monochloride melting at #ac4i;deg and #bg4b;deg1#fc and those of benzophenone at #bf;deg and #dh;deg4#fd ,this class of substance differs from that which we have already studied 7e4g4 sulphur and tin71 in that at all temperatures up to the melting point1 only one of the forms is stable1 the other being metastable4 ,there is1 therefore1 no transition point1 and transformation of the crystalline forms can be observed only in one direction4 ,these two classes of phenomena are distinguished by the names enantiotropy and monotropy2 enantiotropic substances being such that the change of one form into the other is a reversible process 7e4g4 rhombic sulphur into monoclinic1 and monoclinic sulphur into rhombic71 and monotropic substances1 those in which the transformation of the crystalline forms is irreversible4 ,illustration3 ,,fig4 #h4 ,illustration3 ,,fig4 #i4 ,these differences in the behaviour can be explained very well in many cases by supposing that in the case of enantiotropic substances the transition point lies below the melting point1 while in the case of monotropic substances1 it lies above the melting point4#fe ,these conditions would be represented by the ,figs4 #h and #i4 ,in these two figures1 ,o#c is the transition point1 ,o#a and ,o#b the melting points of the metastable and stable forms #de respectively4 ,from ,fig4 #i we see that the crystalline form ,i4 at all temperatures up to its melting point is metastable with respect to the form ,,ii4 ,in such cases the transition point could be reached only at higher pressures4 ,although1 as already stated1 this explanation suffices for many cases1 it does not prove that in all cases of monotropy the transition point is above the melting point of the two forms4 ,it is also quite possible that the transition point may lie below the melting points2#ff in this case we have what is known as pseudomonotropy4 ,it is possible that graphite and diamond1#fg perhaps also the two forms of phosphorus1 stand in the relation of pseudomonotropy 7v4 p4 #di74 ,the disposition of the curves in ,figs4 #h and #i also explains the phenomenon sometimes met with1 especially in organic chemistry1 that the substance first melts1 then solidifies1 and remelts at a higher temperature4 ,on again determining the melting point after re-solidification1 only the higher melting point is obtained4 ,the explanation of such a behaviour is1 that if the determination of the melting point is carried out rapidly1 the point ,o#a1 the melting point of the metastable solid form1 may be realized4 ,at this temperature1 however1 the liquid is metastable with respect to the stable solid form1 and if the temperature is #df not allowed to rise above the melting point of the latter1 the liquid may solidify4 ,the stable solid modification thus obtained will melt only at a higher temperature4 ,d4 ,phosphorus4 ,an interesting case of a monotropic dimorphous substance is found in phosphorus1 which occurs in two crystalline forms2 white phosphorus belonging to the regular system1 and red phosphorus belonging to the hexagonal system4 ,from determinations of the vapour pressures of liquid white phosphorus1 and of solid red phosphorus1#fh it was found that the vapour pressure of red phosphorus was considerably lower than that of liquid white phosphorus at the same temperature1 the values obtained being given in the following table4 ,,vapour ,,pressures ,,of ,,white ,,and ,,red ,,phosphorus4 ---------------------------------------- --------------------------------- ,vapour pressure of liquid white phosphorus4 ,vapour pressure of red phosphorus4 ---------------------------------------- -------------------------------- ,temperature4 ,pressure ,temperature4 ,pressure ,temperature4 ,pressure in cm4 in atm4 in atm4 ---------------------------------------- ---------------------------- #afe;deg #ab #cfj;deg #c4b #cfj;deg #j4a #ahj;deg #bj4d #ddj;deg #g4e #ddj;deg #a4ge #bjj;deg #bf4f #did;deg #ah4j #dhg;deg #f4h #bai;deg #ce4i #ejc;deg #ba4i #eaj;deg #aj4h #bcj;deg #ea4d #eaa;deg #bf4b #eca;deg #af4j #bij;deg #gf4j -- -- #eej;deg #ca4j -- -- -- -- #egg;deg #ef4j ---------------------------------------- --------------------------------- ,these values are also represented graphically in ,fig4 #aj4 ,illustration3 ,,fig4 #aj4 ,at all temperatures above about #bfj;deg1 transformation of the white into the red modification takes place with appreciable velocity1 and this velocity increases as the temperature is raised4 ,even at lower temperatures1 e4g4 at the ordinary temperature1 the velocity of transformation is increased under the influence #dg of light1#fi or by the presence of certain substances1 e4g4 iodine1#gj just as the velocity of transformation of white tin into the grey modification was increased by the presence of a solution of tin ammonium chloride 7p4 #dj74 ,at the ordinary temperature1 therefore1 white phosphorus must be considered as the less stable 7metastable7 form1 for although it can exist in contact with red phosphorus for a long period1 its vapour pressure1 as we have seen1 is greater than that of the red modification1 and also1 its solubility in different solvents is greater#ga than that of the red modification2 as we shall find later1 the solubility of the metastable form is always greater than that of the stable4 ,the relationships which are met with in the case of phosphorus can be best represented by the diagram1 ,fig4 #aa4gb ,in this figure1 ,,bo#a represents the conditions of equilibrium of the univariant system red phosphorus and vapour1 which ends at ,o#a1 the melting point of red phosphorus4 ,by heating in capillary tubes of hard glass1 ,chapman#gc found that red phosphorus melts at the melting point of potassium iodide1 i4e4 about #fcj;deg1#gd but the pressure at this temperature is unknown4 ,at ,o#a1 then1 we have the triple point1 red phosphorus1 liquid1 and vapour1 and starting from it1 we should have the #dh vaporization curve of liquid phosphorus1 ,o#a;,a1 and the fusion curve of red phosphorus1 ,o#a;,f4 ,although these have not been determined1 the latter curve must1 from theoretical considerations 7v4 p4 #eh71 slope slightly to the right2 i4e4 increase of pressure raises the melting point of red phosphorus4 ,illustration3 ,,fig4 #aa4 ,when white phosphorus is heated to #dd;deg1 it melts4 ,at this point1 therefore1 we shall have another triple point1 white phosphorus--liquid--vapour2 the pressure at this point has been calculated to be #c mm4#ge ,this point is the intersection of three curves1 viz4 sublimation curve1 vaporization curve1 and the fusion curve of white phosphorus4 ,the fusion curve1 ,o#b;,e1 has been determined by ,tammann#gf and by ,g4 ,a4 ,hulett1#gg and it was found that increase of pressure by #a atm4 raises the melting point by #j4jbi;deg4 ,the sublimation curve of white phosphorus has not yet been determined4 ,as can be seen from the table of vapour pressures 7p4 #df71 the vapour pressure of white phosphorus has been determined up to #ejj;deg2 at temperatures above this1 however1 the velocity with which transformation into red phosphorus takes place is so great as to render the determination of the vapour pressure #di at higher temperatures impossible4 ,since1 however1 the difference between white phosphorus and red phosphorus disappears in the liquid state1 the vapour pressure curve of white phosphorus must pass through the point ,o#a1 the melting point of red phosphorus1 and must be continuous with the curve ,o#a;,a1 the vapour pressure curve of liquid phosphorus 7vide infra74 ,since1 as ,fig4 #aj shows1 the vapour pressure curve of white phosphorus ascends very rapidly at higher temperatures1 the break between ,,bo#a and ,o#a;,a must be very slight4 ,as compared with monotropic substances like benzophenone1 phosphorus exhibits the peculiarity that transformation of the metastable into the stable modification takes place with great slowness2 and further1 the time required for the production of equilibrium between red phosphorus and phosphorus vapour is great compared with that required for establishing the same equilibrium in the case of white phosphorus4 ,this behaviour can be best explained by the assumption that change in the molecular complexity 7polymerization7 occurs in the conversion of white into red phosphorus1 and when red phosphorus passes into vapour 7depolymerization74#gh ,this is borne out by the fact that measurements of the vapour density of phosphorus vapour at temperatures of #ejj;deg and more1 show it to have the molecular weight represented by ,p#d1gi and the same molecular weight has been found for phosphorus in solution4#hj ,on the other hand1 it has recently been shown by ,r4 ,schenck1#ha that the molecular weight of red phosphorus is at least ,p#h1 and very possibly higher4 ,in the case of phosphorus1 therefore1 it is more than possible that we are dealing1 not simply with two polymorphic #ej forms of the same substance1 but with polymeric forms1 and that there is no transition point at temperatures above the absolute zero1 unless we assume the molecular complexity of the two forms to become the same4 ,the curve for red phosphorus would therefore lie below that of white phosphorus1 for the vapour pressure of the polymeric form1 if produced from the simpler form with evolution of heat1 must be lower than that of the latter4 ,a transition point would1 of course1 become possible if the sign of the heat effect in the transformation of the one modification into the other should change4 ,if1 further1 the liquid which is produced by the fusion of red phosphorus at #fcj;deg under high pressure also exists in a polymeric form1 greater than ,p#d1 then the metastable vaporization curve of white phosphorus would not pass through the melting point of red phosphorus1 as was assumed above4#hb ,we have already seen in the case of water 7p4 #ca7 that the vapour pressure of supercooled water is greater than that of ice1 and that therefore it is possible1 theoretically at least1 by a process of distillation1 to transfer the water from one end of a closed tube to the other1 and to there condense it as ice4 ,on account of the very small difference between the vapour pressure of supercooled water and ice1 this distillation process has not been experimentally realized4 ,in the case of phosphorus1 however1 where the difference in the vapour pressures is comparatively great1 it has been found possible to distil white phosphorus from one part of a closed tube to another1 and to there condense it as red phosphorus2 and since the vapour pressure of red phosphorus at #cej;deg is less than the vapour pressure of white phosphorus at #bjj;deg1 it is possible to carry out the distillation from a colder part of the tube to a hotter1 by having white phosphorus at the former and red phosphorus at the latter4 ,such a process of distillation has been carried out by ,troost and ,hautefeuille between #cbd;deg and #cej;deg4#hc ,relationships similar to those found in the case of phosphorus are also met with in the case of cyanogen and #ea paracyanogen1 which have been studied by ,chappuis1#hd ,troost and ,hautefeuille1#he and ,dewar1#hf and also in the case of other organic substances4 ,enantiotropy combined with ,monotropy4--,not only can polymorphic substances exhibit enantiotropy or monotropy1 but1 if the substance is capable of existing in more than two crystalline forms1 both relationships may be found1 so that some of the forms may be enantiotropic to one another1 while the other forms exhibit only monotropy4 ,this behaviour is seen in the case of sulphur1 which can exist in as many as eight different crystalline varieties4 ,of these only monoclinic and rhombic sulphur exhibit the relationship of enantiotropy1 i4e4 they possess a definite transition point1 while the other forms are all metastable with respect to rhombic and monoclinic sulphur1 and remain so up to the melting point2 that is to say1 they are monotropic modifications4#hg ,e4 ,liquid ,crystals4 ,phenomena observed4--,in #ahhh it was discovered by ,reinitzer#hh that the two substances1 cholesteryl acetate and cholesteryl benzoate1 possess the peculiar property of melting sharply at a definite temperature to milky liquids2 and that the latter1 on being further heated1 suddenly become clear1 also at a definite temperature4 ,other substances1 more especially p-azoxyanisole and p-azoxyphenetole1 were1 later1 found to possess the same property of having apparently a double melting point4#hi ,on cooling the clear liquids1 the reverse series of changes occurred4 ,the turbid liquids which were thus obtained were found to possess not only the usual properties of liquids 7such as the #eb property of flowing and of assuming a perfectly spherical shape when suspended in a liquid of the same density71 but also those properties which had hitherto been observed only in the case of solid crystalline substances1 viz4 the property of double refraction and of giving interference colours when examined by polarized light2 the turbid liquids are anisotropic4 ,to such liquids1 the optical properties of which were discovered by ,o4 ,lehmann1#ij the name liquid crystals1 or crystalline liquids1 was given4 ,nature of ,liquid ,crystals4--,during the past ten years the question as to the nature of liquid crystals has been discussed by a number of investigators1 several of whom have contended strongly against the idea of the term liquid being applied to the crystalline condition2 and various attempts have been made to prove that the turbid liquids are in reality heterogeneous and are to be classed along with emulsions4#ia ,this view was no doubt largely suggested by the fact that the anisotropic liquids were turbid1 whereas the solid crystals were clear4 ,lehmann found1 however1 that1 when examined under the microscope1 the simple liquid crystals were also clear1#ib the apparent turbidity being due to the aggregation of a number of differently oriented crystals1 in the same way as a piece of marble does not appear transparent although composed of transparent crystals4#ic ,further1 no proof of the heterogeneity of liquid crystals has yet been obtained1 but rather all chemical and physical investigations indicate that they are homogeneous4#id ,no separation #ec of a solid substance from the milky1 anisotropic liquids has been effected2 the anisotropic liquid is in some cases less viscous than the isotropic liquid formed at a higher temperature2 and the temperature of liquefaction is constant1 and is affected by pressure and admixture with foreign substances exactly as in the case of a pure substance4#ie ,illustration3 ,,fig4 #ab4 ,equilibrium ,relations in the ,case of ,liquid ,crystals4--,since1 now1 we have seen that we are dealing here with substances in two crystalline forms 7which we may call the solid and liquid#if crystalline form71 which possess a definite transition point1 at which1 transformation of the one form into the other occurs in both directions1 we can represent the conditions of equilibrium by a diagram in all respects similar to that employed in the case of other enantiotropic substances1 e4g4 sulphur 7p4 #ce74 #ed ,in ,fig4 #ab there is given a diagrammatic representation of the relationships found in the case of p-azoxyanisole4#ig ,although the vapour pressure of the substance in the solid1 or liquid state1 has not been determined1 it will be understood from what we have already learned1 that the curves ,,ao1 ,,ob1 ,,bc1 representing the vapour pressure of solid crystals1 liquid crystals1 isotropic liquid1 must have the relative positions shown in the diagram4 ,point ,o1 the transition point of the solid into the liquid crystals1 lies at #aah4bg;deg1 and the change of the transition point with the pressure is #j4jcb;deg pro #a atm4 ,the transition curve ,,oe slopes1 therefore1 slightly to the right4 ,the point ,b1 the melting point of the liquid crystals1 lies at #ace4he;deg1 and the melting point is raised #j4jdhe;deg pro #a atm4 ,the curve ,,bd1 therefore1 also slopes to the right1 and more so than the transition curve4 ,in this respect azoxyanisole is different from sulphur4 ,the areas bounded by the curves represent the conditions for the stable existence of the four single phases1 solid crystals1 liquid crystals1 isotropic liquid and vapour4 ,the most important substances hitherto found to form liquid crystals are#ih3-- ---------------------------------------- -------------- ,substance4 ,transition ,melting point4 point4 ---------------------------------------- -------------- ,cholesteryl benzoate #ade4e;deg #agh4e;deg ,azoxyanisole #aah4c;deg #ace4i;deg ,azoxyphenetole #acd4e;deg #afh4a;deg ,condensation product from benzaldehyde and benzidine #bcd;deg #bfj;deg ,azine of p-oxyethylbenzaldehyde #agb;deg #aif;deg ,condensation product from p-tolylaldehyde and benzidine #bca;deg -- p-,methoxycinnamic acid #afi;deg #ahe;deg ---------------------------------------- -------------- 99 99 99 99 99 #ee ,,chapter ,,iv ,,general ,,summary ,in the preceding pages we have learned how the principles of the ,phase ,rule can be applied to the elucidation of various systems consisting of one component4 ,in the present chapter it is proposed to give a short summary of the relationships we have met with1 and also to discuss more generally how the ,phase ,rule applies to other one-component systems4 ,on account of the fact that beginners are sometimes inclined to expect too much of the ,phase ,rule2 to expect1 for example1 that it will inform them as to the exact behaviour of a substance1 it may here be emphasized that the ,phase ,rule is a general rule2 it informs us only as to the general conditions of equilibrium1 and leaves the determination of the definite1 numerical data to experiment4 ,triple ,point4--,we have already 7p4 #bh7 defined a triple point in a one-component system1 as being that pressure and temperature at which three phases coexist in equilibrium2 it represents1 therefore1 an invariant system 7p4 #af74 ,at the triple point also1 three curves cut1 viz4 the curves representing the conditions of equilibrium of the three univariant systems formed by the combination of the three phases in pairs4 ,the most common triple point of a one-component system is1 of course1 the triple point1 solid1 liquid1 vapour 7,s-,l-,v71 but other triple points#ii are also possible when1 as in the case of #ef sulphur or benzophenone1 polymorphic forms occur4 ,whether or not all the triple points can be experimentally realized will1 of course1 depend on circumstances4 ,we shall1 in the first place1 consider only the triple point ,s-,l-,v4 ,as to the general arrangement of the three univariant curves around the triple point1 the following rules may be given4 7#a7 ,the prolongation of each of the curves beyond the triple point must lie between the other two curves4 7#b7 ,the middle position at one and the same temperature in the neighbourhood of the triple point is taken by that curve 7or its metastable prolongation7 which represents the two phases of most widely differing specific volume4#ajj ,that is to say1 if a line of constant temperature is drawn immediately above or below the triple point so as to cut the three curves--two stable curves and the metastable prolongation of the third--the position of the curves at that temperature will be such that the middle position is occupied by that curve 7or its metastable prolongation7 which represents the two phases of most widely differing specific volume4 ,now1 although these rules admit of a considerable variety of possible arrangements of curves around the triple point1#aja only two of these have been experimentally obtained in the case of the triple point solid--liquid--vapour4 ,at present1 therefore1 we shall consider only these two cases 7,figs4 #ac and #ad74 ,illustration3 ,,fig4 #ac4 ,illustration3 ,,fig4 #ad4 ,an examination of these two figures shows that they satisfy the rules laid down4 ,each of the curves on being prolonged passes between the other two curves4 ,in the case of substances of the first type 7,fig4 #ac71 the specific volume of the solid is greater than that of the liquid 7the substance contracts on fusion72 the difference of specific volume will1 therefore1 be greatest between liquid and vapour4 ,the curve1 therefore1 for liquid and vapour 7or its prolongation7 must lie between the other two curves2 this is seen from the figure to be the case4 ,similarly1 the rule is satisfied by the arrangement of curves in ,fig4 #ad1 where the difference of specific volumes is #eg greatest between the solid and vapour4 ,in this case the curve ,s-,v occupies the intermediate position4 ,as we see1 the two figures differ from one another only in that the fusion curve ,,oc in one case slopes to the right away from the pressure axis1 thus indicating that the melting point is raised by increase of pressure2 in the other case1 to the left1 indicating a lowering of the melting point with the pressure4 ,these conditions are found exemplified in the case of sulphur and ice 7pp4 #bi and #ce74 ,we see further from the two figures1 that ,o in ,fig4 #ac gives the highest temperature at which the solid can exist1 for the curve for solid--liquid slopes back to regions of lower temperature2 in ,fig4 #ad1 ,o gives the lowest temperature at which the liquid phase can exist as stable phase4#ajb ,theorems of van't ,hoff and of ,le ,chatelier4--,so far we have studied only the conditions under which various systems exist in equilibrium2 and we now pass to a consideration of the changes which take place in a system when the external conditions of temperature and pressure are altered4 ,for all such changes there exist two theorems1 based on the laws of thermodynamics1 by means of which the alterations in a system can be qualitatively predicted4#ajc ,the first of these1 usually #eh known as van't ,hoff's law of movable equilibrium1#ajd states3 ,when the temperature of a system in equilibrium is raised1 that reaction takes place which is accompanied by absorption of heat2 and1 conversely1 when the temperature is lowered1 that reaction occurs which is accompanied by an evolution of heat4 ,the second of the two theorems refers to the effect of change of pressure1 and states3#aje ,when the pressure on a system in equilibrium is increased1 that reaction takes place which is accompanied by a diminution of volume2 and when the pressure is diminished1 a reaction ensues which is accompanied by an increase of volume4 ,the demonstration of the universal applicability of these two theorems is due chiefly to ,le ,chatelier1 who showed that they may be regarded as consequences of the general law of action and reaction4 ,for this reason they are generally regarded as special cases of the more general law1 known as the theorem of ,le ,chatelier1 which may be stated in the words of ,ostwald1 as follows3#ajf ,if a system in equilibrium is subjected to a constraint by which the equilibrium is shifted1 a reaction takes place which opposes the constraint1 i4e4 one by which its effect is partially destroyed4 ,this theorem of ,le ,chatelier is of very great importance1 for it applies to all systems and changes of the condition of equilibrium1 whether physical or chemical2 to vaporization and fusion2 to solution and chemical action4 ,in all cases1 whenever changes in the external condition of a system in equilibrium are produced1 processes also occur within the system which tend to counteract the effect of the external changes4 ,changes at the ,triple ,point4--,if now we apply this theorem to equilibria at the triple point ,s-,l-,v1 and ask what changes will occur in such a system when the external conditions of pressure and temperature are altered1 the general answer to the question will be3 ,so long as the three phases are present1 no #ei change in the temperature or pressure of the system can occur1 but only changes in the relative amounts of the phases2 that is to say1 the effect on the system of change in the external conditions is opposed by the reactions or changes which take place within the system 7according to the theorems of van't ,hoff and ,le ,chatelier74 ,we now proceed to discuss what these changes are1 and shall consider first the effect of alteration of the temperature at constant volume and constant pressure1 and then the effect of alteration of the pressure both when the temperature remains constant and when it varies4 ,when the volume is kept constant1 the effect of the addition of heat to a system at the triple point ,s-,l-,v differs somewhat according as there is an increase or diminution of volume when the solid passes into the liquid state4 ,in the former and most general case 7,fig4 #ad71 addition of heat will cause a certain amount of the solid phase to melt1 whereby the heat which is added becomes latent2 the temperature of the system therefore does not rise4 ,since1 however1 the melting of the solid is accompanied by an increase of volume1 whereby an increase of pressure would result1 a certain portion of the vapour must condense to liquid1 in order that the pressure may remain constant4 ,the total effect of addition of heat1 therefore1 is to cause both solid and vapour to pass into liquid1 i4e4 there occurs the change ,s ,v -- ,l4 ,it will1 therefore1 depend on the relative quantities of solid and vapour1 which will disappear first4 ,if the solid disappears first1 then we shall pass to the system ,l-,v2 if vapour disappears first1 we shall obtain the system ,s-,l4 ,withdrawal of heat causes the reverse change1 ,l -- ,s ,v2 at all temperatures below the triple point the liquid is unstable or metastable 7p4 #cj74 ,when fusion is accompanied by a diminution of volume 7e4g4 ice1 ,fig4 #ac71 then1 since the melting of the solid phase would decrease the total volume1 i4e4 would lower the pressure1 a certain quantity of the solid must also pass into vapour in order that the pressure may be maintained constant4 ,on addition of heat1 therefore1 there occurs the reaction ,s -- ,l ,v2 withdrawal of heat causes the reverse change ,l ,v -- ,s4 ,above the temperature of the triple point the #fj solid cannot exist2 below the triple point both systems1 ,s-,l and ,s-,v1 can exist1 and it will therefore depend on the relative amounts of liquid and vapour which of these two systems is obtained on withdrawing heat from the system at constant volume4 ,the same changes in the phases occur when heat is added or withdrawn at constant pressure1 so long as the three phases are present4 ,continued addition of heat1 however1 at constant pressure will ultimately cause the formation of the bivariant system vapour alone2 continued withdrawal of heat will ultimately cause the formation of solid alone4 ,this will be readily understood from ,fig4 #ae4 ,the dotted line ,d',,od is a line of constant pressure2 on adding heat1 the system passes along the line ,,od into the region of vapour2 on heat being withdrawn1 the system passes along ,,od' into the area of solid4 ,illustration3 ,,fig4 #ae4 ,similar changes are produced when the volume of the system is altered4 ,alteration of volume may take place either while transference of heat to or from the system is cut off 7adiabatic change71 or while such transference may occur 7isothermal change74 ,in the latter case1 the temperature of the system will remain constant2 in the former case1 since at the triple point the pressure must be constant so long as the three phases are present1 increase of volume must be compensated by the evaporation of liquid4 ,this1 however1 would cause the temperature to fall 7since communication of heat from the outside is supposed to be cut off71 and a portion of the liquid must therefore freeze4 ,in this way the latent heat of evaporation is counterbalanced by the latent heat of fusion4 ,as the result of increase of volume1 therefore1 the process occurs ,l -- ,s ,v4 ,diminution of volume1 without transference of heat1 will bring about the opposite change1 ,s ,v -- ,l4 ,in the former case there is ultimately obtained the univariant system ,s-,v2 in the latter case there will be #fa obtained either ,s-,l or ,l-,v according as the vapour or solid phase disappears first4 ,this argument holds good for both types of triple point shown in ,figs4 #ac and #ad 7p4 #eg74 ,a glance at these figures will show that increase of volume 7diminution of pressure7 will lead ultimately to the system ,s-,v1 for at pressures lower than that of the triple point1 the liquid phase cannot exist4 ,decrease of volume 7increase of pressure71 on the other hand1 will lead either to the system ,s-,l or ,l-,v1 because these systems can exist at pressures higher than that of the triple point4 ,if the vapour phase disappears and we pass to the curve ,s-,l1 continued diminution of volume will be accompanied by a fall in temperature in the case of systems of the first type 7,fig4 #ac71 and by a rise in temperature in the case of systems of the second type 7,fig4 #ad74 ,illustration3 ,,fig4 #af4 ,illustration3 ,,fig4 #ag4 ,lastly1 if the temperature is maintained constant1 i4e4 if heat can pass into or out of the system1 then on changing the volume the same changes in the phases will take place as described above until one of the phases has disappeared4 ,continued increase of volume 7decrease of pressure7 will then cause the disappearance of a second phase1 the system passing along the dotted line ,,oe' 7,figs4 #af1 #ag71 so that ultimately there remains only the vapour phase4 ,conversely1 diminution of volume 7increase of pressure7 will ultimately lead either to solid 7,fig4 #af7 or to liquid alone 7,fig4 #ag71 the system passing along the dotted line ,,oe4 #fb ,in discussing the alterations which may take place at the triple point with change of temperature and pressure1 we have considered only the triple point ,s-,l-,v4 ,the same reasoning1 however1 applies1 mutatis mutandis1 to all other triple points1 so that if the specific volumes of the phases are known1 and the sign of the heat effects which accompany the transformation of one phase into the other1 it is possible to predict 7by means of the theorem of ,le ,chatelier7 the changes which will be produced in the system by alteration of the pressure and temperature4 ,in all cases of transformation at the triple point1 it should be noted that all three phases are involved in the change1#ajg and not two only2 the fact that in the case1 say1 of the transformation from solid to liquid1 or liquid to solid1 at the melting point with change of temperature1 only these two phases appear to be affected1 is due to there generally being a large excess of the vapour phase present and to the prior disappearance therefore of the solid or liquid phase4 ,in the case of triple points at which two solid phases are in equilibrium with liquid1 other arrangements of the curves around the triple point are found4 ,it is1 however1 unnecessary to give a general treatment of these here1 since the principles which have been applied to the triple point ,s-,l-,v can also be applied to the other triple points4#ajh ,triple ,point ,solid--,solid--,vapour4--,the triple point solid--solid--vapour is one which is of considerable importance4 ,examples of such a triple point have already been given in sulphur and tin1 and a list of other substances capable of yielding two solid phases is given below4 ,the triple point ,s-,s-,v is not precisely the same as the transition point1 but is very nearly so4 ,the transition point is the temperature at which the relative stability of the two solid phases undergoes change1 when the vapour phase is absent and the pressure is #a atm42 whereas at the triple point the pressure is that of the system itself4 ,the transition point1 therefore1 bears the same relation to the triple point ,s-,s-,v as the melting point to the triple point ,s-,l-,v4 #fc ,in the following table is given a list of the most important polymorphous substances1 and the temperatures of the transition point4#aji ---------------------------------------- --------- ,substance4 ,transition temperature4 ---------------------------------------- --------- ,ammonium nitrate-- beta-rhombic -- alpha-rhombic #ce;deg alpha-rhombic -- rhombohedral #hc;deg ,rhombohedral -- regular #abe;deg ,mercuric iodide #abf;deg ,potassium nitrate #abi;deg ,silver iodide #ade;deg ,silver nitrate #afj;deg ,sulphur #ie4e;deg ,tetrabrommethane #df4h;deg ,thallium nitrate-- ,rhombic -- rhombohedral #hj;deg ,rhombohedral -- regular #adb4e;deg ,thallium picrate #df;deg ,tin #bj;deg ---------------------------------------- --------- ,sublimation and ,vaporization ,curves4--,we have already seen1 in the case of ice and liquid water1 that the vapour pressure increases as the temperature rises1 the increase of pressure per degree being greater the higher the temperature4 ,the sublimation and vaporization curves1 therefore1 are not straight lines1 but are bent1 the convex side of the curve being towards the temperature axis in the ordinary pt-diagram4 ,in the case of sulphur and of tin1 we assumed vapour to be given off by the solid substance1 although the pressure of the vapour has not hitherto been measured4 ,the assumption1 however1 is entirely justified1 not only on theoretical grounds1 but also because the existence of a vapour pressure has been observed in the case of many solid substances at temperatures much below the melting point1#aaj and in some cases1 e4g4 camphor1#aaa the vapour pressure is considerable4 #fd ,as the result of a large number of determinations1 it has been found that all vapour pressure curves have the same general form alluded to above4 ,attempts have also been made to obtain a general expression for the quantitative changes in the vapour pressure with change of temperature1 but without success4 ,nevertheless1 the qualitative changes1 or the general direction of the curves1 can be predicted by means of the theorem of ,le ,chatelier4 ,as we have already learned 7p4 #af71 the ,phase ,rule takes no account of the molecular complexity of the substances participating in an equilibrium4 ,a dissociating substance1 therefore1 in contact with its vaporous products of dissociation 7e4g4 ammonium chloride in contact with ammonia and hydrogen chloride71 will likewise constitute a univariant system of one component1 provided the composition of the vapour phase as a whole is the same as that of the solid or liquid phase 7p4 #ac74 ,for all such substances1 therefore1 the conditions of equilibrium will be represented by a curve of the same general form as the vapour pressure curve of a non-dissociating substance4#aab ,the same behaviour is also found in the case of substances which polymerize on passing into the solid or liquid state 7e4g4 red phosphorus74 ,where such changes in the molecular state occur1 however1 the time required for equilibrium to be established is1 as a rule1 greater than when the molecular state is the same in both phases4 ,from an examination of ,figs4 #ac and #ad1 it will be easy to predict the effect of change of pressure and temperature on the univariant systems ,s-,v or ,l-,v4 ,if the volume is kept constant1 addition of heat will cause an increase of pressure1 the system ,s-,v moving along the curve ,,ao until at the triple point the liquid phase is formed1 and the system ,l-,v moving along the curve ,,ob2 so long as two phases are present1 the condition of the system must be represented by these two curves4 ,conversely1 withdrawal of heat will cause condensation of vapour1 and therefore diminution of pressure2 the system will therefore move along the vaporization or sublimation curve to lower temperatures and pressures1 so long as the system remains univariant4 #fe ,if transference of heat to or from the system is prevented1 increase of volume 7diminution of pressure7 will cause the system ,l-,v to pass along the curve ,,bo2 liquid will pass into vapour and the temperature will fall4#aac ,at ,o solid may appear1 and the temperature of the system will then remain constant until the liquid phase has disappeared 7p4 #eg72 the system will then follow the curve ,,oa until the solid phase disappears1 and we are ultimately left with vapour4 ,on the other hand1 diminution of volume 7increase of pressure7 will cause condensation of vapour1 and the system ,s-,v will pass along the curve ,,ao to higher temperatures and pressures2 at ,o the solid will melt1 and the system will ultimately pass to the curve ,,ob or to ,,oc 7p4 #eg74 ,addition or withdrawal of heat at constant pressure1 and increase or diminution of the pressure at constant temperature1 will cause the system to pass along lines parallel to the temperature and the pressure axis respectively2 the working out of these changes may be left to the reader1 guided by what has been said on pp4 #fj and #fa4 ,the sublimation curve of all substances1 so far as yet found1 has its upper limit at the melting point 7triple point71 although the possibility of the existence of a superheated solid is not excluded4 ,the lower limit is1 theoretically at least1 at the absolute zero1 provided no new phase1 e4g4 a different crystalline modification1 is formed4 ,if the sublimation pressure of a substance is greater than the atmospheric pressure at any temperature below the point of fusion1 then the substance will sublime without melting when heated in an open vessel2 and fusion will be possible only at a pressure higher than the atmospheric4 ,this is found1 for example1 in the case of red phosphorus 7p4 #dg74 ,if1 however1 the sublimation pressure of a substance at its triple point ,s-,l-,v is less than one atmosphere1 then the substance will melt when heated in an open vessel4 ,in the case of the vaporization curve1 the upper limit lies at the critical point where the liquid ceases to exist2#aad the #ff lower limit is determined by the range of the metastable state of the supercooled liquid4 ,the interpolation and extrapolation of vapour-pressure curves is rendered very easy by means of a relationship which ,ramsay and ,young#aae found to exist between the vapour-pressure curves of different substances4 ,it was observed that in the case of closely related substances1 the ratio of the absolute temperatures corresponding to equal vapour pressures is constant1 i4e4 ,t#a_/,t'#a ,t#b_/,t'#b4 ,when the two substances are not closely related1 it was found that the relationship could be expressed by the equation ,t#a_/,t'#a ,t#b_/,t'#b c7t' - t7 where c is a constant having a small positive or negative value1 and t' and t are the temperatures at which one of the substances has the two values of the vapour pressure in question4 ,by means of this equation1 if the vapour-pressure curve of one substance is known1 the vapour-pressure curve of any other substance can be calculated from the values at any two temperatures of the vapour pressure of that substance4 ,fusion ,curve--,transition ,curve4--,the fusion curve represents the conditions of equilibrium between the solid and liquid phase2 it shows the change of the melting point of a substance with change of pressure4 ,as shown in ,figs4 #ac and #ad1 the fusion curve is inclined either towards the pressure axis or away from it2 that is1 increase of pressure can either lower or raise the melting point4 ,it is easy to predict in a qualitative manner the different effect of pressure on the melting point in the two cases mentioned1 if we consider the matter in the light of the theorem of ,le ,chatelier 7p4 #eh74 ,water1 on passing into ice1 expands2 therefore1 if the pressure on the system ice--water be increased1 a reaction will take place which is accompanied by a diminution in volume1 i4e4 the ice will melt4 ,consequently1 a lower temperature will be required in order to counteract the effect of increase of pressure2 or1 in other words1 the melting point will #fg be lowered by pressure4#aaf ,in the second case1 the passage of the liquid to the solid state is accompanied by a diminution of volume2 the effect of increase of pressure will therefore be the reverse of that in the previous case4 ,if the value of the heat of fusion and the alteration of volume accompanying the change of state are known1 it is possible to calculate quantitatively the effect of pressure4#aag ,we have already seen 7p4 #be7 that the effect of pressure on the melting point of a substance was predicted as the result of theoretical considerations1 and was first proved experimentally in the case of ice4 ,soon after1 ,bunsen#aah showed that the melting point of other substances is also affected by pressure2 and in more recent years1 ample experimental proof of the change of the melting point with the pressure has been obtained4 ,the change of the melting point is1 however1 small2 as a rule1 increase of pressure by #a atm4 changes the melting point by about #j4jc;deg1 but in the case of water the change is much less 7#j4jjgf;deg71 and in the case of camphor much more 7#j4ac;deg74 ,in other words1 if we take the mean case1 an increase of pressure of more than #cj atm4 is required to produce a change in the melting point of #a;deg4 ,investigations which were made of the influence of pressure on the melting-point1 showed that up to pressures of several hundred atmospheres the fusion curve is a straight line4#aai ,tammann#abj has1 however1 found that on increasing the pressure the fusion curve no longer remains straight1 but bends towards the pressure axis1 so that1 on sufficiently increasing the pressure1 a maximum temperature might at length be reached4 ,this maximum has1 so far1 however1 not been attained1 although the melting point curves of various substances have been studied up to pressures of #dejj atm4 ,this is to be accounted for partly #fh by the fact that the probable maximum temperature in the case of most substances lies at very great pressures1 and also by the fact that other solid phases make their appearance1 as1 for example1 in the case of ice 7p4 #cb74 ,as to the upper limit of the fusion curve1 the view has been expressed#aba that just as in the case of liquid and vapour1 so also in the case of solid and liquid1 there exists a critical point at which the solid and the liquid phase become identical4 ,experimental evidence1 however1 does not appear to favour this view4#abb ,the transition point1 like the melting point1 is also influenced by the pressure1 and in this case also it is found that pressure may either raise or lower the transition point1 so that the transition curve may be inclined either away from or towards the pressure axis4 ,the direction of the transition curve can also be predicted if the change of volume accompanying the passage of one form into the other is known4 ,in the case of sulphur1 we saw that the transition point is raised by increase of pressure2 in the case of the transition of rhombohedral into alpha-rhombic form of ammonium nitrate1 however1 the transition point is lowered by pressure1 as shown by the following table4#abc ----------------------- ,temperature4 ,pressure4 ----------------------- #he4he;deg #a atm4 #hd4ch;deg #ajj #hc4jc;deg #bjj #hb4bi;deg #bej ----------------------- ,so far as investigations have been carried out1 it appears that in most cases the transition curve is practically a straight line4 ,it has1 however1 been found in the case of ,glauber's salt1 that with increase of pressure the transition curve passes through a point of maximum temperature1 and exhibits1 therefore1 a form similar to that assumed by ,tammann for the fusion curve4#abd #fi ,suspended ,transformation4 ,metastable ,equilibria4--,hitherto we have considered only systems in stable equilibrium4 ,we have1 however1 already seen1 in the case of water1 that on cooling the liquid down to the triple point1 solidification did not necessarily take place1 although the conditions were such as to allow of its formation4 ,similarly1 we saw that rhombic sulphur can be heated above the transition point1 and monoclinic sulphur can be obtained at temperatures below the transition point1 although in both cases transformation into a more stable form is possible2 the system becomes metastable4 ,the same reluctance to form a new phase is observed also in the phenomena of superheating of liquids1 and in the hanging of mercury in barometers1 in which case the vapour phase is not formed4 ,in general1 then1 we may say that a new phase will not necessarily be formed immediately the system passes into such a condition that the existence of that phase is possible2 but rather1 instead of the system undergoing transformation so as to pass into the most stable condition under the existing pressure and temperature1 this transformation will be suspended or delayed1 and the system will become metastable4 ,only in the case of the formation of the liquid from the solid phase1 in a one-component system1 has this reluctance to form a new phase not been observed4 ,to ensure the formation of the new phase1 it is necessary to have that phase present4 ,the presence of the solid phase will prevent the supercooling of the liquid2 and the presence of the vapour phase will prevent the superheating of the liquid4 ,however1 even in the presence of the more stable phase1 transformation of the metastable phase occurs with very varying velocity2 in some cases so quickly as to appear almost instantaneous2 while in other cases1 the change takes place so slowly as to require hundreds of years for its achievement4 ,it is this slow rate of transformation that renders the existence of metastable forms possible1 when in contact with the more stable phase4 ,thus1 for example1 although calcite is the most stable form of calcium carbonate at the ordinary temperature1#abe the less stable #gj modification1 aragonite1 nevertheless exists under the ordinary conditions in an apparently very stable state4 ,as to the amount of the new phase required to bring about the transformation of the metastable phase1 quantitative measurements have been carried out only in the case of the initiation of crystallization in a supercooled liquid4#abf ,as the result of these investigations1 it was found that1 in the case of superfused salol1 the very small amount of #a x #aj-g gm4 of the solid phase was sufficient to induce crystallization4 ,crystallization of a supercooled liquid1 however1 can be initiated only by a nucleus of the same substance in the solid state1 or1 as has also been found1 by a nucleus of an isomorphous solid phase2 it is not brought about by the presence of any chance solid4 ,velocity of ,transformation4--,attention has already been drawn to the sluggishness with which reciprocal transformation of the polymorphic forms of a substance may occur4 ,in the case of tin1 for example1 it was found that the white modification1 although apparently possessing permanence1 is in reality in a metastable state1 under the ordinary conditions of temperature and pressure4 ,this great degree of stability is due to the tardiness with which transformation into the grey form occurs4 ,what was found in the case of tin1 is met with also in the case of all transformations in the solid state1 but the velocity of the change is less in some cases than in others1 and appears to decrease with increase of the valency of the element4#abg ,to this fact van't ,hoff attributes the great permanence of many really unstable 7or metastable7 carbon compounds4 ,reference has been made to the fact that the velocity of transformation can be accelerated by various means4 ,one of the most important of these is the employment of a liquid which has a solvent action on the solid phases4 ,just as we have seen that at any given temperature the less stable form has the higher vapour pressure1 but that at the transition point the vapour pressure of both forms becomes identical1 so also it can be proved theoretically1 and be shown experimentally1 that #ga at a given temperature the solubility of the less stable form is greater than that of the more stable1 but that at the transition point the solubility of the two forms becomes identical4#abh ,if1 then1 the two solid phases are brought into contact with a solvent1 the less stable phase will dissolve more abundantly than the more stable2 the solution will therefore become supersaturated with respect to the latter1 which will be deposited4 ,a gradual change of the less stable form1 therefore1 takes place through the medium of the solvent4 ,in this way the more rapid conversion of white tin into grey in presence of a solution of tin ammonium chloride 7p4 #db7 is to be explained4 ,although1 as a rule1 solvents accelerate the transformation of one solid phase into the other1 they may also have a retarding influence on the velocity of transformation1 as was found by ,reinders in the case of mercuric iodide4#abi ,the velocity of inversion1 also1 is variously affected by different solvents1 and in some cases1 at least1 it appears to be slower the more viscous the solvent2#acj indeed1 ,kastle and ,reed state that yellow crystals of mercuric iodide1 which1 ordinarily1 change with considerable velocity into the red modification1 have been preserved for more than a year under vaseline4 ,temperature1 also1 has a very considerable influence on the velocity of transformation4 ,the higher the temperature1 and the farther it is removed from the equilibrium point 7transition point71 the greater is the velocity of change4 ,above the transition point1 these two factors act in the same direction1 and the velocity of transformation will therefore go on increasing indefinitely the higher the temperature is raised4 ,below the transition point1 however1 the two factors act in opposite directions1 and the more the temperature is lowered1 the more is the effect of removal from the equilibrium point counteracted4 ,a point will therefore be reached at which the velocity is a maximum4 ,reduction of the temperature #gb below this point causes a rapid falling off in the velocity of change4 ,the point of maximum velocity1 however1 is not definite1 but may be altered by various causes4 ,thus1 ,cohen found that in the case of tin1 the point of maximum velocity was altered if the metal had already undergone transformation2 and also by the presence of different liquids4#aca ,lastly1 the presence of small quantities of different substances--catalytic agents or catalyzers--has a great influence on the velocity of transformation4 ,thus1 e4g41 the conversion of white to red phosphorus is accelerated by the presence of iodine 7p4 #dg74 ,greater attention1 however1 has been paid to the study of the velocity of crystallization of a supercooled liquid1 the first experiments in this direction having been made by ,gernez#acb on the velocity of crystallization of phosphorus and sulphur4 ,since that time1 the velocity of crystallization of other supercooled liquids has been investigated2 such as acetic acid and phenol by ,moore2#acc supercooled water by ,tumlirz2#acd and a number of organic substances by ,tammann1#ace ,friedlaender and ,tammann1#acf and by ,bogojawlenski4#acg ,in measuring the velocity of crystallization1 the supercooled liquids were contained in narrow glass tubes1 and the time required for the crystallization to advance along a certain length of the tube was determined1 the velocity being expressed in millimetres per minute4 ,the results which have so far been obtained may be summarized as follows4 ,for any given degree of supercooling of a substance1 the velocity of crystallization is constant4 ,as the degree of supercooling increases1 the velocity of crystallization also increases1 until a certain point is reached at which the velocity is a maximum1 which has a definite characteristic value for each substance4 ,this maximum velocity remains constant over a certain range of #gc temperature2 thereafter1 the velocity diminishes fairly rapidly1 and1 with sufficient supercooling1 may become zero4 ,the liquid then passes into a glassy mass1 which will remain 7practically7 permanent even in contact with the crystalline solid4 ,in ordinary glass we have a familiar example of a liquid which has been cooled to a temperature at which crystallization takes place with very great slowness4 ,if1 however1 glass is heated1 a temperature is reached1 much below the melting point of the glass1 at which crystallization occurs with appreciable velocity1 and we observe the phenomenon of devitrification4#ach ,when the velocity of crystallization is studied at temperatures above the maximum point1 it is found that the velocity is diminished by the addition of foreign substances2 and in many cases1 indeed1 it has been found that the diminution is the same for equimolecular quantities of different substances4 ,it would hence appear possible to utilize this behaviour as a method for determining molecular weights4#aci ,the rule is1 however1 by no means a universal one4 ,thus it has been found by ,f4 ,dreyer1#adj in studying the velocity of crystallization of formanilide1 that the diminution in the velocity produced by equivalent amounts of different substances is not the same1 but that the foreign substances exercise a specific influence4 ,further1 von ,pickardt's rule does not hold when the foreign substance forms mixed crystals 7,chap4 ,x47 with the crystallizing substance4#ada ,law of ,successive ,reactions4--,when sulphur vapour is cooled at the ordinary temperature1 it first of all condenses to drops of liquid1 which solidify in an amorphous form1 and only after some time undergo crystallization2 or1 when phosphorus vapour is condensed1 white phosphorus is first formed1 and not the more stable form--red phosphorus4 ,it has also been observed that even at the ordinary temperature 7therefore much below the transition point7 sulphur may crystallize out from solution in benzene1 alcohol1 carbon disulphide1 and other #gd solvents1 in the prismatic form1 the less stable prismatic crystals then undergoing transformation into the rhombic form2#adb a similar behaviour has also been observed in the transformation of the monotropic crystalline forms of sulphur4#adc ,many other examples might be given4 ,in organic chemistry1 for instance1 it is often found that when a substance is thrown out of solution1 it is first deposited as a liquid1 which passes later into the more stable crystalline form4 ,in analysis1 also1 rapid precipitation from concentrated solution often causes the separation of a less stable and more soluble amorphous form4 ,on account of the great frequency with which the prior formation of the less stable form occurs1 ,ostwald#add has put forward the law of successive reactions1 which states that when a system passes from a less stable condition it does not pass directly into the most stable of the possible states2 but into the next more stable1 and so step by step into the most stable4 ,this law explains the formation of the metastable forms of monotropic substances1 which would otherwise not be obtainable4 ,although it is not always possible to observe the formation of the least stable form1 it should be remembered that that may quite conceivably be due to the great velocity of transformation of the less stable into the more stable form4 ,from what we have learned about the velocity of transformation of metastable phases1 we can understand that rapid cooling to a low temperature will tend to preserve the less stable form2 and1 on account of the influence of temperature in increasing the velocity of change1 it can be seen that the formation of the less stable form will be more difficult to observe in superheated than in supercooled systems4 ,the factors1 however1 which affect the readiness with which #ge the less stable modification is produced1 appear to be rather various4#ade ,although a number of at least apparent exceptions to ,ostwald's law have been found1 it may nevertheless be accepted as a very useful generalization which sums up very frequently observed phenomena4 99 99 99 99 99 #gf ,,chapter ,v ,,systems ,,of ,,two ,,components--,,phenomena ,,of ,,dissociation ,in the preceding pages we have studied the behaviour of systems consisting of only one component1 or systems in which all the phases1 whether solid1 liquid1 or vapour1 had the same chemical composition 7p4 #ac74 ,in some cases1 as1 for example1 in the case of phosphorus and sulphur1 the component was an elementary substance2 in other cases1 however1 e4g4 water1 the component was a compound4 ,the systems which we now proceed to study are characterized by the fact that the different phases have no longer all the same chemical composition1 and cannot1 therefore1 according to definition1 be considered as one-component systems4 ,in most cases1 little or no difficulty will be experienced in deciding as to the number of the components1 if the rules given on pp4 #ab and #ac are borne in mind4 ,if the composition of all the phases1 each regarded as a whole1 is the same1 the system is to be regarded as of the first order1 or a one-component system2 if the composition of the different phases varies1 the system must contain more than one component4 ,if1 in order to express the composition of all the phases present when the system is in equilibrium1 two of the constituents participating in the equilibrium are necessary and sufficient1 the system is one of two components4 ,which two of the possible substances are to be regarded as components will1 however1 be to a certain extent a matter of arbitrary choice4 ,the principles affecting the choice of components will best be learned by a study of the examples to be discussed in the sequel4 #gg ,different ,systems of ,two ,components4--,applying the ,phase ,rule ,p ,f ,c #b to systems of two components1 we see that in order that the system may be invariant1 there must be four phases in equilibrium together2 two components in three phases constitute a univariant1 two components in two phases a bivariant system4 ,in the case of systems of one component1 the highest degree of variability found was two 7one component in one phase72 but1 as is evident from the formula1 there is a higher degree of freedom possible in the case of two-component systems4 ,two components existing in only one phase constitute a tervariant system1 or a system with three degrees of freedom4 ,in addition to the pressure and temperature1 therefore1 a third variable factor must be chosen1 and as such there is taken the concentration of the components4 ,in systems of two components1 therefore1 not only may there be change of pressure and temperature1 as in the case of one-component systems1 but the concentration of the components in the different phases may also alter2 a variation which did not require to be considered in the case of one-component systems4 ,illustration3 ,,fig4 #ah4 ,since a two-component system may undergo three possible #gh independent variations1 we should require for the graphic representation of all the possible conditions of equilibrium a system of three co-ordinates in space1 three axes being chosen1 say1 at right angles to one another1 and representing the three variables--pressure1 temperature1 and concentration of components 7,fig4 #ah74 ,a curve 7e4g4 ,,ab7 in the plane containing the pressure and temperature axes would then represent the change of pressure with the temperature1 the concentration remaining unaltered 7pt-diagram72 one in the plane containing the pressure and concentration axes 7e4g4 ,,af or ,,df71 the change of pressure with the concentration1 the temperature remaining constant 7pc-diagram71 while in the plane containing the concentration and the temperature axes1 the simultaneous change of these two factors at constant pressure would be represented 7tc-diagram74 ,if the points on these three curves are joined together1 a surface1 ,,abde1 will be formed1 and any line on that surface 7e4g4 ,,fg1 or ,,gh1 or ,,gi7 would represent the simultaneous variation of the three factors--pressure1 temperature1 concentration4 ,although we shall at a later point make some use of these solid figures1 we shall for the present employ the more readily intelligible plane diagram4 ,the number of different systems which can be formed from two components1 as well as the number of the different phenomena which can there be observed1 is much greater than in the case of one component4 ,in the case of no two substances1 however1 have all the possible relationships been studied2 so that for the purpose of gaining an insight into the very varied behaviour of two-component systems1 a number of different examples will be discussed1 each of which will serve to give a picture of some of the relationships4 ,although the strict classification of the different systems according to the ,phase ,rule would be based on the variability of the systems1 the study of the many different phenomena1 and the correlation of the comparatively large number of different systems1 will probably be rendered easiest by grouping these different phenomena into classes1 each of these classes being studied with the help of one or more typical examples4 ,the order of treatment adopted here is1 of course1 quite arbitrary2 #gi but has been selected from considerations of simplicity and clearness4 ,,phenomena ,,of ,,dissociation4 ,bivariant ,systems4--,as the first examples of the equilibria between a substance and its products of dissociation1 we shall consider very briefly those cases in which there is one solid phase in equilibrium with vapour4 ,reference has already been made to such systems in the case of ammonium chloride4 ,on being heated1 ammonium chloride dissociates into ammonia and hydrogen chloride4 ,since1 however1 in that case the vapour phase has the same total composition as the solid phase1 viz4 ,,nh#c ,h,cl ,,nh#d;,cl1 the system consists of only one component existing in two phases2 it is therefore univariant1 and to each temperature there will correspond a definite vapour pressure 7dissociation pressure74#adf ,if1 however1 excess of one of the products of dissociation be added1 the system becomes one of two components4 ,in the first place1 analysis of each of the two phases yields as the composition of each1 solid3 ,,nh#d;,cl 7 ,,nh#c ,h,cl72 vapour3 m,,nh#c n,h,cl4 ,obviously the smallest number of substances by which the composition of the two phases can be expressed is two2 that is1 the number of components is two4 ,what1 then1 are the components8 ,the choice lies between ,,nh#c ,h,cl1 ,,nh#d;,cl ,,nh#c1 and ,,nh#d;,cl ,h,cl2 for the three substances1 ammonium chloride1 ammonia1 hydrogen chloride1 are the only ones taking part in the equilibrium of the system4 ,of these three pairs of components1 we should obviously choose as the most simple ,,nh#c and ,h,cl1 for we can then represent the composition of the two phases as the sum of the two components4 ,if one of the other two possible pairs of components be chosen1 we should have to introduce negative quantities of one of the components1 in order to represent the composition of the vapour phase4 ,although it must be allowed that the introduction of negative quantities of a component in such cases is quite permissible1 still it will be #hj better to adopt the simpler and more direct choice1 whereby the composition of each of the phases is represented as a sum of two components in varying proportions 7p4 #ab74 ,if1 therefore1 we have a solid substance1 such as ammonium chloride1 which dissociates on volatilization1 and if the products of dissociation are added in varying amounts to the system1 we shall have1 in the sense of the ,phase ,rule1 a two-component system existing in two phases4 ,such a system will possess two degrees of freedom4 ,at any given temperature1 not only the pressure1 but also the composition1 of the vapour-phase1 i4e4 the concentration of the components1 can vary4 ,only after one of these independent variables1 pressure or composition1 has been arbitrarily fixed does the system become univariant1 and exhibit a definite1 constant pressure at a given temperature4 ,now1 although the ,phase ,rule informs us that at a given temperature change of composition of the vapour phase will be accompanied by change of pressure1 it does not cast any light on the relation between these two variables4 ,this relationship1 however1 can be calculated theoretically by means of the ,law of ,mass ,action4#adg ,from this we learn that in the case of a substance which dissociates into equivalent quantities of two gases1 the product of the partial pressures of the gases is constant at a given temperature4 ,this has been proved experimentally in the case of ammonium hydrosulphide1 ammonium cyanide1 phosphonium bromide1 and other substances4#adh ,univariant ,systems4--,in order that a system of two components shall possess only one degree of freedom1 three phases must be present4 ,of such systems1 there are seven possible1 viz4 ,s-,s-,s1 ,s-,s-,l1 ,s-,s-,v1 ,l-,l-,l1 ,s-,l-,l1 ,l-,l-,v1 ,s-,l-,v2 ,s denoting solid1 ,l liquid1 and ,v vapour4 ,in the present chapter we shall consider only the systems ,s-,s-,v1 i4e4 those systems in which there are two solid phases and a vapour phase present4 #ha ,as an example of this1 we may first consider the well-known case of the dissociation of calcium carbonate4 ,this substance on being heated dissociates into calcium oxide1 or quick-lime1 and carbon dioxide1 as shown by the equation ,ca,c,o#c -- ,ca,o ,,co#b4 ,in accordance with our definition 7p4 #i71 we have here two solid phases1 the carbonate and the quick-lime1 and one vapour phase2 the system is therefore univariant4 ,to each temperature1 therefore1 there will correspond a certain1 definite maximum pressure of carbon dioxide 7dissociation pressure71 and this will follow the same law as the vapour pressure of a pure liquid 7p4 #ba74 ,more particularly1 it will be independent of the relative or absolute amounts of the two solid phases1 and of the volume of the vapour phase4 ,if the temperature is maintained constant1 increase of volume will cause the dissociation of a further amount of the carbonate until the pressure again reaches its maximum value corresponding to the given temperature4 ,diminution of volume1 on the other hand1 will bring about the combination of a certain quantity of the carbon dioxide with the calcium oxide until the pressure again reaches its original value4 ,the dissociation pressure of calcium carbonate was first studied by ,debray1#adi but more exact measurements have been made by ,le ,chatelier1#aej who found the following corresponding values of temperature and pressure3-- -------------------------------------- ,temperature4 ,pressure in cm4 mercury4 -------------------------------------- #edg;deg #b4g #faj;deg #d4f #fbe;deg #e4f #gdj;deg #be4e #gde;deg #bh4i #haj;deg #fg4h #hab;deg #gf4c #hfe;deg #acc4c -------------------------------------- ,from this table we see that it is only at a temperature of about #hab;deg that the pressure of the carbon dioxide becomes equal to atmospheric pressure4 ,in a vessel open to #hb the air1 therefore1 the complete decomposition of the calcium carbonate would not take place below this temperature by the mere heating of the carbonate4 ,if1 however1 the carbon dioxide is removed as quickly as it is formed1 say by a current of air1 then the entire decomposition can be made to take place at a much lower temperature4 ,for the dissociation equilibrium of the carbonate depends only on the partial pressure of the carbon dioxide1 and if this is kept small1 then the decomposition can proceed1 even at a temperature below that at which the pressure of the carbon dioxide is less than atmospheric pressure4 ,ammonia ,compounds of ,metal ,chlorides4--,ammonia possesses the property of combining with various substances1 chiefly the halides of metals1 to form compounds which again yield up the ammonia on being heated4 ,thus1 for example1 on passing ammonia over silver chloride1 absorption of the gas takes place with formation of the substances ,ag,cl1#c,,nh#c and #b;,ag,cl1#c,,nh#c1 according to the conditions of the experiment4 ,these were the first known substances belonging to this class1 and were employed by ,faraday in his experiments on the liquefaction of ammonia4 ,similar compounds have also been obtained by the action of ammonia on silver bromide1 iodide1 cyanide1 and nitrate2 and with the halogen compounds of calcium1 zinc1 and magnesium1 as well as with other salts4 ,the behaviour of the ammonia compounds of silver chloride is typical for the compounds of this class1 and may be briefly considered here4 ,it was found by ,isambert#aea that at temperatures below #ae;deg1 silver chloride combined with ammonia to form the compound ,ag,cl1#c,,nh#c1 while at temperatures above #bj;deg the compound #b;,ag,cl1#c,,nh#c was produced4 ,on heating these substances1 ammonia was evolved1 and the pressure of this gas was found in the case of both compounds to be constant at a given temperature1 but was greater in the case of the former than in the case of the latter substance2 the pressure1 further1 was independent of the amount decomposed4 ,the behaviour of these two substances is1 therefore1 exactly analogous to that shown by calcium carbonate1 and the explanation is also similar4 #hc ,regarded from the point of view of the ,phase ,rule1 we see that we are here dealing with two components1 ,ag,cl and ,,nh#c4 ,on being heated1 the compounds decompose according to the equations3-- #b7;,ag,cl1#c,,nh#c7 -- #b;,ag,cl1#c,,nh#c #c,,nh#c4 #b;,ag,cl1#c,,nh#c -- #b;,ag,cl #c,,nh#c4 ,there are1 therefore1 three phases1 viz4 ,ag,cl1#c,,nh#c2 #b;,ag,cl1#c,,nh#c1 and ,,nh#c1 in the one case2 and #b;,ag,cl1#c,,nh#c2 ,ag,cl1 and ,,nh#c in the other4 ,these two systems are therefore univariant1 and to each temperature there must correspond a definite pressure of dissociation1 quite irrespective of the amounts of the phases present4 ,similarly1 if1 at constant temperature1 the volume is increased 7or if the ammonia which is evolved is pumped off71 the pressure will remain constant so long as two solid phases1 ,ag,cl1#c,,nh#c and #b;,ag,cl1#c,,nh#c1 are present1 i4e4 until the compound richer in ammonia is completely decomposed1 when there will be a sudden fall in the pressure to the value corresponding to the system #b;,ag,cl1#c,,nh#c--;,ag,cl--,,nh#c4 ,the pressure will again remain constant at constant temperature1 until all the ammonia has been pumped off1 when there will again be a sudden fall in the pressure to that of the system formed by solid silver chloride in contact with its vapour4 ,the reverse changes take place when the pressure of the ammonia is gradually increased4 ,if the volume is continuously diminished1 the pressure will first increase until it has reached a certain value2 the compound #b;,ag,cl1#c,,nh#c can then be formed1 and the pressure will now remain constant until all the silver chloride has disappeared4 ,the pressure will again rise1 until it has reached the value at which the compound ,ag,cl1#c,,nh#c can be formed1 when it will again remain constant until the complete disappearance of the lower compound4 ,there is no gradual change of pressure on passing from one system to another2 but the changes are abrupt1 as is demanded by the ,phase ,rule1 and as experiment has conclusively proved4#aeb ,the dissociation pressures of the two compounds of silver #hd chloride and ammonia1 as determined by ,isambert1#aec are given in the following table3-- ---------------------------------------- ---------- ,ag,cl1#c,,nh#c4 #b;,ag,cl1#c,,nh#c4 ---------------------------------------- -------- ,temperature4 ,pressure4 ,temperature4 ,pressure4 ---------------------------------------- -------- #j;deg #bi4c cm4 #bj4j;deg #i4c cm4 #aj4f;deg #ej4e #ca4j;deg #ab4e #ag4e;deg #fe4e #dg4j;deg #bf4h #bd4j;deg #ic4g #eh4e;deg #eb4h #bh4j;deg #ace4e #fi4j;deg #gh4f #cd4b;deg #aga4c #ga4e;deg #id4f #dh4e;deg #bda4d #gg4e;deg #aai4h #ea4e;deg #dac4b #hc4e;deg #aei4c #ed4j;deg #dfd4a #hf4a;deg #aha4c #hh4e;deg #bja4c ---------------------------------------- -------- ,the conditions for the formation of these two compounds1 by passing ammonia over silver chloride1 to which reference has already been made1 will be readily understood from the above tables4 ,in the case of the triammonia mono-chloride1 the dissociation pressure becomes equal to atmospheric pressure at a temperature of about #bj;deg2 above this temperature1 therefore1 it cannot be formed by the action of ammonia at atmospheric pressure on silver chloride4 ,the triammonia dichloride can1 however1 be formed1 for its dissociation pressure at this temperature amounts to only #i cm41 and becomes equal to the atmospheric pressure only at a temperature of about #fh;deg2 and this temperature1 therefore1 constitutes the limit above which no combination can take place between silver chloride and ammonia under atmospheric pressure4 ,attention may be here drawn to the fact1 to which reference will also be made later1 that two solid phases are necessary in order that the dissociation pressure at a given temperature shall be definite2 and for the exact definition of this pressure it is necessary to know1 not merely what is the substance undergoing dissociation1 but also what is the solid product of dissociation formed4 ,for the definition of the equilibrium1 the latter is as important as the former4 ,we shall presently find proof of this in the case #he of an analogous class of phenomena1 viz4 the dissociation of salt hydrates4 ,salts with ,water of ,crystallization4--,in the case of the dehydration of crystalline salts containing water of crystallization1 we meet with phenomena which are in all respects similar to those just studied4 ,a salt hydrate on being heated dissociates into a lower hydrate 7or anhydrous salt7 and water vapour4 ,since we are dealing with two components--salt and water#aed--;in three phases1 viz4 hydrate a1 hydrate b 7or anhydrous salt71 and vapour1 the system is univariant1 and to each temperature there will correspond a certain1 definite vapour pressure 7the dissociation pressure71 which will be independent of the relative or absolute amounts of the phases1 i4e4 of the amount of hydrate which has already undergone dissociation or dehydration4 ,illustration3 ,,fig4 #ai4 ,the constancy of the dissociation pressure had been proved experimentally by several investigators#aee a number of years before the theoretical basis for its necessity had been given4 ,in the case of salts capable of forming more than one hydrate1 we should obtain a series of dissociation curves 7pt-curves71 as in the case of the different hydrates of copper sulphate4 ,in ,fig4 #ai there are represented diagrammatically the vapour-pressure curves of the following univariant systems of copper sulphate and water3-- ,curve ,,oa3 ,cu,s,o#d1e;,h#b,o -- ,cu,s,o#d1c;,h#b,o #b;,h#b,o4 ,curve ,,ob3 ,cu,s,o#d1c;,h#b,o -- ,cu,s,o#d1;,h#b,o #b;,h#b,o4 ,curve ,,oc3 ,cu,s,o#d1;,h#b,o -- ,cu,s,o#d ,h#b,o4 ,let us now follow the changes which take place on #hf increasing the pressure of the aqueous vapour in contact with anhydrous copper sulphate1 the temperature being meanwhile maintained constant4 ,if1 starting from the point ,d1 we slowly add water vapour to the system1 the pressure will gradually rise1 without formation of hydrate taking place2 for at pressures below the curve ,,oc only the anhydrous salt can exist4 ,at ,e1 however1 the hydrate ,cu,s,o#d1;,h#b,o will be formed1 and as there are now three phases present1 viz4 ,cu,s,o#d1 ,cu,s,o#d1;,h#b,o1 and vapour1 the system becomes univariant2 and since the temperature is constant1 the pressure must also be constant4 ,continued addition of vapour will result merely in an increase in the amount of the hydrate1 and a decrease in the amount of the anhydrous salt4 ,when the latter has entirely disappeared1 i4e4 has passed into hydrated salt1 the system again becomes bivariant1 and passes along the line ,,ef2 the pressure gradually increases1 therefore1 until at ,f the hydrate #c;,h#b,o is formed1 and the system again becomes univariant2 the three phases present are ,cu,s,o#d1;,h#b,o1 ,cu,s,o#d1c;,h#b,o1 vapour4 ,the pressure will remain constant1 therefore1 until the hydrate #a;,h#b,o has disappeared1 when it will again increase till ,g is reached2 here the hydrate #e;,h#b,o is formed1 and the pressure once more remains constant until the complete disappearance of the hydrate #c;,h#b,o has taken place4 ,conversely1 on dehydrating ,cu,s,o#d1e;,h#b,o at constant temperature1 we should find that the pressure would maintain the value corresponding to the dissociation pressure of the system ,cu,s,o#d1e;,h#b,o--,cu,s,o#d1c;,h#b,o-- vapour1 until all the hydrate #e;,h#b,o had disappeared2 further removal of water would then cause the pressure to fall abruptly to the pressure of the system ,cu,s,o#d1c;,h#b,o--,cu,s,o#d1;,h#b,o--v apour1 at which value it would again remain constant until the tri-hydrate had passed into the monohydrate1 when a further sudden diminution of the pressure would occur4 ,this behaviour is represented diagrammatically in ,fig4 #bj1 the values of the pressure being those at #ej;deg4 ,efflorescence4--,from ,fig4 #ai we are enabled to predict the conditions under which a given hydrated salt will effloresce when exposed to the air4 ,we have just learned that copper #hg sulphate pentahydrate1 for example1 will not be formed unless the pressure of the aqueous vapour reaches a certain value2 and that conversely1 if the vapour pressure falls below the dissociation pressure of the pentahydrate1 this salt will undergo dehydration4 ,from this1 then1 it is evident that a crystalline salt hydrate will effloresce when exposed to the air1 if the partial pressure of the water vapour in the air is lower than the dissociation pressure of the hydrate4 ,at the ordinary temperature the dissociation pressure of copper sulphate is less than the pressure of water vapour in the air1 and therefore copper sulphate does not effloresce4 ,in the case of sodium sulphate decahydrate1 however1 the dissociation pressure is greater than the normal vapour pressure in a room1 and this salt therefore effloresces4 ,illustration3 ,,fig4 #bj4 ,indefiniteness of the ,vapour ,pressure of a ,hydrate4--,reference has already been made 7p4 #hd71 in the case of the ammonia compounds of the metal chlorides1 to the importance of the solid product of dissociation for the definition of the dissociation pressure4 ,similarly also in the case of a hydrated salt4 ,a salt hydrate in contact with vapour constitutes only a bivariant system1 and can exist therefore at different values of temperature and pressure of vapour1 as is seen from the diagram1 ,fig4 #ai4 ,anhydrous copper sulphate can exist in contact with water vapour at all values of temperature and pressure lying in the field below the curve ,,oc2 and the hydrate ,cu,s,o#d1;,h#b,o can exist in contact with vapour at all values of temperature and pressure in the field ,,boc4 ,similarly1 each of the other hydrates can exist in contact with vapour at different values of temperature and pressure4 ,from the ,phase ,rule1 however1 we learn that1 in order that at a given temperature the pressure of a two-component system #hh may be constant1 there must be three phases present4 ,strictly1 therefore1 we can speak only of the vapour pressure of a system2 and since1 in the cases under discussion1 the hydrates dissociate into a solid and a vapour1 any statement as to the vapour pressure of a hydrate has a definite meaning only when the second solid phase produced by the dissociation is given4 ,the everyday custom of speaking of the vapour pressure of a hydrated salt acquires a meaning only through the assumption1 tacitly made1 that the second solid phase1 or the solid produced by the dehydration of the hydrate1 is the next lower hydrate1 where more hydrates than one exist4 ,that a hydrate always dissociates in such a way that the next lower hydrate is formed is1 however1 by no means certain2 indeed1 cases have been met with where apparently the anhydrous salt1 and not the lower hydrate 7the existence of which was possible71 was produced by the dissociation of the higher hydrate4#aef ,that a salt hydrate can exhibit different vapour pressures according to the solid product of dissociation1 can not only be proved theoretically1 but it has also been shown experimentally to be a fact4 ,thus ,ca,cl#b1f;,h#b,o can dissociate into water vapour and either of two lower hydrates1 each containing four molecules of water of crystallization1 and designated respectively as ,ca,cl#b1d;,h#b,oalpha1 and ,ca,cl#b1d;,h#b,obeta4 ,roozeboom#aeg has shown that the vapour pressure which is obtained differs according to which of these two hydrates is formed1 as can be seen from the following figures3-- ---------------------------------------- ------------------------------- ,pressure of ,system4 ,temperature4 ---------------------------------------- ----------------- ,ca,cl#b1f;,h#b,o2 ,ca,cl#b1 ,ca,cl#b1f;,h#b,o2 ,ca,cl#b1 #d;,h#b,oalpha2 vapour4 #d;,h#b,obeta2 vapour4 ---------------------------------------- ------------------------------ -#ae;deg #j4jbg cm4 #j4jbb cm4 #j #j4jib #j4jgf #aj #j4aib #j4afb #bj #j4cgh #j4cae #be #j4ejh #j4dcb #bi4b -- #j4efg #bi4h #j4fhj -- ---------------------------------------- ----------------------------- #hi ,by reason of the non-recognition of the importance of the solid dissociation product for the definition of the dissociation pressure of a salt hydrate1 many of the older determinations lose much of their value4 ,suspended ,transformation4--,just as in systems of one component we found that a new phase was not necessarily formed when the conditions for its existence were established1 so also we find that even when the vapour pressure is lowered below the dissociation pressure of a system1 dissociation does not necessarily occur4 ,this is well known in the case of ,glauber's salt1 first observed by ,faraday4 ,undamaged crystals of ,na#b,,so#d1aj;,h#b,o could be kept unchanged in the open air1 although the vapour pressure of the system ,na#b,,so#d1aj;,h#b,o--,na#b,,so#d--vapo ur is greater than the ordinary pressure of aqueous vapour in the air4 ,that is to say1 the possibility of the formation of the new phase ,na#b,,so#d was given2 nevertheless this new phase did not appear1 and the system therefore became metastable1 or unstable with respect to the anhydrous salt4 ,when1 however1 a trace of the new phase--the anhydrous salt--was brought in contact with the hydrate1 transformation occurred2 the hydrate effloresced4 ,the possibility of suspended transformation or the non-formation of the new phases must also be granted in the case where the vapour pressure is raised above that corresponding to the system hydrate--anhydrous salt 7or lower hydrate7--vapour2 in this case the formation of the higher hydrate becomes a possibility1 but not a certainty4 ,although there is no example of this known in the case of hydrated salts1 the suspension of the transformation has been observed in the case of the compounds of ammonia with the metal chlorides 7p4 #hb74 ,horstmann1#aeh for example1 found that the pressure of ammonia in contact with #b;,ag,cl1#c,,nh#c could be raised to a value higher than the dissociation pressure of ,ag,cl1#c,,nh#c without this compound being formed4 ,we see1 therefore1 that even when the existence of the higher compound in contact with the lower became possible1 the higher compound was not immediately formed4 ,range of ,existence of ,hydrates4--,in ,fig4 #ai the vapour #ij pressure curves of the different hydrates of copper sulphate are represented as maintaining their relative positions throughout the whole range of temperatures4 ,but this is not necessarily the case4 ,it is possible that at some temperature the vapour pressure curve of a lower hydrate may cut that of a higher hydrate4 ,at temperatures above the point of intersection1 the lower hydrate would have a higher vapour pressure than the higher hydrate1 and would therefore be metastable with respect to the latter4 ,the range of stable existence of the lower hydrate would therefore end at the point of intersection4 ,this appears to be the case with the two hydrates of sodium sulphate1 to which reference will be made later4#aei ,constancy of ,vapour ,pressure and the ,formation of ,compounds4--,we have seen in the case of the salt hydrates that the continued addition of the vapour phase to the system caused an increase in the pressure until at a definite value of the pressure a hydrate is formed2 the pressure then becomes constant1 and remains so1 until one of the solid phases has disappeared4 ,conversely1 on withdrawing the vapour phase1 the pressure remained constant so long as any of the dissociating compound was present1 independently of the degree of the decomposition 7p4 #hf74 ,this behaviour1 now1 has been employed for the purpose of determining whether or not definite chemical compounds are formed4 ,should compounds be formed between the vapour phase and the solid1 then1 on continued addition or withdrawal of the vapour phase1 it will be found that the vapour pressure remains constant for a certain time1 and will then suddenly assume a new value1 at which it will again remain constant4 ,by this method1 ,ramsay#afj found that no definite hydrates were formed in the case of ferric and aluminium oxides1 but that two are formed in the case of lead oxide1 viz4 #b,pb,o1,h#b,o and #c,pb,o1,h#b,o4 ,the method has also been applied to the investigation of the so-called palladium hydride1#afa and the results obtained appear to show that no compound is formed4 ,reference will1 however1 be made to this case later 7,chap4 ,x474 #ia ,measurement of the ,vapour ,pressure of ,hydrates4--,for the purpose of measuring the small pressures exerted by the vapour of salt hydrates1 use is very generally made of a differential manometer called the ,bremer-,frowein tensimeter4#afb ,this apparatus has the form shown in ,fig4 #ba4 ,it consists of a ,u-tube1 the limbs of which are bent close together1 and placed in front of a millimetre scale4 ,the bend of the tube is filled with oil or other suitable liquid1 e4g4 bromonaphthalene4 ,if it is desired to measure the dissociation pressure of1 say1 a salt hydrate1 concentrated sulphuric acid is placed in the flask e1 and a quantity of the hydrate1 well dried and powdered1#afc in the bulb d4 ,the necks of the bulbs d and e are then sealed off4 ,since1 as we have learned1 suspended transformation may occur1 it is advisable to first partially dehydrate the salt1 in order to ensure the presence of the second solid product of dissociation2 the value of the dissociation pressure being independent of the degree of dissociation of the hydrate 7p4 #hf74 ,the small bulbs d and e having been filled1 the apparatus is placed on its side1 so as to allow the liquid to run from the bend of the tube into the bulbs a and b2 it is then exhausted through f by means of a mercury pump1 and sealed off4 ,the apparatus is now placed in a perpendicular position in a thermostat1 and kept at constant temperature until equilibrium is established4 ,since the vapour pressure on the side containing the sulphuric acid may be regarded as zero1 the difference in level of the two surfaces of liquid in the ,u-tube gives directly the dissociation pressure of the hydrate in terms of the particular liquid employed2 if the density of the latter is known1 the pressure can then be calculated to cm4 of mercury4 ,illustration3 ,,fig4 #ba4 99 99 99 99 99 #ib ,,chapter ,,vi ,,solutions ,definition4--,in all the cases which have been considered in the preceding pages1 the different phases--with the exception of the vapour phase--consisted of a single substance of definite composition1 or were definite chemical individuals4#afd ,but this invariability of the composition is by no means imposed by the ,phase ,rule2 on the contrary1 we shall find in the examples which we now proceed to study1 that the participation of phases of variable composition in the equilibrium of a system is in no way excluded4 ,to such phases of variable composition there is applied the term solution4 ,a solution1 therefore1 is to be defined as a homogeneous mixture1 the composition of which can undergo continuous variation within certain limits2 the limits1 namely1 of its existence4#afe ,from this definition we see that the term solution is not restricted to any particular physical state of substances1 but includes within its range not only the liquid1 but also the gaseous and solid states4 ,we may therefore have solutions of gases in liquids1 and of gases in solids2 of liquids in liquids or in solids2 of solids in liquids1 or of solids in solids4 ,solutions of gases in gases are1 of course1 also possible2 since1 however1 gas solutions never give rise to more than one phase1 their #ic treatment does not come within the scope of the ,phase ,rule1 which deals with heterogeneous equilibria4 ,it should also be emphasized that the definition of solution given above1 neither creates nor recognizes any distinction between solvent and dissolved substance 7solute72 and1 indeed1 a too persistent use of these terms and the attempt to permanently label the one or other of two components as the solvent or the solute1 can only obscure the true relationships and aggravate the difficulty of their interpretation4 ,in all cases it should be remembered that we are dealing with equilibria between two components 7we confine our attention in the first instance to such71 the solution being constituted of these components in variable and varying amounts4 ,the change from the case where the one component is in great excess 7ordinarily called the solvent7 to that in which the other component predominates1 may be quite gradual1 so that it is difficult or impossible to say at what point the one component ceases to be the solvent and becomes the solute4 ,the adoption of this standpoint need not1 however1 preclude one from employing the conventional terms solvent and solute in ordinary language1 especially when reference is made only to some particular condition of equilibrium of the system1 when the concentration of the two components in the solution is widely different4 ,,solutions ,,of ,,gases ,,in ,,liquids4 ,as the first class of solutions to which we shall turn our attention1 there may be chosen the solutions of gases in liquids1 or the equilibria between a liquid and a gas4 ,these equilibria really constitute a part of the equilibria to be studied more fully in ,chapter ,,viii42 but since the two-phase systems formed by the solutions of gases in liquids are among the best-known of the two-component systems1 a short section may be here allotted to their treatment4 ,when a gas is passed into a liquid1 absorption takes place to a greater or less extent1 and a point is at length reached when the liquid absorbs no more of the gas2 a condition of equilibrium is attained1 and the liquid is said to be saturated #id with the gas4 ,in the light of the ,phase ,rule1 now1 such a system is bivariant 7two components in two phases72 and two of the variable factors1 pressure1 temperature1 and concentration of the components1 must therefore be chosen in order that the condition of the system may be defined4 ,if the concentration and the temperature are fixed1 then the pressure is also defined2 or under given conditions of temperature and pressure1 the concentration of the gas in the solution must have a definite value4 ,if1 however1 the temperature alone is fixed1 the concentration and the pressure can alter2 a fact so well known that it does not require to be further insisted on4 ,as to the way in which the solubility of a gas in a liquid varies with the pressure1 the ,phase ,rule of course does not state2 but guidance on this point is again yielded by the theorem of van't ,hoff and ,le ,chatelier4 ,since the absorption of a gas is in all cases accompanied by a diminution of the total volume1 this process must take place with increase of pressure4 ,this1 indeed1 is stated in a quantitative manner in the law of ,henry1 according to which the amount of a gas absorbed is proportional to the pressure4 ,but this law must be modified in the case of gases which are very readily absorbed2 the direction of change of concentration with the pressure will1 however1 still be in accordance with the theorem of ,le ,chatelier4 ,if1 on the other hand1 the pressure is fixed1 then the concentration will vary with the temperature2 and since the absorption of gases is in all cases accompanied by the evolution of heat1 the solubility is found1 in accordance with the theorem of ,le ,chatelier1 to diminish with rise of temperature4 ,in considering the changes of pressure accompanying changes of concentration and temperature1 a distinction must be drawn between the total pressure and the partial pressure of the dissolved gas1 in cases where the solvent is volatile4 ,in these cases1 the law of ,henry applies not to the total pressure of the vapour1 but only to the partial pressure of the dissolved gas4 #ie ,,solutions ,,of ,,liquids ,,in ,,liquids4 ,when mercury and water are brought together1 the two liquids remain side by side without mixing4 ,strictly speaking1 mercury undoubtedly dissolves to a certain extent in the water1 and water no doubt dissolves1 although to a less extent1 in the mercury2 the amount of substance passing into solution is1 however1 so minute1 that it may1 for all practical purposes1 be left out of account1 so long as the temperature does not rise much above the ordinary4#aff ,on the other hand1 if alcohol and water be brought together1 complete miscibility takes place1 and one homogeneous solution is obtained4 ,whether water be added in increasing quantities to pure alcohol1 or pure alcohol be added in increasing amount to water1 at no point1 at no degree of concentration1 is a system obtained containing more than one liquid phase4 ,at the ordinary temperature1 water and alcohol can form only two phases1 liquid and vapour4 ,if1 however1 water be added to ether1 or if ether be added to water1 solution will not occur to an indefinite extent2 but a point will be reached when the water or the ether will no longer dissolve more of the other component1 and a further addition of water on the one hand1 or ether on the other1 will cause the formation of two liquid layers1 one containing excess of water1 the other excess of ether4 ,we shall1 therefore1 expect to find all grades of miscibility1 from almost perfect immiscibility to perfect miscibility1 or miscibility in all proportions4 ,in cases of perfect immiscibility1 the components do not affect one another1 and the system therefore remains unchanged4 ,such cases do not call for treatment here4 ,we have to concern ourselves here only with the second and third cases1 viz4 with cases of complete and of partial miscibility4 ,there is no essential difference between the two classes1 for1 as we shall see1 #if the one passes into the other with change of temperature4 ,the formal separation into two groups is based on the miscibility relations at ordinary temperatures4 ,partial or ,limited ,miscibility4--,in accordance with the ,phase ,rule1 a pure liquid in contact with its vapour constitutes a univariant system4 ,if1 however1 a small quantity of a second substance is added1 which is capable of dissolving in the first1 a bivariant system will be obtained2 for there are now two components and1 as before1 only two phases--the homogeneous liquid solution and the vapour4 ,at constant temperature1 therefore1 both the composition of the solution and the pressure of the vapour can undergo change2 or1 if the composition of the solution remains unchanged1 the pressure and the temperature can alter4 ,if the second 7liquid7 component is added in increasing amount1 the liquid will at first remain homogeneous1 and its composition and pressure will undergo a continuous change2 when1 however1 the concentration has reached a definite value1 solution no longer takes place2 two liquid phases are produced4 ,since there are now three phases present1 two liquids and vapour1 the system is univariant2 at a given temperature1 therefore1 the concentration of the components in the two liquid phases1 as well as the vapour pressure1 must have definite values4 ,addition of one of the components1 therefore1 cannot alter the concentrations or the pressure1 but can only cause a change in the relative amounts of the phases4 ,the two liquid phases can be regarded1 the one as a solution of the component ,i4 in component ,,ii41 the other as a solution of component ,,ii4 in component ,i4 ,if the pressure is maintained constant1 then to each temperature there will correspond a definite concentration of the components in the two liquid phases2 and addition of excess of one will merely alter the relative amounts of the two solutions4 ,as the temperature changes1 the composition of the two solutions will change1 and there will therefore be obtained two solubility curves1 one showing the solubility of component ,i4 in component ,,ii41 the other showing the solubility of component ,,ii4 in component ,i4 ,since heat may be either evolved or absorbed when one liquid dissolves in another1 the solubility may diminish or increase #ig with rise of temperature4 ,the two solutions which at a given temperature correspond to one another are known as conjugate solutions4 ,the solubility relations of partially miscible liquids have been studied by ,guthrie1#afg and more especially by ,alexejeff#afh and by ,rothmund4#afi ,a considerable variety of curves have been obtained1 and we shall therefore discuss only a few of the different cases which may be taken as typical of the rest4 ,phenol and ,water4--,when phenol is added to water at the ordinary temperature1 solution takes place1 and a homogeneous liquid is produced4 ,when1 however1 the concentration of the phenol in the solution has risen to about #h per cent41 phenol ceases to be dissolved2 and a further addition of it causes the formation of a second liquid phase1 which consists of excess of phenol and a small quantity of water4 ,in ordinary language it may be called a solution of water in phenol4 ,if now the temperature is raised1 this second liquid phase will disappear1 and a further amount of phenol must be added in order to produce a separation of the liquid into two layers4 ,in this way1 by increasing the amount of phenol and noting the temperature at which the two layers disappear1 the so-called solubility curve of phenol in water can be obtained4 ,by noting the change of the solubility with the temperature in this manner1 it is found that at all temperatures below #fh4d;deg1 the addition of more than a certain amount of phenol causes the formation of two layers2 at temperatures above this1 however1 two layers cannot be formed1 no matter how much phenol is added4 ,at temperatures above #fh4d;deg1 therefore1 water and phenol are miscible in all proportions4 ,on the other hand1 if water is added to phenol at the ordinary temperature1 a liquid is produced which consists chiefly of phenol1 and on increasing the amount of water beyond a certain point1 two layers are formed4 ,on raising the temperature these two layers disappear1 and a homogeneous solution is again obtained4 ,the phenomena are exactly analogous to those already described4 ,since1 now1 in the second #ih case the concentration of the phenol in the solution gradually decreases1 while in the former case it gradually increases1 a point must at length be reached at which the composition of the two solutions becomes the same4 ,on mixing the two solutions1 therefore1 one homogeneous liquid will be obtained4 ,but the point at which two phases become identical is called a critical point1 so that1 in accordance with this definition1 the temperature at which the two solutions of phenol and water become identical may be called the critical solution temperature1 and the concentration at this point may be called the critical concentration4 ,illustration3 ,,fig4 #bb4 ,from what has been said above1 it will be seen that at any temperature below the critical solution temperature1 two conjugate solutions containing water and phenol in different concentration can exist together1 one containing excess of water1 the other excess of phenol4 ,the following table gives the composition of the two layers1 and the values are represented graphically in ,fig4 #bb4agj ,,phenol ,,and ,,water4 ,c#a is the percentage amount of phenol in the first layer4 ,c#b second layer4 ----------------------------- ,temperature4 ,c#a4 ,c#b4 ----------------------------- #bj;deg #h4e #gb4b #cj;deg #h4g #fi4i #dj;deg #i4g #ff4h #ej;deg #ab4j #fb4g #ee;deg #ad4b #fj4j #fj;deg #ag4e #ef4b #fe;deg #bb4g #di4g #fh4d;deg #cf4a #cf4a ----------------------------- #ii ,the critical solution temperature for phenol and water is #fh4d;deg1 the critical concentration #cf4a per cent4 of phenol4 ,at all temperatures above #fh4d;deg1 only homogeneous solutions of phenol and water can be obtained2 water and phenol are then miscible in all proportions4 ,at the critical solution point the system exists in only two phases--liquid and vapour4 ,it ought1 therefore1 to possess two degrees of freedom4 ,the restriction is1 however1 imposed that the composition of the two liquid phases1 coexisting at a point infinitely near to the critical point1 becomes the same1 and this disposes of one of the degrees of freedom4 ,the system is therefore univariant2 and at a given temperature the pressure will have a definite value4 ,conversely1 if the pressure is fixed 7as is the case when the system is under the pressure of its own vapour71 then the temperature will also be fixed2 that is1 the critical solution temperature has a definite value depending only on the substances4 ,if the vapour phase is omitted1 the temperature will alter with the pressure2 in this case1 however1 as in the case of other condensed systems1 the effect of pressure is slight4 ,from ,fig4 #bb it is easy to predict the effect of bringing together water and phenol in any given quantities at any temperature4 ,start with a solution of phenol and water having the composition represented by the point x4 ,if to this solution phenol is added at constant temperature1 it will dissolve1 and the composition of the solution will gradually change1 as shown by the dotted line xy4 ,when1 however1 the concentration has reached the value represented by the point y1 two liquid layers will be formed1 the one solution having the composition represented by y1 the other that represented by y'4 ,the system is now univariant1 and on further addition of phenol1 the composition of the two liquid phases will remain unchanged1 but their relative amounts will alter4 ,the phase richer in phenol will increase in amount2 that richer in water will decrease1 and ultimately disappear1 and there will remain the solution y'4 ,continued addition of phenol will then lead to the point x'1 there being now only one liquid phase present4 ,since the critical solution point represents the highest temperature at which two liquid phases consisting of phenol and #ajj water can exist together1 these two substances can be brought together in any amount whatever at temperatures higher than #fh4d;deg1 without the formation of two layers4 ,it will therefore be possible to pass from a system represented by x to one represented by x'1 without at any time two liquid phases appearing4 ,starting with x1 the temperature is first raised above the critical solution temperature2 phenol is then added until the concentration reaches the point x#b4 ,on allowing the temperature to fall1 the system will then pass into the condition represented by x'4 ,illustration3 ,,fig4 #bc4 ,methylethylketone and ,water4--,in the case just described1 the solubility of each component in the other increased continuously with the temperature4 ,there are1 however1 cases where a maximum or minimum of solubility is found1 e4g4 methylethylketone and water4 ,the curve which represents the equilibria between these two substances is given in ,fig4 #bc1 the concentration values being contained in the following table3#aga-- ,,methylethylketone ,,and ,,water4 ---------------------------------------- -------- ,temperature4 ,c#a per cent4 ,c#b per cent4 ---------------------------------------- -------- -#aj;deg #cd4e #hi4g #aj;deg #bf4a #ij4j #cj;deg #ba4i #hi4i #ej;deg #ag4e #hi4j #gj;deg #af4b #he4g #ij;deg #af4a #hd4h #aaj;deg #ag4g #hj4j #acj;deg #ba4h #ga4i #adj;deg #bf4j #fd4j #aea4h;deg #dd4b #dd4b ---------------------------------------- -------- #aja ,these numbers and ,fig4 #bc show clearly the occurrence of a minimum in the solubility of the ketone in water1 and also a minimum 7at about #aj;deg7 in the solubility of water in methylethylketone4 ,minima of solubility have also been found in other cases4 ,illustration3 ,,fig4 #bd4 ,triethylamine and ,water4--,although in most of the cases studied the solubility of one liquid in another increases with rise of temperature1 this is not so in all cases4 ,thus1 at temperatures below #ah;deg1 triethylamine and water mix together in all proportions2 but1 on raising the temperature1 the homogeneous solution becomes turbid and separates into two layers4 ,in this case1 therefore1 the critical solution temperature is found in the direction of lower temperature1 not in the direction of higher4#agb ,this behaviour is clearly shown by the graphic representation in ,fig4 #bd1 and also by the numbers in the following table3-- ,,triethylamine ,,and ,,water4 ---------------------------------------- ------ ,temperature4 ,c#a per cent4 ,c#b per cent4 ---------------------------------------- ------ #gj;deg #a4f -- #ej;deg #b4i -- #cj;deg #e4f #if #be;deg #g4c #ie4e #bj;deg #ae4e #gc _/-#ah4e;deg _/-#cj _/-#cj ---------------------------------------- ------ ,general ,form of ,concentration-,temperature ,curve4--,from the preceding figures it will be seen that the general #ajb form of the solubility curve is somewhat parabolic in shape2 in the case of triethylamine and water1 the closed end of the curve is very flat4 ,since for all liquids there is a point 7critical point7 at which the liquid and gaseous states become identical1 and since all gases are miscible in all proportions1 it follows that there must be some temperature at which the liquids become perfectly miscible4 ,in the case of triethylamine and water1 which has just been considered1 there must therefore be an upper critical solution temperature1 so that the complete solubility relations would be represented by a closed curve of an ellipsoidal aspect4 ,an example of such a curve is furnished by nicotine and water4 ,at temperatures below #fj;deg and above #baj;deg1 nicotine and water mix in all proportions4#agc ,although it is possible that this is the general form of the curve for all pairs of liquids1 there are as yet insufficient data to prove it4 ,with regard to the closed end of the curve it may be said that it is continuous2 the critical solution point is not the intersection of two curves1 for such a break in the continuity of the curve could occur only if there were some discontinuity in one of the phases4 ,no such discontinuity exists4 ,the curve is1 therefore1 not to be considered as two solubility curves cutting at a point2 it is a curve of equilibrium between two components1 and so long as the phases undergo continuous change1 the curve representing the equilibrium must also be continuous4 ,as has already been emphasized1 a distinction between solvent and solute is merely conventional 7p4 #ic74 ,pressure-,concentration ,diagram4--,in considering the pressure-concentration diagram of a system of two liquid components1 a distinction must be drawn between the total pressure of the system and the partial pressures of the components4 ,on studying the total pressure of a system1 it is found that two cases can be obtained4#agd ,so long as there is only one liquid phase1 the system is bivariant4 ,the pressure therefore can change with the concentration and the temperature4 ,if the temperature is maintained #ajc constant1 the pressure will vary only with the concentration1 and this variation can therefore be represented by a curve4 ,if1 however1 two liquid phases are formed1 the system becomes univariant3 and if one of the variables1 say the temperature1 is arbitrarily fixed1 the system no longer possesses any degree of freedom4 ,when two liquid phases are formed1 therefore1 the concentrations and the vapour pressure have definite values1 which are maintained so long as the two liquid phases are present2 the temperature being supposed constant4 ,in ,fig4 #be is given a diagrammatic representation of the two kinds of pressure-concentration curves which have so far been obtained4 ,in the one case1 the vapour pressure of the invariant system 7at constant temperature7 lies higher than the vapour pressure of either of the pure components2 a phenomenon which is very generally found in the case of partially miscible liquids1 e4g4 ether and water4#age ,accordingly1 by the addition of water to ether1 or of ether to water1 there is an increase in the total vapour pressure of the system4 ,illustration3 ,,fig4 #be4 ,with regard to the second type1 the vapour pressure of the systems with two liquid phases lies between that of the two single components4 ,an example of this is found in sulphur dioxide and water4#agf ,on adding sulphur dioxide to water there is an increase of the total vapour pressure2 but on adding water to liquid sulphur dioxide1 the total vapour pressure is diminished4 ,the case that the vapour pressure of the system with two #ajd liquid phases is less than that of each of the components is not possible4 ,with regard to the partial pressure of the components1 the behaviour is more uniform4 ,the partial pressure of one component is in all cases lowered by the addition of the other component1 the diminution being approximately proportional to the amount added4 ,if two liquid phases are present1 the partial pressure of the components1 as well as the total pressure1 is constant1 and is the same for both phases4 ,that is to say1 in the case of the two liquids1 saturated solution of water in ether1 and of ether in water1 the partial pressure of the ether in the vapour in contact with the one solution is the same as that in the vapour over the other solution4#agg ,complete ,miscibility4--,although the phenomena of complete miscibility are here treated under a separate heading1 it must not be thought that there is any essential difference between those cases where the liquids exhibit limited miscibility and those in which only one homogeneous solution is formed4 ,as has been already pointed out1 the solubility relations alter with the temperature2 and liquids which at one temperature can dissolve in one another only to a limited extent1 are found at some other temperature to possess the property of complete miscibility4 ,conversely1 we may expect that liquids which at one temperature1 say at the ordinary temperature1 are miscible in all proportions1 will be found at some other temperature to be only partially miscible4 ,thus1 for example1 it was found by ,guthrie that ethyl alcohol and carbon disulphide1 which are miscible in all proportions at the ordinary temperature1 possess only limited miscibility at temperatures below -#ad4d;deg4#agh ,nevertheless1 it is doubtful if the critical solution temperature is in all cases experimentally realizable4 ,pressure-,concentration ,diagram4--,since1 in the cases of complete miscibility of two liquid components1 there are never more than two phases present1 the system must always be bivariant2 and two of the variables pressure1 temperature or concentration of the components1 must be arbitrarily chosen #aje before the system becomes defined4 ,for this reason the ,phase ,rule affords only a slight guidance in the study of such equilibria2 and we shall therefore not enter in detail into the behaviour of these homogeneous mixtures4 ,all that the ,phase ,rule can tell us in connection with these solutions1 is that at constant temperature the vapour pressure of the solution varies with the composition of the liquid phase2 and if the composition of the liquid phase remains unchanged1 the pressure also must remain unchanged4 ,this constancy of composition is exhibited not only by pure liquids1 but also by liquid solutions in all cases where the vapour pressure of the solution reaches a maximum or minimum value4 ,this is the case1 for example1 with mixtures of constant boiling point4#agi 99 99 99 99 99 #ajf ,,chapter ,,vii ,,solutions ,,of ,,solids ,,in ,,liquids1 ,,only ,,one ,,of ,,the ,,components ,,being ,,volatile ,general4--,when a solid is brought into contact with a liquid in which it can dissolve1 a certain amount of it passes into solution2 and the process continues until the concentration reaches a definite value independent of the amount of solid present4 ,a condition of equilibrium is established between the solid and the solution2 the solution becomes saturated4 ,since the number of components is two1 and the number of phases three1 viz4 solid1 liquid solution1 vapour1 the system is univariant4 ,if1 therefore1 one of the factors1 pressure1 temperature1 or concentration of the components 7in the solution#ahj71 is arbitrarily fixed1 the state of the system becomes perfectly defined4 ,thus1 at any given temperature1 the vapour pressure of the system and the concentration of the components have a definite value4 ,if the temperature is altered1 the vapour pressure and also1 in general1 the concentration will undergo change4 ,likewise1 if the pressure varies1 while the system is isolated so that no heat can pass between it and its surroundings1 the concentration and the temperature must also undergo variation until they attain values corresponding to the particular pressure4 ,that the temperature has an influence1 sometimes a very considerable influence1 on the amount of substance passing into solution1 is sufficiently well known2 the effect of pressure1 although less apparent1 is no less certain4 ,if at any given temperature the volume of the vapour phase is diminished1 #ajg vapour will condense to liquid1 in order that the pressure may remain constant1 and so much of the solid will pass into solution that the concentration may remain unchanged2 for1 so long as the three phases are present1 the state of the system cannot alter4 ,if1 however1 one of the phases1 e4g4 the vapour phase1 disappears1 the system becomes bivariant2 at any given temperature1 therefore1 there may be different values of concentration and pressure4 ,the direction in which change of concentration will occur with change of pressure can be predicted by means of the theorem of ,le ,chatelier1 if it is known whether solution is accompanied by increase or diminution of the total volume4 ,if diminution of the total volume of the system occurs on solution1 increase of pressure will increase the solubility2 in the reverse case1 increase of pressure will diminish the solubility4 ,this conclusion has also been verified by experiment1 as is shown by the following figures4#aha ---------------------------------------- ----------------------- ,change of ,solubility 7at #ah;deg7 7grams salt volume by in #a gram of solution74 dissolving #a gm4--------------------------- ,salt4 of salt in the saturated ,pressure ,pressure solution4 #a atm4 #ejj atm4 ---------------------------------------- -------------------- ,sodium chloride -#j4jg #j4bfd #j4bgj ,ammonium chloride #j4aj #j4bgb #j4beh ,alum -#j4jfg #j4aae #j4adb 7p #djj atm47 ---------------------------------------- --------------------- ,as can be seen1 a large increase of the pressure brings about a no more than appreciable alteration of the solubility2 a result which is due1 as in the case of the alteration of the fusion point with the pressure1 to the small change in volume accompanying solution or increase of pressure4 ,for all practical purposes1 therefore1 the solubility as determined under atmospheric pressure may be taken as equal to the true #ajh solubility1 that is1 the solubility when the system is under the pressure of its own vapour4 ,the ,saturated ,solution4--,from what has been said above1 it will be seen that the condition of saturation of a solution can be defined only with respect to a certain solid phase2 if no solid is present1 the system is undefined1 for it then consists of only two phases1 and is therefore bivariant4 ,under such circumstances not only can there be at one given temperature solutions of different concentration1 all containing less of one of the components than when that component is present in the solid form1 but there can also exist solutions containing more of that component than corresponds to the equilibrium when the solid is present4 ,in the former case the solutions are unsaturated1 in the latter case they are supersaturated with respect to a certain solid phase2 in themselves1 the solutions are stable1 and are neither unsaturated nor supersaturated4 ,further1 if the solid substance can exist in different allotropic modifications1 the particular form of the substance which is in equilibrium with the solution must be known1 in order that the statement of the solubility may be definite2 for each form has its own solubility1 and1 as we shall see presently1 the less stable form has the greater solubility 7cf4 p4 #dg74 ,in all determinations of the solubility1 therefore1 not only must the concentration of the components in the solution be determined1 but equal importance should be attached to the characterisation of the solid phase present4 ,in this connection1 also1 one other point may be emphasised4 ,for the production of the equilibrium between a solid and a liquid1 time is necessary1 and this time not only varies with the state of division of the solid and the efficiency of the stirring1 but is also dependent on the nature of the substance4#ahb ,considerable care must therefore be taken that sufficient time is allowed for equilibrium to be established4 ,such care is more especially needful when changes may occur in the solid phase1 and neglect of it has greatly diminished the value of many of the older determinations of solubility4 ,form of the ,solubility ,curve4--,the solubility curve--that #aji is1 the curve representing the change of concentration of the components in the solution with the temperature--differs markedly from the curve of vapour pressure 7p4 #fc71 in that it possesses no general form1 but may vary in the most diverse manner4 ,not only may the curve have an almost straight and horizontal course1 or slope or curve upwards at varying angles2 but it may even slope downwards1 corresponding to a decrease in the solubility with rise of temperature2 may exhibit maxima or minima of solubility1 or may1 as in the case of some hydrated salts1 pass through a point of maximum temperature4 ,in the latter case the salt may possess two values of solubility at the same temperature4 ,we shall consider these cases in the following chapter4 ,illustration3 ,,fig4 #bf4 ,the great variety of form shown by solubility curves is at once apparent from ,fig4 #bf1 in which the solubility curves of various substances 7not1 however1 drawn to scale7 are reproduced4#ahc ,varied as is the form of the solubility curve1 its direction1 nevertheless1 can be predicted by means of the theorem of van't ,hoff and ,le ,chatelier2 for in accordance with that theorem 7p4 #eg7 increase of solubility with the temperature must occur in those cases where the process of solution is accompanied by an absorption of heat2 and a decrease in the solubility with rise of temperature will be found in cases where solution occurs with evolution of heat4 ,where there is no heat effect accompanying solution1 #aaj change of temperature will be without influence on the solubility2 and if the sign of the heat of solution changes1 the direction of the solubility curve must also change1 i4e4 must show a maximum or minimum point4 ,this has in all cases been verified by experiment4#ahd ,in applying the theorem of ,le ,chatelier to the course of the solubility curve1 it should be noted that by heat of solution there is meant1 not the heat effect produced on dissolving the salt in a large amount of solvent 7which is the usual signification of the expression71 but the heat which is absorbed or evolved when the salt is dissolved in the almost saturated solution 7the so-called last heat of solution74 ,not only does the heat effect in the two cases have a different value1 but it may even have a different sign4 ,a striking example of this is afforded by cupric chloride1 as the following figures show3#ahe-- ---------------------------------------- ------------------- ,number of gram-molecules of ,cu,cl#b1 #b;,h#b,o dissolved in #aih ,heat effect4 gram-molecules of water4 ---------------------------------------- ------------------ #a #cg ,k #b4jb #ff #d4ae #aje #g4jg #aag #i4ie #aag #aa #ia #ah4h -#aj #ai4f -#ca #bd4ge -#aih ---------------------------------------- -------------------- ,in the above table the positive sign indicates evolution of heat1 the negative sign1 absorption of heat2 and the values of the heat effect are expressed in centuple calories4 ,judging from the heat effect produced on dissolving cupric chloride in a large bulk of water1 we should predict that the solubility of that salt would diminish with rise of temperature2 as a matter of fact1 it increases4 ,this is in accordance with the fact that #aaa the last heat of solution is negative 7as expressed above71 i4e4 solution of the salt in the almost saturated solution is accompanied by absorption of heat4 ,we are led to expect this from the fact that the heat of solution changes sign from positive to negative as the concentration increases2 experiment also showed it to be the case4 ,despite its many forms1 it should be particularly noted that the solubility curve of any substance is continuous1 so long as the solid phase1 or solid substance in contact with the solution1 remains unchanged4 ,if any break or discontinuous change in the direction of the curve occurs1 it is a sign that the solid phase has undergone alteration4 ,conversely1 if it is known that a change takes place in the solid phase1 a break in the solubility curve can be predicted4 ,we shall presently meet with examples of this4#ahf ,a4--,,anhydrous ,,salt ,,and ,,water4 ,the ,solubility ,curve4--,in studying the equilibria in those systems of two components in which the liquid phase is a solution or phase of varying composition1 we shall in the present chapter limit the discussion to those cases where no compounds are formed1 but where the components crystallise out in the pure state4 ,since some of the best-known examples of such systems are yielded by the solutions of anhydrous salts in water1 we shall first of all briefly consider some of the results which have been obtained with them4 ,for the most part the solubility curves have been studied only at temperatures lying between #j;deg and #ajj;deg1 the solid phase in contact with the solution being the anhydrous salt4 ,for the representation of these equilibria1 the concentration-temperature #aab diagram is employed1 the concentration being expressed as the number of grams of the salt dissolved in #ajj grams of water1 or as the number of gram-molecules of salt in #ajj gram-molecules of water4 ,the curves thus obtained exhibit the different forms to which reference has already been made4 ,so long as the salt remains unchanged the curve will be continuous1 but if the salt alters its form1 then the solubility curve will show a break4 ,illustration3 ,,fig4 #bg4 ,now1 we have already seen in ,chapter ,,iii4 that certain substances are capable of existing in various crystalline forms1 and these forms are so related to one another that at a given temperature the relative stability of each pair of polymorphic forms undergoes change4 ,since each crystalline variety of a substance must have its own solubility1 there must be a break in the solubility curve at the temperature of transition of the two enantiotropic forms4 ,at this point the two solubility curves must cut1 for since the two forms are in equilibrium with respect to their vapour1 they must also be in equilibrium with respect to their solutions4 ,from the table on p4 #fc it is seen that potassium nitrate1 ammonium nitrate1 silver nitrate1 thallium nitrate1 thallium picrate1 are capable of existing in two or more different enantiotropic crystalline forms1 the range of stability of these forms being limited by definite temperatures 7transition temperature74 ,since the transition point is not altered by a solvent 7provided the latter is not absorbed by the solid phase71 we should find on studying the solubility of these substances in water that the solubility curve would exhibit a change in direction at the temperature of transition4 ,as a matter of fact this has been verified1 more especially in the case of ammonium nitrate#ahg #aac and thallium picrate4#ahh ,the following table contains the values of the solubility of ammonium nitrate obtained by ,mueller and ,kaufmann1 the solubility being expressed in gram-molecules ,,nh#d,,no#c in #ajj gram-molecules of water4 ,in ,fig4 #bg these results are represented graphically4 ,the equilibrium point was approached both from the side of unsaturation and of supersaturation1 and the condition of equilibrium was controlled by determinations of the density of the solution4 ,,solubility ,,of ,,ammonium ,,nitrate4 ---------------------------------------- -------------------- ,temperature4 ,solubility4 ,temperature4 ,solubility4 ---------------------------------------- ----------------- #ab4b;deg #cd4ej #cb4g;deg #eg4ij #bj4b;deg #dc4cj #cd4j;deg #eh4hi #be4je;deg #dh4ai #ce4j;deg #ei4hj #bh4j;deg #ea4hf #cf4j;deg #fa4jj #cj4j;deg #ed4dj #cg4e;deg #fb4ij #cj4b;deg #ed4fa #ch4j;deg #fc4fj #ca4i;deg #eg4bj #ci4j;deg #fe4ji #cb4a;deg #eg4fj #dj4j;deg #ff4hj ---------------------------------------- -------------------- ,from the graphic representation of the solubility given in ,fig4 #bg1 there is seen to be a distinct change in the direction of the curve at a temperature of #cb;deg2 and this break in the curve corresponds to the transition of the beta-rhombic into the alpha-rhombic form of ammonium nitrate 7p4 #fc74 ,suspended ,transformation and ,supersaturation4--,as has already been learned1 the transformation of the one crystalline form into the other does not necessarily take place immediately the transition point has been passed2 and it has therefore been found possible in a number of cases to follow the solubility curve of a given crystalline form beyond the point at which it ceases to be the most stable modification4 ,now1 it will be readily seen from ,fig4 #bg that if the two solubility curves be prolonged beyond the point of intersection1 the solubility of the less stable form is greater than that of the more stable4 ,a solution1 therefore1 which is saturated with respect to the less stable form1 i4e4 which is in equilibrium with that form1 is supersaturated with respect to the more stable modification4 ,if1 #aad therefore1 a small quantity of the more stable form is introduced into the solution1 the latter must deposit such an amount of the more stable form that the concentration of the solution corresponds to the solubility of the stable form at the particular temperature4 ,since1 however1 the solution is now unsaturated with respect to the less stable variety1 the latter1 if present1 must pass into solution2 and the two processes1 deposition of the stable and solution of the metastable form1 must go on until the latter form has entirely disappeared and a saturated solution of the stable form is obtained4 ,there will thus be a conversion1 through the medium of the solvent1 of the less stable into the more stable modification4 ,this behaviour is of practical importance in the determination of transition points 7v4 ,appendix74 ,from the above discussion it will be seen how important is the statement of the solid phase for the definition of saturation and supersaturation4#ahi ,solubility ,curve at ,higher ,temperatures4--,on passing to the consideration of the solubility curves at higher temperatures1 two chief cases must be distinguished4 7#a7 ,the two components in the fused state can mix in all proportions4 7#b7 ,the two components in the fused state cannot mix in all proportions4 #a4 ,complete ,miscibility of the ,fused ,components4 ,illustration3 ,,fig4 #bh4 ,the best example of this which has been studied1 so far as anhydrous salts and water are concerned1 is that of silver nitrate and water4 ,the solubility of this salt at temperatures #aae above #ajj;deg has been studied chiefly by ,etard#aij and by ,tilden and ,shenstone4#aia ,the values obtained by ,etard are given in the following table1 and represented graphically in ,fig4 #bh4 ,,solubility ,,of ,,silver ,,nitrate4 ---------------------------------------- ----------- ,temperature4 ,parts of dry salt in #ajj parts of solution4 ---------------------------------------- ---------- -#g;deg #df4b -#a;deg #eb4a #e;deg #ef4c #aj;deg #fa4b #bj;deg #fg4h #dj4e;deg #gf4h #gc;deg #hd4j #ace;deg #ib4h #ahb;deg #if4i ---------------------------------------- ----------- ,in this figure the composition of the solution is expressed in parts of silver nitrate in #ajj parts by weight of the solution1 so that #ajj per cent4 represents pure silver nitrate4 ,as can be seen1 the solubility increases with the temperature4 ,at a temperature of about #afj;deg there should be a break in the curve due to change of crystalline form 7p4 #fc74 ,such a change in the direction of the solubility curve1 however1 does not in any way alter the essential nature of the relationships discussed here1 and may for the present be left out of account4 ,on following the solubility curve of silver nitrate to higher temperatures1 therefore1 the concentration of silver nitrate in the solution gradually increases1 until at last1 at a temperature of #bjh;deg1#aib the melting point of pure silver nitrate is reached1 and the concentration of the water has become zero4 ,the curve throughout its whole extent represents the equilibrium between silver nitrate1 solution1 and vapour4 ,conversely1 starting with pure silver nitrate in contact with the fused salt1 addition of water will lower the melting point1 i4e4 will lower the temperature at which the solid salt can exist in contact with the liquid2 #aaf and the depression will be all the greater the larger the amount of water added4 ,as the concentration of the water in the liquid phase is increased1 therefore1 the system will pass back along the curve from higher to lower temperatures1 and from greater to smaller concentrations of silver nitrate in the liquid phase4 ,the curve in ,fig4 #bh may1 therefore1 be regarded either as the solubility curve of silver nitrate in water1 or as the freezing point curve for silver nitrate in contact with a solution consisting of that salt and water4 ,as the temperature of the saturated solution falls1 silver nitrate is deposited1 and on lowering the temperature sufficiently a point will at last be reached at which ice also begins to separate out4 ,since there are now four phases co-existing1 viz4 silver nitrate1 ice1 solution1 vapour1 the system is invariant1 and the point is a quadruple point4 ,this quadruple point1 therefore1 forms the lower limit of the solubility curve of silver nitrate4 ,below this point the solution becomes metastable4 ,ice as ,solid ,phase4--,ice melts or is in equilibrium with water at a temperature of #j;deg4 ,the melting point1 will1 however1 be lowered by the solution of silver nitrate in the water2 and the greater the concentration of the salt in the solution the greater will be the depression of the temperature of equilibrium4 ,on continuing the addition of silver nitrate1 a point will at length be reached at which the salt is no longer dissolved1 but remains in the solid form along with the ice4 ,we again obtain1 therefore1 the invariant system ice--salt--solution--vapour4 ,the temperature at which this invariant system can exist has been found by ,middelberg#aic to be -#g4c;deg1 the solution at this point containing #dg4a per cent4 of silver nitrate4 ,the same general behaviour will be found in the case of all other systems of two components belonging to this class2 that is1 in the case of systems from which the components crystallise out in the pure state1 and in which the fused components are miscible in all proportions4 ,in all such cases1 therefore1 the solubility curves 7curves of equilibrium7 can be represented diagrammatically as in ,fig4 #bi4 ,in this figure ,,oa represents the solubility curve of the salt1 and ,,ob the freezing #aag point curve of ice4 ,o is the quadruple point at which the invariant system exists1 and may be regarded as the point of intersection of the solubility curve with the freezing-point curve4 ,since this point is fixed1 the condition of the system as regards temperature1 vapour pressure1 and concentration of the components 7or composition of the solution71 is perfectly definite4 ,from the way1 also1 in which the condition is attained1 it is evident that the quadruple point is the lowest temperature that can be obtained with mixtures of the two components in presence of vapour4 ,it is known as the cryohydric point1 or1 generally1 the eutectic point4#aid ,illustration3 ,,fig4 #bi4 ,cryohydrates4#aie--,on cooling a solution of common salt in water to a temperature of -#c;deg1 ,guthrie observed that the hydrate ,na,cl1#b;,h#b,o separated out4 ,this salt continued to be deposited until at a temperature of -#bb;deg opaque crystals made their appearance1 and the liquid passed into the solid state without change of temperature4 ,a similar behaviour was found by ,guthrie in the case of a large number of other salts1 a temperature below that of the melting point of ice being reached at which on continued withdrawal of heat1 the solution solidified at a constant temperature4 ,when the system had attained this minimum temperature1 it was found that the composition of the solid and the liquid phases was the same1 and remained unchanged throughout the period of solidification4 ,this is shown by the following figures1 which give the composition of different samples of the solid phase deposited from the solution at constant temperature4#aif #aah --------------------------------- ,no4 ,temperature of ,na,cl4 solidification4 ,per cent4 ------------------------------- #a -#ba;deg to -#bb;deg #bc4gb #b -#bb;deg #bc4ff #c -#bb;deg #bc4gc #d -#bc;deg #bc4hb #e -#bc;deg #bc4cd #f -#bc;deg #bc4ce --------------------------------- ,mean #bc4f --------------------------------- ,conversely1 a mixture of ice and salt containing #bc4f per cent4 of sodium chloride will melt at a definite and constant temperature1 and exhibit1 therefore1 a behaviour supposed to be characteristic of a pure chemical compound4 ,this1 then1 combined with the fact that the solid which was deposited was crystalline1 and that the same constant temperature was attained1 no matter with what proportions of water and salt one started1 led ,guthrie to the belief that the solids which thus separated at constant temperature were definite chemical compounds1 to which he gave the general name cryohydrate4 ,a large number of such cryohydrates were prepared and analysed by ,guthrie1 and a few of these are given in the following table1 together with the temperature of the cryohydric point3#aig-- ,,cryohydrates4 ---------------------------------------- -------------------------- ,salt4 ,cryohydric point4 ,percentage of anhydrous salt in the cryohydrate4 ---------------------------------------- -------------------------- ,sodium bromide -#bd;deg #da4cc ,sodium chloride -#bb;deg #bc4fj ,potassium iodide -#bb;deg #eb4jg ,sodium nitrate -#ag4e;deg #dj4hj ,ammonium sulphate -#ag;deg #da4gj ,ammonium chloride -#ae;deg #ai4bg ,sodium iodide -#ae;deg #ei4de ,potassium bromide -#ac;deg #cb4ae ,potassium chloride -#aa4d;deg #bj4jc ,magnesium sulphate -#e;deg #ba4hf ,potassium nitrate -#b4f;deg #aa4bj ,sodium sulphate -#j4g;deg #d4ee ---------------------------------------- -------------------------- #aai ,the chemical individuality of these cryohydrates was1 however1 called in question by ,pfaundler1#aih and disproved by ,offer1#aii who showed that in spite of the constancy of the melting point1 the cryohydrates had the properties1 not of definite chemical compounds1 but of mixtures2 the arguments given being that the heat of solution and the specific volume are the same for the cryohydrate as for a mixture of ice and salt of the same composition2 and it was further shown that the cryohydrate had not a definite crystalline form1 but separated out as an opaque mass containing the two components in close juxtaposition4 ,the heterogeneous nature of cryohydrates can also be shown by a microscopical examination4 ,at the cryohydric point1 therefore1 we are not dealing with a single solid phase1 but with two solid phases1 ice and salt2 the cryohydric point1 therefore1 as already stated1 is a quadruple point and represents an invariant system4 ,although on cooling a solution to the cryohydric point1 separation of ice may occur1 it will not necessarily take place2 the system may become metastable4 ,similarly1 separation of salt may not take place immediately the cryohydric point is reached4 ,it will1 therefore1 be possible to follow the curves ,,bo and ,,ao beyond the quadruple point1#bjj which is thereby clearly seen to be the point of intersection of the solubility curve of the salt and the freezing-point curve of ice4 ,at this point1 also1 the curves of the univariant systems ice--salt--vapour and ice--salt--solution intersect4 ,changes at the ,quadruple ,point4--,since the invariant system ice--salt--solution--vapour can exist only at a definite temperature1 addition or withdrawal of heat must cause the disappearance of one of the phases1 whereby the system will become univariant4 ,so long as all four phases are present the temperature1 pressure1 and concentration of the components in the solution must remain constant4 ,when1 therefore1 heat is added to or withdrawn from the system1 mutually compensatory changes will take place within the system whereby the #abj condition of the latter is preserved4 ,these changes can in all cases be foreseen with the help of the theorem of van't ,hoff and ,le ,chatelier2 and1 after what was said in ,chap4 ,,iv41 need only be briefly referred to here4 ,in the first place1 addition of heat will cause ice to melt1 and the concentration of the solution will be thereby altered2 salt must therefore dissolve until the original concentration is reached1 and the heat of fusion of ice will be counteracted by the heat of solution of the salt4 ,changes of volume of the solid and liquid phases must also be taken into account2 an alteration in the volume of these phases being compensated by condensation or evaporation4 ,all four phases will therefore be involved in the change1 and the final state of the system will be dependent on the amounts of the different phases present2 the ultimate result of addition or withdrawal of heat or of change of pressure at the quadruple point will be one of the four univariant systems3 ice--solution--vapour2 salt--solution--vapour2 ice--salt--vapour2 ice--salt--solution4 ,if the vapour phase disappear1 there will be left the univariant system ice--salt--solution1 and the temperature at which this system can exist will alter with the pressure4 ,since in this case the influence of pressure is comparatively slight1 the temperature of the quadruple point will differ only slightly from that of the cryohydric point as determined under atmospheric pressure4 ,freezing ,mixtures4--,not only will the composition of a univariant system undergo change when the temperature is varied1 but1 conversely1 if the composition of the system is caused to change1 corresponding changes of temperature must ensue4 ,thus1 if ice is added to the univariant system salt--solution--vapour1 the ice must melt and the temperature fall2 and if sufficient ice is added1 the temperature of the cryohydric point must be at length reached1 for it is only at this temperature that the four phases ice--salt--solution--vapour can coexist4 ,or1 on the other hand1 if salt is added to the system ice--solution--vapour1 the concentration of the solution will increase1 ice must melt1 and the temperature must thereby fall2 and this process also will go on until the cryohydric point is reached4 ,in both cases ice melts and there is a change in the #aba composition of the solution2 in the former case1 salt will be deposited#bja because the solubility diminishes as the temperature falls2 in the latter1 salt will pass into solution4 ,this process may be accompanied either by an evolution or1 more generally1 by absorption of heat2 in the former case the effect of the addition of ice will be partially counteracted2 in the latter case it will be augmented4 ,these principles are made use of in the preparation of freezing mixtures4 ,the lowest temperature which can be reached by means of these 7under atmospheric pressure7 is the cryohydric point4 ,this temperature-minimum is1 however1 not always attained in the preparation of a freezing mixture1 and that for various reasons4 ,the chief of these are radiation and the heat absorbed in cooling the solution produced4 ,the lower the temperature falls1 the more rapid does the radiation become2 and the rate at which the temperature sinks decreases as the amount of solution increases4 ,both these factors counteract the effect of the latent heat of fusion and the heat of solution1 so that a point is reached 7which may lie considerably above the cryohydric point7 at which the two opposing influences balance4 ,the absorption of heat by the solution can be diminished by allowing the solution to drain off as fast as it is produced2 and the effect of radiation can be partially annulled by increasing the rate of cooling4 ,this can be done by the more intimate mixing of the components4 ,since1 under atmospheric pressure1 the temperature of the cryohydric point is constant1 the cryohydrates are very valuable for the production of baths of constant low temperature4 #b4 ,partial ,miscibility of the ,fused ,components4 ,on passing to the study of the second class of systems of two components belonging to this group1 namely1 those in which the fused components are not miscible in all proportions1 we find that the relationships are not quite so simple as #abb in the case of silver nitrate and water4 ,in the latter case1 only one liquid phase was possible2 in the cases now to be studied1 two liquid phases can be formed1 and there is a marked discontinuity in the solubility curve on passing from the cryohydric point to the melting point of the second 7non-volatile7 component4 ,paratoluidine dissolves in water1 and the solubility increases as the temperature rises4#bjb ,at #dd4b;deg1 however1 paratoluidine in contact with water melts1 and two liquid phases are formed1 viz4 a solution of water in fused paratoluidine and a solution of fused paratoluidine in water4 ,we have1 therefore1 the phenomenon of melting under the solvent4 ,this melting point will1 of course1 be lower than the melting point of the pure substance1 because the solid is now in contact with a solution1 and1 as we have already seen1 addition of a foreign substance lowers the melting point4 ,such cases of melting under the solvent are by no means rare1 and a review of the relationships met with may1 therefore1 be undertaken here4 ,as an example1 there may be chosen the equilibrium between succinic nitrile1 ,c#b;,h#d7;,,cn7#b and water1 which has been fully studied by ,schreinemakers4#bjc ,illustration3 ,,fig4 #cj4 ,if to the system ice--water at #j;deg succinic nitrile is added1 the temperature will fall2 and continued addition of the nitrile will lead at last to the cryohydric point b 7,fig4 #cj71 at which solid nitrile1 ice1 solution1 and vapour can coexist4 ,the temperature of the cryohydric point is -#a4b;deg1 and the composition of the solution is #a4bi mol4 of nitrile in #ajj mol4 of solution4 ,from a to b the solid phase in contact with the solution is ice4 #abc ,if the temperature be now raised so as to cause the disappearance of the ice1 and the addition of nitrile be continued1 the concentration of the nitrile in the solution will increase as represented by the curve bc4 ,at the point c 7#ah4e;deg71 when the concentration of the nitrile in the solution has increased to #b4e molecules per cent41 the nitrile melts and two liquid phases are formed2 the concentration of the nitrile in these two phases is given by the points c and c'4 ,as there are now four phases present1 viz4 solid nitrile1 solution of fused nitrile in water1 solution of water in fused nitrile1 and vapour1 the system is invariant4 ,since at this point the concentration1 temperature1 and pressure are completely defined1 addition or withdrawal of heat can only cause a change in the relative amounts of the phases1 but no variation of the concentrations of the respective phases4 ,as a matter of fact1 continued addition of nitrile and addition of heat will cause an increase in the amount of the liquid phase containing excess of nitrile 7i4e4 the solution of water in fused nitrile71 whereas the other liquid phase1 the solution of fused nitrile in water1 will gradually disappear4 ,when it has completely disappeared1 the system will be represented by the point c'1 where the molecular concentration of nitrile is now #ge per cent41 and again becomes univariant1 the three phases being solid nitrile1 liquid phase containing excess of nitrile1 and vapour2 and as the amount of the water is diminished the temperature of equilibrium rises1 until at #ed;deg the melting point of the pure nitrile is reached4 ,return now to the point c4 ,at this point there exists the invariant system solid nitrile1 two liquid phases1 vapour4 ,if heat be added1 the solid nitrile will disappear1 and there will be left the univariant system1 consisting of two liquid phases and vapour4#bjd ,such a system will exhibit relationships similar to those already studied in the previous chapter4 ,as the temperature rises1 the mutual solubility of the two fused components becomes greater1 until at d 7#ee4e;deg7 the critical solution temperature is reached1 and the fused components become miscible in all proportions4 ,at all temperatures and concentrations lying to the right #abd of the curve abcdc'e there can be only one liquid phase2 in the field cdc' there are two liquid phases4 ,from the figure it will be easy to see what will be the result of bringing together succinic nitrile and water at different temperatures and in different amounts4 ,since b is the lowest temperature at which liquid can exist in stable equilibrium with solid1 ice and succinic nitrile can be mixed in any proportions at temperatures below b without undergoing change4 ,between b and c succinic nitrile will be dissolved until the concentration reaches the value on the curve bc1 corresponding to the given temperature4 ,on adding the nitrile to water at temperatures between c and d1 it will dissolve until a concentration lying on the curve cd is attained2 at this point two liquid phases will be formed1 and further addition of nitrile will cause the one liquid phase 7that containing excess of nitrile7 to increase1 while the other liquid phase will decrease1 until it finally disappears and there is only one liquid phase left1 that containing excess of nitrile4 ,this can dissolve further quantities of the nitrile1 and the concentration will increase until the curve c'e is reached1 when the concentration will remain unchanged1 and addition of solid will merely increase the amount of the solid phase4 ,if a solution represented by any point in the field lying below the curve bcd is heated to a temperature above d1 the critical solution temperature1 then the concentration of the nitrile can be increased to any desired amount without at any time two liquid phases making their appearance2 the system can then be cooled down to a temperature represented by any point between the curves dc'e4 ,in this way it is possible to pass continuously from a solution containing excess of one component to solutions containing excess of the other1 as represented by the dotted line xxxx 7v4 p4 #ajj74 ,at no point is there formation of two liquid phases4 ,supersaturation4--,just as suspended transformation is rarely met with in the passage from the solid to the liquid state1 so also it is found in the case of the melting of substances under the solvent that suspended fusion does not occur2 but that when the temperature of the invariant point is reached at which1 therefore1 the formation of two liquid layers is possible1 #abe these two liquid layers1 as a matter of fact1 make their appearance4 ,suspended transformation can1 however1 take place from the side of the liquid phase1 just as water or other liquid can be cooled below the normal freezing point without solidification occurring4 ,the question1 therefore1 arises as to the relative solubilities of the solid and the supercooled liquid at the same temperature4 ,illustration3 ,,fig4 #ca4 ,the answer to this question can at once be given from what we have already learned 7p4 #aac71 if we recollect that at temperatures below the point of fusion under the solvent1 the solid form1 at temperatures above that point1 the liquid form1 is the more stable2 at this temperature1 therefore1 the relative stability of the solid and liquid forms changes4 ,since1 as we have already seen1 the less stable form has the greater solubility1 it follows that the supercooled liquid1 being the less stable form1 must have the greater solubility4 ,this was first proved experimentally by ,alexejeff#bje in the case of benzoic acid and water1 the solubility curves for which are given in ,fig4 #ca4 ,as can be seen from the figure1 the prolongation of the curve for liquid--liquid1 which represents the solubility of the supercooled liquid benzoic acid1 lies above that for the solubility of the #abf solid benzoic acid in water2 the solution saturated with respect to the supercooled liquid is therefore supersaturated with respect to the solid form4 ,a similar behaviour has been found in the case of other substances4#bjf ,pressure-,temperature ,diagram4--,having considered the changes which occur in the concentration of the components in a solution with the temperature1 we may conclude the discussion of the equilibrium between a salt and water by studying the variation of the vapour pressure4 ,since in systems of two components the two phases1 solution and vapour1 constitute a bivariant system1 the vapour pressure is undefined1 and may have different values at the same temperature1 depending on the concentration4 ,in order that there may be for each temperature a definite corresponding pressure of the vapour1 a third phase must be present4 ,this condition is satisfied by the system solid--liquid 7solution7--vapour2 that is1 by the saturated solution 7p4 #ajh74 ,in the case of a saturated solution1 therefore1 the pressure of the vapour at any given temperature is constant4 ,vapour ,pressure of ,solid--,solution--,vapour4--,it has long been known that the addition of a non-volatile solid to a liquid in which it is soluble lowers the vapour pressure of the solvent2 and the diminution of the pressure is approximately proportional to the amount of substance dissolved 7,law of ,babo74 ,the vapour-pressure curve1 therefore1 of a solution of a salt in water must lie below that for pure water4 ,further1 in the case of a pure liquid1 the vaporization curve is a function only of the temperature 7p4 #fc71 whereas1 in the case of a solution1 the pressure varies both with the temperature and the concentration4 ,these two factors1 however1 act in opposite directions2 for although the vapour pressure in all cases increases as the temperature rises1 increase of concentration1 as we have seen1 lowers the vapour pressure4 ,again1 since the concentration itself varies with the temperature1 two cases have to be considered1 viz4 where the concentration increases with rise of #abg temperature1 and where the concentration diminishes with rise of temperature4 ,the relations which are found here will be best understood with the help of ,fig4 #cb4bjg ,in this figure1 ,,ob represents the sublimation curve of ice1 and ,,bc the vaporization curve of water2 the curve for the solution must lie below this1 and must cut the sublimation curve of ice at some temperature below the melting point4 ,the point of intersection ,a is the cryohydric point4 ,if the solubility increases with rise of temperature1 the increase of the vapour pressure due to the latter will be partially annulled4 ,since at first the effect of increase of temperature more than counteracts the depressing action of increase of concentration1 the vapour pressure will increase on raising the temperature above the cryohydric point4 ,if the elevation of temperature is continued1 however1 to the melting point of the salt1 the effect of increasing concentration makes itself more and more felt1 so that the vapour-pressure curve of the solution falls more and more below that of the pure liquid1 and the pressure will ultimately become equal to that of the pure salt2 that is to say1 practically equal to zero4 ,the curve will therefore be of the general form ,,amf shown in ,fig4 #cb4 ,if the solubility should diminish with rise of temperature1 the two factors1 temperature and concentration1 will act in the same direction1 and the vapour-pressure curve will rise relatively more rapid than that of the pure liquid2 since1 however1 the pure salt is ultimately obtained1 the vapour-pressure curve must in this case also finally approach the value zero4 ,illustration3 ,,fig4 #cb4 ,other ,univariant ,systems4--,besides the univariant system #abh salt--solution--vapour already considered1 three others are possible1 viz4 ice--solution--vapour1 ice--salt--solution1 and ice--salt--vapour4 ,the fusion point of a substance is lowered1 as we have seen1 by the addition of a foreign substance1 and the depression is all the greater the larger the quantity of substance added4 ,the vapour pressure of the water1 also1 is lowered by the solution in it of other substances1 so that the vapour pressure of the system ice--solution--vapour must decrease as the temperature falls from the fusion point of ice to the cryohydric point4 ,this curve is represented by ,,ba 7,fig4 #cb71 and is coincident with the sublimation curve of ice4 ,this1 at first sight1 strange fact will be readily understood when we consider that since ice and solution are together in equilibrium with the same vapour1 they must have the same vapour pressure4 ,for suppose at any given temperature equilibrium to have been established in the system ice--solution--vapour1 removal of the ice will not alter this equilibrium4 ,suppose1 now1 the ice and the solution placed under a bell-jar so that they have a common vapour1 but are not themselves in contact2 then1 if they do not have the same vapour pressure1 distillation must take place and the solution will become more dilute or more concentrated4 ,since1 at the completion of this process1 the ice and solution are now in equilibrium when they are not in contact1 they must also be in equilibrium when they are in contact 7p4 #cb74 ,but if distillation has taken place the concentration of the solution must have altered1 so that the ice will now be in equilibrium with a solution of a different concentration from before4 ,but according to the ,phase ,rule ice cannot at one and the same temperature be in equilibrium with two solutions of different concentration1 for the system ice--solution--vapour is univariant1 and at any given temperature1 therefore1 not only the pressure but also the concentration of the components in the solution must be constant4 ,distillation could not1 therefore1 take place from the ice to the solution or vice versa2 that is to say1 the solution and the ice must have the same vapour pressure--the sublimation pressure of ice4 ,the reason of the coincidence is the non-volatility of the salt3 had #abi the salt a measurable vapour pressure itself1 the sublimation curve of ice and the curve for ice--solution--vapour would no longer fall together4 ,the curve ,,ao represents the pressures of the system ice--salt--vapour4 ,this curve will also be coincident with the sublimation curve of ice1 on account of the non-volatility of the salt4 ,the equilibria of the fourth univariant system ice--salt--solution are represented by ,,ae4 ,since this is a condensed system1 the effect of a small change of temperature will be to cause a large change of pressure1 as in the case of the fusion point of a pure substance4 ,the direction of this curve will depend on whether there is an increase or diminution of volume on solidification2 but the effect in any given case can be predicted with the help of the theorem of ,le ,chatelier4 ,since the cryohydric point is a quadruple point in a two-component system1 it represents an invariant system4 ,the condition of the system is1 therefore1 completely defined2 the four phases1 ice1 salt1 solution1 vapour1 can co-exist only when the temperature1 pressure1 and concentration of the solution have constant and definite values4 ,addition or withdrawal of heat1 therefore1 can cause no alteration of the condition of the system except a variation of the relative amounts of the phases4 ,addition of heat at constant volume will ultimately lead to the system salt--solution--vapour or the system ice--solution--vapour1 according as ice or salt disappears first4 ,this is readily apparent from the diagram 7,fig4 #cb71 for the systems ice--salt--solution and ice--salt--vapour can exist only at temperatures below the cryohydric point 7provided the curve for ice--salt--solution slopes towards the pressure axis74 ,bivariant ,systems4--,besides the univariant systems already discussed1 various bivariant systems are possible1 the conditions for the existence of which are represented by the different areas of ,fig4 #cb4 ,they are as follows3-- ,area4 ,system4 ,,oamf ,salt--vapour4 ,,cbamf ,solution--vapour2 salt--solution4 ,,eabd ,salt--solution2 ice--solution4 ,,eao ,ice--salt4 #acj ,deliquescence4--,as is evident from ,fig4 #cb1 salt can exist in contact with water vapour at pressures under those represented by ,,oamf4 ,if1 however1 the pressure of the vapour is increased until it reaches a value lying on this curve at temperatures above the cryohydric point1 solution will be formed2 for the curve ,,amf represents the equilibria between salt--solution--vapour4 ,from this1 therefore1 it is clear that if the pressure of the aqueous vapour in the atmosphere is greater than that of the saturated solution of a salt1 that salt will1 on being placed in the air1 form a solution2 it will deliquesce4 ,separation of ,salt on ,evaporation4--,with the help of ,fig4 #cb it is possible to state in a general manner whether or not salt will be deposited when a solution is evaporated under a constant pressure4#bjh ,the curve ,,amf 7,fig4 #cb7 is the vapour-pressure curve of the saturated solutions of the salt1 i4e4 it represents1 as we have seen1 the maximum vapour pressure at which salt can exist in contact with solution and vapour4 ,the dotted line aa represents atmospheric pressure4 ,if1 now1 an unsaturated solution1 the composition of which is represented by the point x1 is heated in an open vessel1 the temperature will rise1 and the vapour pressure of the solution will increase4 ,the system will1 therefore1 pass along a line represented diagrammatically by xx'4 ,at the point x' the vapour pressure of the system becomes equal to #a atm42 and as the vessel is open to the air1 the pressure cannot further rise2 the solution boils4 ,if the heating is continued1 water passes off1 the concentration increases1 and the boiling point rises4 ,the system will therefore pass along the line x'm1 until at the point m solid salt separates out 7provided supersaturation is excluded74 ,the system is now univariant1 and continued heating will no longer cause an alteration of the concentration2 as water passes off1 solid salt will be deposited1 and the solution will evaporate to dryness4 ,if1 however1 the atmospheric pressure is represented not by aa but by bb1 then1 as ,fig4 #cb shows1 the maximum vapour #aca pressure of the system salt--solution--vapour never reaches the pressure of #a atm4 ,further1 since the curve bb lies in the area of the bivariant system solution--vapour there can at no point be a separation of the solid form2 for the system solid--solution--vapour can exist only along the curve ,,amf4 ,on evaporating the solution of a salt in an open vessel1 therefore1 salt can be deposited only if at some temperature the pressure of the saturated solution is equal to the atmospheric pressure4 ,this is found to be the case with most salts4 ,in the case of aqueous solutions of sodium and potassium hydroxide1 however1 the vapour pressure of the saturated solution never reaches the value of #a atm41 and on evaporating these solutions1 therefore1 in an open vessel1 there is no separation of the solid4 ,only a homogeneous fused mass is obtained4 ,if1 however1 the evaporation be carried out under a pressure which is lower than the maximum pressure of the saturated solution1 separation of the solid substance will be possible4 ,general ,summary4--,the systems which have been discussed in the present chapter contained water as one of their components1 and an anhydrous salt as the other4 ,it will1 however1 be clear that the relationships which were found in the case of these will be found also in other cases where it is a question of the equilibria between two components1 which crystallize out in the pure state1 and only one of which possesses a measurable vapour pressure4 ,a similar behaviour will1 for example1 be found in the case of many pairs of organic substances2 and in all cases the equilibria will be represented by a diagram of the general appearance of ,fig4 #bi or ,fig4 #cj4 ,that is to say3 ,starting from the fusion point of component ,i41 the system will pass1 by progressive addition of component ,,ii41 to regions of lower temperature1 until at last the cryohydric or eutectic point is reached4 ,on further addition of component ,,ii41 the system will pass to regions of higher temperature1 the solid phase now being component ,,ii4 ,if the fused components are miscible with one another in all proportions a continuous curve will be obtained leading up to the point of fusion of component ,,ii4 ,slight changes of direction1 it is true1 due to changes in the crystalline form1 may be found along this curve1 #acb but throughout its whole course there will be but one liquid phase4 ,if1 on the other hand1 the fused components are not miscible in all proportions1 then the second curve will exhibit a marked discontinuity1 and two liquid phases will make their appearance4 99 99 99 99 99 #acc ,,chapter ,,viii ,,solutions ,,of ,,solids ,,in ,,liquids1 ,,only ,,one ,,of ,,the ,,components ,,being ,,volatile ,b4--,,hydrated ,,salt ,,and ,,water4 ,in the preceding chapter we discussed the behaviour of systems formed of two components1 only one of which was volatile1 in those cases where the two components separated from solution in the pure state4 ,in the present chapter we shall consider those systems in which combination between the components can occur with the formation of definite compounds2 such as are found in the case of crystalline salt hydrates4 ,since a not inconsiderable amount of study has been devoted to the systems formed by hydrated salts and water1 systems which are of great chemical interest and importance1 the behaviour of these will first call for discussion in some detail1 and it will be found later that the relationships which exist in such systems appear also in a large number of other two-component systems4 ,the systems belonging to this group may be divided into two classes according as the compounds formed possess a definite melting point1 i4e4 form a liquid phase of the same composition1 or do not do so4 ,we shall consider the latter first4 #a4 ,the ,compounds formed do not have a ,definite ,melting ,point4 ,concentration-,temperature ,diagram4--,in the case of salts which can form crystalline hydrates1 the temperature-concentration diagram1 representing the equilibria of the #acd different possible systems1 must necessarily be somewhat more complicated than where no such combination of the components occurs4 ,for1 as has already been pointed out1 each substance has its own solubility curve2 and there will therefore be as many solubility curves as there are solid phases possible1 the curve for each particular solid phase being continuous so long as it remains unchanged in contact with the solution4 ,as an example of the relationships met with in such cases1 we shall first of all consider the systems formed of sodium sulphate and water4 ,illustration3 ,,fig4 #cc4 ,sodium ,sulphate and ,water4--,at the ordinary temperatures1 sodium sulphate crystallises from water with ten molecules of water of crystallisation1 forming ,glauber's salt4 ,on determining the solubility of this salt in water1 it is found that the solubility increases as the temperature rises1 the values of the solubility1 represented graphically by the curve ,,ac 7,fig4 #cc71 being given in the following table4#bji ,the numbers denote grams of sodium sulphate1 calculated as anhydrous salt1 dissolved by #ajj grams of water4 ,,solubility ,,of ,na#b,,so#d1aj;,h#b,o4 -------------------------- ,temperature4 ,solubility4 -------------------------- #j;deg #e4jb #aj;deg #i4jj #ae;deg #ac4bj #ah;deg #af4hj #bj;deg #ai4dj #be;deg #bh4jj #cj;deg #dj4jj #cc;deg #ej4gf #cd;deg #ee4jj -------------------------- #ace ,on continuing the investigation at higher temperatures1 it was found that the solubility no longer increased1 but decreased with rise of temperature4 ,at the same time1 it was observed that the solid phase was now different from that in contact with the solution at temperatures below #cc;deg2 for whereas in the latter case the solid phase was sodium sulphate decahydrate1 at temperatures above #cc;deg the solid phase was the anhydrous salt4 ,the course of the solubility curve of anhydrous sodium sulphate is shown by ,,bd1 and the values of the solubility are given in the following table3--#baj ,,solubility ,,of ,,anhydrous ,,sodium ,,sulphate4 -------------------------- ,temperature4 ,solubility4 -------------------------- #ah;deg #ec4be #bj;deg #eb4gf #be;deg #ea4ec #cj;deg #ej4cg #cc;deg #di4ga #cd;deg #di4ec #cf;deg #di4bg #dj4ae;deg #dh4gh #ej4dj;deg #df4hb -------------------------- ,as is evident from the figure1 the solubility curve which is obtained when anhydrous sodium sulphate is present as the solid phase1 cuts the curve representing the solubility of the decahydrate1 at a temperature of about #cc;deg4 ,if a solution of sodium sulphate which has been saturated at a temperature of about #cd;deg be cooled down to a temperature below #ag;deg1 while care is taken that the solution is protected against access of particles of ,glauber's salt1 crystals of a second hydrate of sodium sulphate1 having the composition ,na#b,,so#d1g;,h#b,o1 separate out4 ,on determining the composition of the solutions in equilibrium with this hydrate at different temperatures1 the following values were obtained1 these values being represented by the curve ,,fe 7,fig4 #cc73-- #acf ,,solubility ,,of ,na#b,,so#d1g;,h#b,o4 -------------------------- ,temperature4 ,solubility4 -------------------------- #j;deg #ai4fb #aj;deg #cj4di #ae;deg #cg4dc #ah;deg #da4fc #bj;deg #dd4gc #be;deg #eb4id #bf;deg #ed4ig -------------------------- ,since1 as has already been stated1 each solid substance has its own solubility curve1 there are three separate curves to be considered in the case of sodium sulphate and water4 ,where two curves cut1 the solution must be saturated with respect to two solid phases2 at the point ,b1 therefore1 the point of intersection of the solubility curve of anhydrous sodium sulphate with that of the decahydrate1 the solution must be saturated with respect to these two solid substances4 ,but a system of two components existing in four phases1 anhydrous salt--hydrated salt--solution--vapour1 is invariant2 and this invariability will remain even if only three phases are present1 provided that one of the factors1 pressure1 temperature1 or concentration of components retains a constant value4 ,this is the case when solubilities are determined in open vessels2 the pressure is then equal to atmospheric pressure4 ,under these circumstances1 then1 the system1 anhydrous sodium sulphate--decahydrate--solution1 will possess no degree of freedom1 and can exist1 therefore1 only at one definite temperature and when the solution has a certain definite composition4 ,the temperature of this point is #cb4dhb;deg on a mercury thermometer1 or #cb4cgi;deg on the hydrogen thermometer4#baa #acg ,suspended ,transformation4--,although it is possible for the anhydrous salt to make its appearance at the temperature of the quadruple point1 it will not necessarily do so2 and it is therefore possible to follow the solubility curve of sodium sulphate decahydrate to a higher temperature4 ,since1 however1 the solubility of the decahydrate at temperatures above the quadruple point is greater than that of the anhydrous salt1 the solution which is saturated with respect to the former will be supersaturated with respect to the latter4 ,on bringing a small quantity of the anhydrous salt in contact with the solution1 therefore1 anhydrous salt will be deposited2 and all the hydrated salt present will ultimately undergo conversion into the anhydrous salt1 through the medium of the solution4 ,in this case1 as in all cases1 the solid phase1 which is the most stable at the temperature of the experiment1 has at that temperature the least solubility4 ,similarly1 the solubility curve of anhydrous sodium sulphate has been followed to temperatures below #cb4e;deg4 ,below this temperature1 however1 the solubility of this salt is greater than that of the decahydrate1 and the saturated solution of the anhydrous salt will therefore be supersaturated for the decahydrate1 and will deposit this salt if a nucleus is added to the solution4 ,from this we see that at temperatures above #cb4e;deg the anhydrous salt is the stable form1 while the decahydrate is unstable 7or metastable72 at temperatures below #cb4e;deg the decahydrate is stable4 ,this temperature1 therefore1 is the transition temperature for decahydrate and anhydrous salt4 ,from ,fig4 #cc we see further that the solubility curve of the anhydrous salt 7which at all temperatures below #cb4e;deg is metastable7 is cut by the solubility curve of the heptahydrate2 and this point of intersection 7at a temperature of #bd4b;deg7 must be the transition point for heptahydrate and anhydrous salt4 ,since at all temperatures the solubility of the heptahydrate is greater than that of the decahydrate1 the former hydrate must be metastable with respect to the latter2 so that throughout its whole course the solubility curve of the heptahydrate #ach represents only metastable equilibria4 ,sodium sulphate1 therefore1 forms only one stable hydrate1 the decahydrate4 ,the solubility relations of sodium sulphate illustrate very clearly the importance of the solid phase for the definition of saturation and supersaturation4 ,since the solubility curve of the anhydrous salt has been followed backwards to a temperature of about #ah;deg1 it is readily seen1 from ,fig4 #cc1 that at a temperature of1 say1 #bj;deg three different saturated solutions of sodium sulphate are possible1 according as the anhydrous salt1 the heptahydrate or the decahydrate1 is present as the solid phase4 ,two of these solutions1 however1 would be metastable and supersaturated with respect to the decahydrate4 ,further1 the behaviour of sodium sulphate and water furnishes a very good example of the fact that a break in the solubility curve occurs when1 and only when1 the solid phase undergoes change4 ,so long as the decahydrate1 for example1 remained unaltered in contact with the solution1 the solubility curve was continuous2 but when the anhydrous salt appeared in the solid phase1 a distinct change in the direction of the solubility curve was observed4 ,dehydration by ,means of ,anhydrous ,sodium ,sulphate4--,the change in the relative stability of sodium sulphate decahydrate and anhydrous salt in presence of water at a temperature of #cb4e;deg explains why the latter salt cannot be employed for dehydration purposes at temperatures above the transition point4 ,the dehydrating action of the anhydrous salt depends on the formation of the decahydrate2 but since at temperatures above #cc;deg the latter is unstable1 and cannot be formed in presence of the anhydrous salt1 this salt cannot1 of course1 effect a dehydration above that temperature4 ,pressure-,temperature ,diagram4--,the consideration of the pressure-temperature relations of the two components1 sodium sulphate and water1 must include not only the vapour pressure of the saturated solutions1 but also that of the crystalline hydrates4 ,the vapour pressures of salt hydrates have already been treated in a general manner 7,chap4 ,v471 so that it is only necessary here to point out the connection between the two classes of systems4 #aci ,in most cases the vapour pressure of a salt hydrate1 i4e4 the vapour pressure of the system hydrate--anhydrous salt 7or lower hydrate7--vapour1 is at all temperatures lower than that of the system anhydrous salt 7or lower hydrate7--solution--vapour4 ,this1 however1 is not a necessity2 and cases are known where the vapour pressure of the former system is1 under certain circumstances1 equal to or higher than that of the latter4 ,an example of this is found in sodium sulphate decahydrate4 ,on heating ,na#b,,so#d1aj;,h#b,o1 a point is reached at which the dissociation pressure into anhydrous salt and water vapour becomes equal to the vapour pressure of the saturated solution of the anhydrous salt1 as is apparent from the following measurements2#bab the differences in pressure being expressed in millimetres of a particular oil4 ,temperature3 #bi4j;deg #cj4hc;deg #ca4gi;deg #cb4ji;deg #cb4ce;deg #cb4f;deg ,difference of pressure3 #bc4h #aj4h #e4f #c4f #a4f #j ,at #cb4f;deg1 therefore1 the vapour pressures of the two systems ,na#b,,so#d1aj;,h#b,o--,na#b,,so#d--vapo ur ,na#b,,so#d--solution--vapour are equal2 at this temperature the four phases1 ,na#b,,so#d1aj;,h#b,o2 ,na#b,,so#d2 solution2 vapour1 can coexist4 ,from this it is evident that when sodium sulphate decahydrate is heated to #cb4f;deg1 the two new phases anhydrous salt and solution will be formed 7suspended transformation being supposed excluded71 and the hydrate will appear to undergo partial fusion2 and during the process of melting the vapour pressure and temperature will remain constant4#bac ,this is1 however1 not a true but a so-called incongruent melting point2 for the composition of the liquid phase is not the same as that of the solid4 ,as has already been pointed out 7p4 #acg71 we are dealing here with the transition point of the decahydrate and anhydrous salt1 i4e4 with the reaction ,na#b,,so#d1aj;,h#b,o -- ,na#b,,so#d #aj;,h#b,o4 ,since at the point of partial fusion of the decahydrate four #adj phases can coexist1 the point is a quadruple point in a two-component system1 and the system at this point is therefore invariant4 ,the temperature of this point is therefore perfectly definite1 and on this account the proposal has been made to adopt this as a fixed point in thermometry4#bad ,the temperature is1 of course1 practically the same as that at which the two solubility curves intersect 7p4 #aab74 ,if1 however1 the vapour phase disappears1 the system becomes univariant1 and the equilibrium temperature undergoes change with change of pressure4 ,the transition curve has been determined by ,tammann1#bae and shown to pass through a point of maximum temperature4 ,illustration3 ,,fig4 #cd4 ,the vapour pressure of the different systems of sodium sulphate and water can best be studied with the help of the diagram in ,fig4 #cd4baf ,the curve ,,abcd represents the vapour-pressure curve of the saturated solution of anhydrous sodium sulphate4 ,,gc is the pressure curve of decahydrate anhydrous salt1 which1 as we have seen1 cuts the curve ,,abcd at the transition temperature1 #cb4f;deg4 ,since at this point the solution is saturated with respect to both the anhydrous salt and the decahydrate1 the vapour-pressure curve of the saturated solution of the latter must also pass through the point ,c4#bag ,as at temperatures below this point the solubility of the decahydrate is less than that of the anhydrous salt1 the vapour pressure of the solution will1 in accordance with ,babo's law 7p4 #abf71 be higher than that of the solution of the anhydrous salt2 which was also found experimentally to be the case 7curve ,,hc74 #ada ,in connection with the vapour pressure of the saturated solutions of the anhydrous salt and the decahydrate1 attention must be drawn to a conspicuous deviation from what was found to hold in the case of one-component systems in which a vapour phase was present 7p4 #ca74 ,there1 it was seen that the vapour pressure of the more stable system was always lower than that of the less stable2 in the present case1 however1 we find that this is no longer so4 ,we have already learned that at temperatures below #cb4e;deg the system decahydrate--solution--vapour is more stable than the system anhydrous salt--solution--vapour2 but the vapour pressure of the latter system is1 as has just been stated1 lower than that of the former4 ,at temperatures above the transition point the vapour pressure of the saturated solution of the decahydrate will be lower than that of the saturated solution of the anhydrous salt4 ,this behaviour depends on the fact that the less stable form is the more soluble1 and that the diminution of the vapour pressure increases with the amount of salt dissolved4 ,with regard to sodium sulphate heptahydrate the same considerations will hold as in the case of the decahydrate4 ,since at #bd;deg the four phases heptahydrate1 anhydrous salt1 solution1 vapour can coexist1 the vapour-pressure curves of the systems hydrate--anhydrous salt--vapour 7curve ,,eb7 and hydrate--solution--vapour 7curve ,,fb7 must cut the pressure curve of the saturated solution of the anhydrous salt at the above temperature1 as represented in ,fig4 #cd by the point ,b4 ,this constitutes1 therefore1 a second quadruple point1 which is1 however1 metastable4 ,from the diagram it is also evident that the dissociation pressure of the heptahydrate is higher than that of the decahydrate1 although it contains less water of crystallization4 ,the system heptahydrate--anhydrous salt--vapour must be metastable with respect to the system decahydrate--anhydrous salt--vapour1 and will pass into the latter4#bah ,whether or not there is a temperature at which the vapour-pressure curves of the two systems intersect1 and below which the heptahydrate becomes the more stable form1 is not known4 #adb ,in the case of sodium sulphate there is only one stable hydrate4 ,other salts are known which exhibit a similar behaviour2 and we shall therefore expect that the solubility relationships will be represented by a diagram similar to that for sodium sulphate4 ,a considerable number of such cases have1 indeed1 been found1#bai and in some cases there is more than one metastable hydrate4 ,this is found1 for example1 in the case of nickel iodate1#bbj the solubility curves for which are given in ,fig4 #ce4 ,as can be seen from the figure1 suspended transformation occurs1 the solubility curves having in some cases been followed to a considerable distance beyond the transition point4 ,one of the most brilliant examples1 however1 of suspended transformation in the case of salt hydrates1 and the sluggish transition from the less stable to the more stable form1 is found in the case of the hydrates of calcium chromate4#bba ,illustration3 ,,fig4 #ce4 ,in the preceding cases1 the dissociation-pressure curve of the hydrated salt cuts the vapour-pressure curve of the saturated #adc solution of the anhydrous salt4 ,it can1 however1 happen that the dissociation-pressure curve of one hydrate cuts the solubility curve1 not of the anhydrous salt1 but of a lower hydrate2 in this case there will be more than one stable hydrate1 each having a stable solubility curve2 and these curves will intersect at the temperature of the transition point4 ,various examples of this behaviour are known1 and we choose for illustration the solubility relationships of barium acetate and its hydrates#bbb 7,fig4 #cf74 ,illustration3 ,,fig4 #cf4 ,at temperatures above #j;deg1 barium acetate can form two stable hydrates1 a trihydrate and a monohydrate4 ,the solubility of the trihydrate increases very rapidly with rise of temperature1 and has been determined up to #bf4a;deg4 ,at temperatures above #bd4g;deg1 however1 the trihydrate is metastable with respect to the monohydrate2 for at this temperature the solubility curve of the latter hydrate cuts that of the former4 ,this is1 therefore1 the transition temperature for the trihydrate and monohydrate4 ,the solubility curve of the monohydrate succeeds that of the trihydrate1 and exhibits a conspicuous point of minimum solubility at about #cj;deg4 ,below #bd4g;deg the #add monohydrate is the less stable hydrate1 but its solubility has been determined to a temperature of #bb;deg4 ,at #da;deg the solubility curve of the monohydrate intersects that of the anhydrous salt1 and this is therefore the transition temperature for the monohydrate and anhydrous salt4 ,above this temperature the anhydrous salt is the stable solid phase4 ,its solubility curve also passes through a minimum4 ,the diagram of solubilities of barium acetate not only illustrates the way in which the solubility curves of the different stable hydrates of a salt succeed one another1 but it has also an interest and importance from another point of view4 ,in ,fig4 #cf there is also shown a faintly drawn curve which is continuous throughout its whole course4 ,this curve represents the solubility of barium acetate as determined by ,krasnicki4#bbc ,since1 however1 three different solid phases can exist under the conditions of experiment1 it is evident1 from what has already been stated 7p4 #aaa71 that the different equilibria between barium acetate and water could not be represented by one continuous curve4 ,another point which these experiments illustrate and which it is of the highest importance to bear in mind is1 that in making determinations of the solubility of salts which are capable of forming hydrates1 it is not only necessary to determine the composition of the solution1 but it is of equal importance to determine the composition of the solid phase in contact with it4 ,in view of the fact1 also1 that the solution equilibrium is in many cases established with comparative slowness1 it is necessary to confirm the point of equilibrium1 either by approaching it from higher as well as from lower temperatures1 or by actually determining the rate with which the condition of equilibrium is attained4 ,this can be accomplished by actual weighing of the dissolved salt or by determinations of the density of the solution1 as well as by other methods4 #ade #b4 ,the ,compounds formed have a ,definite ,melting ,point4 ,in the cases which have just been considered we saw that the salt hydrates on being heated did not undergo complete fusion1 but that a solid was deposited consisting of a lower hydrate or of the anhydrous salt4 ,it has1 however1 been long known that certain crystalline salt hydrates 7e4g4 sodium thiosulphate1 ,na#b,s#b,o#c1e;,h#b,o1 sodium acetate1 ,na,c#b;,h#c,o#b1c;,h#b,o7 melt completely in their water of crystallization1 and yield a liquid of the same composition as the crystalline salt4 ,in the case of sodium thiosulphate pentahydrate the temperature of liquefaction is #ef;deg2 in the case of sodium acetate trihydrate1 #eh;deg4 ,these two salts1 therefore1 have a definite melting point4 ,for the purpose of studying the behaviour of such salt hydrates1 we shall choose not the cases which have just been mentioned1 but two others which have been more fully studied1 viz4 the hydrates of calcium chloride and of ferric chloride4 ,solubility ,curve of ,calcium ,chloride ,hexahydrate4#bbd--;,although calcium chloride forms several hydrates1 each of which possesses its own solubility1 it is nevertheless the solubility curve of the hexahydrate which will chiefly interest us at present1 and we shall therefore first discuss that curve by itself4 ,illustration3 ,,fig4 #cg4 ,the solubility of this salt has been determined from the cryohydric point1 which lies at about -#ee;deg1 up to the melting point of the salt4#bbe ,the solubility increases with rise of temperature1 as is shown by the figures in the following table1 and by the 7diagrammatic7 curve ,,ab in ,fig4 #cg4 ,in the table1 the numbers under the heading solubility denote the number of grams of ,ca,cl#b dissolved in #ajj grams #adf of water2 those under the heading composition1 the number of gram-molecules of water in the solution to one gram-molecule of ,ca,cl#b4 ,,solubility ,,of ,,calcium ,,chloride ,,hexahydrate4 ---------------------------------------- - ,temperature4 ,solubility4 ,composition4 ---------------------------------------- - -#ee;deg #db4e #ad4e -#be;deg #ej4j #ab4c -#aj;deg #ee4j #aa4b #j;deg #ei4e #aj4cg #aj;deg #fe4j #i4di #bj;deg #gd4e #h4bh #be;deg #hb4j #g4eb #bh4e;deg #ij4e #f4ha #bi4e;deg #ie4e #f4df #cj4b;deg #ajb4g #f4jj #bi4f;deg #aji4j #e4gj #bi4b;deg #aab4h #e4da ---------------------------------------- - ,so far as the first portion of the curve is concerned1 it resembles the most general type of solubility curve4 ,in the present case the solubility is so great and increases so rapidly with rise of temperature1 that a point is reached at which the water of crystallization of the salt is sufficient for its complete solution4 ,this temperature is #cj4b;deg2 and since the composition of the solution is the same as that of the solid salt1 viz4 #a mol4 of ,ca,cl#b to #f mols4 of water1 this temperature must be the melting point of the hexahydrate4 ,at this point the hydrate will fuse or the solution will solidify without change of temperature and without change of composition4 ,such a melting point is called a congruent melting point4 ,but the solubility curve of calcium chloride hexahydrate differs markedly from the other solubility curves hitherto considered in that it possesses a retroflex portion1 represented in the figure by ,,bc4 ,as is evident from the figure1 therefore1 calcium chloride hexahydrate exhibits the peculiar and1 as it was at first thought1 impossible behaviour that it can be in equilibrium at one and the same temperature with two different solutions1 one of which contains more1 the other less1 water than the solid hydrate2 for it must be remembered that #adg throughout the whole course of the curve ,,abc the solid phase present in equilibrium with the solution is the hexahydrate4 ,such a behaviour1 however1 on the part of calcium chloride hexahydrate will appear less strange if one reflects that the melting point of the hydrate will1 like the melting point of other substances1 be lowered by the addition of a second substance4 ,if1 therefore1 water is added to the hydrate at its melting point1 the temperature at which the solid hydrate will be in equilibrium with the liquid phase 7solution7 will be lowered2 or if1 on the other hand1 anhydrous calcium chloride is added to the hydrate at its melting point 7or what is the same thing1 if water is removed from the solution71 the temperature at which the hydrate will be in equilibrium with the liquid will also be lowered2 i4e4 the hydrate will melt at a lower temperature4 ,in the former case we have the hydrate in equilibrium with a solution containing more water1 in the latter case with a solution containing less water than is contained in the hydrate itself4 ,it has already been stated 7p4 #aji7 that the solubility curve 7in general1 the equilibrium curve7 is continuous so long as the solid phase remains unchanged2 and we shall therefore expect that the curve ,,abc will be continuous4 ,formerly1 however1 it was considered by some that the curve was not continuous1 but that the melting point is the point of intersection of two curves1 a solubility curve and a fusion curve4 ,although the earlier solubility determinations were insufficient to decide this point conclusively1 more recent investigation has proved beyond doubt that the curve is continuous and exhibits no break4#bbf #adh ,although in taking up the discussion of the equilibria between calcium chloride and water1 it was desired especially to call attention to the form of the solubility curve in the case of salt hydrates possessing a definite melting point1 nevertheless1 for the sake of completeness1 brief mention may be made of the other systems which these two components can form4 ,illustration3 ,,fig4 #ch4 ,besides the hexahydrate1 the solubility curve of which has already been described1 calcium chloride can also crystallize in two different forms1 each of which contains four molecules #adi of water of crystallization2 these are distinguished as alpha-tetrahydrate1 and beta-tetrahydrate4 ,two other hydrates are also known1 viz4 a dihydrate and a monohydrate4 ,the solubility curves of these different hydrates are given in ,fig4 #ch4 ,on following the solubility curve of the hexahydrate from the ordinary temperature upwards1 it is seen that at a temperature of #bi4h;deg represented by the point ,h1 it cuts the solubility curve of the alpha-tetrahydrate4 ,this point is therefore a quadruple point at which the four phases hexahydrate1 alpha-tetrahydrate1 solution1 and vapour can coexist4 ,it is also the transition point for these two hydrates4 ,since1 at temperatures above #bi4h;deg1 the alpha-tetrahydrate is the stable form1 it is evident from the data given before 7p4 #adf71 as also from ,fig4 #ch1 that the portion of the solubility curve of the hexahydrate lying above this temperature represents metastable equilibria4 ,the realization of the metastable melting point of the hexahydrate is1 therefore1 due to suspended transformation4 ,at the transition point1 #bi4h;deg1 the solubility of the hexahydrate and alpha-tetrahydrate is #ajj4f parts of ,ca,cl#b in #ajj parts of water4 ,the retroflex portion of the solubility curve of the hexahydrate extends to only #a;deg below the melting point of the hydrate4 ,at #bi4b;deg crystals of a new hydrate1 beta-tetrahydrate1 separate out1 and the solution1 which now contains #aab4h parts of ,ca,cl#b to #ajj parts of water1 is saturated with respect to the two hydrates4 ,throughout its whole extent the solubility curve ,,edf of the beta-tetrahydrate represents metastable equilibria4 ,the upper limit of the solubility curve of beta-tetrahydrate is reached at #ch4d;deg 7,f71 the point of intersection with the curve for the dihydrate4 ,above #bi4h;deg the stable hydrate is the alpha-tetrahydrate2 and its solubility curve extends to #de4c;deg 7,k71 at which temperature it cuts the solubility curve of the dihydrate4 ,the curve of the latter hydrate extends to #age4e;deg 7,l71 and is then succeeded by the curve for the monohydrate4 ,the solubility curve of the anhydrous salt does not begin until a temperature of about #bfj;deg4 ,the whole diagram1 therefore1 shows a succession of stable hydrates1 a metastable hydrate1 a metastable melting point and retroflex solubility curve4 #aej ,pressure-,temperature ,diagram4--,the complete study of the equilibria between the two components calcium chloride and water would require the discussion of the vapour pressure of the different systems1 and its variation with the temperature4 ,for our present purpose1 however1 such a discussion would not be of great value1 and will therefore be omitted here2 in general1 the same relationships would be found as in the case of sodium sulphate 7p4 #ach71 except that the rounded portion of the solubility curve of the hexahydrate would be represented by a similar rounded portion in the pressure curve4#bbg ,as in the case of sodium sulphate1 the transition points of the different hydrates would be indicated by breaks in the curve of pressures4 ,finally1 mention may again be made of the difference of the pressure of dissociation of the hexahydrate according as it becomes dehydrated to the alpha- or the beta-tetrahydrate 7p4 #hh74 ,the ,indifferent ,point4--,we have already seen that at #cj4b;deg calcium chloride hexahydrate melts congruently1 and that1 provided the pressure is maintained constant1 addition or withdrawal of heat will cause the complete liquefaction or solidification1 without the temperature of the system undergoing change4 ,this behaviour1 therefore1 is similar to1 but is not quite the same as the fusion of a simple substance such as ice2 and the difference is due to the fact that in the case of the hexahydrate the emission of vapour by the liquid phase causes an alteration in the composition of the latter1 owing to the non-volatility of the calcium chloride2 whereas in the case of ice this is1 of course1 not so4 ,consider1 however1 for the present that the vapour phase is absent1 and that we are dealing with the two-phase system solid--solution4 ,then1 since there are two components1 the system is bivariant4 ,for any given value of the pressure1 therefore1 we should expect that the system could exist at different temperatures2 which1 indeed1 is the case4 ,it has1 however1 already been noted that when the composition of the liquid phase becomes the same as that of the solid1 the system then behaves as a univariant system2 for1 at a given pressure1 the system solid--solution can exist only at one temperature1 change of temperature producing complete transformation in #aea one or other direction4 ,the variability of the system has therefore been diminished4 ,this behaviour will perhaps be more clearly understood when one reflects that since the composition of the two phases is the same1 the system may be regarded as being formed of one component1 just as the system ,,nh#d;,cl -- ,,nh#c ,h,cl was regarded as being composed of one component when the vapour had the same total composition as the solid 7p4 #ac74 ,one component in two phases1 however1 constitutes a univariant system1 and we can therefore see that calcium chloride hexahydrate in contact with solution of the same composition will constitute a univariant system4 ,the temperature of equilibrium will1 however1 vary with the pressure2#bbh if the latter is constant1 the temperature will also be constant4 ,a point such as has just been referred to1 which represents the special behaviour of a system of two 7or more7 components1 in which the composition of two phases becomes identical1 is known as an indifferent point1#bbi and it has been shown#bcj that at a given pressure the temperature in the indifferent point is the maximum or minimum temperature possible at the particular pressure#bca 7cf4 critical solution temperature74 ,at such a point a system loses one degree of freedom1 or behaves like a system of the next lower order4 ,the ,hydrates of ,ferric ,chloride4--,a better illustration of the formation of compounds possessing a definite melting point1 and of the existence of retroflex solubility curves1 is afforded by the hydrates of ferric chloride1 which not only possess definite points of fusion1 but these melting points are stable4 ,a very brief description of the relations met with will suffice4#bcb #aeb ,ferric chloride can form no less than four stable hydrates1 viz4 ,fe#b;,cl#f1ab;,h#b,o1 ,fe#b;,cl#f1g;,h#b,o1 ,fe#b;,cl#f1e;,h#b,o1 and ,fe#b;,cl#f1d;,h#b,o1 and each of these hydrates possesses a definite1 stable melting point4 ,on analogy with the behaviour of calcium chloride1 therefore1 we shall expect that the solubility curves of these different hydrates will exhibit a series of temperature maxima2 the points of maximum temperature representing systems in which the composition of the solid and liquid phases is the same4 ,a graphical representation of the solubility relations is given in ,fig4 #ci1 and the composition of the different saturated solutions which can be formed is given in the following tables1 the composition being expressed in molecules of ,fe#b;,cl#f to #ajj molecules of water4 ,the figures printed in thick type refer to transition and melting points4 ,illustration3 ,,fig4 #ci4 #aec ,,composition ,,of ,,the ,,saturated ,,solutions ,,of ,,ferric ,,chloride ,,and ,,its ,,hydrates4 7,the name placed at the head of each table is the solid phase47 ,,ice4 --------------------------- ,temperature4 ,composition4 --------------------------- _/--#ee;deg _/-#b4ge -#dj;deg #b4cg -#bg4e;deg #a4ij -#bj4e;deg #a4fd -#aj;deg #a4jj #j;deg #j --------------------------- ,fe#b;,cl#f1ab;,h#b,o4 --------------------------- ,temperature4 ,composition4 --------------------------- -#ee;deg _/-#b4ge -#da;deg #b4ha -#bg;deg #b4ih #j;deg #d4ac #aj;deg #d4ed #bj;deg #e4aj #cj;deg #e4ic #ce;deg #f4gh #cf4e;deg #g4ic #cg;deg #h4cc #cf;deg #i4bi #cc;deg #aj4de #cj;deg #aa4bj #bg4d;deg #ab4ae #bj;deg #ab4hc #aj;deg #ac4bj #h;deg #ac4gj --------------------------- ,fe#b;,cl#f1g;,h#b,o4 --------------------------- ,temperature4 ,composition4 --------------------------- #bj;deg #aa4ce #bg4d;deg #ab4ae #cb;deg #ac4ee #cb4e;deg #ad4bi #cj;deg #ae4ab #be;deg #ae4ed --------------------------- ,fe#b;,cl#f1e;,h#b,o4 --------------------------- ,temperature4 ,composition4 --------------------------- #bj;deg #aa4ce #ab;deg #ab4hg #bj;deg #ac4ie #bg;deg #ad4he #cj;deg #ae4ab #ce;deg #ae4fd #ej;deg #ag4ej #ee;deg #ai4ae #ef;deg #bj4jj #ee;deg #bj4cb --------------------------- ,fe#b;,cl#f1d;,h#b,o --------------------------- ,temperature4 ,composition4 --------------------------- #bj;deg #aa4ce #ej;deg #ai4if #ee;deg #bj4cb #fj;deg #bj4gj #fi;deg #ba4ec #gb4e;deg #bc4ce #gc4e;deg #be4jj #gb4e;deg #bf4ae #gj;deg #bg4ij #ff;deg #bi4bj --------------------------- ,fe#b;,cl#f 7,,anhydrous74 --------------------------- ,temperature4 ,composition4 --------------------------- #bj;deg #aa4ce #ff;deg #bi4bj #gj;deg #bi4db #ge;deg #bh4ib #hj;deg #bi4bj #ajj;deg #bi4ge --------------------------- ,the lowest portion of the curve1 ,,ab1 represents the equilibria between ice and solutions containing ferric chloride4 ,it represents1 in other words1 the lowering of the fusion point of ice by addition of ferric chloride4 ,at the point ,b 7-#ee;deg71 the cryohydric point 7p4 #aag7 is reached1 at which the solution is in equilibrium with ice and ferric chloride dodecahydrate4 ,as #aed has already been shown1 such a point represents an invariant system2 and the liquid phase will1 therefore1 solidify to a mixture of ice and hydrate without change of temperature4 ,if heat is added1 ice will melt and the system will pass to the curve ,,bcdn1 which is the solubility curve of the dodecahydrate4 ,at ,c 7#cg;deg71 the point of maximum temperature1 the hydrate melts completely4 ,the retroflex portion of this curve can be followed backwards to a temperature of #h;deg1 but below #bg4d;deg 7,d71 the solutions are supersaturated with respect to the heptahydrate2 point ,d is the eutectic point for dodecahydrate and heptahydrate4 ,the curve ,,def is the solubility curve of the heptahydrate1 ,e being the melting point1 #cb4e;deg4 ,on further increasing the quantity of ferric chloride1 the temperature of equilibrium is lowered until at ,f 7#cj;deg7 another eutectic point is reached1 at which the heptahydrate and pentahydrate can co-exist with solution4 ,then follow the solubility curves for the pentahydrate1 the tetrahydrate1 and the anhydrous salt2 ,g 7#ef;deg7 is the melting point of the former hydrate1 ,j 7#gc4e;deg7 the melting point of the latter4 ,h and ,k1 the points at which the curves intersect1 represent eutectic points2 the temperature of the former is #ee;deg1 that of the latter #ff;deg4 ,the dotted portions of the curves represent metastable equilibria4 ,as is seen from the diagram1 a remarkable series of solubility curves is obtained1 each passing through a point of maximum temperature1 the whole series of curves forming an undulating festoon4 ,to the right of the series of curves the diagram represents unsaturated solutions2 to the left1 supersaturated4 ,if an unsaturated solution1 the composition of which is represented by a point in the field to the right of the solubility curves1 is cooled down1 the result obtained will differ according as the composition of the solution is the same as that of a cryohydric point1 or of a melting point1 or has an intermediate value4 ,thus1 if a solution represented by x#a is cooled down1 the composition will remain unchanged as indicated by the horizontal dotted line1 until the point ,d is reached4 ,at this point1 dodecahydrate and heptahydrate will separate out1 and the liquid will ultimately solidify completely to a mixture or conglomerate of these two hydrates2 the temperature of #aee the system remaining constant until complete solidification has taken place4 ,if1 on the other hand1 a solution of the composition x#c is cooled down1 ferric chloride dodecahydrate will be formed when the temperature has fallen to that represented by ,c1 and the solution will completely solidify1 without alteration of temperature1 with formation of this hydrate4 ,in both these cases1 therefore1 a point is reached at which complete solidification occurs without change of temperature4 ,somewhat different1 however1 is the result when the solution has an intermediate composition1 as represented by x#b or x#d4 ,in the former case the dodecahydrate will first of all separate out1 but on further withdrawal of heat the temperature will fall1 the solution will become relatively richer in ferric chloride1 owing to separation of the hydrate1 and ultimately the eutectic point ,d will be reached1 at which complete solidification will occur4 ,similarly with the second solution4 ,ferric chloride dodecahydrate will first be formed1 and the temperature will gradually fall1 the composition of the solution following the curve ,,cb until the cryohydric point ,b is reached1 when the whole will solidify to a conglomerate of ice and dodecahydrate4 ,suspended ,transformation4--,not only can the upper branch of the solubility curve of the dodecahydrate be followed backwards to a temperature of #h;deg1 or about #ai;deg below the temperature of transition to the heptahydrate2 but suspended transformation has also been observed in the case of the heptahydrate and the pentahydrate4 ,to such an extent is this the case that the solubility curve of the latter hydrate has been followed downwards to its point of intersection with the curve for the dodecahydrate4 ,this point of intersection1 represented in ,fig4 #ci by ,m1 lies at a temperature of about #ae;deg2 and at this temperature1 therefore1 it is possible for the two solid phases dodecahydrate and pentahydrate to coexist1 so that ,m is a eutectic point for the dodecahydrate and the pentahydrate4 ,it is1 however1 a metastable eutectic point1 for it lies in the region of supersaturation with respect to the heptahydrate2 and it can be realized only because of the fact that the latter hydrate is not readily formed4 ,evaporation of ,solutions at ,constant ,temperature4--,on #aef evaporating dilute solutions of ferric chloride at constant temperature1 a remarkable series of changes is observed1 which1 however1 will be understood with the help of ,fig4 #dj4 ,suppose an unsaturated solution1 the composition of which is represented by the point x#a1 is evaporated at a temperature of about #ag;deg - #ah;deg4 ,as water passes off1 the composition of the solution will follow the dotted line of constant temperature1 until at the point where it cuts the curve ,,bc the solid hydrate ,fe#b;,cl#f1ab;,h#b,o separates out4 ,as water continues to be removed1 the hydrate must be deposited 7in order that the solution shall remain saturated71 until finally the solution dries up to the hydrate4 ,as dehydration proceeds1 the heptahydrate can be formed1 and the dodecahydrate will finally pass into the heptahydrate2 and this1 in turn1 into the pentahydrate4 ,illustration3 ,,fig4 #dj4 ,but the heptahydrate is not always formed by the dehydration of the dodecahydrate1 and the behaviour on evaporation is therefore somewhat perplexing at first sight4 ,after the solution has dried to the dodecahydrate1 as explained above1 further removal of water causes liquefaction1 and the system is now represented by the point of intersection at a2 at this point the solid hydrate is in equilibrium with a solution containing relatively more ferric chloride4 ,if1 therefore1 evaporation is continued1 the solid hydrate must pass into solution in order that the composition of the latter may remain unchanged1 so that ultimately a liquid will again be obtained4 ,a very slight further dehydration will bring the solution into the state represented by b1 at which the pentahydrate is formed1 and the solution will at last disappear and leave this hydrate alone4 ,without the information to be obtained from the curves in ,figs4 #ci and #dj1 the phenomena which would be observed on carrying out the evaporation at a temperature of about #ca - #cb;deg #aeg would be still more bewildering4 ,the composition of the different solutions formed will be represented by the perpendicular line x#babcde4 ,evaporation will first cause the separation of the dodecahydrate1 and then total disappearance of the liquid phase4 ,then liquefaction will occur1 and the system will now be represented by the point #b1 in which condition it will remain until the solid hydrate has disappeared4 ,following this there will be deposition of the heptahydrate 7point #c71 with subsequent disappearance of the liquid phase4 ,further dehydration will again cause liquefaction1 when the concentration of the solution will be represented by the point #d2 the heptahydrate will ultimately disappear1 and then will ensue the deposition of the pentahydrate1 and complete solidification will result4 ,on evaporating a solution1 therefore1 of the composition x#b1 the following series of phenomena will be observed3 solidification to dodecahydrate2 liquefaction2 solidification to heptahydrate2 liquefaction2 solidification to pentahydrate4#bcc ,although ferric chloride and water form the largest and best-studied series of hydrates possessing definite melting points1 examples of similar hydrates are not few in number2 and more careful investigation is constantly adding to the list4#bcd ,in all these cases the solubility curve will show a point of maximum temperature1 at which the hydrate melts1 and will end1 above and below1 in a cryohydric point4 ,conversely1 if such a curve is found in a system of two components1 we can argue that a definite compound of the components possessing a definite melting point is formed4 ,inevaporable ,solutions4--,if a saturated solution in contact with two hydrates1 or with a hydrate and anhydrous salt is heated1 the temperature and composition of the solution will1 of course1 remain unchanged so long as the two solid phases are present1 for such a system is invariant4 ,in addition to this1 however1 the quantity of the solution will also remain unchanged1 the water which evaporates being supplied by the higher hydrate4 ,the same phenomenon is also observed in the case of cryohydric points when ice is a solid phase2 so long as the latter is present1 evaporation will be accompanied #aeh by fusion of the ice1 and the quantity of solution will remain constant4 ,such solutions are called inevaporable4#bce ,illustration3 ,,fig4 #da4 ,illustration4--,in order to illustrate the application of the principles of the ,phase ,rule to the study of systems formed by a volatile and a non-volatile component1 a brief description may be given of the behaviour of sulphur dioxide and potassium iodide1 which has formed the subject of a recent investigation4 ,after it had been found#bcf that liquid sulphur dioxide has the property of dissolving potassium iodide1 and that the solutions thus obtained present certain peculiarities of behaviour1 the question arose as to whether or not compounds are formed between the sulphur dioxide and the potassium iodide1 and if so1 what these compounds are4 ,to find an answer to this question1 ,walden and ,centnerszwer#bcg made a complete investigation of the solubility curves 7equilibrium curves7 of these two components1 the investigation extending from the freezing point to the critical point of sulphur dioxide4 ,for convenience of reference1 the results which they obtained are represented diagrammatically in ,fig4 #da4 ,the freezing point 7,a7 of pure sulphur dioxide was found to be -#gb4g;deg4 ,addition of potassium iodide lowered the freezing point1 but the maximum depression obtained was very small1 and was reached when the concentration of the potassium iodide in the solution was only #j4ccf mols4 per cent4 ,beyond this point1 an increase in the concentration of the iodide was accompanied by an elevation of the freezing point1 the change of the freezing point with the concentration being represented by the curve ,,bc4 ,the solid #aei which separated from the solutions represented by ,,bc was a bright yellow crystalline substance4 ,at the point ,c 7-#bc4d;deg7 a temperature-maximum was reached2 and as the concentration of the potassium iodide was continuously increased1 the temperature of equilibrium first fell and then slowly rose1 until at #j4bf;deg 7,e7 a second temperature-maximum was registered4 ,on passing the point ,d1 the solid which was deposited from the solution was a red crystalline substance4 ,on withdrawing sulphur dioxide from the system1 the solution became turbid1 and the temperature remained constant4 ,the investigation was not pursued farther at this point1 the attention being then directed to the equilibria at higher temperatures4 ,when a solution of potassium iodide in liquid sulphur dioxide containing #a4di per cent4 of potassium iodide was heated1 solid 7potassium iodide7 was deposited at a temperature of #if4d;deg4 ,solutions containing more than about #c per cent4 of the iodide separated1 on being heated1 into two layers1 and the temperature at which the liquid became heterogeneous fell as the concentration was increased2 a temperature-minimum being obtained with solutions containing #ab per cent4 of potassium iodide4 ,on the other hand1 solutions containing #cj4i per cent4 of the iodide1 on being heated1 deposited potassium iodide2 while a solution containing #bd4e per cent4 of the salt first separated into two layers at #hi4c;deg1 and then1 on cooling1 solid was deposited and one of the liquid layers disappeared4 ,such are1 in brief1 the results of experiment2 their interpretation in the light of the ,phase ,rule is the following3-- ,the curve ,,ab is the freezing-point curve of solid sulphur dioxide in contact with solutions of potassium iodide4 ,,bcd is the solubility curve of the yellow crystalline solid which is deposited from the solutions4 ,c1 the temperature-maximum1 is the melting point of this yellow solid1 and the composition of the latter must be the same as that of the solution at this point 7p4 #ade71 which was found to be that represented by the formula ,,ki1#ad,,so#b4 ,b is therefore the eutectic point1 at which solid sulphur dioxide and the compound ,,ki1#ad,,so#b can exist together in equilibrium with solution and vapour4 ,the curve ,,de is the solubility curve of the red crystalline solid1 and the #afj point ,e1 at which the composition of solution and solid is the same1 is the melting point of the solid4 ,the composition of this substance was found to be ,,ki1#d,,so#b4bch ,d is1 therefore1 the eutectic point at which the compounds ,,ki1#ad,,so#b and ,,ki1#d,,so#b can coexist in equilibrium with solution and vapour4 ,the curve ,,de does not exhibit a retroflex portion2 on the contrary1 on attempting to obtain more concentrated solutions in equilibrium with the compound ,,ki1#d,,so#b1 a new solid phase 7probably potassium iodide7 was formed4 ,since at this point there are four phases in equilibrium1 viz4 the compound ,,ki1#d,,so#b1 potassium iodide1 solution1 and vapour1 the system is invariant4 ,e is1 therefore1 the transition point for ,,ki1#d,,so#b and ,,ki4 ,passing to higher temperatures1 ,,fg is the solubility curve of potassium iodide in sulphur dioxide2 at ,g two liquid phases are formed1 and the system therefore becomes invariant 7cf4 p4 #aba74 ,the curve ,,ghk is the solubility curve for two partially miscible liquids2 and since complete miscibility occurs on lowering the temperature1 the curve is similar to that obtained with triethylamine and water 7p4 #aja74 ,k is also an invariant point at which potassium iodide is in equilibrium with two liquid phases and vapour4 ,the complete investigation of the equilibria between sulphur dioxide and potassium iodide1 therefore1 shows that these two components form the compounds ,,ki1#ad,,so#b and ,,ki1#d,,so#b2 and that when solutions having a concentration between those represented by the points ,g and ,k are heated1 separation into two layers occurs4 ,the temperatures and concentrations of the different characteristic points are as follows3-- ---------------------------------------- --------------------- ,composition of ,point4 ,temperature4 the solution per cent4 ,,ki4 ---------------------------------------- --------------------- ,a 7m4p4 of ,,so#b7 -#gb4g;deg -- ,b 7eutectic point7 -- #j4hf ,c 7m4p4 of ,,ki1#ad,,so#b7 -#bc4d;deg #ag4fc ,e 7m4p4 of ,,ki1#d,,so#b7 #j4bf;deg #ci4cc ,g 7,,ki two liquid phases7 7about7 #hh;deg #bd4j ,h 7critical solution point7 #gg4c;deg #ab ,k 7,,ki two liquid phases7 7about7 #hh;deg #b4g ---------------------------------------- --------------------- 99 99 99 99 99 #afa ,,chapter ,,ix ,,equilibria ,,between ,,two ,,volatile ,,components ,general4--,in the two preceding chapters certain restrictions were imposed on the discussion of the equilibria between two components2 but in the present chapter the restriction that only one of the components is volatile will be allowed to fall1 and the general behaviour of two volatile#bci components1 each of which is capable of forming a liquid solution with the other1 will be studied4 ,as we shall see1 however1 the removal of the previous restriction produces no alteration in the general aspect of the equilibrium curves for concentration and temperature1 but changes to some extent the appearance of the pressure-temperature diagram4 ,the latter would become still more complicated if account were taken not only of the total pressure but also of the partial pressures of the two components in the vapour phase2 this complication1 however1 will not be introduced in the present discussion4#bdj ,in this chapter we shall consider the systems formed by the two components iodine and chlorine1 and sulphur dioxide and water4 ,iodine and ,chlorine4--,the different systems furnished by iodine and chlorine1 rendered classical by the studies of ,stortenbeker1#bda form a very complete example of equilibria in a two-component system4 ,we shall first of all consider the #afb relations between concentration and temperature1 with the help of the accompanying diagram1 ,fig4 #db4 ,illustration3 ,,fig4 #db4 ,concentration-,temperature ,diagram4--,in this diagram the temperatures are taken as the abscissae1 and the composition of the solution1 expressed in atoms of chlorine to one atom of iodine1#bdb is represented by the ordinates4 ,in the diagram1 ,a represents the melting point of pure iodine1 #aad;deg4 ,if chlorine is added to the system1 a solution of chlorine in liquid iodine is obtained1 and the temperature at which solid iodine is in equilibrium with the liquid solution will be all the lower the greater the concentration of the chlorine4 ,we therefore obtain the curve ,,abf1 which represents the composition of the solution #afc with which solid iodine is in equilibrium at different temperatures4 ,this curve can be followed down to #j;deg1 but at temperatures below #g4i;deg 7,b7 it represents metastable equilibria4 ,at ,b iodine monochloride can be formed1 and if present the system becomes invariant2 ,b is therefore a quadruple point at which the four phases1 iodine1 iodine monochloride1 solution1 and vapour1 can coexist4 ,continued withdrawal of heat at this point will therefore lead to the complete solidification of the solution to a mixture or conglomerate of iodine and iodine monochloride1 while the temperature remains constant during the process4 ,b is the eutectic point for iodine and iodine monochloride4 ,just as we found in the case of aqueous salt solutions that at temperatures above the cryohydric or eutectic point1 two different solutions could exist1 one in equilibrium with ice1 the other in equilibrium with the salt 7or salt hydrate71 so in the case of iodine and chlorine there can be two solutions above the eutectic point ,b1 one containing a lower proportion of chlorine in equilibrium with iodine1 the other containing a higher proportion of chlorine in equilibrium with iodine monochloride4 ,the composition of the latter solution is represented by the curve ,,bcd4 ,as the concentration of chlorine is increased1 the temperature at which there is equilibrium between iodine monochloride and solution rises until a point is reached at which the composition of the solution is the same as that of the solid4 ,at this point 7,c71 iodine monochloride melts4 ,addition of one of the components will lower the temperature of fusion1 and a continuous curve1#bdc exhibiting a retroflex portion as in the case of ,ca,cl#b1f;,h#b,o1 will be obtained4 ,at temperatures below its melting point1 therefore1 iodine monochloride can be in equilibrium with two different solutions4 ,the upper portion of this curve1 ,,cd1 can be followed downwards to a temperature of #bb4g;deg4 ,at this temperature iodine trichloride can separate out1 and a second quadruple #afd point 7,d7 is obtained4 ,this is the eutectic point for iodine monochloride and iodine trichloride4 ,by addition of heat and increase in the amount of chlorine1 the iodine monochloride disappears1 and the system passes along the curve ,,de1 which represents the composition of the solutions in equilibrium with solid iodine trichloride4 ,the concentration of chlorine in the solution increases as the temperature is raised1 until at the point ,e1 where the solution has the same composition as the solid1 the maximum temperature is reached2 the iodine trichloride melts4 ,on increasing still further the concentration of chlorine in the solution1 the temperature of equilibrium falls1 and a continuous curve1 similar to that for the monochloride1 is obtained4 ,the upper branch of this curve has been followed down to a temperature of #cj;deg1 the solution at this point containing #ii4f per cent4 of chlorine4#bdd ,the very rounded form of the curve is due to the trichloride being largely dissociated in the liquid state4 ,one curve still remains to be considered4 ,as has already been mentioned1 iodine monochloride can exist in two crystalline forms1 only one of which1 however1 is stable at temperatures below the melting point2 the two forms are monotropic 7p4 #dd74 ,the stable form which melts at #bg4b;deg1 is called the alpha-form1 while the less stable variety1 melting at #ac4i;deg1 is known as the beta-form4 ,if1 now1 the presence of alpha-,i,cl is excluded1 it is possible to obtain the beta-form1 and to study the conditions of equilibrium between it and solutions of iodine and chlorine1 from the eutectic point ,f to the melting point ,g4 ,as the beta-,i,cl becomes less stable in presence of excess of chlorine1 it has not been possible to study the retroflex portion of the curve represented by the dotted continuation of ,,fg4 ,the following table gives some of the numerical data from which ,fig4 #db was constructed4#bde #afe ,,iodine ,,and ,,chlorine4 ,i4 ,invariant systems4 ---------------------------------------- --------------------------------- ,phases present4 ,temper- ,pressure4------------------------------ --------------------- ature4 ,solid4 ,liquid4 ,vapour4 ---------------------------------------- ----------------------------- #g4i;deg #aa mm4 ,i#b1;alpha-,i,cl ,iwavy,cl#j4ff ,i ,cl#j4ib #j4i;deg -- ,i#b1;beta-,i,cl ,iwavy,cl#j4gb -- #bb4g;deg #db mm4 alpha-,i,cl1,i,cl#c ,iwavy,cl#a4ai ,i ,cl#a4ge -#ajb;deg #a atm4 ,i,cl#c1;,cl#b ,iwavy,clm ,i ,cln ---------------------------------------- ----------------------------- ,,ii4 ,melting points4 ,a4 ,iodine1#bdf #aad4ae;deg 7pressure #hi4h mm474 ,c4 alpha-,iodine monochloride1 #bg4b;deg 7pressure #cg mm474 ,e4 ,iodine trichloride1 #aja;deg 7pressure #af atm474 ,g4 beta-,iodine monochloride1 #ac4i;deg4 ,since the vapour pressure at the melting point of iodine trichloride amounts to #af atm41 the experiments must of course be carried out in closed vessels4 ,at #fc4g;deg the vapour pressure of the system trichloride--solution--vapour is equal to #a atm4 ,pressure-,temperature ,diagram4--,in this diagram there are represented the values of the vapour pressure of the saturated solutions of chlorine and iodine4 ,to give a complete picture of the relations between pressure1 temperature1 and concentration1 a solid model would be required1 with three axes at right angles to one another along which could be measured the values of pressure1 temperature1 and concentration of the components in the solution4 ,instead of this1 however1 there may be employed the accompanying projection figure#bdg 7,fig4 #dc71 the lower portion of which shows the projection of the equilibrium curve on the surface containing the concentration and temperature axes1 while the upper portion is the projection on the plane containing the pressure and temperature axes4 ,the lower portion is therefore a concentration-temperature diagram2 #aff the upper portion1 a pressure-temperature diagram4 ,the corresponding points of the two diagrams are joined by dotted lines4 ,illustration3 ,,fig4 #dc4 ,corresponding to the point ,c1 the melting point of pure iodine1 there is the point ,c#a1 which represents the vapour pressure of iodine at its melting point4 ,at this point three curves cut3 #a1 the sublimation curve of iodine2 #b1 the vaporization curve of fused iodine2 #c1 ,c#a;,b#a1 the vapour-pressure curve of the saturated solutions in equilibrium with solid iodine4 ,starting1 therefore1 with the system solid iodine--liquid iodine1 addition of chlorine will cause the temperature of equilibrium to fall continuously1 while the vapour pressure will first increase1 pass through a maximum and then fall continuously #afg until the eutectic point1 ,b 7,b#a71 is reached4#bdh ,at this point the system is invariant1 and the pressure will therefore remain constant until all the iodine has disappeared4 ,as the concentration of the chlorine increases in the manner represented by the curve ,bf,h1 the pressure of the vapour also increases as represented by the curve ,b#a;f#a;,h#a4 ,at ,h#a1 the eutectic point for iodine monochloride and iodine trichloride1 the pressure again remains constant until all the monochloride has disappeared4 ,as the concentration of the solution passes along the curve ,,hf1 the pressure of the vapour increases as represented by the curve ,h#a;,f#a2 ,f#a represents the pressure of the vapour at the melting point of iodine trichloride4 ,if the concentration of the chlorine in the solution is continuously increased from this point1 the vapour pressure first increases and then decreases1 until the eutectic point for iodine trichloride and solid chlorine is reached 7,d#a74 ,curves ,cl#b solid and ,cl#b liquid represent the sublimation and vaporization curves of chlorine1 the melting point of chlorine being -#ajb;deg4 ,although complete measurements of the vapour pressure of the different systems of pure iodine to pure chlorine have not been made1 the experimental data are nevertheless sufficient to allow of the general form of the curves being indicated with certainty4 ,bivariant ,systems4--,to these1 only a brief reference need be made4 ,since there are two components1 two phases will form a bivariant system4 ,the fields in which these systems can exist are shown in ,fig4 #dc and ,fig4 #dd1 which is a more diagrammatic representation of a portion of ,fig4 #dc4 ,i4 ,iodine--vapour4 ,,ii4 ,solution--vapour4 ,,iii4 ,iodine trichloride--vapour4 ,,iv4 ,iodine monochloride--vapour4 ,illustration3 ,,fig4 #dd4 ,the conditions for the existence of these systems will probably be best understood from ,fig4 #dd4 ,since the curve ,b',a' #afh represents the pressures under which the system iodine--solution--vapour can exist1 increase of volume 7diminution of pressure7 will cause the volatilization of the solution1 and the system iodine--vapour will remain4 ,if1 therefore1 we start with a system represented by a1 diminution of pressure at constant temperature will lead to the condition represented by x4 ,on the other hand1 increase of pressure at a will lead to the condensation of a portion of the vapour phase4 ,since1 now1 the concentration of chlorine in the vapour is greater than in the solution1 condensation of vapour would increase the concentration of chlorine in the solution2 a certain amount of iodine must therefore pass into solution in order that the composition of the latter shall remain unchanged4#bdi ,if1 therefore1 the volume of vapour be sufficiently great1 continued diminution of volume will ultimately lead to the disappearance of all the iodine1 and there will remain only solution and vapour 7field ,,ii474 ,as the diminution of volume is continued1 the vapour pressure and the concentration of the chlorine in the solution will increase1 until when the pressure has reached the value b1 iodine monochloride can separate out4 ,the system1 therefore1 again becomes univariant1 and at constant temperature the pressure and composition of the phases must remain unchanged4 ,diminution of volume will therefore not effect an increase of pressure1 but a condensation of the vapour2 and since this is richer in chlorine than the #afi solution1 solid iodine monochloride must separate out in order that the concentration of the solution remain unchanged4#bej ,as the result1 therefore1 we obtain the bivariant system iodine monochloride--vapour4 ,a detailed discussion of the effect of a continued increase of pressure will not be necessary4 ,from what has already been said and with the help of ,fig4 #dd1 it will readily be understood that this will lead successively to the univariant system 7c71 iodine monochloride--solution--vapour2 the bivariant system solution--vapour 7field ,,ii472 the univariant system 7d71 iodine trichloride--solution--vapour2 and the bivariant system x'1 iodine trichloride--vapour4 ,if the temperature of the experiment is above the melting point of the monochloride1 then the systems in which this compound occurs will not be formed4 ,sulphur ,dioxide and ,water4--,in the case just studied we have seen that the components can combine to form definite compounds possessing stable melting points4 ,the curves of equilibrium1 therefore1 resemble in their general aspect those of calcium chloride and water1 or of ferric chloride and water4 ,in the case of sulphur dioxide and water1 however1 the melting point of the compound formed cannot be realized1 because transition to another system occurs2 retroflex concentration-temperature curves are therefore not found here1 but the curves exhibit breaks or sudden changes in direction at the transition points1 as in the case of the systems formed by sodium sulphate and water4 ,the case of sulphur dioxide and water is also of interest from the fact that two liquid phases can be formed4 ,the phases which occur are--,solid3 ice1 sulphur dioxide hydrate1 ,,so#b1g;,h#b,o4 ,liquid3 two solutions1 the one containing excess of sulphur dioxide1 the other excess of water1 and represented by the symbols ,,so#b wavy x,h#b,o 7solution ,i471 and ,h#b,o wavy y,,so#b 7solution ,,ii474 ,vapour3 a mixture of sulphur dioxide and water vapour in varying proportions4 ,since there are two components1 sulphur dioxide and water1 the number of #agj possible systems is considerable4 ,only the following1 however1 have been studied3-- ,i4 ,invariant ,systems3 ,four co-existing phases4 7a7 ,ice1 hydrate1 solution1 vapour4 7b7 ,hydrate1 solution ,i41 solution ,,ii41 vapour4 ,,ii4 ,univariant ,systems3 ,three co-existing phases4 7a7 ,hydrate1 solution ,i41 vapour4 7b7 ,hydrate1 solution ,,ii41 vapour4 7c7 ,solution ,i41 solution ,,ii41 vapour4 7d7 ,hydrate1 solution ,i41 solution ,,ii4 7e7 ,hydrate1 ice1 vapour4 7f7 ,ice1 solution ,,ii41 vapour4 7g7 ,ice1 hydrate1 solution ,,ii4 ,,iii4 ,bivariant ,systems3 ,two co-existing phases4 7a7 ,hydrate1 solution ,i4 7b7 ,hydrate1 solution ,,ii4 7c7 ,hydrate1 vapour4 7d7 ,hydrate1 ice4 7e7 ,solution ,i41 solution ,,ii4 7f7 ,solution ,i41 vapour4 7g7 ,solution ,i41 ice4 7h7 ,solution ,,ii41 vapour4 7i7 ,solution ,,ii41 ice4 7j7 ,ice1 vapour4 ,illustration3 ,,fig4 #de4 ,pressure-,temperature ,diagram4#bea--;,if sulphur dioxide is passed into water at #j;deg1 a solution will be formed and the temperature at which ice can exist in equilibrium with this solution will fall more and more as the concentration of the sulphur dioxide increases4 ,at -#b4f;deg1 however1 a cryohydric point is reached at which solid hydrate separates out1 and the system becomes invariant4 ,the curve ,,ab 7,fig4 #de7 therefore represents the pressure of the system ice--solution ,,ii4--vapour1 and ,b represents the temperature and pressure at which the invariant system ice--hydrate--solution ,,ii4--vapour can exist4 ,at this point the temperature is -#b4f;deg1 and the pressure #ba4a cm4 ,if heat is withdrawn from this system1 the solution will ultimately #aga solidify to a mixture of ice and hydrate1 and there will be obtained the univariant system ice--hydrate--vapour4 ,the vapour pressure of this system has been determined down to a temperature of -#i4e;deg1 at which temperature the pressure amounts to #ae cm4 ,the pressures for this system are represented by the curve ,,bc4 ,if at the point ,b the volume is diminished1 the pressure must remain constant1 but the relative amounts of the different phases will undergo change4 ,if suitable quantities of these are present1 diminution of volume will ultimately lead to the total condensation of the vapour phase1 and there will remain the univariant system ice--hydrate--solution4 ,the temperature of equilibrium of this system will alter with the pressure1 but1 as in the case of the melting point of a simple substance1 great differences of pressure will cause only comparatively small changes in the temperature of equilibrium4 ,the change of the cryohydric point with the pressure is represented by the line ,,be2 the actual values have not been determined1 but the curve must slope towards the pressure axis because fusion is accompanied by diminution of volume1 as in the case of pure ice4 #agb ,a fourth univariant system can be formed at ,b4 ,this is the system hydrate--solution ,,ii4--vapour4 ,the conditions for the existence of this system are represented by the curve ,,bf1 which may therefore be regarded as the vapour-pressure curve of the saturated solution of sulphur dioxide heptahydrate in water4 ,unlike the curve for iodine trichloride--solution--vapour1 this curve cannot be followed to the melting point of the hydrate4 ,before this point is reached1 a second liquid phase appears1 and an invariant system consisting of hydrate--solution ,i4--solution ,,ii4--vapour is formed4 ,we have here1 therefore1 the phenomenon of melting under the solution as in the case of succinic nitrile and water 7p4 #abb74 ,this point is represented in the diagram by ,f2 the temperature at this point is #ab4a;deg1 and the pressure #agg4c cm4 ,the range of stable existence of the hydrate is therefore from -#b4f;deg to #ab4a;deg2 nevertheless1 the curve ,,fb has been followed down to a temperature of -#f;deg1 at which point ice formed spontaneously4 ,so long as the four phases hydrate1 two liquid phases1 and vapour are present1 the condition of the system is perfectly defined4 ,by altering the conditions1 however1 one of the phases can be made to disappear1 and a univariant system will then be obtained4 ,thus1 if the vapour phase is made to disappear1 the univariant system solution ,i4--solution ,,ii4--hydrate1 will be left1 and the temperature at which this system is in equilibrium will vary with the pressure4 ,this is represented by the curve ,,fi2 under a pressure of #bbe atm4 the temperature of equilibrium is #ag4a;deg4 ,increase of pressure1 therefore1 raises the temperature at which the three phases can coexist4 ,again1 addition of heat to the invariant system at ,f will cause the disappearance of the solid phase1 and there will be formed the univariant system solution ,i4--solution ,,ii4--vapour4 ,in the case of this system the vapour pressure increases as the temperature rises1 as represented by the curve ,,fg4 ,such a system is analogous to the case of ether and water1 or other two partially miscible liquids 7p4 #ajc74 ,as the temperature changes1 the composition of the two liquid phases will undergo change2 but this system has not been studied fully4 ,the fourth curve1 which ends at the quadruple point ,f1 is #agc that representing the vapour pressure of the system hydrate--solution ,i4--vapour 7,,fh74 ,this curve has been followed to a temperature of #j;deg1 the pressure at this point being #aac cm4 ,the metastable prolongation of ,,gf has also been determined4 ,although1 theoretically1 this curve must lie below ,,fh1 it was found that the difference in the pressure for the two curves was within the error of experiment4 ,bivariant ,systems4--,the different bivariant systems1 consisting of two phases1 which can exist within the range of temperature and pressure included in ,fig4 #de1 were given on p4 #agj4 ,the conditions under which these systems can exist are represented by the areas in the diagram1 and the fields of the different bivariant systems are indicated by letters1 corresponding to the letters on p4 #agj4 ,just as in the case of one-component systems 7p4 #bi71 we found that the field lying between any two curves gave the conditions of existence of that phase which was common to the two curves1 so also in the case of two-component systems1 a bivariant two-phase system occurs in the field enclosed#beb by the two curves to which the two phases are common4 ,as can be seen1 the same bivariant system can occur in more than one field4 ,as is evident from ,fig4 #de1 three different bivariant systems are capable of existing in the area ,,hfi2 which of these will be obtained will depend on the relative masses of the different phases in the univariant or invariant system4 ,thus1 starting with a system represented by a point on the curve ,,hf1 diminution of volume at constant temperature will cause the condensation of a portion of the vapour1 which is rich in sulphur dioxide2 since this would increase the concentration of sulphur dioxide in the solution1 it must be counteracted by the passage of a portion of the hydrate 7which is relatively poor in sulphur dioxide7 into the solution4 ,if1 therefore1 the amount of hydrate present is relatively very small1 the final result of the compression will be the production of the system f1 solution ,i4--vapour4 ,on the other hand1 if the vapour is present in relatively small amount1 it will be the first phase to disappear1 #agd and the bivariant system a1 hydrate--solution ,i41 will be obtained4 ,finally1 if we start with the invariant system at ,f1 compression will cause the condensation of vapour1 while the composition of the two solutions will remain unchanged4 ,when all the vapour has disappeared1 the univariant system hydrate--solution ,i4--solution ,,ii4 will be left4 ,if1 now1 the pressure is still further increased1 while the temperature is kept below #ab;deg1 more and more hydrate must be formed at the expense of the two liquid phases 7because #ab;deg is the lower limit for the coexistence of the two liquid phases71 and if the amount of the solution ,i4 7containing excess of sulphur dioxide7 is relatively small1 it will disappear before solution ,,ii41 and there will be obtained the bivariant system hydrate--solution ,,ii4 7bivariant system b74 ,in a similar manner1 account can be taken of the formation of the other bivariant systems4 ,a behaviour similar to that of sulphur dioxide and water is shown by chlorine and water and by bromine and water1 although these have not been so fully studied4#bec ,in the case of hydrogen bromide and water1 and of hydrogen chloride and water1 a hydrate1 viz4 ,h,br1#b;,h#b,o and ,h,cl1#b;,h#b,o1 is formed which possesses a definite melting point1 as in the case of iodine trichloride4 ,in these cases1 therefore1 a retroflex curve is obtained4 ,further1 just as in the case of the chlorides of iodine the upper branch of the retroflex curve ended in a eutectic point1 so also in the case of the hydrate ,h,br1#b;,h#b,o the upper branch of the curve ends in a eutectic point at which the system dihydrate--monohydrate--solution--vapour can exist4 ,before the melting point of the monohydrate is reached1 two liquid phases are formed1 as in the case of sulphur dioxide and water4 99 99 99 99 99 #age ,,chapter ,x ,,solid ,,solutions4 ,,mixed ,,crystals ,general4--,with the conception of gaseous and liquid solutions1 every one is familiar4 ,gases can mix in all proportions to form homogeneous solutions4 ,gases can dissolve in or be absorbed by liquids2 and solids1 also1 when brought in contact with liquids1 pass into solution and yield a homogeneous liquid phase4 ,on the other hand1 the conception of a solid solution is one which in many cases is found more difficult to appreciate2 and the existence and behaviour of solid solutions1 in spite of their not uncommon occurrence and importance1 are in general comparatively little known4 ,the reason of this is to be found1 to some extent1 no doubt1 in the fact that the term solid solution was introduced at a comparatively recent date1#bed but it is probably also due in some measure to a somewhat hazy comprehension of the definition of the term solution itself4 ,as has already been said 7p4 #ib71 a solution is a homogeneous phase1 the composition of which can vary continuously within certain limits2 the definition involves1 therefore1 no condition as to the physical state of the substances4 ,accordingly1 solid solutions are homogeneous solid phases1 the composition of which can undergo continuous variation within certain limits4 ,just as we saw that the range of variation of composition is more limited in the case of liquids than in the case of gases1 so also we find that the limits of miscibility are in general still more restricted in the case of solids4 ,examples of complete miscibility are1 however1 not unknown even in the case of solid substances4 ,solid solutions have long been known1 although1 of course1 #agf they were not defined as such4 ,thus1 the phenomena of occlusion of gases by metals and other substances 7occlusion of hydrogen by palladium2 occlusion of hydrogen by iron7 are due to the formation of solid solutions4 ,the same is probably also true of the phenomena of adsorption1 as in the removal of organic colouring matter by charcoal1 although1 in this case1 surface tension no doubt plays a considerable part4#bee ,as examples of the solution of gases in solids there may be cited 7in addition to the phenomena of occlusion already mentioned71 the hydrated silicates and the zeolites4 ,during dehydration these crystalline substances remain clear and transparent1 and the pressure of the water vapour which they emit varies with the degree of hydration or the concentration of water in the mineral4#bef ,as examples of the solution of solids in solids we have the cementation of iron by charcoal1 the formation of glass1 and the crystallization together of isomorphous substances4 ,although we have here spoken of the glasses as solid solutions1 it should be mentioned that the term solid is used in its popular sense4 ,strictly speaking1 the glasses are to be regarded as supercooled liquids 7see also p4 #ec1 footnote74 ,in discussing the equilibria in systems containing a solid solution1 it is of essential importance to remember that a solid solution constitutes only one phase1 a phase of varying composition1 as in the case of liquid solutions4 ,solution of ,gases in ,solids4--,comparatively little work has been done in this connection1 the investigations being limited chiefly to the phenomena of occlusion or adsorption of gases by charcoal4#beg ,we shall1 therefore1 indicate only briefly #agg and in a general manner1 the behaviour which the ,phase ,rule enables us to foresee4#beh ,in dealing with the systems formed by the two phases gas--solid1 three chief cases call for mention3-- ,i4 ,the gas is not absorbed by the solid1 but when the pressure reaches a certain value1 combination of the two components can result4 ,illustration3 ,fig4 #df4 ,the graphic representation of such a system is shown in ,fig4 #df1 the ordinates being the pressures of the gas1 and the abscissae the concentrations of the gaseous component in the solid phase4 ,since there is no formation of a solid solution1 the concentration of gas in the solid phase remains zero until the pressure has increased to the point ,a4 ,at this point combination can take place4 ,there will now be three phases present1 viz4 solid component1 compound1 and vapour4 ,the system is therefore univariant1 and if the temperature is maintained constant1 the vapour pressure will be constant1 irrespective of the amount of compound formed1 i4e4 irrespective of the relative amounts of gas and solid4 ,this is indicated by the line ,,ab4 ,when the solid component has entirely disappeared1 the system ceases to be univariant1 and if no absorption occurs1 the pressure will increase again1 as shown by ,,bc4 ,if a second compound can be formed1 then a second pc-line will be obtained1 similar to the preceding4 ,to this group belong the salt hydrates 7,chap4 ,,vii474 ,,ii4 ,the gas may be absorbed and may also form a compound4 ,if absorption of gas occurs with formation of a solid solution1 then1 as the system consists of two phases1 solution--vapour1 it is bivariant4 ,at constant temperature1 therefore1 the pressure will still vary with the concentration of the gaseous component in the solid phase4 ,this is represented by the curve ,,ab in ,fig4 #dg4 ,when1 however1 the pressure has reached a certain value1 combination can take place2 and since there are now three phases present1 the system is #agh univariant1 and at constant temperature the pressure is constant1 as shown by the line ,,bc4 ,,iii4 ,absorption of gas occurs1 but at a certain concentration the solid solution can separate into two immiscible solid solutions4 ,we have seen1 in ,chapter ,,vi41 that two liquids can form two immiscible solutions1 and the same has also been found true of solid solutions1 as we shall presently learn more fully4 ,if1 now1 two immiscible solutions are formed1 then the system will become univariant1 and at constant temperature the pc-curve will be a straight line1 as in the case of the formation of a compound 7cf4 p4 #hf74 ,the behaviour of this system will1 therefore1 also be represented diagrammatically by ,fig4 #dg4 ,illustration3 ,,fig4 #dg4 ,palladium and ,hydrogen4--,the phenomenon of the absorption of hydrogen by palladium1 to which ,graham gave the name occlusion1 is one that has claimed the attention of several investigators4 ,although ,graham was not of opinion that a compound is formed1 but rather that the gas undergoes very great condensation1 acts as a quasi-metal 7to which he gave the name hydrogenium71 and forms a homogeneous alloy with the palladium1 later investigations1 especially those of ,troost and ,hautefeuille1#bei pointed to the formation of a definite chemical compound1 having the formula ,pd#b;,h4 ,this conclusion has1 however1 not been confirmed by subsequent investigation4#bfj ,roozeboom and ,hoitsema#bfa sought to arrive at a final decision as to the nature of the phenomenon by an investigation of the equilibrium between hydrogen and palladium on the basis of the ,phase ,rule classification given above4 ,if a compound is formed1 diminution of volume would cause no increase of pressure1 but only an increase in the amount of the compound4 ,as this is the only case of gas absorption which has been #agi accurately studied from this point of view1 a brief account of the results obtained will be given here1 although these are not so clear and free from ambiguity as one would desire4 ,the scientists just mentioned investigated the variation of the pressure of hydrogen with the amount absorbed by the metal at different temperatures1 and a few of their results1 typical of all1 are represented graphically in ,fig4 #dh2 the curves indicating the variation of the gas pressure with the concentration of the hydrogen in the palladium at the temperatures #abj;deg1 #agj;deg1 and #bjj;deg4 ,as can be seen1 the curve consists of three parts1 an ascending portion which passes gradually and continuously into an almost horizontal but slightly ascending middle part1 which in turn passes without break into a second rapidly ascending curve4 ,this1 as ,fig4 #dh indicates1 is the general form of the curve2 but the length of the middle portion varies with the temperature1 being shorter at higher than at lower temperatures4 ,illustration3 ,,fig4 #dh4 ,what is the interpretation to be put on these curves8 ,with regard to the two end portions1 these represent bivariant1 two-phase systems1 consisting of a solid solution and gas4 ,they correspond1 therefore1 to curve ,,ab in ,fig4 #dg4 ,if the middle portion were horizontal1 it would indicate either the formation of a compound or of two immiscible solid solutions4 ,if a compound ,pd#b;,h were formed1 then the middle portion would at all temperatures end at the same value of the concentration1 viz4 that corresponding to #j4e atoms of hydrogen to #a atom of palladium4 ,as the figure shows1 however1 this is not the case2 the higher the temperature1 the lower is the concentration at which the middle passes into the terminal portion of the curve4 #ahj ,such a behaviour would1 however1 agree with the assumption of the formation of two solid solutions1 the miscibility of which increases with the temperature1 as in the case of the liquid solutions of phenol and water 7p4 #ig74 ,nevertheless1 although the assumption of the formation of two solid solutions is more satisfactory than that of the formation of a compound1 it does not entirely explain the facts4 ,if two solid solutions are formed1 the pressure curve should be horizontal1 but this is not the case2 and the deviation from the horizontal does not appear to be due to impurities either in the gas or in the metal1 but is apparently a peculiarity of the system4 ,further1 the gradual instead of abrupt passage of the three portions of the curve into one another remains unexplained4 ,hoitsema has expressed the opinion that the occlusion of hydrogen by palladium is a process of continuous absorption1 the peculiar form of the curve--the flat middle portion--being possibly due to a condensation of the gas1 even at temperatures far above the critical temperature of liquid hydrogen4 ,while1 therefore1 the occlusion of hydrogen by palladium still presents some unexplained phenomena1 the behaviour found by ,hoitsema would appear to disprove conclusively the formation of a definite chemical compound4#bfb ,,solution ,,of ,,solids ,,in ,,solids4 ,,mixed ,,crystals4 ,the introduction by van't ,hoff of the term solid solution resulted from the discovery of a number of deviations from the ,raoult-van't ,hoff law for the depression of the freezing point by dissolved substances4 ,in all cases1 the depression was too small2 in some instances1 indeed1 the freezing point may be raised4 ,to explain these irregularities1 van't ,hoff assumed that the dissolved substance crystallized out along with the solid solvent2 and he showed how this would account for the #aha deviations from the law of the depression of the freezing point1 which had been developed on the assumption that only the pure solvent crystallized out from the solution4#bfc ,the mixed crystals which were thus obtained1 and which van't ,hoff called dilute solid solutions1 showed great resemblance in their behaviour to ordinary liquid solutions1 and obeyed the laws applicable to these4 ,these laws1 however1 can no longer be applied in the case of the concentrated solid solutions formed by the crystallization together of isomorphous substances1 and known as isomorphous mixtures4 ,indeed1 it has been contended#bfd that these isomorphous mixtures should not be considered as solid solutions at all1 although no sharp line of demarcation can be drawn between the two classes4 ,the differences1 however1 in the behaviour of the two groups are of a quantitative rather than a qualitative nature2 and since we are concerned at present only with the qualitative behaviour1 we shall make no distinction between the crystalline solid solutions and the isomorphous mixtures1 but shall study the behaviour of the two classes under the head of mixed crystals4 ,mixed crystals can be formed either by sublimation#bfe or from a liquid phase2 and in the latter case the mixed crystals can be deposited either from solution in a common solvent or from a mixture of the fused components4 ,in this method of formation1 which alone will be discussed in the present chapter1 we are dealing with the fusion curves of two substances1 where1 however1 the liquid solution is in equilibrium not with one of the pure components1 but with a solid solution or mixed crystal4 ,the simple scheme 7,fig4 #bi1 p4 #aag7 which was obtained in the case of two components which crystallize out in the pure state1 is no longer sufficient in the case of the formation of mixed crystals4 ,with the help of the ,phase ,rule1 however1 the different possible systems can be classified2 and examples of the different cases predicted by the ,phase ,rule have also been obtained by experiment4 #ahb ,we shall now consider briefly the formation of mixed crystals by isomorphous substances2 the consideration of the formation of mixed crystals of isodimorphous substances will1 on account of the complexity of the relationships1 not be undertaken here4#bff ,formation of ,mixed ,crystals of ,isomorphous ,substances4 ,for the purpose of representing the relationships found here we shall employ a temperature-concentration diagram1#bfg in which the ordinates represent the temperature and the abscissae the concentration of the components4 ,since there are two solutions1 the liquid and the solid1 and since the concentration of the components in these two phases is not1 in general1 the same1 two curves will be required for each system1 one relating to the liquid phase1 the other relating to the solid4 ,the temperature at which solid begins to be deposited from the liquid solution will be called the freezing point of the mixture1 and the temperature at which the solid solution just begins to liquefy will be called the melting point of the solid solution4 ,the temperature-concentration curve for the liquid phase will therefore be the freezing-point curve2 that for the solid solution1 the melting-point curve4 ,the latter will be represented by a dotted line4#bfh #ahc ,i4--,,the ,,two ,,components ,,can ,,form ,,an ,,unbroken ,,series ,,of ,,mixed ,,crystals4 ,since1 as has already been pointed out 7p4 #agf71 a mixed crystal 7solid solution7 constitutes only one phase1 it is evident that if the two components are miscible with one another in all proportions in the solid state1 there can never be more than one solid phase present1 viz4 the solid solution or mixed crystal4 ,if the components are completely miscible in the solid state1 they will also be completely miscible in the liquid state1 and there can therefore be only one liquid phase4 ,the system can at no point become invariant1 because there can never be more than three phases present4 ,when1 therefore1 the two components form a continuous series of mixed crystals1 the equilibrium curve must also be continuous4 ,of these systems three types are found4 ,illustration3 ,,fig4 #di4 7a7 ,the freezing points of all mixtures lie between the freezing points of the pure components 7,curve ,i41 ,fig4 #di74 ,examples4--,this type of curve is represented by the mixed crystals of naphthalene and beta-naphthol4#bfi ,the addition of beta-naphthol to naphthalene raises the freezing point of the latter1 and the rise is directly proportional to the amount of naphthol added4 ,the freezing point curve is therefore a straight line joining the melting points of the two components4 ,this behaviour1 however1 is rather exceptional1 the freezing-point curve lying generally above1 sometimes also below1 the straight line joining the melting points of the pure components4 ,thus the freezing-point curve of mixtures of alpha-monochlorocinnamic aldehyde and alpha-monobromocinnamic aldehyde#bgj lies above the #ahd straight line joining the melting points of the pure components 7#ca4bb;deg and #fi4ef;deg71 as is evident from the following table3-- ---------------------------------------- ------------------------------ ,molecules of bromo- cinnamic aldehyde in ,freezing point4 ,deviation from straight #ajj mols4 of mixture4 line4 ---------------------------------------- ------------------------------ #j4jj #ca4bb;deg -- #aj4dh #cg4bh;deg #b4jd;deg #ba4ia #dc4ab;deg #c4ej;deg #cj4jg #df4hj;deg #d4je;deg #de4jd #eb4id;deg #d4de;deg #fb4af #eh4hb;deg #c4gg;deg #hb4ih #fe4jg;deg #b4jc;deg #ic4ej #fg4ia;deg #j4hd;deg #ajj4jj #fi4ef;deg -- ---------------------------------------- ------------------------------ ,melting-point ,curve4--,this curve1 like the freezing-point curve1 must also be continuous1 and the melting points of the different solid solutions will lie between the melting points of the pure components4 ,this is represented by the dotted line in ,fig4 #di1 ,i4 ,the relative position of the two curves1 which can be deduced with the help of thermodynamics and also by experimental determination1 is found in all cases to be in accordance with the following rule3 ,at any given temperature1 the concentration of that component by the addition of which the freezing point is depressed1 is greater in the liquid than in the solid phase2 or1 conversely1 the concentration of that component by the addition of which the freezing point is raised1 is greater in the solid than in the liquid phase4 ,an illustration of this rule is afforded by the two substances chloro- and bromo-cinnamic aldehyde already mentioned4 ,as can be seen from the above table1 the addition of chlorocinnamic aldehyde lowers the melting point of the bromo-compound4 ,in accordance with the rule1 therefore1 the concentration of the chloro-compound in the liquid phase must be greater than in the solid phase2 and this was found experimentally4 ,at a temperature of #di4dd;deg1 the liquid contained #eh4eb per cent41 the solid only #eb4eg per cent4 of the chlorocinnamic aldehyde4 ,from this it will also be clear that on cooling a fused mixture of two substances capable of forming mixed crystals1 #ahe the temperature of solidification will not remain constant during the separation of the solid2 nor1 on the other hand1 will the temperature of liquefaction of the solid solution be constant4 ,thus1 for example1 if a liquid solution of two components1 ,a and ,b1 having the composition represented by the point x 7,fig4 #ej71 is allowed to cool1 the system will pass along the line xx'4 ,at the temperature of the point a1 mixed crystals will be deposited1 the composition of which will be that represented by b4 ,as the temperature continues to fall1 more and more solid will be deposited2 and since the solid phase is relatively rich in the component ,b1 the liquid will become relatively poorer in this4 ,the composition of the liquid solution will therefore pass along the curve ad1 the composition of the solid solution at the same time passing along the curve bc2 at the point c the liquid will solidify completely4#bga ,illustration3 ,,fig4 #ej4 ,conversely1 if mixed crystals of the composition and at the temperature x' are heated1 liquefaction will begin at the temperature c1 yielding a liquid of the composition d4 ,on continuing to add heat1 the temperature of the mass will rise1 more of the solid will melt1 and the composition of the two phases will change as represented by the curves da and cb4 ,when the temperature has risen to a1 complete liquefaction will have occurred4 ,the process of solidification or of liquefaction is therefore extended over a temperature interval ac4 ,even when the freezing-point curve is a straight line joining #ahf the melting points of the pure components1 the melting-point curve will not necessarily coincide with the freezing-point curve1 although it may approach very near to it2 complete coincidence can take place only when the melting points of the two components are identical4 ,an example of this will be given later 7,chap4 ,,xii474 7b7 ,the freezing-point curve passes through a maximum 7,curve ,,ii41 ,fig4 #di74 ,illustration3 ,,fig4 #ea4 ,this curve exhibits the greatest degree of contrast to the freezing-point curve which is obtained when the pure components crystallize out4 ,for1 since the curve passes through a maximum1 it is evident that the freezing point of each of the components must be raised by the addition of the other component4 ,example4--,very few cases belonging to this type are known4 ,the best example is found in the freezing-point curve of mixtures of d- and l-carvoxime#bgb 7,c#aj;,h#ad,n4,,oh74 ,the freezing points and melting points of the different mixtures of d- and l-carvoxime are given in the following table1 and represented graphically in ,fig4 #ea3-- ---------------------------------------- ------------------------- ,per cent4 of ,per cent4 of ,freezing point4 ,melting point4 d-carvoxime4 l-carvoxime4 ---------------------------------------- ------------------------- #ajj #j #gb4j;deg #gb4j;deg #ii #a #gb4d;deg -- #ih #b #gc4j;deg -- #ie #e #ge4d;deg #gc4j;deg #ij #aj #gi4j;deg #ge4j;deg #hj #bj #hd4f;deg #hj4j;deg #gj #cj #hh4b;deg #he4j;deg #fj #dj #ij4d;deg -- #ej #ej #ia4d;deg #ia4d;deg #be #ge #hf4d;deg #hb4j;deg #h #ib #gg4d;deg -- #a #ii #gb4d;deg -- #j #ajj #gb4j;deg #gb4j;deg ---------------------------------------- ------------------------- #ahg ,in this figure1 the melting-point curve1 i4e4 the temperature-concentration curve for the mixed crystals1 is represented by the lower curve4 ,since the addition of the laevo-form to the dextro-form raises the melting point of the latter1 the concentration of the laevo-form 7on the right-hand branch of the curve7 must1 in accordance with the rule given1 be greater in the solid phase than in the liquid4 ,similarly1 since addition of the dextro-form raises the melting point of the laevo-form1 the solid phase 7on the left-hand branch of the curve7 must be richer in dextro- than in laevo-carvoxime4 ,at the maximum point1 the melting-point and freezing-point curves touch2 at this point1 therefore1 the composition of the solid and liquid phases must be identical4 ,it is evident1 therefore1 that at the maximum point the liquid will solidify1 or the solid will liquefy completely without change of temperature2 and1 accordingly1 mixed crystals of the composition represented by the maximum point will exhibit a definite melting point1 and will in this respect behave like a simple substance4 7c7 ,the freezing-point curve passes through a minimum 7,curve ,,iii41 ,fig4 #di74 ,in this case1 as in the case of those systems where the pure components are deposited1 a minimum freezing point is obtained4 ,in the latter case1 however1 there are two freezing-point curves which intersect at a eutectic point2 in the case where mixed crystals are formed there is only one continuous curve4 ,on one side of the minimum point the liquid phase contains relatively more1 on the other side relatively less1 of the one component than does the solid phase2 while at the minimum point the composition of the two phases is the same4 ,at this point1 therefore1 complete solidification or complete liquefaction will occur without change of temperature1 and the mixed crystals will accordingly exhibit a definite melting point4 ,illustration3 ,,fig4 #eb4 #ahh ,example4--,as an example of this there may be taken the mixed crystals of mercuric bromide and iodide4#bgc ,mercuric bromide melts at #bcf4e;deg1 and mercuric iodide at #bee4d;deg4 ,the mixed crystal of definite constant melting point 7minimum point7 contains #ei mols4 per cent4 of mercuric bromide1 the melting point being #baf4a;deg4 ,the numerical data are contained in the following table1 and represented graphically in ,fig4 #eb3-- ---------------------------------------- ------------- ,mols4 per cent4 of ,hg,br#b4 ,freezing point4 ,melting point4 ---------------------------------------- ------------- #ajj #bcf4e;deg #bcf;deg #ij #bbh4h;deg #bbf;deg #hj #bbb4b;deg #bai;deg #gj #bag4h;deg #bag;deg #fe #baf4f;deg #baf;deg #fj #baf4a;deg #bae4e;deg #ee #baf4c;deg #baf;deg #ej #bag4c;deg #baf;deg #dj #bba4a;deg #bah;deg #cj #bbg4h;deg #bbc;deg #bj #bcf4b;deg #bca;deg #aj #bde4e;deg #bdb;deg #j #bee4d;deg #bed;deg ---------------------------------------- ------------- ,illustration3 ,,fig4 #ec4 ,fractional ,crystallization of ,mixed ,crystals4--,with the help of the diagrams already given it will be possible to predict what will be the result of the fractional crystallization of a fused mixture of two substances which can form mixed crystals4 ,suppose1 for example1 a fused mixture of the composition x 7,fig4 #ec7 is cooled down2 then1 as we have already seen1 when the temperature has fallen to a1 mixed crystals of composition1 b1 are deposited4 ,if the temperature is allowed to fall #ahi to x'1 and the solid then separated from the liquid1 the mixed crystals so obtained will have the composition represented by e4 ,if1 now1 the mixed crystals e are completely fused and the fused mass allowed to cool1 separation of solid will occur when the temperature has fallen to the point f4 ,the mixed crystals which are deposited have now the composition represented by g1 i4e4 they are richer in ,b than the original mixed crystals4 ,by repeating this process1 the composition of the successive crops of mixed crystals which are obtained approximates more and more to that of the pure component ,b1 while1 on the other hand1 the composition of the liquid phase produced tends to that of pure ,a4 ,by a systematic and methodical repetition of the process of fractional crystallization1 therefore1 a practically complete separation of the components can be effected2 a perfect separation is theoretically impossible4 ,from this it will be readily understood that in the case of substances the freezing point of which passes through a maximum1 fractional crystallization will ultimately lead to mixed crystals having the composition of the maximum point1 while the liquid phase will more and more assume the composition of either pure ,a or pure ,b1 according as the initial composition was on the ,a side or the ,b side of the maximum point4 ,in those cases1 however1 where the curves exhibit a minimum1 the solid phase which separates out will ultimately be one of the pure components1 while a liquid phase will finally be obtained which has the composition of the minimum point4 ,,ii4--,,the ,,two ,,components ,,do ,,not ,,form ,a ,,continuous ,,series ,,of ,,mixed ,,crystals4 ,this case corresponds to that of the partial miscibility of liquids4 ,the solid component ,a can dissolve the component ,b until the concentration of the latter in the mixed crystal has reached a certain value4 ,addition of a further amount of ,b will not alter the composition of the mixed crystal1 but there will be formed a second solid phase consisting #aij of a solution of ,a in ,b4 ,at this point the four phases1 mixed crystals containing excess of ,a1 mixed crystals containing excess of ,b1 liquid solution1 vapour1 can coexist2 this will therefore be an invariant point4 ,the temperature-concentration curves will therefore no longer be continuous1 but will exhibit a break or discontinuity at the point at which the invariant system is formed4 7a7 ,the freezing-point curve exhibits a transition point 7,curve ,i41 ,fig4 #ed74 ,as is evident from the figure1 addition of ,b raises the melting point of ,a1 and1 in accordance with the rule previously given1 the concentration of ,b in the mixed crystals will be greater than in the solution4 ,this is represented in the figure by the dotted curve ,,ad4 ,on the other hand1 addition of ,a lowers the melting point of ,b1 and the two curves ,,bc and ,,be are obtained for the liquid and solid phases respectively4 ,at the temperature of the line ,,cde the liquid solution of the composition represented by ,c is in equilibrium with the two different mixed crystals represented by ,d and ,e4 ,at this temperature1 therefore1 the tc-curve for the solid phase exhibits a discontinuity2 and1 since the solid phase undergoes change at this point1 the freezing-point curve must show a break 7p4 #aaa74 ,illustration3 ,,fig4 #ed4 ,example4--,curves of the form given in ,fig4 #ed ,i4 have been found experimentally in the case of silver nitrate and sodium nitrate4#bgd ,the following table contains the numerical data1 which are also represented graphically in ,fig4 #ee3-- #aia ---------------------------------------- ------------- ,molecules ,na,n,o#c ,freezing point4 ,melting point4 per cent4 ---------------------------------------- ------------- #j #bjh4f;deg #bjh4f;deg #h #baa4d;deg #baj;deg #ae4jf #bae;deg #bab;deg #ai4df #bag4b;deg #bad4h;deg #ba4i #bbb;deg #bae;deg #bf #bbh4d;deg #baf4e;deg #bi4g #bcd4h;deg #bag4e;deg #cf4b #bdd4d;deg #bag4e;deg #dg4c #bei4d;deg #bcg4f;deg #eh4i #bgb;deg #beg;deg #gb #bhd;deg #bgd;deg #ajj #cjh;deg #cjh;deg ---------------------------------------- ------------- ,the temperature of the transition point is #bag4e;deg2 at this point the liquid contains #ai4e1 and the two conjugate solid solutions #bf and #ch molecules of sodium nitrate per cent4 respectively4 ,illustration3 ,,fig4 #ee4 ,illustration3 ,,fig4 #ef4 7b7 ,the freezing-point curve exhibits a eutectic point 7,curve ,,ii41 ,fig4 #ed74 #aib ,in this case the freezing point of each of the components is lowered by the addition of the other1 until at last a point is reached at which the liquid solution solidifies to a mixture or conglomerate of two mixed crystals4 ,examples4--,curves belonging to this class have been obtained in the case of potassium and thallium nitrates#bge and of naphthalene and monochloracetic acid4#bgf ,the data for the latter are given in the following table and represented in ,fig4 #ef3-- ---------------------------------------- --------------------------------- ,liquid solution4 ,solid solution4 ---------------------------------------- -------------------- ,temperature4 ,per cent4 ,per cent4 ,per cent4 ,per cent4 naphthalene4 acid4 naphthalene4 acid4 ---------------------------------------- --------------------------------- #fb;deg -- #ajj -- #ajj #fj;deg #d4j #if4j #a4g #ih4c #ee;deg #ba4j #gi4j #b4a #ig4i #ec4e;deg #bi4d #gj4j -- -- #ee;deg #ca4c #fh4g #ei4f #dj4d #fj;deg #db4d #eg4f #hj4c #ai4g #fe;deg #ec4c #df4g #hi4b #aj4h #gj;deg #fi4g #b4c #ie4d #d4f #ge;deg #hd4d #ae4f #if4f #c4d #gi4i;deg #ajj -- #ajj -- ---------------------------------------- --------------------------------- ,at the eutectic point the liquid solution is in equilibrium with two different mixed crystals the composition of which is represented by ,d and ,e respectively4 ,if1 therefore1 a fused mixture containing the two components ,a and ,b in the proportions represented by ,c is cooled down1 it will1 when the temperature has reached the point ,c1 solidify completely to a conglomerate of mixed crystals1 ,d and ,e4 ,illustration3 ,,fig4 #eg4 ,illustration3 ,,fig4 #eh4 ,changes in ,mixed ,crystals with the ,temperature4--,in the case of the different types of systems represented in ,fig4 #di1 a homogeneous liquid solution of the two components will exist at temperatures above the freezing-point curve1 a homogeneous mixed crystal at temperatures below the melting-point curve1 while at any point between the freezing-point and melting-point #aic curves the mixture will separate into a solid phase and a liquid phase4 ,in the case1 however1 of the two types shown in ,fig4 #ed the relationships are somewhat more complicated4 ,as before1 the area above the freezing-point curve gives the conditions under which homogeneous liquid solutions can exist2 but below the melting-point curve two different mixed crystals can coexist4 ,this will be best understood from ,figs4 #eg and #eh4 ,d and ,e represent1 as we have seen1 the composition of two mixed crystals which are in equilibrium with the liquid solution at the temperature of the point ,c4 ,these two mixed crystals represent1 in the one case1 a saturated solution of ,b in ,a 7point ,d71 and the other a saturated solution of ,a in ,b 7point ,e74 ,just as we saw that the mutual solubility of two liquids varied with the temperature1 so also in the case of two solids2 as the temperature alters1 the solubility of the two solid components in one another will change4 ,this alteration is indicated diagrammatically in ,figs4 #eg and #eh by the dotted curve similar to the solubility curves for two mutually soluble liquids 7p4 #aja74 ,suppose1 now1 that a mixed crystal of the composition x is cooled down1 it will remain unchanged until1 when the temperature has fallen to t'1 the homogeneous mixed crystal breaks up into a conglomerate of two mixed crystals the composition of #aid which is represented by x' and x respectively4 ,from this1 then1 it can be seen that in the case of substances which form two solid solutions1 the mixed crystals which are desposited from the liquid fused mass need not remain unchanged in the solid state1 but may at some lower temperature lose their homogeneity4 ,this fact is of considerable importance for the formation of alloys4#bgg ,a good example of this will soon be met with in the case of the iron and carbon alloys4 ,the alloys of copper and tin also furnish examples of the great changes which may take place in the alloy between the temperature at which it separates out from the fused mass and the ordinary temperature4 ,thus1 for example1 one of the alloys of copper and tin which separates out from the liquid as a solid solution breaks up1 on cooling1 into the compound ,cu#c,sn and liquid3#bgh a striking example of a solid substance partially liquefying on being cooled4 99 99 99 99 99 #aie ,,chapter ,,xi ,,equilibrium ,,between ,,dynamic ,,isomerides ,it has long been known that certain substances1 e4g4 acetoacetic ester1 are capable when in solution or in the fused state1 of reacting as if they possessed two different constitutions2 and in order to explain this behaviour the view was advanced 7by ,laar7 that in such cases a hydrogen atom oscillated between two positions in the molecule1 being at one time attached to oxygen1 at another time to carbon1 as represented by the formula-- ,,ch#c4;,c--,,ch4,,co#b;,c#b;,h#e 4 4 ,o-,h ,when the hydrogen is in one position1 the substance will act as an hydroxy-compound2 with hydrogen in the other position1 as a ketone4 ,substances possessing this double function are called tautomeric4 ,doubt1 however1 arose as to the validity of the above explanation1 and this doubt was confirmed by the isolation of the two isomerides in the solid state1 and also by the fact that the velocity of change of the one isomeride into the other could in some cases be quantitatively measured4 ,these and other observations then led to the view1 in harmony with the laws of chemical dynamics1 that tautomeric substances in the dissolved or fused state represent a mixture of two isomeric forms1 and that equilibrium is established not by intra- but by inter-molecular change1 as expressed by the equation-- ,,ch#c4;,,co4,,ch#b4;,,co#b;,c#b;,h#e -- ,,ch#c4;,c7,,oh73,,ch4,,co#b;,c#b;,h#e #aif ,in the solid state1 the one or other of the isomerides represents the stable form2 but in the liquid state 7solution or fusion7 the stable condition is an equilibrium between the two forms4 ,a similar behaviour is also found in the case of other isomeric substances where the isomerism is due to difference of structure1 i4e4 structure isomerism 7e4g4 in the case of the oximes ,c#f;,h#e4;,c4,h ,c#f;,h#e4;,c4,h and 71 ,n4,,oh ,,ho4,n or to difference in configuration1 i4e4 stereoisomerism 7e4g4 optically active substances71 or to polymerism 7e4g4 acetaldehyde and paraldehyde74 ,in all such cases1 although the different solid forms correspond to a single definite constitution1 in the liquid state a condition of equilibrium between the two modifications is established4 ,as a general name for these different classes of substances1 the term dynamic isomerides has been introduced2 and the different kinds of isomerism are classed together under the title dynamic isomerism4#bgi ,by reason of the importance of these phenomena in the study more especially of ,organic ,chemistry1 a brief account of the equilibrium relations exhibited by systems composed of dynamic isomerides may be given here4#bhj ,in studying the fusion and solidification of those substances which exhibit the relationships of dynamic isomerism1 the phenomena observed will vary somewhat according as the reversible transformation of the one form into the other takes place with measurable velocity at temperatures in the neighbourhood of the melting points1 or only at some higher temperature4 ,if the transformation is very rapid1 the system will behave like a one-component system1 but if the isomeric change is comparatively slow1 the behaviour will be that of a two-component system4 ,temperature-,concentration ,diagram4--,the relationships which are met with here will be most readily understood with #aig the help of ,fig4 #ei4 ,suppose1 in the first instance1 that isomeric transformation does not take place at the temperature of the melting point1 then the freezing point curve will have the simple form ,,acb2 the formation of compounds being for the present excluded4 ,this is the simplest type of curve1 and gives the composition of the solutions in equilibrium with the one modification 7alpha modification7 at different temperatures 7curve ,,ac72 and of the solutions in equilibrium with the other modification 7beta modification7 at different temperatures 7curve ,,bc74 ,c is the eutectic point at which the two solid isomerides can exist side by side in contact with the solution4 ,illustration3 ,,fig4 #ei4 ,now1 suppose that isomeric transformation takes place with measurable velocity4 ,if the pure alpha-modification is heated to a temperature t' above its melting point1 and the liquid maintained at that temperature until equilibrium has been established1 a certain amount of the beta-form will be present in the liquid1 the composition of which will be represented by the point x'4 ,the same condition of equilibrium will also be reached by starting with pure beta4 ,similarly1 if the temperature of the liquid is maintained at the temperature t1 equilibrium will be reached1 we shall suppose1 when the solution has the composition x4 ,the curve ,,de1 therefore1 which passes through all the different values of x corresponding to different values of t1 will represent the change of equilibrium with the temperature4 ,it will slope to the right 7as in the figure7 if the transformation of alpha into beta is accompanied by absorption of heat2 to the left if the transformation is accompanied by evolution of heat1 in accordance with van't ,hoff's ,law of movable equilibrium4 ,if transformation occurs without heat effect1 the equilibrium will be independent of the #aih temperature1 and the equilibrium curve ,,de will therefore be perpendicular and parallel to the temperature axis4 ,we must now find the meaning of the point ,d4 ,suppose the pure alpha- or pure beta-form heated to the temperature t'1 and the temperature maintained constant until the liquid has the composition x' corresponding to the equilibrium at that temperature4 ,if the temperature is now allowed to fall sufficiently slowly so that the condition of equilibrium is continually readjusted as the temperature changes1 the composition of the solution will gradually alter as represented by the curve x',d4 ,since ,d is on the freezing point curve of pure alpha1 this form will be deposited on cooling2 and since ,d is also on the equilibrium curve of the liquid1 ,d is the only point at which solid can exist in stable equilibrium with the liquid phase4 7,the vapour phase may be omitted from consideration1 as we shall suppose the experiments carried out in open vessels47 ,all systems consisting of the two hylotropic#bha isomeric substances alpha and beta will1 therefore1 ultimately freeze at the point ,d1 which is called the natural freezing point#bhb of the system2 provided1 of course1 that sufficient time is allowed for equilibrium to be established4 ,from this it is apparent that the stable modification at temperatures in the neighbourhood of the melting point is that which is in equilibrium with the liquid phase at the natural freezing point4 ,from what has been said1 it will be easy to predict what will be the behaviour of the system under different conditions4 ,if pure alpha is heated1 a temperature will be reached at which it will melt1 but this melting point will be sharp only if the velocity of isomeric transformation is comparatively slow2 i4e4 slow in comparison with the determination of the melting point4 ,if the substance be maintained in the fused condition for some time1 a certain amount of the beta modification will be formed1 and on lowering the temperature the pure alpha form will be deposited1 not at the temperature of the melting point1 but at some lower temperature depending on the concentration of the beta modification in the liquid phase4 ,if isomeric transformation #aii takes place slowly in comparison with the rate at which deposition of the solid occurs1 the liquid will become increasingly rich in the beta modification1 and the freezing point will1 therefore1 sink continuously4 ,at the eutectic point1 however1 the beta modification will also be deposited1 and the temperature will remain constant until all has become solid4 ,if1 on the other hand1 the velocity of transformation is sufficiently rapid1 then as quickly as the alpha modification is deposited1 the equilibrium between the two isomeric forms in the liquid phase will continuously readjust itself1 and the end-point of solidification will be the natural freezing point4 ,similarly1 starting with the pure beta modification1 the freezing point after fusion will gradually fall owing to the formation of the alpha modification2 and the composition of the liquid phase will pass along the curve ,,bc4 ,if1 now1 the rate of cooling is not too great1 or if the velocity of isomeric transformation is sufficiently rapid1 complete solidification will not occur at the eutectic point2 for at this temperature solid and liquid are not in stable equilibrium with one another4 ,on the contrary1 a further quantity of the beta modification will undergo isomeric change1 the liquid phase will become richer in the alpha form1 and the freezing point will rise2 the solid phase in contact with the liquid being now the alpha modification4 ,the freezing point will continue to rise until the point ,d is reached1 at which complete solidification will take place without further change of temperature4 ,the diagram also allows us to predict what will be the result of rapidly cooling a fused mixture of the two isomerides4 ,suppose that either the alpha or the beta modification has been maintained in the fused state at the temperature t' sufficiently long for equilibrium to be established4 ,the composition of the liquid phase will be represented by x'4 ,if the liquid is now rapidly cooled1 the composition will remain unchanged as represented by the dotted line x',g4 ,at the temperature of the point ,g solid alpha modification will be deposited4 ,if the cooling is not carried below the point ,g1 so as to cause complete solidification1 the freezing point will be found to rise with time1 owing to the conversion of some of the beta form into the alpha form #bjj in the liquid phase2 and this will continue until the composition of the liquid has reached the point ,d4 ,from what has just been said1 it can also be seen that if the freezing point curves can be obtained by actual determination of the freezing points of different synthetic mixtures of the two isomerides1 it will be possible to determine the condition of equilibrium in the fused state at any given temperature without having recourse to analysis4 ,all that is necessary is to rapidly cool the fused mass1 after equilibrium has been established1 and find the freezing point at which solid is deposited2 that is1 find the point at which the line of constant temperature cuts the freezing point curve4 ,the composition corresponding to this temperature gives the composition of the equilibrium mixture at the given temperature4 ,it will be evident1 from what has gone before1 that the degree of completeness with which the different curves can be realised will depend on the velocity with which isomeric change takes place1 and on the rapidity with which the determinations of the freezing point can be carried out4 ,as the two extremes we have1 on the one hand1 practically instantaneous transformation1 and on the other1 practically infinite slowness of transformation4 ,in the former case1 only one melting and freezing point will be found1 viz4 the natural freezing point2 in the latter case1 the two isomerides will behave as two perfectly independent components1 and the equilibrium curve ,,de will not be realised4 ,the diagram which is obtained when isomeric transformation does not occur within measurable time at the temperature of the melting point is somewhat different from that already given in ,fig4 #ei4 ,in this case1 the two freezing point curves ,,ac and ,,bc 7,fig4 #fj7 can be readily realized1 as no isomeric change occurs in the liquid phase4 ,suppose1 however1 that at a higher temperature1 t'1 reversible isomeric transformation can take place1 the composition of the liquid phase will alter until at the point x' a condition of equilibrium is reached2 and the composition of the liquid at higher temperatures will be represented by the curve x',f4 ,below the temperature t' the position of the equilibrium curve is hypothetical2 but as the temperature #bja falls the velocity of transformation diminishes1 and at last becomes practically zero4 ,the equilibrium curve can therefore be regarded as dividing into two branches x',g and x',h4 ,at temperatures between ,g and t' the alpha modification can undergo isomeric change leading to a point on the curve ,gx'2 and the beta modification can undergo change leading to a point on the curve ,hx'4 ,the same condition of equilibrium is therefore not reached from each side1 and we are therefore dealing not with true but with false equilibrium 7p4 #e74 ,below the temperatures ,g and ,h1 isomeric transformation does not occur in measurable time4 ,we shall not1 however1 enter into a detailed discussion of the equilibria in such systems1 more especially as they are not systems in true equilibrium1 and as the temperature at which true equilibrium can be established with appreciable velocity alters under the influence of catalytic agents4#bhc ,examples of such systems will no doubt be found in the case of optically active substances1 where both isomerides are apparently quite stable at the melting point4 ,in the case of such substances1 also1 the action of catalytic agents in producing isomeric transformation 7racemisation7 is well known4 ,illustration3 ,,fig4 #fj4 ,transformation of the ,unstable into the ,stable ,form4--,as has already been stated1 the stable modification in the neighbourhood of the melting point is that one which is in equilibrium with the liquid phase at the natural freezing point4 ,in the case of polymorphic substances1 we have seen 7p4 #ci7 that that form which is stable in the neighbourhood of the melting point melts at the higher temperature4 ,that was a #bjb consequence of the fact that the two polymorphic forms on melting gave identical liquid phases4 ,in the present case1 however1 the above rule does not apply1 for the simple reason that the liquid phase obtained by the fusion of the one modification is not identical with that obtained by the fusion of the other4 ,in the case of isomeric substances1 therefore1 the form of lower melting point may be the more stable2 and where this behaviour is found it is a sign that the two forms are isomeric 7or polymeric7 and not polymorphic4#bhd ,an example of this is found in the case of the isomeric benzaldoximes 7p4 #bjc74 ,since in ,fig4 #ei the alpha modification has been represented as the stable form1 the transformation of the beta into the alpha form will be possible at all temperatures down to the transition point4 ,at temperatures below the eutectic point1 transformation will occur without formation of a liquid phase2 but at temperatures above the eutectic point liquefaction can take place4 ,this will be more readily understood by drawing a line of constant temperature1 ,,hk1 at some point between ,c and ,b4 ,then if the beta modification is maintained for a sufficiently long time at that temperature1 a certain amount of the alpha modification will be formed2 and when the composition of the mixture has reached the point ,h1 fusion will occur4 ,if the temperature is maintained constant1 isomeric transformation will continue to take place in the liquid phase until the equilibrium point for that temperature is reached4 ,if this temperature is higher than the natural melting point1 the mixture will remain liquid all the time2 but if it is below the natural melting point1 then the alpha modification will be deposited when the system reaches the condition represented by the point on the curve ,,ac corresponding to the particular temperature4 ,as isomeric transformation continues1 the freezing point of the system will rise until it reaches the natural freezing point ,d4 ,similarly1 if the alpha modification is maintained at a temperature above that of the point ,d1 liquefaction will ultimately occur1 and the system will again reach the final state represented by ,d4#bhe #bjc ,examples4--,benzaldoximes4 ,the relationships which have just been discussed from the theoretical point of view will be rendered clearer by a brief description of cases which have been experimentally investigated4 ,the first we shall consider is that of the two isomeric benzaldoximes3#bhf-- ,c#f;,h#e4;,c4,h ,c#f;,h#e4;,c4,h ,,ho4,n ,n4,,oh ,benzantialdoxime ,benzsynaldoxime 7alpha-modification74 7beta-modification74 ,fig4 #fa gives a graphic representation of the results obtained4 ,the melting point of the alpha modification is #cd-ce;deg2 the melting point of the unstable beta-modification being #acj;deg4 ,the freezing curves ,,ac and ,,bc were obtained by determining the freezing points of different mixtures of known composition1 and the numbers so obtained are given in the following table4 #bjd ---------------------------------------- ------------ ,grams of the alpha modification in #ajj gm4 of mixture4 ,freezing point4 ---------------------------------------- ----------- #bf4b #aja;deg #di4b #gi;deg #gc4g #df;deg #ia4g #bf4b;deg #ie4j #bh4f;deg #if4j #cj4j;deg ---------------------------------------- ------------ ,illustration3 ,,fig4 #fa4 ,the eutectic point ,c was found to lie at #be-bf;deg1 and the natural freezing point ,d was found to be #bg4g;deg4 ,the equilibrium curve ,,de was determined by heating the liquid mixtures at different temperatures until equilibrium was attained1 and then rapidly cooling the liquid4 ,in all cases the freezing point was practically that of the point ,d4 ,from this it is seen that the equilibrium curve must be a straight line parallel to the temperature axis2 and1 therefore1 isomeric transformation in the case of the two benzaldoximes is not accompanied by any heat effect 7p4 #aig74 ,this behaviour has also been found in the case of acetaldoxime4#bhg ,the isomeric benzaldoximes are also of interest from the fact that the stable modification has the lower melting point 7v4 p4 #bjb74 ,acetaldehyde and ,paraldehyde4--,as a second example of the equilibria between two isomerides1 we shall take the two isomeric 7polymeric7 forms of acetaldehyde1 which have recently been exhaustively studied4#bhh #bje ,in the case of these two substances the reaction #c;,,ch#c4;,,cho -- 7,,ch#c4;,,cho7#c takes place at the ordinary temperature with very great slowness4 ,for this reason it is possible to determine the freezing point curves of acetaldehyde and paraldehyde4 ,the three chief points on these curves1 represented graphically in ,fig4 #fb1 are3-- m4p4 of acetaldehyde - #aah4de;deg m4p4 of paraldehyde #ab4ee;deg eutectic point - #aai4i;deg ,illustration3 ,,fig4 #fb4 ,in order to determine the position of the natural melting point1 it was necessary1 on account of the slowness of transformation1 to employ a catalytic agent in order to increase the velocity with which the equilibrium was established4 ,a drop of concentrated sulphuric acid served the purpose4 ,in presence of a trace of this substance1 isomeric transformation very speedily occurs1 and leads to the condition of equilibrium4 ,starting in the one case with fused paraldehyde1 and in the other case with acetaldehyde1 the same freezing point1 viz4 #f4ge;deg1 was obtained1 the solid phase being paraldehyde4 ,this temperature1 #f4ge;deg1 is therefore the natural freezing point1 and paraldehyde1 the solid in equilibrium with the liquid phase at this point1 is the stable form4 ,with regard to the change of equilibrium with the temperature1 it was found that whereas the liquid phase contained #aa4g molecules per cent4 of acetaldehyde at the natural freezing point1 the liquid at the temperature of #da4f;deg contains #df4f molecules per cent4 of acetaldehyde4 ,as the temperature #bjf rises1 therefore1 there is increased formation of acetaldehyde1 or a decreasing amount of polymerisation4 ,this is in harmony with the fact that the polymerisation of acetaldehyde is accompanied by evolution of heat4 ,while speaking of these isomerides1 it may be mentioned that at the temperature #da4f;deg the equilibrium mixture has a vapour pressure equal to the atmospheric pressure4 ,at this temperature1 therefore1 the equilibrium mixture 7obtained quickly with the help of a trace of sulphuric acid7 boils4#bhi 99 99 99 99 99 #bjg ,,chapter ,,xii ,,summary4--,,application ,,of ,,the ,,phase ,,rule ,,to ,,the ,,study ,,of ,,systems ,,of ,,two ,,components ,in this concluding chapter on two-component systems1 it is proposed to indicate briefly how the ,phase ,rule has been applied to the elucidation of a number of problems connected with the equilibria between two components1 and how it has been employed for the interpretation of the data obtained by experiment4 ,it is hoped that the practical value of the ,phase ,rule may thereby become more apparent1 and its application to other cases be rendered easier4 ,the interest and importance of investigations into the conditions of equilibrium between two substances1 lie in the determination not only of the conditions for the stable existence of the participating substances1 but also of whether or not chemical action takes place between these two components2 and if combination occurs1 in the determination of the nature of the compounds formed and the range of their existence4 ,in all such investigations1 the ,phase ,rule becomes of conspicuous value on account of the fact that its principles afford1 as it were1 a touchstone by which the character of the system can be determined1 and that from the form of the equilibrium curves obtained1 conclusions can be drawn as to the nature of the interaction between the two substances4 ,in order to exemplify the application of the principles of the ,phase ,rule more fully than has already been done1 illustrations will be drawn from investigations on the interaction of organic compounds2 on the equilibria between optically active compounds2 and on alloys4 #bjh ,summary of the ,different ,systems of ,two ,components4--,before passing to the consideration of the application of the ,phase ,rule to the investigation of particular problems1 it will be well to collect together the different types of equilibrium curves with which we are already acquainted2 to compare them with one another1 in order that we may then employ these characteristic curves for the interpretation of the curves obtained as the result of experiment4 ,in investigating the equilibria between two components1 three chief classes of curves will be obtained according as-- ,i4 ,no combination takes place between the two components4 ,,ii4 ,the components can form definite compounds4 ,,iii4 ,the components separate out in the form of mixed crystals4 ,the different types of curves which are obtained in these three cases are represented in ,figs4 #fc1 #fd1 #fe4 ,these different diagrams represent the whole series of equilibria1 from the melting point of the one component 7,a7 to that of the other component 7,b74 ,the curves represent1 in all cases1 the composition of the solution1 or phase of variable composition2 the temperature being measured along one axis1 and the composition along the other4 ,we shall now recapitulate very briefly the characteristics of the different curves4 ,illustration3 ,,fig4 #fc4 ,if no compound is formed between the two components1 #bji the general form of the equilibrium curve will be that of curve ,i4 or ,,ii41 ,fig4 #fc4 ,type ,i4 is the simplest form of curve found1 and consists1 as the diagram shows1 of only two branches1 ,,ac and ,,bc1 meeting at the point ,c1 which lies below the melting point of either component4 ,the solid phase which is in equilibrium with the solutions ,,ac is pure ,a2 that in equilibrium with ,,bc1 pure ,b4 ,c is the eutectic point4 ,although at the eutectic point the solution solidifies entirely without change of temperature1 the solid which is deposited is not a homogeneous solid phase1 but a mixture1 or conglomerate of the two components4 ,the eutectic point1 therefore1 represents the melting or freezing point1 not of a compound1 but of a mixture 7p4 #aai74 ,curve ,,ii41 ,fig4 #fc1 is obtained when two liquid phases are formed4 ,c is an eutectic point1 ,d and ,f are transition points at which there can co-exist the four phases--solid1 two liquid phases1 vapour4 ,,def represents the change in the composition of the two liquid phases with rise of temperature2 the curve might also have the reversed form with the critical solution point below the transition points ,d and ,f4 ,illustration3 ,,fig4 #fd4 ,in the second class of systems 7,fig4 #fd71 that in which combination between the components occurs1 there are again two types according as the compound formed has a definite melting point 7i4e4 can exist in equilibrium with a solution of the same composition71 or undergoes only partial fusion2 that is1 exhibits a transition point4 ,if a compound possessing a definite melting point is formed1 the equilibrium curve will have the general form shown by curve ,i41 ,fig4 #fd4 ,a1 ,b1 and ,d are the melting points of pure ,a1 pure ,b1 and of the compound ,ax,by respectively4 ,,ac #baj is the freezing point curve of ,a in presence of ,b2 ,,be that of ,b in presence of ,a2 and ,,dc and ,,de the freezing point curves of the compound in presence of a solution containing excess of one of the components4 ,c and ,e are eutectic points at which mixtures of ,a and ,ax,by1 or ,b and ,ax,by can co-exist in contact with solution4 ,the curve ,,cde may be large or small1 and the melting point of the compound1 ,d1 may lie above or below that of each of the components1 or may have an intermediate position4 ,if more than one compound can be formed1 a series of curves similar to ,,cde will be obtained 7cf4 p4 #aeb74 ,on the other hand1 if the compound undergoes transition to another solid phase at a temperature below its melting point1 a curve of the form ,,ii41 ,fig4 #fd1 will be found4 ,this corresponds to the case where a compound can exist only in contact with solutions containing excess of one of the components4 ,the metastable continuation of the equilibrium curve for the compound is indicated by the dotted line1 the summit of which would be the melting point of the compound4 ,before this temperature is reached1 however1 the solid compound ceases to be able to exist in contact with solution1 and transition to a different solid phase occurs at the point ,e 7cf4 p4 #acd74 ,this point1 therefore1 represents the limit of the existence of the compound ,,ab4 ,if a series of compounds can be formed none of which possess a definite melting point1 then a series of curves will be obtained which do not exhibit a temperature-maximum1 and there will be only one eutectic point4 ,the limits of existence of each compound will be marked by a break in the curve 7cf4 p4 #adc74 ,illustration3 ,,fig4 #fe4 ,turning1 lastly1 to the third class of systems1 in which formation of mixed crystals can occur1 five different types of curves can be obtained1 as shown in ,fig4 #fe4 ,with regard to the first three types1 curves ,i41 ,,ii41 and ,,iii41 #baa these differ entirely from those of the previous classes1 in that they are continuous2 they exhibit no eutectic point1 and no transition point4 ,curve ,,ii4 bears some resemblance to the melting-point curve of a compound 7e4g4 ,,cde1 ,fig4 #fd1 ,i471 but differs markedly from it in not ending in eutectic points4 ,further1 in the case of the formation of a compound1 the composition of the solid phase remains unchanged throughout the whole curve between the eutectic points2 whereas1 when mixed crystals are produced1 the composition of the solid phase varies with the composition of the liquid solution4 ,on passing through the maximum1 the relative proportions of ,a and ,b in the solid and the liquid phase undergo change2 on the one side of the maximum1 the solid phase contains relatively more ,a1 and on the other side of the maximum1 relatively more ,b than the liquid phase4 ,lastly1 when mixed crystals are formed1 the temperature at which complete solidification occurs changes as the composition of the solution changes1 whereas in the case of the formation of compounds1 the temperature of complete solidification for all solutions is a eutectic point4 ,the third type of curve1 ,fig4 #fe1 can be distinguished in a similar manner from the ordinary eutectic curve1 ,fig4 #fc1 ,i41 to which it bears a certain resemblance4 ,whereas in the case of the latter1 the eutectic point is the temperature of complete solidification of all solutions1 the point of minimum temperature in the case of the formation of mixed crystals1 is the solidification point only of solutions having one particular composition2 that1 namely1 of the minimum point4 ,for all other solutions1 the temperature of complete solidification is different4 ,whereas1 also1 in the case of the simple eutectic curve1 the solid which separates out from the solutions represented by either curve remains the same throughout the whole extent of that curve1 the composition of the mixed crystal varies with variation of the composition of the liquid phase1 and the relative proportions of the two components in the solid and the liquid phase are reversed on passing through the minimum4#bij ,in a similar manner1 type ,,iv41 ,fig4 #fe1 can be distinguished from type ,,ii41 ,fig4 #fd1 by the fact that it does not exhibit a #bab eutectic point1 and that the composition of the solid phase undergoes continuous variation with variation of the liquid phase on either side of the transition point4 ,lastly1 type ,v41 which does exhibit a eutectic point1 differs from the eutectic curve of ,fig4 #fc1 in that the eutectic point does not constitute the point of complete solidification for all solutions1 and that the composition of the solid phase varies with the composition of the liquid phase4 ,such1 then1 are the chief general types of equilibrium curves for two-components2 they are the pattern curves with which other curves1 experimentally determined1 can be compared2 and from the comparison it will be possible to draw conclusions as to the nature of the equilibria between the two components under investigation4 #a4 ,organic ,compounds4 ,illustration3 ,,fig4 #ff4 ,the principles of the ,phase ,rule have been applied to the investigation of the equilibria between organic compounds1 and ,figs4 #ff-fi reproduce some of the results which have been obtained4#bia #bac ,fig4 #ff1 the freezing point curve 7curve of equilibrium7 for o-nitrophenol and p-toluidine1 shows a curve of the simplest type#bib 7type ,i41 ,fig4 #fc71 in which two branches meet at an eutectic point4 ,the solid phase in equilibrium with solutions represented by the left-hand branch of the curve was o-nitrophenol 7m4p4 #dd4a;deg72 that in equilibrium with the solutions represented by the right-hand branch1 was p-toluidine 7m4p4 #dc4c;deg74 ,at the eutectic point 7#ae4f;deg71 these two solid phases could co-exist with the liquid phase4 ,this equilibrium curve1 therefore1 shows that o-nitrophenol and p-toluidine do not combine with one another4 ,in connection with this curve1 attention may be called to the interesting fact that although the solid produced by cooling the liquid phase at the eutectic point has a composition approximating to that of a compound of equimolecular proportions of the phenol and toluidine1 and a constant melting point1 it is nevertheless a mixture4 ,although1 as a rule1 the constituents of the eutectic mixture are not present in simple molecular proportions1 there is no reason why they should not be so2 and it is therefore necessary to beware of assuming the formation of compounds in such cases4#bic ,fig4 #fg1 on the other hand1 indicates with perfect certainty the formation of a compound between phenol and alpha-naphthylamine4#bid 7,cf4 curve ,i41 ,fig4 #fd47 ,phenol freezes at #dj4d;deg1 but the addition of alpha-naphthylamine lowers the freezing point as represented by the curve ,,ac4 ,at ,c 7#af4j;deg7 the compound ,c#f;,h#e,,oh1,c#aj;,h#g,,nh#b is formed1 and the system becomes invariant4 ,on increasing the amount of the amine1 the temperature of equilibrium rises1 the solid phase now being the compound4 ,at ,d1 the curve passes through a maximum 7#bh4h;deg71 at which the solid and liquid phases have the same composition4 ,this is the melting point of the compound4 ,further addition of the amine lowers the temperature of equilibrium1 until at ,e solid alpha-naphthylamine separates out1 and a second eutectic point 7#bd4j;deg7 is obtained4 ,,be is the #bad freezing-point curve of alpha-naphthylamine in presence of phenol1 the freezing point of the pure amine being #dh4c;deg4 ,on account of the great sluggishness with which the compound of phenol and alpha-naphthylamine crystallizes1 it was found possible to follow the freezing point curves of phenol and the amine to temperatures considerably below the eutectic points1 as shown by the curves ,,cf and ,,eg4 ,illustration3 ,,fig4 #fg4 ,phenol can also combine with p-toluidine in equimolecular proportions2 and this compound is of interest1 from the fact that it exists in two crystalline forms melting at #bh4e;deg and #cj;deg4 ,each of these forms now must have its own equilibrium curve1 and it was found that the intermediate portion of the freezing point curve was duplicated1 as shown in ,fig4 #fh4bie #bae ,illustration3 ,,fig4 #fh4 ,illustration3 ,,fig4 #fi4 #baf ,lastly1 a curve is given1 ,fig4 #fi1bif which corresponds with curve ,,ii41 ,fig4 #fd4 ,picric acid and benzene can form a compound1 which1 however1 can exist only in contact with solutions containing excess of benzene4 ,when the temperature is raised1 a point 7,k7 is reached at which the compound melts with separation of solid picric acid4 ,the point1 ,k1 is1 therefore1 a transition point2 analysis1 however1 showed that the composition of the solution at this point is very nearly that of the compound ,c#f;,h#b7,,no#b7c,,oh1,c#f;,h#f1 so that the melting point of the compound can almost be reached4 ,the fusion of the compound of benzene and picric acid with separation of the latter is analogous to the 7partial7 fusion of ,glauber's salt with separation of anhydrous sodium sulphate4 #b4 ,optically ,active ,substances4 ,the question as to whether a resolvable inactive body is a mixture of the two oppositely active constituents 7a dl-mixture71 or a racemic compound1 is one which has given rise to considerable discussion during the past decade2 and several investigators have endeavoured to establish general rules by which the question could be decided4 ,in the case of inactive liquids it is a matter of great difficulty to arrive at a certain conclusion as to whether one is dealing with a mixture or a compound1 for in this case the usual physical methods give but a dubious answer2 and although the existence of a racemate in the liquid state 7in the case of conine7 has been asserted1#big most chemists incline to the belief that such a thing is improbable4 ,even in the case of crystalline substances1 where the differences between the various forms is greater1 it was not always easy to discriminate between the dl-mixture and the racemic compound4 ,the occurrence of hemihedral faces was considered by ,pasteur to be a sufficient criterion for an optically active substance4 ,it has1 however1 been found that hemihedry in crystals1 although a frequent accompaniment of #bag optical activity1 is by no means a necessary or constant expression of this property4 ,other rules1 also1 which were given1 although in some cases reliable1 were in other cases insufficient2 and all were in so far unsatisfactory that they lacked a theoretical basis4 ,with the help of the ,phase ,rule1 however1 it is possible from a study of the solubility or fusion curves of the optically active and inactive substances1 to decide the nature of the inactive substance1 at least under certain conditions4 ,on account of the interest and importance which these compounds possess1 a brief description of the application of the ,phase ,rule to the study of such substances will be given here2#bih the two optical antipodes being regarded as the two components4 ,in the present chapter we shall consider only the fusion curves1 the solubility curves being discussed in the next section on three-component systems4 ,the rules which are hereby obtained1 have reference only to the nature of the inactive substance in the neighbourhood of the melting points4 ,i4 ,the inactive substance is a dl-mixture4 ,in this case the fusion curves will have the simple form shown in type ,i1 ,fig4 #fc4 ,a and ,b are the melting points of the two optical isomerides1 and ,c the eutectic point at which the inactive mixture consisting of equal amounts of d- and l-form melts4 ,owing to the similar effect of the one form on the freezing point of the other1 the figure is symmetrical4 ,no example of this simple case has been investigated4 ,,ii4 ,the two components form a racemic compound4 ,in this case there will be three melting point curves as in ,fig4 #fd1 type ,i4 ,in this case also the figure must be symmetrical4 ,examples4--,as examples of this1 may be taken dimethyl tartrate and mandelic acid1 the freezing point curves of which are given in ,figs4 #gj and #ga4bii ,as can be seen1 the curve for the racemic tartrate occupies a large part of the diagram1 #bah while that for racemic mandelic acid is much smaller4 ,in the case of dimethyldiacetyl tartrate1 this middle portion is still less4 ,illustration3 ,,fig4 #gj4 ,illustration3 ,,fig4 #ga4 ,illustration3 ,,fig4 #gb4 ,active dimethyl tartrate melts at #dc4c;deg2 racemic dimethyl tartrate at #hi4d;deg4 ,active mandelic acid melts at #acb4h;deg2 the racemic acid at #aah4j;deg4 ,in the one case1 therefore1 the racemic compound has a higher1 in the other a lower melting point than the active forms4 #bai ,in the case of partially racemic compounds 7i4e4 the compound of a racemate with an optically active substance7 the type of curve will be the same1 but the figure will no longer be symmetrical4 ,such a curve has been found in the case of the l-menthyl esters of d- and l-mandelic acid 7,fig4 #gb74cjj ,the freezing point of l-menthyl d-mandelate is #ig4b;deg1 of l-menthyl l-mandelate #gg4f;deg1 and of l-menthyl r-mandelate #hc4g4;deg ,it will be observed that the summit of the curve for the partially racemic mandelate is very flat1 indicating that the compound is largely dissociated into its components at the temperature of fusion4 ,,iii4 ,the inactive substance is a pseudo-racemic mixed crystal4 ,in cases where the active components can form mixed crystals1 the freezing-point curve will exhibit one of the forms given in ,fig4 #fe4 ,the inactive mixed crystal containing #ej per cent4 of the dextro and laevo compound1 is known as a pseudo-racemic mixed crystal4#cja ,so far1 only curves of the types ,i4 and ,,ii4 have been obtained4 ,examples4--,the two active camphor oximes are of interest from the fact that they form a continuous series of mixed crystals1 all of which have the same melting point4 ,the curve which is obtained in this case is1 therefore1 a straight line joining the melting points of the pure active components2 the melting point of the active isomerides and of the whole series of mixed crystals being #aah4h;deg4 ,illustration3 ,,fig4 #gc4 ,in the case of the carvoximes mixed crystals are also formed1 but the equilibrium curve in this case exhibits a maximum 7,fig4 #gc74 ,at this maximum point the composition of the solid and of the liquid solution is the same4 ,since the curve must be symmetrical1 this maximum point must occur in the case of the solution containing #ej per cent4 #bbj of each component1 which will therefore be inactive4 ,further1 this inactive mixed crystal will melt and solidify at the same temperature1 and behave1 therefore1 like a chemical compound 7p4 #ahg74 ,the melting point of the active compounds is #gb;deg2 that of the inactive pseudo-racemic mixed crystal is #ia4d;deg4 ,transformations4--,as has already been remarked1 the conclusions which can be drawn from the fusion curves regarding the nature of the inactive substances formed hold only for temperatures in the neighbourhood of the melting points4 ,at temperatures below the melting point transformation may occur2 e4g4 a racemate may break up into a dl-mixture1 or a pseudo-racemic mixed crystal may form a racemic compound4 ,we shall at a later point meet with examples of a racemic compound changing into a dl-mixture at a definite transition point2 and the pseudo-racemic mixed crystal of camphoroxime is an example of the second transformation4 ,although at temperatures in the neighbourhood of the melting point the two active camphoroximes form only mixed crystals but no compound1 a racemic compound is formed at temperatures below #ajc;deg4 ,at this temperature the inactive pseudo-racemic mixed crystal changes into a racemic compound2 and in the case of the other mixed crystals transformation to racemate and 7excess of7 active component also occurs1 although at a lower temperature than in the case of the inactive mixed crystal4 ,although this behaviour is one of considerable importance1 this brief reference to it must suffice here4#cjb #c4 ,alloys4 ,one of the most important classes of substances in the study of which the ,phase ,rule has been of very considerable importance1 is that formed by the mixtures or compounds of metals with one another known as alloys4 ,although in the investigation of the nature of these bodies various methods are employed1 one of the most important is the determination of the character of the freezing-point curve2 for from the form of this1 valuable information can1 as we have already learned1 be #bba obtained regarding the nature of the solid substances which separate out from the molten mixture4 ,although it is impossible here to discuss fully the experimental results and the oftentimes very complicated relationships which the study of the alloys has brought to light1 a brief reference to these bodies will be advisable on account both of the scientific interest and of the industrial importance attaching to them4#cjc ,we have already seen that there are three chief types of freezing-point curves in systems of two components1 viz4 those obtained when 7#a7 the pure components crystallize out from the molten mass2 7#b7 the components form one or more compounds2 7#c7 the components form mixed crystals4 ,in the case of the metals1 representatives of these three classes are also found4 #a4 ,the components separate out in the pure state4 ,in this case the freezing-point curve is of the simple type1 ,fig4 #fc1 ,i4 ,such curves have been obtained in the case of a number of pairs of metals1 e4g4 zinc--cadmium1 zinc--aluminium1 copper--silver 7,heycock and ,neville71 tin--zinc1 bismuth--lead 7,gautier71 and in other cases4 ,from molten mixtures represented by one branch of the freezing-point curve one of the metals will be deposited2 while from mixtures represented by the other branch1 the other metal will separate out4 ,at the eutectic point the molten mass will solidify to a heterogeneous mixture of the two metals1 forming what is known as the eutectic alloy4 ,such an alloy1 therefore1 will melt at a definite temperature lower than the melting point of either of the pure metals4 #bbb ,in the following table are given the temperature and the composition of the liquid at the eutectic point1 for three pairs of metals3-- ---------------------------------------- --------------------------- ,temperature4 ,composition of liquid4 ---------------------------------------- --------------------------- ,zinc--cadmium #bfd4e;deg #gc4e atoms per cent4 of cadmium4 ,zinc--aluminium #chj4e;deg #aa aluminium4 ,copper--silver #ggh;deg #dj copper4 ---------------------------------------- --------------------------- ,the melting points of the pure metals are1 zinc1 #dai;deg2 cadmium1 #cbb;deg2 silver1 #ifj;deg2 copper1 #ajha;deg2 aluminium1 #fej;deg4 #b4 ,the two metals can form one or more compounds4 ,in this case there will be obtained not only the freezing-point curves of the pure metals1 but each compound formed will have its own freezing-point curve1 exhibiting a point of maximum temperature1 and ending on either side in an eutectic point4 ,the simplest curve of this type will be obtained when only one compound is formed1 as is the case with mercury and thallium4#cjd ,this curve is represented in ,fig4 #gd1 where the summit of the intermediate curve corresponds with a composition ,tl,hg#b4 ,similar curves are also given by nickel and tin1 by aluminium and silver1 and by other metals1 the formation of definite compounds between these pairs of metals being thereby indicated4#cje ,illustration3 ,,fig4 #gd4 #bbc ,a curve belonging to the same type1 but more complicated1 is obtained with gold and aluminium2#cjf in this case1 several compounds are formed1 some of which have a definite melting point1 while others exhibit only a transition point4 ,the chief compound is ,au,al#b1 which has practically the same melting point as pure gold4 #c4 ,the two metals form mixed crystals 7solid solutions74 ,the simplest case in which the metals crystallize out together is found in silver and gold4#cjg ,the freezing-point curve in this case is an almost straight line joining the freezing points of the pure metals 7cf4 curve ,i41 ,fig4 #fe1 p4 #baj74 ,these two metals1 therefore1 can form an unbroken series of mixed crystals4 ,in some cases1 however1 the two metals do not form an unbroken series of mixed crystals4 ,in the case of zinc and silver1#cjh for example1 the addition of silver raises the freezing point of the mixture1 until a transition point is reached4 ,this corresponds with curve ,,iv41 ,fig4 #fe4 ,silver and copper1 and gold and copper1 on the other hand1 do not form unbroken series of mixed crystals1 but the freezing-point curve exhibits an eutectic point1 as in curve ,v41 ,fig4 #fe4 ,not only may there be these three different types of curves1 but there may also be combinations of these4 ,thus the two metals may not only form compounds1 but one of the metals may not separate out in the pure state at all1 but form mixed crystals4 ,in this case the freezing point may rise 7as in the case of silver and zinc71 and one of the eutectic points will be absent4 ,iron-,carbon ,alloys4--,of all the different binary alloys1 probably the most important are those formed by iron and carbon3 alloys consisting not of two metals1 but of a metal and a non-metal4 ,on account of the importance of these alloys1 an attempt will be made to describe in brief some of the most important relationships met with4 ,before proceeding to discuss the applications of the ,phase ,rule to the study of the iron-carbon alloys1 however1 the main #bbd facts with which we have to deal may be stated very briefly4 ,with regard to the metal itself1 it is known to exist in three different allotropic modifications1 called alpha-1 beta-1 and gamma-ferrite respectively4 ,like the two modifications of sulphur and of tin1 these different forms exhibit transition points at which the relative stability of the forms changes4 ,thus the transition point for alpha- and beta-ferrite is about #ghj;deg2 and below this temperature the alpha- form1 above it the beta- form is stable4 ,for beta- and gamma-ferrite1 the transition point is about #hgj;deg1 the gamma- form being the stable modification above this temperature4 ,the different modifications of iron also possess different properties4 ,thus1 alpha-ferrite is magnetic1 but does not possess the power of dissolving carbon2 beta-ferrite is non-magnetic1 and likewise does not dissolve carbon2 gamma-ferrite is also non-magnetic1 but possesses the power of dissolving carbon1 and of thus giving rise to solid solutions of carbon in iron4 ,various alloys of iron and carbon1 also1 have to be distinguished4 ,first of all1 there is hard steel1 which contains varying amounts of carbon up to #b per cent4 ,microscopic examination shows that these mixtures are all homogeneous2 and they are therefore to be regarded as solid solutions of carbon in iron 7gamma-ferrite74 ,to these solutions the name martensite has been given4 ,pearlite contains about #j4h per cent4 of carbon1 and1 on microscopic examination1 is found to be a heterogeneous mixture4 ,if heated above #fgj;deg1 pearlite becomes homogeneous1 and forms martensite4 ,lastly1 there is a definite compound of iron and carbon1 iron carbide or cementite1 having the formula ,fe#c;,c4 ,a short description may now be given of the application of the ,phase ,rule to the two-component system iron--carbon2 and of the diagram showing how the different systems are related1 and with the help of which the behaviour of the different mixtures under given conditions can be predicted4 ,although1 with regard to the main features of this diagram1 the different areas to be mapped and the position of the frontier lines1 there is general agreement2 a final decision has not yet been reached with regard to the interpretation to be put on all the curves4 ,illustration3 ,,fig4 #ge4 ,the chief relationships met with in the case of the #bbe iron-carbon alloys are represented graphically in ,fig4 #ge4cji ,the curve ,,ac is the freezing-point curve for iron1#caj ,,bc the unknown freezing-point curve for graphite4 ,c is an eutectic point4 ,suppose1 now1 that we start with a mixture of iron and carbon1 represented by the point x4 ,on lowering the temperature1 a point1 y1 will be reached at which solid begins to separate out4 ,this solid phase1 however1 is not pure iron1 but a solid solution of carbon in iron1 having the composition represented by y' 7cf4 p4 #ahe74 ,as the temperature continues to fall1 the #bbf composition of the liquid phase changes in the direction of y,c1 while the composition of the solid which separates out changes in the direction y',d2 and1 finally1 when the composition of the molten mass is that of the point ,c 7#d4c per cent4 of carbon71 the whole mass solidifies to a heterogeneous mixture of two solid solutions1 one of which is represented by ,d 7containing #b per cent4 of carbon71 while the other will consist practically of pure graphite1 and is not shown in the figure4 ,the temperature of the eutectic point is #aacj;deg4 ,even below the solidification point1 however1 changes can take place4 ,as has been said1 the solid phase which finally separates out from the molten mass is a solid solution represented by the point ,d2 and the curve ,,de represents the change in the composition of this solid solution with the temperature4 ,as indicated in the figure1 ,,de forms a part of a curve representing the mutual solubility of graphite in iron and iron in graphite2 the latter solutions1 however1 not being shown1 as they would lie far outside the diagram4 ,as the temperature falls below #aacj;deg1 more and more graphite separates out1 until at ,e1 when the temperature is #ajjj;deg1 the solid solution contains only #a4h per cent4 of carbon4 ,at this temperature cementite also begins to be formed1 so that as the temperature continues to fall1 separation of cementite 7represented by the line ,e',f'7 occurs1 and the composition of the solid solution undergoes alteration1 as represented by the curve ,,ef4 ,below the temperature of the point ,f 7#fgj;deg7 the martensite becomes heterogeneous1 and forms pearlite4 ,from the above description1 therefore1 it follows that if we start with a molten mixture of iron and carbon1 the composition of which is represented by any point between ,d and ,c 7from #b to #d4c per cent4 of carbon71 we shall obtain1 on cooling the mass1 first of all solid solutions1 the composition of which will be represented by points on the line ,,ad2 that then1 after the mass has completely solidified at #aacj;deg1 further cooling will lead to a separation of graphite and a change in the composition of the martensite 7from #b to #a4h per cent4 of carbon74 ,on cooling below #ajjj;deg1 however1 the martensite and graphite will give rise to cementite and solid solutions #bbg containing less carbon than before1 until1 at temperatures below #fgj;deg1 we are left with a mixture of pearlite and cementite4 ,we have already said that iron consists in three allotropic modifications1 the regions of stability of which are separated by definite transition points4 ,the transition point for alpha- and beta-ferrite 7#ghj;deg7 is represented in ,fig4 #ge by the point ,h2 and the transition point for beta- and gamma-ferrite 7#hgj;deg7 by the point ,i4 ,since neither the alpha- nor the beta-ferrite dissolves carbon1 the transition point will be unaffected by addition of carbon1 and we therefore obtain the horizontal transition curve ,,hg4 ,in the case of the beta- and gamma-ferrite1 however1 the latter dissolves carbon1 and the transition point is consequently affected by the amount of carbon present4 ,this is shown by the line ,,ig4 ,if a martensite containing less carbon than that represented by the point ,g is cooled down from a temperature of1 say1 #ijj;deg1 then when the temperature has fallen to that1 represented by a point on the curve ,,ig1 beta-ferrite will separate out1 and1 as the temperature falls1 the composition of the solid solution will alter as represented by ,,ig4 ,on passing below the temperature of ,,hg1 the beta-ferrite will be converted into alpha-ferrite1 and1 as the temperature falls1 the latter will separate out more and more1 while the composition of the solid solution alters in the direction ,,gf4 ,on passing to still lower temperatures1 the solid solution at ,f 7#j4h per cent4 of carbon7 breaks up into pearlite4 ,if the percentage of carbon in the original solid solution was between that represented by the points ,g and ,f1 then1 on cooling down1 no beta-ferrite1 but only alpha-ferrite would separate out4 ,we see1 therefore1 that when martensite is allowed to cool slowly1 it yields a heterogeneous mixture either of ferrite and pearlite 7when the original mixture contained up to #j4h per cent4 of carbon71 or pearlite and cementite 7when the original mixture contained between #j4h and #b per cent4 of carbon74 ,these heterogeneous mixtures constitute soft steels1 or1 when the carbon content is low1 wrought iron4 ,the case1 however1 is different if the solid solution of carbon in iron is rapidly cooled 7quenched7 from a temperature above the curve ,,igfe to a temperature below this #bbh curve4 ,in this case1 the rapid cooling does not allow time for the various changes which have been described to take place2 so that the homogeneous solid solution1 on being rapidly cooled1 remains homogeneous4 ,in this way hard steel is obtained4 ,by varying the rapidity of cooling1 as is done in the tempering of steel1 varying degrees of hardness can be obtained4 ,the interpretation of the curves given above is that due essentially to ,roozeboom1 who concluded from the experimental data that at temperatures below #ajjj;deg the stable systems are martensite and cementite1 or ferrite and cementite1 graphite being labile4 ,it has1 however1 been pointed out1 more especially by ,e4 ,heyn1#caa that this is not in harmony with the facts of metallurgy1 which show that graphite is undoubtedly formed on slow cooling1 and more especially when small quantities of silicon are present in the iron4#cab ,while1 therefore1 the relationships represented by ,fig4 #ge are obtained under certain conditions 7especially when manganese is present71 ,heyn considers that all the curves in that figure1 except ,,acb1 represent metastable systems--systems1 therefore1 akin to supercooled liquids4 ,rapid cooling will favour the production of the metastable systems containing cementite1 and therefore give rise to relationships represented by ,fig4 #ge2 whereas slow cooling will lead to the stable system ferrite and graphite4 ,presence of silicon tends to prevent1 presence of manganese tends to assist1 the production of the metastable systems4 ,although this view put forward by ,heyn has not been conclusively proved1 it must be said that there is much evidence in its favour4 ,further investigation is1 however1 required before a final decision as to the interpretation of the curves can be reached4 ,determination of the ,composition of ,compounds1 without ,analysis4--,since the equilibrium between a solid and a liquid phase depends not only on the composition of the liquid 7solution7 but also on that of the solid1 it is necessary #bbi to determine the composition of the latter4 ,in some cases this is easily effected by separating the solid from the liquid phase and analyzing it4 ,in other cases1 however1 this method is inapplicable1 or is accompanied by difficulties1 due either to the fact that the solid phase undergoes decomposition 7e4g4 when it contains a volatile constituent71 or to the difficulty of completely separating the mother liquor2 as1 for example1 in the case of alloys4 ,in all such cases1 therefore1 recourse must be had to other methods4 ,in the first place1 synthetic methods may be employed4#cac ,in this case we start with a solution of the two components1 to which a third substance is added1 which1 however1 does not enter into the solid phase4#cad ,we will assume that the initial solution contains x gm4 of ,a and y gm4 of ,b to #a gm4 of ,c4 ,after the solution has been cooled down to such a temperature that solid substance separates out1 a portion of the liquid phase is removed with a pipette and analyzed4 ,if1 now1 the composition of the solution is such that there are x' gm4 of ,a and y' gm4 of ,b to #a gm4 of ,c41 then the composition of the solid phase is x - x' gm4 of ,a and y - y' gm4 of ,b4 ,when x x'1 the solid phase is pure ,b2 when y y'1 the solid phase is pure ,a4 ,we have assumed here that there is only one solid phase present1 containing ,a and ,b4 ,to make sure that the solid phase is not a solid solution in which ,a and ,b are present in the same ratio as in the liquid solution1 a second determination of the composition must be made1 with different initial and end concentrations4 ,if the solid phase is a solid solution1 the composition will now be found different from that found previously4 ,the composition of the solid phase can1 however1 be determined in another manner1 viz4 by studying the fusion curve and the curve of cooling4 ,from the form of the fusion curve alone1 it is possible to decide whether the two components #bcj form a compound or not2 and if the compounds which may be formed have a definite melting point1 the position of the latter gives at once the composition of the compounds 7cf4 p4 #bca74 ,this method1 however1 cannot be applied when the compounds undergo decomposition before the melting point is reached4 ,in such cases1 however1 the form of the cooling curve enables one to decide the composition of the solid phase4#cae ,if a solution is allowed to cool slowly1 and the temperature noted at definite times1 the graphic representation of the rate of cooling will give a continuous curve2 e4g4 ab in ,fig4 #gf4 ,so soon1 however1 as a solid phase begins to be formed1 the rate of cooling alters abruptly1 and the cooling curve then exhibits a break1 or change in direction 7point b74 ,when the eutectic point is reached1 the temperature remains constant1 until all the liquid has solidified4 ,this is represented by the line cd4 ,when complete solidification has occurred1 the fall of temperature again becomes uniform 7de74 ,illustration3 ,,fig4 #gf4 ,illustration3 ,,fig4 #gg4 ,illustration3 ,,fig4 #gh4 ,the length of time during which the temperature remains constant at the point c1 depends1 of course1 on the eutectic solution4 ,if1 therefore1 we take equal amounts of solution having a different initial composition1 the period of constant temperature in the cooling curve will evidently be greatest in the case of the solution having the composition of the eutectic point2 and the period will become less and less as we increase the amount of one of the components4 ,the relationship between initial composition of solution and the duration of constant temperature at the eutectic point is represented by the curve a'c'b' 7,fig4 #gg74 ,when a compound possessing a definite melting point is formed1 it behaves as a pure substance4 ,if1 therefore1 the initial composition of the #bca solution is the same as that of the compound1 no eutectic solution will be obtained2 and therefore no line of constant temperature1 such as cd 7,fig4 #gf74 ,in such a case1 if we represent graphically the relation between the initial composition of the solution and the duration of constant temperature1 a diagram is obtained such as shown in ,fig4 #gh4 ,the two maxima on the time-composition curve represent eutectic points1 and the minima1 a'1 b'1 e'1 pure substances4 ,the position of e' gives the composition of the compound4 ,when a series of compounds is formed1 then for each compound a minimum is found on the time-composition curve4 ,illustration3 ,,fig4 #gi4 ,if the compound formed has no definite melting point1 the diagram obtained is like that shown in ,fig4 #gi4 ,if we start with a solution1 the composition of which is represented by a point between d and b1 then1 on cooling1 b will separate out first1 and the temperature will fall until the point d is reached4 ,the temperature then remains constant until the component b1 which has separated out1 is converted into the compound4 ,after this the temperature again falls1 until it again remains constant at the eutectic point c4 ,in the case of the first halt1 the period of constant temperature is greatest when the initial composition of the solution is the same as that of the compound2 and it becomes shorter and shorter with #bcb increase in the amount of either component4 ,in this way we obtain the time-composition curve b'ed'1 of which the maximum point e gives the composition of the compound4 ,on the other hand1 the period of constant temperature for the eutectic point c is greatest in the case of solutions having the same initial composition as that corresponding with the eutectic point2 and it decreases the more the initial composition approaches that of the pure component a or the component e4 ,in this way we obtain the time-composition curve a'c'e'4 ,here also the point e' represents the composition of the compound4 ,we see1 therefore1 that from the graphic representation of the freezing-point curve1 and from the duration of the temperature-arrests on the cooling curve1 for solutions of different initial composition1 it is possible1 without having recourse to analysis1 to decide what solid phases are formed1 and what is their composition4 ,formation of ,minerals4--,important and interesting as is the application of the ,phase ,rule to the study of alloys1 its application to the study of the conditions regulating the formation of minerals is no less so2 and although we do not propose to consider different cases in detail here1 still attention must be drawn to certain points connected with this interesting subject4 ,in the first place1 it will be evident from what has already been said1 that that mineral which first crystallizes out from a molten magma is not necessarily the one with the highest melting point4 ,the composition of the fused mass must be taken into account4 ,when the system consists of two components which do not form a compound1 one or other of these will separate out in a pure state1 according as the composition of the molten mass lies on one or other side of the eutectic composition2 and the separation of the one component will continue until the composition of the eutectic point is reached4 ,further cooling will then lead to the simultaneous separation of the two components4 ,if1 however1 the two components form a stable compound 7e4g4 orthoclase1 from a fused mixture of silica and potassium aluminate71 then the freezing-point curve will resemble that #bcc shown in ,fig4 #fd2 i4e4 there will be a middle curve possessing a dystectic point1 and ending on either side at a eutectic point4 ,this curve would represent the conditions under which orthoclase is in equilibrium with the molten magma4 ,if the initial composition of the magma is represented by a point between the two eutectic points1 orthoclase will separate first4 ,the composition of the magma will thereby change1 and the mass will finally solidify to a mixture of orthoclase and silica1 or orthoclase and potassium aluminate1 according to the initial composition4 ,what has just been said holds1 however1 only for stable equilibria1 and it must not be forgotten that complications can arise owing to suspended transformation 7when1 for example1 the magma is rapidly cooled7 and the production of metastable equilibria4 ,these conditions occur very frequently in nature4 ,the study of the formation of minerals from the point of view of the ,phase ,rule is still in its initial stages1 but the results which have already been obtained give promise of a rich harvest in the future4#caf 99 99 99 99 99 #bcd ,,chapter ,,xiii ,,systems ,,of ,,three ,,components ,general4--,it has already been made evident that an increase in the number of the components from one to two gives rise to a considerable increase in the possible number of systems1 and introduces not a few complications into the equilibrium relations of these4 ,no less is this the case when the number of components increases from two to three2 and although examples of all the possible types of systems of three components have not been investigated1 nor1 indeed1 any one type fully1 nevertheless1 among the systems which have been studied experimentally1 cases occur which not only possess a high scientific interest1 but are also of great industrial importance4 ,on account not only of the number1 but more especially of the complexity of the systems constituted of three components1 no attempt will be made to give a full account1 or1 indeed1 even a survey of all the cases which have been subjected to a more or less complete experimental investigation2 on the contrary1 only a few of the more important classes will be selected1 and the most important points in connection with the behaviour of these described4 ,on applying the ,phase ,rule ,p ,f ,c #b to the systems of three components1 we see that in order that the system shall be invariant1 no fewer than five phases must be present together1 and an invariant system will therefore exist at a quintuple point4 ,since the number of liquid phases can never exceed the number of the components1 and since there can be only one vapour phase1 it is evident that in this case1 #bce as in others1 there must always be at least one solid phase present at the quintuple point4 ,as the number of phases diminishes1 the variability of the system can increase from one to four1 so that in the last case the condition of the system will not be completely defined until not only the temperature and the total pressure of the system1 but also the concentrations of two of the components have been fixed4 ,or1 instead of the concentrations1 the partial pressures of the components may also be taken as independent variables4 ,graphic ,representation4--,hitherto the concentrations of the components have been represented by means of rectangular co-ordinates1 although the numerical relationships have been expressed in two different ways4 ,in the one case1 the concentration of the one component was expressed in terms of a fixed amount of the other component4 ,thus1 the solubility of a salt was expressed by the number of grams of salt dissolved by #ajj grams of water or other solvent2 and the numbers so obtained were measured along one of the co-ordinates4 ,the second co-ordinate was then employed to indicate the change of another independent variable1 e4g4 temperature4 ,in the other case1 the combined weights of the two components ,a and ,b were put equal to unity1 and the concentration of the one expressed as a fraction of the whole amount4 ,this method allows of the representation of the complete series of concentrations1 from pure ,a to pure ,b1 and was employed1 for example1 in the graphic representation of the freezing point curves4 ,even in the case of three components rectangular co-ordinates can also be employed1 and1 indeed1 are the most convenient in those cases where the behaviour of two of the components to one another is very different from their behaviour to the third component2 as1 for example1 in the case of two salts and water4 ,in these cases1 the composition of the system can be represented by measuring the amounts of each of the two components in a given weight of the third1 along two co-ordinates at right angles to one another2 and the change of the system with the temperature can then be represented by a third axis at right angles to the first two4 ,in those cases1 #bcf however1 where the three components behave in much the same manner towards one another1 the rectangular co-ordinates are not at all suitable1 and instead of these a triangular diagram is employed4 ,various methods have been proposed for the graphic representation of systems of three components by means of a triangle1 but only two of these have been employed to any considerable extent2 and a short description of these two methods will therefore suffice4#cag ,illustration3 ,,fig4 #hj4 ,in the method proposed by ,gibbs an equilateral triangle of unit height is used 7,fig #hj74cah ,the quantities of the different components are expressed as fractional parts of the whole1 and the sum of their concentrations is therefore equal to unity1 and can be represented by the height of the triangle4 ,the corners #bcg of the triangle represent the pure substances ,a1 ,b1 and ,c respectively4 ,a point on one of the sides of the triangle will give the composition of a mixture in which only two components are present1 while a point within the triangle will represent the composition of a ternary mixture4 ,since every point within the triangle has the property that the sum of the perpendiculars from that point on the sides of the triangle is equal to unity 7the height of the triangle71 it is evident that the composition of a ternary mixture can be represented by fixing a point within the triangle such that the lengths of the perpendiculars from the point to the sides of the triangle are equal respectively to the fractional amounts of the three components present2 the fractional amount of ,a1 ,b1 or ,c being represented by the perpendicular distance from the side of the triangle opposite the corners ,a1 ,b1 and ,c respectively4 ,the location of this point is simplified by dividing the normals from each of the corners on the opposite side into ten or one hundred parts1 and drawing through these divisions lines at right angles to the normal and parallel to the side of the triangle4 ,a network of rhombohedra is thus obtained1 and the position of any point can be read off in practically the same manner as in the case of rectangular co-ordinates4 ,thus the point ,p in ,fig4 #hj represents a ternary mixture of the composition ,a #j4e1 ,b #j4c1 ,c #j4b2 the perpendiculars ,pa1 ,pb1 and ,pc being equal respectively to #j4e1 #j4b1 and #j4c of the height of the triangle4 ,another method of representation1 due to ,roozeboom1 consists in employing an equilateral triangle1 the length of whose side is made equal to unity1 or one hundred2 the sum of the fractional or percentage amounts of the three components being represented therefore by a side of the triangle4 ,in this case the composition of a ternary mixture is obtained by determining1 not the perpendicular distance of a point ,p from the three sides of the triangle1 but the distance in a direction parallel to the sides of the triangle 7,fig4 #ha74 ,conversely1 in order to represent a mixture consisting of a1 b1 and c parts of the components ,a1 ,b1 and ,c respectively1 one side of the triangle1 say ,,ab1 is first of all divided into ten or one #bch hundred parts2 a portion1 ,bx a1 is then measured off1 and represents the amount of ,a present4 ,similarly1 a portion1 ,ax' b1 is measured off and represents the fractional amount of ,b1 while the remainder1 xx' c1 represents the amount of ,c4 ,from x and x' lines are drawn parallel to the sides of the triangle1 and the point of intersection1 ,p1 represents the composition of the ternary mixture of given composition2 for1 as is evident from the figure1 the distance of the point ,p from the three sides of the triangle1 when measured in directions parallel to the sides1 is equal to a1 b1 and c respectively4 ,from the division marks on the side ,,ab1 it is seen that the point ,p in this figure also represents a mixture of #j4e parts of ,a1 #j4b parts of ,b1 and #j4c parts of ,c4 ,this gives exactly the same result as the previous method4 ,the employment of a right-angled isosceles triangle has also been suggested1#cai but is not in general use4 ,illustration3 ,,fig4 #ha4 ,in employing the triangular diagram1 it will be of use to note a property of the equilateral triangle4 ,a line drawn from one corner of the triangle to the opposite side1 represents the composition of all mixtures in which the relative amounts of two of the components remain unchanged4 ,thus1 as ,fig4 #hb shows1 if the component ,c is added to a mixture x1 in which ,a and ,b are present in the proportions of a 3 b1 a mixture x'1 which is thereby obtained1 also contains ,a and ,b in the ratio a 3 b4 ,for the two triangles ,,acx and ,,bcx are similar to the two triangles ,,hcx' and ,,kcx'2 and1 #bci therefore1 ,ax 3 ,bx ,hx' 3 ,kx'4 ,but ,ax ,dx and ,bx ,ex2 further ,hx' ,fx' and ,kx' ,gx'4 ,therefore1 ,dx 3 ,ex ,fx' 3 ,gx' b 3 a4 ,at all points on the line ,cx1 therefore1 the ratio of ,a to ,b is the same4 ,illustration3 ,,fig4 #hb4 ,illustration3 ,,fig4 #hc4 ,if it is desired to represent at the same time the change of another independent variable1 e4g4 temperature1 this can be done by measuring the latter along axes drawn perpendicular to the corners of the triangle4 ,in this way a right prism 7,fig4 #hc7 is obtained1 and each section of this cut parallel to the base represents therefore an isothermal surface4 99 99 99 99 99 #bdj ,,chapter ,,xiv ,,solutions ,,of ,,liquids ,,in ,,liquids ,we have already seen 7p4 #ie7 that when two liquids are brought together1 they may mix in all proportions and form one homogeneous liquid phase2 or1 only partial miscibility may occur1 and two phases be formed consisting of two mutually saturated solutions4 ,in the latter case1 the concentration of the components in either phase and also the vapour pressure of the system had1 at a given temperature1 perfectly definite values4 ,in the case of three liquid components1 a similar behaviour may be found1 although complete miscibility of three components with the formation of only one liquid phase is of much rarer occurrence than in the case of two components4 ,when only partial miscibility occurs1 various cases are met with according as the three components form one1 two1 or three pairs of partially miscible liquids4 ,further1 when two of the components are only partially miscible1 the addition of the third may cause either an increase or a diminution in the mutual solubility of these4 ,an increase in the mutual solubility is generally found when the third component dissolves readily in each of the other two2 but when the third component dissolves only sparingly in the other two1 its addition diminishes the mutual solubility of the latter4 ,we shall consider here only a few examples illustrating the three chief cases which can occur1 viz4 7#a7 ,a and ,b1 and also ,b and ,c are miscible in all proportions1 while ,a and ,c are only partially miscible4 7#b7 ,a and ,b are miscible in all proportions1 but ,a and ,c and ,b and ,c are only partially miscible4 7#c7 ,a and ,b1 ,b and ,c1 and ,a and ,c are only partially miscible4 ,a1 ,b1 and ,c here represent the three components4 #a4--,the three components form only one pair of partially miscible liquids4 #bda ,an example of this is found in the three substances3 chloroform1 water1 and acetic acid4#cbj ,chloroform and acetic acid1 and water and acetic acid1 are miscible with one another in all proportions1 but chloroform and water are only partially miscible with one another4 ,if1 therefore1 chloroform is shaken with a larger quantity of water than it can dissolve1 two layers will be formed consisting one of a saturated solution of water in chloroform1 the other of a saturated solution of chloroform in water4 ,the composition of these two solutions at a temperature of about #ah;deg1 will be represented by the points a and b in ,fig4 #hd2 a representing a solution of the composition3 chloroform1 #ii per cent42 water1 #a per cent42 and b a solution of the composition3 chloroform1 #j4h per cent42 water1 #ii4b per cent4 ,when acetic acid is added1 it distributes itself between the two liquid layers1 and two conjugate ternary solutions1 consisting of chloroform1 water1 and acetic acid are thereby produced which are in equilibrium with one another1 and the composition of which will be represented by two points inside the triangle4 ,in this way a series of pairs of ternary solutions will be obtained by the addition of acetic acid to the mixture of chloroform and water4 ,by this addition1 also1 not only do the two liquid phases become increasingly rich in acetic acid1 but the mutual solubility of the chloroform and water increases2 so that the layer a becomes relatively richer in water1 and layer b relatively richer in chloroform4 ,this is seen from the following table1 which gives the percentage composition of different conjugate ternary solutions at #ah;deg4 ---------------------------------------- --------------------------------- ,heavier layer4 ,lighter layer4 ---------------------------------------- --------------------------------- ,chloroform4 ,water4 ,acetic acid4 ,chloroform4 ,water4 ,acetic acid4 ---------------------------------------- --------------------------------- #ii4ja #j4ii #j #j4hd #ii4af #j #ia4he #a4ch #f4gg #a4ba #gc4fi #be4aj #hj4jj #b4bh #ag4gb #g4cj #dh4eh #dd4ab #gj4ac #d4ab #be4ge #ae4aa #cd4ga #ej4ah #fg4ae #e4bj #bg4fe #ah4cc #ca4aa #ej4ef #ei4ii #g4ic #cb4jh #be4bj #be4ci #di4da #ee4ha #i4eh #cd4fa #bh4he #bc4bh #dg4hg ---------------------------------------- --------------------------------- #bdb ,by the continued addition of acetic acid1 the composition of the successive conjugate solutions in equilibrium with one another becomes1 as the table shows1 more nearly the same1 and a point is at length reached at which the two solutions become identical4 ,this will therefore be a critical point 7p4 #ih74 ,increased addition of acetic acid beyond this point will lead to a single homogeneous solution4 ,these relationships are represented graphically by the curve a,kb1 ,fig4 #hd4 ,the points on the branch a,k represent the composition of the solutions relatively rich in chloroform 7heavier layer71 those on the curve b,k the composition of solutions relatively rich in water 7lighter layer72 and the points on these two branches representing conjugate solutions are joined together by tie-lines4 ,thus1 the points a'b' represent conjugate solutions1 and the line a'b' is a tie-line4 ,illustration3 ,,fig4 #hd4 ,since1 now1 acetic acid when added to a heterogeneous mixture of chloroform and water does not enter in equal amounts into the two layers1 but in amounts depending on its coefficient of distribution between chloroform and water1#cba the #bdc tie-lines will not be parallel to ,,ab1 but will be inclined at an angle4 ,as the solutions become more nearly the same1 the tie-lines diminish in length1 and at last1 when the conjugate solutions become identical1 shrink to a point4 ,for the reason that the tie-lines are1 in general1 not parallel to the side of the triangle1 the critical point at which the tie-line vanishes will not be at the summit of the curve1 but somewhere below this1 as represented by the point ,k4 ,the curve a,kb1 further1 forms the boundary between the heterogeneous and homogeneous systems4 ,a mixture of chloroform1 water1 and acetic acid represented by any point outside the curve a,kb1 will form only one homogeneous phase2 while any mixture represented by a point within the curve1 will separate into two layers having the composition represented by the ends of the tie-line passing through that point4 ,thus1 a mixture of the total composition x1 will separate into two layers having the composition a' and b' respectively4 ,since three components existing in three phases 7two liquid and a vapour phase7 constitute a bivariant system1 the final result1 i4e4 the composition of the two layers and the total vapour pressure1 will not depend merely on the temperature1 as in the case of two-component systems 7p4 #ajb71 but also on the composition of the mixture with which we start4 ,at constant temperature1 however1 all mixtures1 the composition of which is represented by a point on one and the same tie-line1 will separate into the same two liquid phases1 although the relative amounts of the two phases will vary4 ,if we omit the vapour phase1 the condition of the system will depend on the pressure as well as on the temperature and composition of the initial mixture4 ,by keeping the pressure constant1 e4g4 at atmospheric pressure 7by working with open vessels71 the system again becomes bivariant4 ,we see1 therefore1 that the position of the curve a,kb1 or1 in other words1 the composition of the different conjugate ternary solutions1 will vary with the temperature1 and only with the temperature1 if we assume either constancy of pressure or the presence of the vapour phase4 ,since at the critical point the condition is imposed that the two liquid phases become identical1 one degree of freedom is thereby #bdd lost1 and therefore only one degree of freedom remains4 ,the critical point1 therefore1 depends on the temperature1 and only on the temperature2 always on the assumption1 of course1 that the pressure is constant1 or that a vapour phase is present4 ,fig4 #hd1 therefore1 represents an isothermal 7p4 #bci74 ,it is of importance to note that the composition of the different ternary solutions obtained by the addition of acetic acid to a heterogeneous mixture of chloroform and water1 will depend not only on the amount of acetic acid added1 but also on the relative amounts of chloroform and water at the commencement4 ,suppose1 for example1 that we start with chloroform and water in the proportions represented by the point c' 7,fig4 #hd74 ,on mixing these1 two liquid layers having the composition a and b respectively will be formed4 ,since by the addition of acetic acid the relative amounts of these two substances in the system as a whole cannot undergo alteration1 the total composition of the different ternary systems which will be obtained must be represented by a point on the line ,cc' 7p4 #bch74 ,thus1 for example1 by the addition of acetic acid a system may be obtained1 the total composition of which is represented by the point c4 ,such a system1 however1 will separate into two conjugate ternary solutions1 the composition of which will be represented by the ends of the tie-line passing through the point c4 ,so long as the total composition of the system lies below the point ,s1 i4e4 the point of intersection of the line ,cc' with the boundary curve1 two liquid layers will be formed2 while all systems having a total composition represented by a point on the line ,cc'1 above ,s1 will form only one homogeneous solution4 ,from the figure1 also1 it is evident that as the amount of acetic acid is increased1 the relative amounts of the two liquid layers formed differ more and more until at ,s a limiting position is reached1 when the amount of the one liquid layer dwindles to nought1 and only one solution remains4 ,the same reasoning can be carried through for different initial amounts of chloroform and water1 but it would be fruitless to discuss all the different systems which can be obtained4 ,the reason for the preceding discussion was to show that #bde although the addition of acetic acid to a mixture of chloroform and water will1 in all cases1 lead ultimately to a limiting system1 beyond which homogeneity occurs1 that point is not necessarily the critical point4 ,on the contrary1 in order that addition of acetic acid shall lead to the critical mixture1 it is necessary to start with a binary mixture of chloroform and water in the proportions represented by the point c'4 ,in this case1 addition of acetic acid will give rise to a series of conjugate ternary solutions1 the composition of which will gradually approach to one another1 and at last become identical4 ,from the foregoing it will be evident that the amount of acetic acid required to produce a homogenous solution1 will depend on the relative amounts of chloroform and water from which we start1 and can be ascertained by joining the corner ,c with the point on the line ,,ab representing the total composition of the initial binary system4 ,the point where this line intersects the boundary curve a,kb will indicate the minimum amount of acetic acid which1 under these particular conditions1 is necessary to give one homogeneous solution4 ,retrograde ,solubility4--,as a consequence of the fact that acetic acid distributes itself unequally between chloroform and water1 and the critical point ,k1 therefore1 does not lie at the summit of the curve1 it is possible to start with a homogeneous solution in which the percentage amount of acetic acid is greater than at the critical point1 and to pass from this first to a heterogenous and then again to a homogenous system merely by altering the relative amounts of chloroform and water4 ,this phenomenon1 to which the term retrograde solubility is applied1 will be observed not only in the case of chloroform1 water1 and acetic acid1 but in all other systems in which the critical point lies below the highest point of the boundary curve for heterogeneous systems4 ,this will be seen from the diagram1 ,fig4 #he4 ,starting with the homogeneous system represented by x1 in which1 therefore1 the concentration of ,c is greater than in the critical mixture 7,k71 if the relative amounts of ,a and ,b are altered in the direction xx'1 while the amount of ,c is maintained constant1 the system will become heterogeneous when the composition reaches the point y1 and will remain #bdf heterogeneous with changing composition until the point y' is passed1 when it will again become homogeneous4 ,if the relative concentration of ,c is increased above that represented by the line ,,ss1 this phenomenon will1 of course1 no longer be observed4 ,illustration3 ,,fig4 #he4 ,relationships similar to those described for chloroform1 water1 and acetic acid are also found in the case of a number of other trios1 e4g4 ether1 water1 and alcohol2 chloroform1 water1 and alcohol4#cbb ,they have also been observed in the case of a considerable number of molten metals4#cbc ,thus1 molten lead and silver1 as well as molten zinc and silver1 mix in all proportions2 but molten lead and zinc are only partially miscible with one another4 ,when melted together1 therefore1 the last two metals will separate into two liquid layers1 one rich in lead1 the other rich in zinc4 ,if silver is now added1 and the temperature maintained above the freezing point of the mixture1 the silver passes for the most part1 in accordance with the law of distribution1 into the upper layer1 which is rich in zinc2 silver being more soluble in molten zinc than in molten lead4 ,this is clearly shown by the following figures3--#cbd #bdg ---------------------------------------- ---------- ,heavier alloy4 ,lighter alloy4 ---------------------------------------- ---------- ,percentage amount of ,percentage amount of ,silver4 ,lead4 ,zinc4 ,silver4 ,lead4 ,zinc4 ---------------------------------------- ---------- #a4be #if4fi #b4jf #ch4ia #c4ab #eg4ig #a4ga #if4dc #a4hf #de4ja #c4cg #ea4fb #e4ee #ic4af #a4bi #ed4ic #d4ba #dj4hf ---------------------------------------- ---------- ,the numbers in the same horizontal row give the composition of the conjugate alloys1 and it is evident that the upper layer consists almost entirely of silver and zinc4 ,on allowing the mixture to cool slightly1 the upper layer solidifies first1 and can be separated from the still molten lead layer4 ,it is on this behaviour of silver towards a mixture of molten lead and zinc that the ,parkes's method for the desilverization of lead depends4#cbe ,if aluminium is also added1 a still larger proportion of silver passes into the lighter layer1 and the desilverization of the lead is more complete4#cbf ,illustration3 ,,fig4 #hf4 ,illustration3 ,,fig4 #hg4 ,the ,influence of ,temperature4--,as has already been said1 a ternary system existing in three phases possesses two degrees of freedom2 and the state of the system is therefore dependent not only on the relative concentration of the components1 but also on the temperature4 ,as the temperature changes1 therefore1 the boundary curve of the heterogeneous system will also alter2 and in order to represent this alteration we shall make use of the right prism1 in which the temperature is measured upwards4 ,in this way the boundary curve passes into a boundary surface 7called a dineric surface71 as shown in ,fig4 #hf4 ,in this figure the curve akb is the isothermal for the ternary system2 the curve a,kb shows the change in the binary system ,,ab with the temperature1 with #bdh a critical point at ,k4 ,this curve has the same meaning as those given in ,chapter ,,vi4 ,the curve k,k is a critical curve joining together the critical points of the different isothermals4 ,in such a case as is shown in ,fig4 #hf1 there does not exist any real critical temperature for the ternary system1 for as the temperature is raised1 the amount of ,c in the critical solution becomes less and less1 and at ,k only two components1 ,a and ,b1 are present4 ,in the case1 however1 represented in ,fig4 #hg1 a real ternary critical point is found4 ,in this figure ak'b is an isothermal1 ak is the curve for the binary system1 and ,k is the ternary critical point4 ,all points outside the helmet-shaped boundary surface represent homogeneous ternary solutions1 while all points within the surface belong to heterogeneous systems4 ,above the temperature of the point ,k1 the three components are miscible in all proportions4 ,an example of a ternary system yielding such a boundary surface is that consisting of phenol1 water1 and acetone4#cbg ,in this case the critical temperature ,k is #ib;deg1 and the composition at this ternary critical point is-- ,water #ei per cent4 ,acetone #ab ,phenol #bi ,illustration3 ,,fig4 #hh4 ,the difference between the two classes of systems just mentioned1 is seen very clearly by a glance at the ,figs4 #hh and #hi1 which show the projection of the isothermals on the base of the prism4 ,in ,fig4 #hh1 the projections yield paraboloid curves1 the two branches of which are cut by one side of the triangle2 and the critical point is represented by a point on #bdi this side4 ,in the second case 7,fig4 #hi71 however1 the projections of the isothermals form ellipsoidal curves surrounding the supreme critical point1 which now lies inside the triangle4 ,at lower temperatures1 these isothermal boundary curves are cut by a side of the triangle2 at the critical temperature1 k1 of the binary system ,,ab1 the boundary curve touches the side ,,ab1 while at still higher temperatures the boundary curve comes to lie entirely within the triangle4 ,at any given temperature1 therefore1 between the critical point of the binary system 7k71 and the supreme critical point of the ternary system 7,k71 each pair of the three components are miscible with one another in all proportions2 for the region of heterogeneous systems is now bounded by a closed curve lying entirely within the triangle4 ,outside this curve only homogeneous systems are found4 ,binary mixtures1 therefore1 represented by any point on one of the sides of the triangle must be homogeneous1 for they all lie outside the boundary curve for heterogeneous states4 ,illustration3 ,,fig4 #hi4 #b4 ,the three components can form two pairs of partially miscible liquids4 ,in the case of the three components water1 alcohol1 and succinic nitrile1 water and alcohol are miscible in all proportions1 but not so water and succinic nitrile1 or alcohol and succinic nitrile4 ,illustration3 ,,fig4 #ij4 ,illustration3 ,,fig4 #ia4 ,as we have already seen 7p4 #abb71 water and succinic nitrile can form two liquid layers between the temperatures #ah4e;deg and #ee4e;deg2 while alcohol and nitrile can form two liquid layers between #ac;deg and #ca;deg4 ,if1 then1 between these two temperature limits1 alcohol is added to a heterogeneous mixture of water and nitrile1 or water is added to a mixture of alcohol and nitrile1 two heterogeneous ternary systems will be formed1 #bej and two boundary curves will be obtained in the triangular diagram1 as shown in ,fig4 #ij4cbh ,on changing the temperature1 the boundary curves will also undergo alteration1 in a manner similar to that just discussed4 ,as the temperature falls1 the two curves will spread out more and more into the centre of the triangle1 and might at last meet one another2 while at still lower temperatures we may imagine the curves still further expanding so that the two heterogeneous regions flow into one another and form a band on the triangular diagram 7,fig4 #ia74 ,this1 certainly1 has not been realized in the case of the three components mentioned1 because at a temperature higher than that at which the two heterogeneous regions could fuse together1 solid separates out4 ,illustration3 ,,fig4 #ib4 ,the gradual expansion of a paraboloid into a band-like area of heterogeneous ternary systems1 has1 however1 been observed in the case of water1 phenol1 and aniline4#cbi ,in ,fig4 #ib are shown three isothermals1 viz4 those for #adh;deg1 #ie;deg1 and #ej;deg4 ,at #adh;deg1 water and aniline form two layers having the composition-- ,water1 #hc4e per cent4 water1 #bj per cent4 and ,aniline1 #af4e aniline1 #hj #bea and the critical point k' has the composition-- ,water1 #fe2 phenol1 #ac4b2 aniline1 #ba4h per cent4 ,at #ie;deg1 the composition of the two binary solutions is-- ,water1 #ic per cent4 water #h per cent4 and ,aniline1 #g aniline1 #ib while the point k has the composition ,water1 #fi4i2 phenol1 #bf4f2 aniline1 #c4e per cent4 ,at #ej;deg1 the region of heterogeneous states now forms a band1 and the two layers formed by water and aniline have the composition-- ,water1 #if4e per cent4 water1 #e4e per cent4 and ,aniline1 #c4e aniline1 #id4e while the two layers formed by water and phenol have the composition-- ,water1 #hi per cent4 water1 #ch per cent4 and ,phenol1 #aa phenol1 #fb ,all mixtures of water1 phenol1 and aniline1 therefore1 the composition of which is represented by any point within the band abcd1 will form two ternary solutions2 while if the composition is represented by a point outside the band1 only one homogeneous solution will be produced4 #c4 ,the three components form three pairs of partially miscible liquids4 ,illustration3 ,,fig4 #ic4 ,the third chief case which can occur is that no two of the components are completely miscible with one another4 ,in this case1 therefore1 we shall obtain three paraboloid boundary curves1 as shown in ,fig4 #ic4 ,if1 now1 we imagine these three curves to expand in towards the centre of the triangle1 as might happen1 for example1 by lowering the temperature1 a point will #beb be reached at which the curves partly overlap1 and we shall get the appearance shown in ,fig4 #id4 ,the points a1 b1 and c represent the points where the three curves cut1 and the triangle abc is a region where the curves overlap4 ,from this diagram we can see that any mixture having a composition represented by a point in one of the clear spaces at the corners of the larger triangle1 will form a homogeneous solution2 if the composition corresponds to any point lying in one of the quadrilateral regions x#a1 x#b or x#c1 two ternary solutions will be formed2 while1 if the composition is represented by any point in the inner triangle1 separation into three layers will occur4 ,illustration3 ,,fig4 #id4 ,since in the clear regions at the corners of the triangle we have three components in two phases1 liquid and vapour1 the systems have three degrees of freedom4 ,at constant temperature1 therefore1 the condition of the system is not defined until the concentrations of two of the components are fixed4 ,a system belonging to one of the quadrilateral spaces has1 as we have seen1 two degrees of freedom2 besides the temperature1 one concentration must be fixed4 ,lastly1 a system the composition of which falls within the inner triangle abc1 will form three layers1 and will therefore possess only one degree of freedom4 ,if the temperature is fixed1 the composition of the three layers is also determined1 viz4 that of the points a1 b1 and c respectively2 and a change in the composition of the original mixture can lead only to a difference in the relative amounts of the three layers1 not to a difference in their composition4 ,an example of a system which can form three liquid phases is found in water1 ether1 and succinic nitrile4#ccj 99 99 99 99 99 #bec ,,chapter ,,xv ,,presence ,,of ,,solid ,,phases ,a4 ,the ,ternary ,eutectic ,point4--,in passing to the consideration of those ternary systems in which one or more solid phases can exist together with one liquid phase1 we shall first discuss not the solubility curves1 as in the case of two-component systems1 but the simpler relationships met with at the freezing point4 ,that is1 we shall first of all examine the freezing point curves of ternary systems4 ,illustration3 ,,fig4 #ie4 ,since it is necessary to take into account not only the changing composition of the liquid phase1 but also the variation of the temperature1 we shall employ the right prism for the graphic representation of the systems1 as shown in ,fig4 #ie4 ,a1 ,b1 and ,c in this figure1 therefore1 denote the melting points of the pure components4 ,if we start with the component ,a at its melting point1 and add ,b1 which is capable of dissolving in liquid ,a1 the freezing point of ,a will be lowered2 and1 similarly1 the freezing point of ,b by addition of ,a4 ,in this way we get the freezing point curve ,ak#a;,b for the binary system2 k#a2 being an eutectic point4 ,this curve will of course lie in the plane formed by one face of the prism4 ,in a similar manner we obtain the freezing point curves ,ak#b;,c and ,bk#c;,c4 ,these curves give the composition of the binary liquid phases in equilibrium #bed with one of the pure components1 or at the eutectic points1 with a mixture of two solid components4 ,if1 now1 to the system represented say by the point k#a1 a small quantity of the third component1 ,c1 is added1 the temperature at which the two solid phases ,a and ,b can exist in equilibrium with the liquid phase is lowered2 and this depression of the eutectic point is all the greater the larger the addition of ,c4 ,in this way we obtain the curve k#a,k1 which slopes inwards and downwards1 and indicates the varying composition of the ternary liquid phase with which a mixture of solid ,a and ,b are in equilibrium4 ,similarly1 the curves k#b,k and k#c,k are the corresponding eutectic curves for ,a and ,c1 and ,b and ,c in equilibrium with ternary solutions4 ,at the point ,k1 the three solid components are in equilibrium with the liquid phase2 and this point1 therefore1 represents the lowest temperature attainable with the three components given4 ,each of the ternary eutectic curves1 as they may be called1 is produced by the intersection of two surfaces1 while at the ternary eutectic point1 three surfaces1 viz4 ,ak#a,kk#b1 ,bk#a,kk#c1 and ,ck#a,kk#c intersect4 ,any point on one of these surfaces represents a ternary solution in equilibrium with only one component in the solid state2 the lines or curves of intersection of these represent equilibria with two solid phases1 while at the point ,k1 the ternary eutectic point1 there are three solid phases in equilibrium with a liquid and a vapour phase4 ,the surfaces just mentioned represent bivariant systems4 ,one component in the solid state can exist in equilibrium with a ternary liquid phase under varying conditions of temperature and concentration of the components in the solution2 and before the state of the system is defined1 these two variables1 temperature and composition of the liquid phase1 must be fixed4 ,on the other hand1 the curves formed by the intersection of these planes represent univariant systems2 at a given temperature two solid phases can exist in equilibrium with a ternary solution1 only when the latter has a definite composition4 ,lastly1 the ternary eutectic point1 ,k1 represents an invariant system2 three solid phases can exist in equilibrium with a ternary solution1 only when the latter has one fixed composition and when the temperature has a definite value4 ,this eutectic point1 therefore1 #bee has a perfectly definite position1 depending only on the nature of the three components4 ,instead of employing the prism1 the change in the composition of the ternary solutions can also be indicated by means of the projections of the curves k#a,k1 k#b,k1 and k#c,k on the base of the prism1 the particular temperature being written beside the different eutectic points and curves4 ,this is shown in ,fig4 #if4 ,illustration3 ,,fig4 #if4 ,the numbers which are given in this diagram refer to the eutectic points for the system bismuth--lead--tin1 the data for which are as follows3--#cca ---------------------------------------- ---------------------------- ,melting point of ,percentage composition of ,temperature of binary pure metal4 binary eutectic mixture4 eutectic point4 ---------------------------------------- ---------------------------- ,bi ,pb ,sn ,bismuth1 #bfh;deg #ee #de -- ,bi--,pb1 #abg;deg ,lead1 #cbe;deg #eh -- #db ,bi--,sn1 #acc;deg ,tin1 #bcb;deg -- #cg #fc ,pb--,sn1 #ahb;deg ---------------------------------------- ---------------------------- ---------------------------------------- ---------- ,percentage composition of ,temperature of ternary ternary eutectic mixture4 eutectic point4 ---------------------------------------- ---------- ,bi ,pb ,sn #eb #cb #af #if;deg ---------------------------------------- ---------- ,formation of ,compounds4--,in the case just discussed1 the components crystallized out from solution in the pure state4 ,if1 however1 combination can take place between two of the components1 the relationships will be somewhat different2 the curves which are obtained in such a case being represented in ,fig4 #ig4 ,from the figure1 we see that the two components ,b #bef and ,c form a compound1 and the freezing point curve of the binary system has therefore the form shown in ,fig4 #fd 7p4 #bji74 ,further1 there are two ternary eutectic points1 ,k#a and ,k#b1 the solid phases present being ,a1 ,b1 and compound1 and ,a1 ,c1 and compound respectively4 ,illustration3 ,,fig4 #ig4 ,the particular point1 now1 to which it is desired to draw attention is this4 ,suppose the ternary eutectic curves projected on a plane parallel to the face of the prism containing ,b and ,c1 i4e4 suppose the concentrations of the two components ,b and ,c1 between which interaction can occur1 expressed in terms of a constant amount of the third component ,a1#ccb curves will then be obtained which are in every respect analogous to the freezing point curves of binary systems4 ,thus1 suppose the eutectic curves k#a,k and k#b,k in ,fig4 #ie projected on the face ,,bc of the prism1 then evidently a curve will be obtained consisting of two branches meeting in an eutectic point4 ,on the other hand1 the projection of the ternary eutectic curves in ,fig4 #ig on the face ,,bc of the prism1 will give a curve consisting of three portions1 as shown by the outline k#a,k#a,k#bk#b in ,fig4 #ig4 ,various examples of this have been studied1 and the following table contains some of the data for the system ethylene bromide 7,a71 picric acid 7,b71 and beta-naphthol 7,c71 obtained by ,bruni4#ccc #beg ---------------------------------------- --------------------------------- ,temperature ,solid phases present4 ---------------------------------------- --------------------------------- ,point k#a #i4da;deg ,ethylene bromide1 picric acid4 ,curve k#a,k#a -- ,point ,k#a #i4cb;deg ,ethylene bromide1 picric acid1 and beta-naphthol picrate4 ,curve ,k#a;,d',k#b -- ,ethylene bromide1 beta-naphthol picrate4 ,point ,d' #i4ge;deg ,point ,k#b #h4hi;deg beta-naphthol1 and picrate4 ,curve ,k#bk#b -- beta-naphthol4 ,point k#b #i4jd;deg ---------------------------------------- --------------------------------- ,from what has been said1 it will be apparent that if the ternary eutectic curve of a three-component system 7in which one of the components is present in constant amount7 is determined1 it will be possible to state1 from the form of curve obtained1 whether or not the two components present in varying amount crystallize out pure or combine with one another to form a compound4 ,it may be left to the reader to work out the curves for the other possible systems2 but it will be apparent1 that the projections of the ternary eutectic curves in the manner given will yield a series of curves alike in all points to the binary curves given in ,figs4 #fc-fe1 pp4 #bjh-baj4 ,since1 from the method of investigation1 the temperatures of the eutectic curves will depend on the melting point of the third component 7,a71 it is possible1 by employing substances with widely differing melting points1 to investigate the interaction of the two components 7e4g4 two optical antipodes7 ,b and ,c over a range of temperature2 and thus determine the range of stability of the compound1 if one is formed4 ,since1 in some cases1 two substances which at one temperature form mixed crystals combine at another temperature to form a definite compound1 the relationships which have just been described can be employed1 and indeed1 have been employed1 to determine the temperature at which this change occurs4#ccd ,by means of this method1 ,adriani found that below #ajc;deg i-camphoroxime exists as a racemic compound1 while above #beh that temperature it occurs as a racemic mixed crystal#cce 7cf4 p4 #bai74 ,b4 ,equilibria at ,higher ,temperatures4 ,formation of ,double ,salts4--,after having studied the relationships which are found in the neighbourhood of the freezing points of the components1 we now pass to the discussion of the equilibria which are met with at higher temperatures4 ,in this connection we shall confine the discussion entirely to the systems formed of two salts and water1 dealing more particularly with those cases in which the water is present in relatively large amount and acts as solvent4 ,further1 in studying these systems1 one restriction must be made1 viz4 that the single salts are salts either of the same base or of the same acid2 or are1 in other words1 capable of yielding a common ion in solution4 ,such a restriction is necessary1 because otherwise the system would be one not of three but of four components4#ccf ,transition ,point4--,as is very well known1 there exist a number of hydrated salts which1 on being heated1 undergo apparent partial fusion2 and in ,chapter ,v4 the behaviour of such hydrates was more fully studied in the light of the ,phase ,rule4 ,glauber's salt1 or sodium sulphate decahydrate1 for example1 on being heated to a temperature of about #cb4e;deg1 partially liquefies1 owing to the fact that the water of crystallization is split off and anhydrous sodium sulphate formed1 as shown by the equation-- ,na#b,,so#d1aj;,h#b,o ,na#b,,so#d #aj;,h#b,o ,the temperature of #cb4e;deg1 it was learned1 constituted a transition point for the decahydrate and anhydrous salt plus water2 decomposition of the hydrated salt occurring above this temperature1 combination of the anhydrous salt and water below it4 ,analogous phenomena are met with in systems constituted of two salts and water in which the formation of double salts can take place4 ,thus1 for example1 if d-sodium potassium #bei tartrate is heated to above #ee;deg1 apparent partial fusion occurs1 and the two single salts1 d-sodium tartrate and d-potassium tartrate1 are deposited1 the change which occurs being represented by the equation-- #d,na,k,c#d,o#f;,h#d1d;,h#b,o #b,na#b;,c#d,o#f;,h#d1b;,h#b,o #b,k#b;,c#d,o#f;,h#d1a_/b;,h#b,o #aa;,h#b,o ,on the other hand1 if sodium and potassium tartrates are mixed with water in the proportions shown on the right side of the equation1 the system will remain partially liquid so long as the temperature is maintained above #ee;deg 7in a closed vessel to prevent loss of water71 but on allowing the temperature to fall below this point1 complete solidification will ensue1 owing to the formation of the hydrated double salt4 ,below #ee;deg1 therefore1 the hydrated double salt is the stable system1 while above this temperature the two single salts plus saturated solution are stable4#ccg ,a similar behaviour is found in the case of the double salt copper dipotassium chloride 7,cu,cl#b1b,k,cl1#b;,h#b,o or ,cu,k#b;,cl#d1b;,h#b,o74#cch ,when this salt is heated to #ib;deg1 partial liquefaction occurs1 and the original blue plate-shaped crystals give place to brown crystalline needles and white cubes2 while on allowing the temperature to fall1 re-formation of the blue double salt ensues4 ,the temperature #ib;deg is1 therefore1 a transition point at which the reversible reaction-- ,cu,k#b;,cl#d1b;,h#b,o -- ,cu,k,cl#c ,k,cl #b;,h#b,o takes place4 ,the decomposition of sodium potassium tartrate1 or of copper dipotassium chloride1 differs in so far from that of ,glauber's salt that two new solid phases are formed2 and in the case of copper dipotassium chloride1 one of the decomposition products is itself a double salt4 ,in the two examples of double salt decomposition which have just been mentioned1 sufficient water was yielded to cause a partial liquefaction2 but other cases are known where this is not so4 ,thus1 when copper calcium acetate is heated to a #bfj temperature of #ge;deg1 although decomposition of the double salt into the two single salts occurs as represented by the equation#cci-- ,cu,ca7,c#b;,h#c,o#b7d1h;,h#b,o ,cu7,c#b;,h#c,o#b7b1;,h#b,o ,ca7,c#b;,h#c,o#b7b1;,h#b,o #f;,h#b,o the amount of water split off is insufficient to give the appearance of partial fusion1 and1 therefore1 only a change in the crystals is observed4 ,the preceding examples1 in which decomposition of the double salt was effected by a rise of temperature1 were chosen for first consideration as being more analogous to the case of ,glauber's salt2 but not a few examples are known where the reverse change takes place1 formation of the double salt occurring above the transition point1 and decomposition into the constituent salts below it4 ,instances of this behaviour are found in the case of the formation of astracanite from sodium and magnesium sulphates1 and of sodium ammonium racemate from the two sodium ammonium tartrates1 to which reference will be made later4 ,between these various systems1 however1 there is no essential difference2 and whether decomposition or formation of the double salt occurs at temperatures above the transition point1 will of course depend on the heat of change at that point4 ,for1 in accordance with van't ,hoff's law of movable equilibrium 7p4 #eh71 that change will take place at the higher temperature which is accompanied by an absorption of heat4 ,if1 therefore1 the formation of the double salt from the single salts is accompanied by an absorption of heat1 the double salt will be formed from the single salts on raising the temperature2 but if the reverse is the case1 then the double salt on being heated will decompose into the constituent salts4#cdj ,in those cases1 now1 which have so far been studied1 the change at the transition point is accompanied by a taking up or a splitting off of water2 and in such cases the general rule can be given1 that if the water of crystallization of the two constituent #bfa salts together is greater than that of the double salt1 the latter will be produced from the former on raising the temperature 7e4g4 astracanite from sodium and magnesium sulphates72 but if the double salt contains more water of crystallization than the two single salts1 increase of temperature will effect the decomposition of the double salt4 ,when we seek for the connection between this rule and the law of van't ,hoff1 it is found in the fact that the heat effect involved in the hydration or dehydration of the salts is much greater than that of the other changes which occur1 and determines1 therefore1 the sign of the total heat effect4#cda ,vapour ,pressure4 ,quintuple ,point4--,in the case of ,glauber's salt1 we saw that at a certain temperature the vapour pressure curve of the hydrated salt cut that of the saturated solution of anhydrous sodium sulphate4 ,that point1 it will be remembered1 was a quadruple point at which the four phases sodium sulphate decahydrate1 anhydrous sodium sulphate1 solution1 and vapour1 could co-exist2 and was also the point of intersection of the curves for four univariant systems4 ,in the case of the formation of double salts1 similar relationships are met with2 and also certain differences1 due to the fact that we are now dealing with systems of three components4 ,two cases will be chosen here for brief description1 one in which formation1 the other in which decomposition of the double salt occurs with rise of temperature4 ,on heating a mixture of sodium sulphate decahydrate and magnesium sulphate heptahydrate1 it is found that at #bb;deg partial liquefaction occurs with formation of astracanite4 ,at this temperature1 therefore1 there can coexist the five phases-- ,na#b,,so#d1aj;,h#b,o2 ,mg,s,o#d1g;,h#b,o2 ,na#b,mg7,,so#d7b1d;,h#b,o2 solution2 vapour4 ,this constitutes1 therefore1 a quintuple point2 and since there are three components present in five phases1 the system is invariant4 ,this point1 also1 will be the point of intersection of curves for five univariant systems1 which1 in this case1 must each be composed of four phases4 ,these systems are-- #bfb ,i4 ,na#b,,so#d1aj;,h#b,o2 ,mg,s,o#d1g;,h#b,o2 ,na#b,mg7,,so#d7b1d;,h#b,o2 vapour4 ,,ii4 ,na#b,,so#d1aj;,h#b,o2 ,mg,s,o#d1g;,h#b,o2 solution2 vapour4 ,,iii4 ,mg,s,o#d1g;,h#b,o2 ,na#b,mg7,,so#d7b1d;,h#b,o2 solution2 vapour4 ,,iv4 ,na#b,,so#d1aj;,h#b,o2 ,na#b,mg7,,so#d7b1d;,h#b,o2 solution2 vapour4 ,v4 ,na#b,,so#d1aj;,h#b,o2 ,mg,s,o#d1g;,h#b,o2 ,na#b,mg7,,so#d7b1d;,h#b,o2 solution4 ,illustration3 ,,fig4 #ih4 ,on representing the vapour pressures of these different systems graphically1 a diagram is obtained such as is shown in ,fig4 #ih1cdb the curves being numbered in accordance with the above list4 ,when the system ,i4 is heated1 the vapour pressure increases until at the quintuple point the liquid phase 7solution7 is formed1 and it will then depend on the relative amounts of the different phases whether on further heating there is formed system ,,iii41 ,,iv41 or ,v4 ,if either of the first two is produced1 we shall obtain the vapour pressure of the solutions saturated with respect to both double salt and one of the single salts2 while if the vapour phase disappears1 there will be obtained the pressure of the condensed systems formed of double salt1 two single salts and solution4 ,this curve1 therefore1 indicates the change of the transition point with pressure2 and since in the ordinary determinations of the transition point in open vessels1 we are in reality dealing with condensed systems under the pressure of #a atm41 it will be evident that the transition point does not accurately coincide with the quintuple point 7at which the system is under the pressure of its own vapour74 ,as in the case of other condensed systems1 however1 pressure has only a slight influence on the temperature of the transition point4 ,whether or not pressure raises or lowers the transition point will depend on whether transformation is accompanied by an increase or #bfc diminution of volume 7theorem of ,le ,chatelier1 p4 #eh74 ,in the case of the formation of astracanite1 expansion occurs1 and the transition point will therefore be raised by increase of pressure4 ,although measurements have not been made in the case of this system1 the existence of such a curve has been experimentally verified in the case of copper and calcium acetates and water 7v4 infra74#cdc ,illustration3 ,,fig4 #ii4 ,the vapour pressure diagram in the case of copper calcium acetate and water 7,fig4 #ii71 is almost the reverse of that already discussed4 ,in this case1 the double salt decomposes on heating1 and the decomposition is accompanied by a contraction4 ,curve ,i4 is the vapour pressure curve for double salt1 two single salts 7p4 #bfj71 and vapour2 curves ,,ii4 and ,,iii4 give the vapour pressures of solutions saturated with respect to double salt and one of the single salts2 curve ,,iv4 is the curve of pressures for the solutions saturated with respect to the two single salts2 while curve ,v4 again represents the change of the transition point with pressure4 ,on examining this diagram1 it is seen that whereas #bfd astracanite could exist both above and below the quintuple point1 copper calcium acetate can exist only below the quintuple point4 ,this behaviour is found only in those cases in which the double salt is decomposed by rise of temperature1 and where the decomposition is accompanied by a diminution of volume4#cdd ,as already mentioned1 the decomposition of copper calcium acetate into the single salts and saturated solution is accompanied by a contraction1 and it was therefore to be expected that increase of pressure would lower the transition point4 ,this expectation of theory was confirmed by experiment1 for van't ,hoff and ,spring found that although the transition point under atmospheric pressure is about #ge;deg1 decomposition of the double salt took place even at the ordinary temperature when the pressure was increased to #fjjj atm4#cde ,solubility ,curves at the ,transition ,point4--,at the transition point1 as has already been shown1 the double salt and the two constituent salts can exist in equilibrium with the same solution4 ,the transition point1 therefore1 must be the point of intersection of two solubility curves2 the solubility curve of the double salt and the solubility curve of the mixtures of the two constituent salts4 ,it should be noted here that we are not dealing with the solubility curves of the single salts separately1 for since the systems are composed of three components1 a single solid phase can1 at a given temperature1 be in equilibrium with solutions of different composition1 and two solid phases in contact with solution 7and vapour7 are therefore necessary to give an univariant system4 ,the same applies1 of course1 to the solubility of the double salt2 for a double salt also constitutes a single phase1 and can therefore exist in equilibrium with solutions of varying composition4 ,if1 however1 we make the restriction 7which we do for the present7 that the double salt is not decomposed by water1 then the solution will contain the constituent salts in the same relative proportions as they are contained in the double salt1 and the system may therefore be regarded as one of two components1 viz4 double salt and water4 ,in this case one solid phase is sufficient1 with solution and #bfe vapour1 to give an univariant system2 and at a given temperature1 therefore1 the solubility will have a perfectly definite value4 ,since in almost all cases the solubility is determined in open vessels1 we shall in the following discussion consider that the vapour phase is absent1 and that the system is under a constant pressure1 that of the atmosphere4 ,with this restriction1 therefore1 four phases will constitute an invariant system1 three phases an univariant1 and two phases a bivariant system4 ,it has already been learned that in the case of sodium sulphate and water1 the solubility curve of the salt undergoes a sudden change in direction at the transition point1 and that this is accompanied by a change in the solid phase in equilibrium with the solution4 ,the same behaviour is also found in the case of double salts4 ,to illustrate this1 we shall briefly discuss the solubility relations of a few double salts1 beginning with one of the simplest cases1 that of the formation of rubidium racemate from rubidium d- and l-tartrates4 ,the solubilities are represented diagrammatically in ,fig4 #ajj1 the numerical data being contained in the following table1 in which the solubility is expressed as the number of gram-molecules ,rb#b;,c#d;,h#d,o#f in #ajj gm4-molecules of water4#cdf ---------------------------------------- ----------------------- ,temperature4 ,solubility of tartrate ,solubility of racemate4 mixture4 ---------------------------------------- ----------------------- #be;deg #ac4jc #aj4ia #ce;deg -- #ab4fc #dj4d;deg -- #ac4dh #dj4g;deg #ac4df -- #ed;deg #ac4hc -- ---------------------------------------- ----------------------- ,in ,fig4 #ajj the curve ,,ab represents the solubility of the racemate1 while ,a',,bc represents the solubility of the mixed tartrates4 ,below the transition point1 therefore1 the solubility of the racemate is less than that of the mixed tartrates4 ,the solution1 saturated with respect to the latter1 will be supersaturated with respect to the racemate2 and if a nucleus of this is present1 racemate will be deposited1 and the mixed tartrates1 if present in equimolecular amounts1 will ultimately #bff entirely disappear1 and only racemate will be left as solid phase4 ,the solution will then have the composition represented by a point on the curve ,,ab4 ,conversely1 above the transition point1 the saturated solution of the racemate would be supersaturated with respect to the two tartrates1 and transformation into the latter would ensue4 ,if1 therefore1 a solution of equimolecular proportions of rubidium d- and l-tartrates is allowed to evaporate at a temperature above #dj;deg1 a mixture of the two tartrates will be deposited2 while at temperatures below #dj;deg the racemate will separate out4 ,illustration3 ,,fig4 #ajj4 ,similar relationships are met with in the case of sodium ammonium d- and l-tartrate and sodium ammonium racemate2 but in this case the racemate is the stable form in contact with solution above the transition point 7#bg;deg74#cdg ,below the transition point1 therefore1 the solubility curve of the mixed tartrates will lie below the solubility curve of the racemate4 ,below the transition point1 therefore1 sodium ammonium racemate will break up in contact with solution into a mixture of sodium ammonium d- and l-tartrates4 ,at a higher temperature1 #ce;deg1 sodium ammonium racemate undergoes decomposition into sodium racemate and ammonium racemate4#cdh ,the behaviour of sodium ammonium racemate is of interest from the fact that it was the first racemic substance to be resolved into its optically active forms by a process of crystallization4 ,on neutralizing a solution of racemic tartaric acid1 half with soda and half with ammonia1 and allowing the solution to evaporate1 ,pasteur#cdi obtained a mixture of sodium ammonium #bfg d- and l-tartrates4 ,since ,pasteur was unaware of the existence of a transition point1 the success of his experiment was due to the happy chance that he allowed the solution to evaporate at a temperature below #bg;deg2 for had he employed a temperature above this1 separation of the racemate into the two enantiomorphous forms would not have occurred4 ,for this reason the attempt of ,staedel to perform the same resolution met only with failure4#cej ,decomposition of the ,double ,salt by ,water4--,in the two cases just described1 the solubility relationships at the transition point are of a simpler character than in the case of most double salts4 ,if1 at a temperature above the transition point1 a mixture of rubidium d- and l-tartrates in equimolecular proportions is brought in contact with water a solution will be obtained1 which is saturated with respect to both enantiomorphous forms2 and since the solubility of the two optical antipodes is identical1 and the effect of one on the solubility of the other also the same1 the solution will contain equimolecular amounts of the d- and l-salt4 ,if1 now1 the solution is cooled down in contact with the solid salts to just below the transition point1 it becomes supersaturated with respect to the racemate1 and this will be deposited4 ,the solution thereby becomes unsaturated with respect to the mixture of the active salts1 and these must therefore pass into solution4 ,as the latter are equally soluble1 equal amounts of each will dissolve1 and a further quantity of the racemate will be deposited4 ,these processes of solution and deposition will continue until the single tartrates have completely disappeared1 and only racemate is left as solid phase4 ,as a consequence of the identical solubility of the two tartrates1 therefore1 no excess of either form will be left on passing through the transition point4 ,from this it will be evident that the racemate can exist as single solid phase in contact with its saturated solution at the transition point2 or1 in other words1 the racemate is not decomposed by water at the transition point4 ,the same behaviour will evidently be exhibited by sodium ammonium racemate at #bg;deg1 for the two enantiomorphous sodium ammonium tartrates have also identical solubility4 #bfh ,very different1 however1 is the behaviour of1 say1 astracanite1 or of the majority of double salts2 for the solubility of the constituent salts is now no longer the same4 ,if1 for example1 excess of a mixture of sodium sulphate and magnesium sulphate1 in equimolecular proportions1 is brought in contact with water below the transition point 7#bb;deg71 more magnesium sulphate than sodium sulphate will dissolve1 the solubility of these two salts in a common solution being given by the following figures1 which express number of molecules of the salt in #ajj molecules of water4#cea ,,composition ,,of ,,solutions ,,saturated ,,with ,,respect ,,to ,na#b,,so#d1aj;,h#b,o ,,and ,mg,s,o#d1g;,h#b,o4 ---------------------------------------- ,temperature4 ,na#b,,so#d4 ,mg,s,o#d4 ---------------------------------------- #ah4e;deg #b4af #d4eg #bd4e;deg #c4dc #d4fh ---------------------------------------- ,at the transition point1 then1 it is evident that the solution contains more magnesium sulphate than sodium sulphate3 and this must still be the case when astracanite1 which contains sodium sulphate and magnesium sulphate in equimolecular proportions1 separates out4 ,if1 therefore1 the temperature is raised slightly above the transition point1 magnesium sulphate and sodium sulphate will pass into solution1 the former1 however1 in larger quantities than the latter1 and astracanite will be deposited2 and this will go on until all the magnesium sulphate has disappeared1 and a mixture of astracanite and sodium sulphate decahydrate is left as solid phases4 ,since there are now three phases present1 the system is univariant 7by reason of the restriction previously made that the vapour phase is absent71 and at a given temperature the solution will have a definite composition2 as given in the following table3-- ,,composition ,,of ,,solutions ,,saturated ,,with ,,respect ,,to ,na#b,mg7,,so#d7b1d;,h#b,o ,,and ,na#b,,so#d1aj;,h#b,o4 ---------------------------------------- ,temperature4 ,na#b,,so#d4 ,mg,s,o#d4 ---------------------------------------- #bb;deg #b4ie #d4gj #bd4e;deg #c4de #c4fb ---------------------------------------- #bfi ,from the above figures1 therefore1 it will be seen that at a temperature just above the transition point a solution in contact with the two solid phases1 astracanite and ,glauber's salt1 contains a relatively smaller amount of sodium sulphate than a pure solution of astracanite would2 for in this case there would be equal molecular amounts of ,na#b,,so#d and ,mg,s,o#d4 ,a solution which is saturated with respect to astracanite alone1 will contain more sodium sulphate than the solution saturated with respect to astracanite plus ,glauber's salt1 and the latter will therefore be deposited4 ,from this1 therefore1 it is clear that if astracanite is brought in contact with water at about the transition point1 it will undergo decomposition with separation of ,glauber's salt 7supersaturation being excluded74 ,illustration3 ,,fig4 #aja4 ,this will perhaps be made clearer by considering ,fig4 #aja4 ,in this diagram the ordinates represent the ratio of sodium sulphate to magnesium sulphate in the solutions1 and the abscissae represent the temperatures4 ,the line ,,ab represents solutions saturated with respect to a mixture of the single salts 7p4 #bfh72 ,,bc refers to solutions in equilibrium with astracanite and magnesium sulphate2 while ,,bx represents the composition of solutions in contact with the solid phases astracanite and ,glauber's salt4 ,the values of the solubility are contained in the following table1 and in that on p4 #bfh1 and are1 as before1 expressed in gm4-molecules of salt in #ajj gm4-molecules of water4#ceb #bgj ---------------------------------------- --------------------------------- ,astracanite ,astracanite ,temperature4 sodium sulphate4 magnesium sulphate4 ---------------------------------------- ------------------ ,na#b,,so#d4 ,mg,s,o#d4 ,na#b,,so#d4 ,mg,s,o#d4 ---------------------------------------- --------------------------------- #ah4e;deg -- -- #c4da #d4bg #bb;deg #b4ie #d4gj #b4he #d4fc #bd4e;deg #c4de #c4fb #b4fh #d4gf #cj;deg #d4eh #b4ia #b4cj #e4ca #ce;deg #d4cj #b4gf #a4gc #e4hh ---------------------------------------- --------------------------------- ,at the transition point the ratio of sodium sulphate to magnesium sulphate is approximately #a 3 #a4f4 ,in the case of solutions saturated with respect to both astracanite and ,glauber's salt1 the relative amount of sodium sulphate increases as the temperature rises1 while in the solutions saturated for astracanite and magnesium sulphate1 the ratio of sodium sulphate to magnesium sulphate decreases4 ,if1 now1 we consider only the temperatures above the transition point1 we see from the figure that solutions represented by points above the line ,,bx contain relatively more sodium sulphate than solutions in contact with astracanite and ,glauber's salt2 and solutions lying below the line ,,bc contain relatively more magnesium sulphate than solutions saturated with this salt and astracanite4 ,these solutions will therefore not be stable1 but will deposit in the one case1 astracanite and ,glauber's salt1 and in the other case1 astracanite and magnesium sulphate1 until a point on ,,bx or ,,bc is reached4 ,all solutions1 however1 lying to the right of ,,cbx1 will be unsaturated with respect to these two pairs of salts1 and only the solutions represented by the line ,,xy 7and which contain equimolecular amounts of sodium and magnesium sulphates7 will be saturated with respect to the pure double salt4 ,transition ,interval4--,fig4 #aja will also render intelligible a point of great importance in connection with astracanite1 and of double salts generally4 ,at temperatures between those represented by the points ,b and ,x1 the double salt when brought in contact with water will be decomposed with separation of sodium sulphate4 ,above the temperature of the point #bga ,x1 however1 the solution of the pure double salt is stable1 because it can still take up a little of either of the components4 ,at temperatures1 then1 above that at which the solution in contact with the double salt and the less soluble single salt1 contains the single salts in the ratio in which they are present in the double salt1 solution of the latter will take place without decomposition4 ,the range of temperature between that at which double salt can begin to be formed 7the transition point7 and that at which it ceases to be decomposed by water is called the transition interval4#cec ,if the two single salts have identical solubility at the transition point1 the transition interval diminishes to nought4 ,in those cases where the double salt is the stable form below the transition point1 the transition interval will extend downwards to a lower temperature4 ,fig4 #aja will then have the reverse form4 ,summary4--,with regard to double salts we have learned that their formation from and their decomposition into the single salts1 is connected with a definite temperature1 the transition temperature4 ,at this transition temperature two vapour pressure curves cut1 viz4 a curve of dehydration of a mixture of the single salts and the solubility curve of the double salt2 or the dehydration curve of the double salt and the solubility curve of the mixed single salts4 ,the solubility curves1 also1 of these two systems intersect at the transition point1 but although the formation of the double salt commences at the transition point1 complete stability in contact with water may not be attained till some temperature above 7or below7 that point4 ,only when the temperature is beyond the transition interval1 will a double salt dissolve in water without decomposition 7e4g4 the alums74 99 99 99 99 99 #bgb ,,chapter ,,xvi ,,isothermal ,,curves ,,and ,,the ,,space ,,model ,in the preceding chapter we considered the changes in the solubility of double salts and of mixtures of their constituent salts with the temperature2 noting1 more especially1 the relationships between the two systems at the transition point4 ,it is now proposed to conclude the study of the three-component systems by discussing very briefly the solubility relations at constant temperature1 or the isothermal solubility curves4 ,in this way fresh light will be thrown on the change in the solubility of one component by the addition of another component1 and also on the conditions of formation and stable existence of double salts in solution4 ,with the help of these isothermal curves1 also1 the phenomena of crystallization at constant temperature--phenomena which have not only a scientific interest but also an important bearing on the industrial preparation of double salts--will be more clearly understood4#ced ,a brief description will also be given of the method of representing the variation of the concentration of the two salts in the solution with the temperature4 ,non-formation of ,double ,salts4--,in ,fig4 #ajb are shown the solubility curves of two salts1 ,a and ,b1 which at the given temperature do not form a double salt4#cee ,the ordinates represent the amount of ,a1 the abscissae the amount of ,b in a constant amount of the third component1 the solvent4 ,the #bgc point ,a1 therefore1 represents the solubility of the salt ,a at the given temperature2 and similarly1 point ,b represents the solubility of ,b4 ,since we are dealing with a three-component system1 one solid phase in contact with solution will constitute a bivariant system 7in the absence of the vapour phase and under a constant pressure74 ,at any given temperature1 therefore1 the concentration of the solution in equilibrium with the solid can undergo change4 ,if1 now1 to a pure solution of ,a a small quantity of ,b is added1 the solubility of ,a will in general be altered2 as a rule it is diminished1 but sometimes it is increased4#cef ,the curve ,,ac represents the varying composition of the solution in equilibrium with the solid component ,a4 ,similarly1 the curve ,,bc represents the composition of the solutions in contact with pure ,b as solid phase4 ,at the point1 ,c1 where these two curves intersect1 there are two solid phases1 viz4 pure ,a and pure ,b1 in equilibrium with solution1 and the system becomes invariant4 ,at this point the solution is saturated with respect to both ,a and ,b1 and at a given temperature must have a perfectly definite composition4 ,to take an example1 if we suppose ,a to represent sodium sulphate decahydrate1 and ,b1 magnesium sulphate heptahydrate1 and the temperature to be #ah4e;deg 7i4e4 below the transition point71 the point ,c would represent a solution containing #b4af gm4-molecules ,na#b,,so#d and #d4eg gm4-molecules ,mg,s,o#d per #ajj gm4-molecules of water 7p4 #bfh74 ,the curve ,,acb is the boundary curve for saturated solutions2 solutions lying outside this curve are supersaturated1 those lying within the area ,,acbo1 are unsaturated4 ,illustration3 ,,fig4 #ajb4 ,illustration3 ,,fig4 #ajc4 ,illustration3 ,,fig4 #ajd4 ,formation of ,double ,salt4--,we have already learned in the preceding chapter that if the temperature is outside#ceg the #bgd transition interval1 it is possible to prepare a pure saturated solution of the double salt4 ,if1 now1 we suppose the double salt to contain the two constituent salts in equimolecular proportions1 its saturated solution must be represented by a point lying on the line which bisects the angle ,,aob2 e4g4 point ,d1 ,fig4 #ajc4 ,but a double salt constitutes only a single phase1 and can exist1 therefore1 in contact with solutions of varying concentration1 as represented by ,,edf4 ,let us compare1 now1 the relations between the solubility curve for the double salt1 and those for the two constituent salts4 ,we shall suppose that the double salt is formed from the single salts when the temperature is raised above a certain point 7as in the formation of astracanite74 ,at a temperature below the transition point1 as we have already seen1 the solubility of the double salt is greater than that of a mixture of the single salts4 ,the curve ,,edf1 therefore1 must lie above the point ,c1 in the region representing solutions supersaturated with respect to the single salts 7,fig4 #ajd74 ,such a solution1 however1 would be metastable1 and on being brought in contact with the single salts would deposit these and yield a solution represented by the point ,c4 ,at this particular temperature1 therefore1 the isothermal solubility curve will consist of only two branches4 ,illustration3 ,,fig4 #aje4 ,suppose1 now1 that the temperature is that of the transition point4 ,at this point1 the double salt can exist together with the single salts in contact with solution4 ,the solubility curve #bge of the double salt must1 therefore1 pass through the point ,c1 as shown in ,fig4 #aje4 ,from this figure1 now1 it is seen that a solution saturated with respect to double salt alone 7point ,d71 is supersaturated with respect to the component ,a4 ,if1 then1 at the temperature of the transition point1 excess of the double salt is brought in contact with water1#ceh and if supersaturation is excluded1 the double salt will undergo decomposition and the component ,a will be deposited4 ,the relative concentration of the component ,b in the solution will1 therefore1 increase1 and the composition of the solution will be thereby altered in the direction ,,dc4 ,when the solution has the composition of ,c1 the single salt ceases to be deposited1 for at this point the solution is saturated for both double and single salt2 and the system becomes invariant4 ,this diagram explains very clearly the phenomenon of the decomposition of a double salt at the transition point4 ,as is evident1 this decomposition will occur when the solution which is saturated at the temperature of the transition point1 with respect to the two single salts 7point ,c71 does not contain these salts in the same ratio in which they are present in the double salt4 ,if point ,c lay on the dotted line bisecting the right angle1 then the pure saturated solution of the double salt would not be supersaturated with respect to either of the single salts1 and the double salt would1 therefore1 not be decomposed by water4 ,as has already been mentioned1 this behaviour is found in the case of optically active isomerides1 the solubilities of which are identical4 ,at the transition point1 therefore1 the isothermal curve also consists of two branches2 but the point of intersection of the two branches now represents a solution which is saturated not #bgf only with respect to the single salts1 but also for the double salt in presence of the single salts4 ,we have just seen that by a change of temperature the two solubility curves1 that for the two single salts and that for the double salt1 were made to approach one another 7cf4 ,figs4 #ajd and #aje74 ,in the previous chapter1 however1 we found that on passing the transition point to the region of stability for the double salt1 the solution which is saturated for a mixture of the two constituent salts1 is supersaturated for the double salt4 ,in this case1 therefore1 point ,c must lie above the solubility curve of the pure double salt 7,fig4 #ajf71 and a solution of the composition ,c1 if brought in contact with double salt1 will deposit the latter4 ,if the single salts were also present1 then as the double salt separated out1 the single salts would pass into solution1 because so long as the two single salts are present1 the composition of the solution must remain unaltered4 ,if one of the single salts disappear before the other1 there will be left double salt plus ,a or double salt plus ,b1 according to which was in excess2 and the composition of the solution will be either that represented by ,d 7saturated for double salt plus ,a71 or that of the point ,f 7saturated for double salt plus ,b74 ,illustration3 ,,fig4 #ajf4 ,in connection with the isothermal represented in ,fig4 #ajf1 it should be noted that at this particular temperature a solution saturated with respect to the pure double salt is no longer supersaturated for one of the single salts 7point ,d72 so that at the temperature of this isothermal the double salt is not decomposed by water4 ,at this temperature1 further1 the boundary curve consists of three branches ,,ad1 ,,df1 and ,,fb1 which give the composition of the solutions in equilibrium with pure ,a1 double salt1 and pure ,b respectively2 while the points ,d and ,f represent solutions saturated for double salt plus ,a and double salt plus ,b4 ,on continuing to alter the temperature in the same direction #bgg as before1 the relative shifting of the solubility curves becomes more marked1 as shown in ,fig4 #ajg4 ,at the temperature of this isothermal1 the solution saturated for the double salt now lies in a region of distinct unsaturation with respect to the single salts2 and the double salt can now exist as solid phase in contact with solutions containing both relatively more of ,a 7curve ,,ed71 and relatively more of ,b 7curve ,,df71 than is contained in the double salt itself4 ,illustration3 ,,fig4 #ajg4 ,transition ,interval4--,from what has been said1 and from an examination of the isothermal diagrams1 ,figs4 #ajd-ajg1 it will be seen that by a variation of the temperature we can pass from a condition where the double salt is quite incapable of existing in contact with solution 7supersaturation being excluded71 to a condition where the existence of the double salt in presence of solution becomes possible2 only in the presence1 however1 of one of the single salts 7transition point1 ,fig4 #aje74 ,a further change of temperature leads to a condition where the stable existence of the pure double salt in contact with solution just becomes possible 7,fig4 #ajf72 and from this point onwards1 pure saturated solutions of the double salt can be obtained 7,fig4 #ajg74 ,at any temperature1 therefore1 between that represented by ,fig4 #aje1 and that represented by ,fig4 #ajf1 the double salt undergoes partial decomposition1 with deposition of one of the constituent salts4 ,the temperature range between the transition point and the temperature at which a stable saturated solution of the pure double salt just begins to be possible1 is known as the transition interval 7p4 #bgj74 ,as the figures show1 the transition interval is limited on the one side by the transition temperature1 and on the other by the temperature at which the solution saturated for double salt and the less soluble of the single salts1 contains the component salts in the same ratio as they are present in the double salt4 ,the greater the difference in the solubility of the single salts1 the larger will be the transition interval4 #bgh ,isothermal ,evaporation4--,the isothermal solubility curves are of great importance for obtaining an insight into the behaviour of a solution when subjected to isothermal evaporation4 ,to simplify the discussion of the relationships found here1 we shall still suppose that the double salt contains the single salts in equimolecular proportions2 and we shall1 in the first instance1 suppose that the unsaturated solution with which we commence1 also contains the single salts in the same ratio4 ,the composition of the solution must1 therefore1 be represented by some point lying on the line ,,od1 the bisectrix of the right angle4 ,from what has been said1 it is evident that when the formation of a double salt can occur1 three temperature intervals can be distinguished1 viz4 the single-salt interval1 the transition interval1 and the double-salt interval4#cei ,when the temperature lies in the first interval1 evaporation leads first of all to the crystallization of one of the single salts1 and then to the separation of both the single salts together4 ,in the second temperature interval1 evaporation again leads1 in the first place1 to the deposition of one of the single salts1 and afterwards to the crystallization of the double salt4 ,in the third temperature interval1 only the double salt crystallizes out4 ,this will become clearer from what follows4 ,illustration3 ,,fig4 #ajh4 ,illustration3 ,,fig4 #aji4 ,if an unsaturated solution of the two single salts in equimolecular proportion 7e4g4 point x1 ,fig4 #ajh7 is evaporated at a temperature at which the formation of double salt is impossible1 the component ,a1 the solubility curve of which is #bgi cut by the line ,,od1 will first separate out2 the solution will thereby become richer in ,b4 ,on continued evaporation1 more ,a will be deposited1 and the composition of the solution will change until it attains the composition represented by the point ,c1 when both ,a and ,b will be deposited1 and the composition of the solution will remain unchanged4 ,the result of evaporation will therefore be a mixture of the two components4 ,if the formation of double salt is possible1 but if the temperature lies within the transition interval1 the relations will be represented by a diagram like ,fig4 #aji4 ,isothermal evaporation of the solution ,x will lead to the deposition of the component ,a1 and the composition of the solution will alter in the direction ,,de2 at the latter point the double salt will be formed1 and the composition of the solution will remain unchanged so long as the two solid phases are present4 ,as can be seen from the diagram1 however1 the solution in ,e contains less of component ,a than is contained in the double salt4 ,deposition of the double salt at ,e1 therefore1 would lead to a relative decrease in the concentration of ,a in the solution1 and to counterbalance this1 the salt which separated out at the commencement must redissolve4 ,since the salts were originally present in equimolecular proportions1 the final result of evaporation will be the pure double salt4 ,if when the solution has reached the point ,e the salt ,a which had separated out is removed1 double salt only will be left as solid phase4 ,at a given temperature1 however1 a single solid phase can exist in equilibrium with solutions of different composition4 ,if1 therefore1 isothermal evaporation is continued after the removal of the salt ,a1 double salt will be deposited1 and the composition of the solution will change in the direction ,,ef4 ,at the point ,f the salt ,b will separate out1 and on evaporation both double salt and the salt ,b will be deposited4 ,in the former case 7when the salt ,a disappears on evaporation7 we are dealing with an incongruently saturated solution2 but in the latter case1 where both solid phases continue to be deposited1 the solution is said to be congruently saturated4#cfj ,a congruently saturated solution is one from which the #bhj solid phases are continuously deposited during isothermal evaporation to dryness1 whereas in the case of incongruently saturated solutions1 at least one of the solid phases disappears during the process of evaporation4 ,illustration3 ,,fig4 #aaj4 ,lastly1 if the temperature lies outside the transition interval1 isothermal evaporation of an unsaturated solution of the composition ,x 7,fig4 #aaj7 will lead to the deposition of pure double salt from beginning to end4 ,if a solution of the composition ,y is evaporated1 the component ,a will first be deposited and the composition of the solution will alter in the direction of ,e1 at which point double salt will separate out4 ,since the solution at this point contains relatively more of ,a than is present in the double salt1 both the double salt and the single salt ,a will be deposited on continued evaporation1 in order that the composition of the solution shall remain unchanged4 ,in the case of solution ,z1 first component ,b and afterwards the double salt will be deposited4 ,the result will1 therefore1 be a mixture of double salt and the salt ,b 7congruently saturated solutions71 ,it may be stated here that the same relationships as have been explained above for double salts are also found in the resolution of racemic compounds by means of optically active substances 7third method of ,pasteur74 ,in this case the single salts are doubly active substances 7e4g4 strychnine-d-tartrate and strychnine-l-tartrate71 and the double salt is a partially racemic compound4#cfa ,crystallization of ,double ,salt from ,solutions containing ,excess of ,one ,component4--,one more case of isothermal crystallization may be discussed4 ,it is well known that a double salt which is decomposed by pure water can nevertheless be obtained pure by crystallization from a solution containing excess of one of the single salts 7e4g4 in the case of carnallite74 ,since the double salt is partially decomposed by water1 the temperature of the experiment must be within the transition #bha interval1 and the relations will1 therefore1 be represented by a diagram like ,fig4 #aji4 ,if1 now1 instead of starting with an unsaturated solution containing the single salts in equimolecular proportions1 we commence with one in which excess of one of the salts is present1 as represented by the point ,y1 isothermal evaporation will cause the composition to alter in the direction ,,yd'1 the relative amounts of the single salts remaining the same throughout4 ,when the composition of the solution reaches the point ,d'1 pure double salt will be deposited4 ,the separation of double salt will1 however1 cause a relative decrease in the concentration of the salt ,a1 and the composition of the solution will1 therefore1 alter in the direction ,d',f4 ,if the evaporation is discontinued before the solution has attained the composition ,f1 only double salt will have separated out4 ,even within the transition interval1 therefore1 pure double salt can be obtained by crystallization1 provided the original solution has a composition represented by a point lying between the two lines ,,oe and ,,of4 ,since1 as already shown1 the composition of the solution alters on evaporation in the direction ,,ef1 it will be best to employ a solution having a composition near to the line ,,oe4 ,formation of ,mixed ,crystals4--,if the two single salts ,a and ,b do not crystallize out pure from solution1 but form an unbroken series of mixed crystals1 it is evident that an invariant system cannot be produced4 ,the solubility curve will therefore be continuous from ,a to ,b2 the liquid solutions of varying composition being in equilibrium with solid solutions also of varying composition4 ,if1 however1 the series of mixed crystals is not continuous1 there will be a break in the solubility curve at which two solid solutions of different composition will be in equilibrium with liquid solution4 ,this1 of course1 will constitute an invariant system1 and the point will correspond to the point ,c in ,fig4 #ajh4 ,a full discussion of these systems would1 however1 lead us too far1 and the above indication of the behaviour must suffice4#cfb #bhb ,application to the ,characterization of ,racemates4--,the form of the isothermal solubility curves is also of great value for determining whether an inactive substance is a racemic compound or a conglomerate of equal proportions of the optical antipodes4#cfc ,as has already been pointed out1 the formation of racemic compounds from the two enantiomorphous isomerides1 is analogous to the formation of double salts4 ,the isothermal solubility curves1 also1 have a similar form4 ,in the case of the latter1 indeed1 the relationships are simplified by the fact that the two enantiomorphous forms have identical solubility1 and the solubility curves are therefore symmetrical to the line bisecting the angle of the co-ordinates4 ,further1 with the exception of the partially racemic compounds to be mentioned later1 there is no transition interval4 ,in ,fig4 #aaa1 are given diagrammatically two isothermal solubility curves for optically active substances4 ,from what has been said in the immediately preceding pages1 the figure ought really to explain itself4 ,the upper isothermal acb represents the solubility relations when the formation of a racemic compound is excluded1 as1 e4g4 in the case of rubidium d- and l-tartrates above the transition point 7p4 #bfe74 ,the solution at the point c is1 of course1 inactive1 and is unaffected by addition of either the d- or l- form4 ,the lower isothermal1 on the other hand1 would be obtained at a temperature at which the racemic compound could be formed4 ,the curve a'e is the solubility curve for the l- form2 b'f1 that for the d- form2 and edf1 that for the racemic compound in presence of solutions of varying concentration4 ,the point d corresponds to saturation for the pure racemic compound4 ,illustration3 ,,fig4 #aaa4 ,from these curves now1 it will be evident that it will be possible1 in any given case1 to decide whether or not an inactive body is a mixture or a racemic compound4 ,for this purpose1 #bhc two solubility determinations are made1 first with the inactive material alone 7in excess71 and then with the inactive material plus excess of one of the optically active forms4 ,if we are dealing with a mixture1 the two solutions thus obtained will be identical2 both will have the composition corresponding to the point c1 and will be inactive4 ,if1 however1 the inactive material is a racemic compound1 then two different solutions will be obtained2 namely1 an inactive solution corresponding to the point d 7,fig4 #aaa71 and an active solution corresponding either to e or to f1 according to which enantiomorphous form was added4 ,partially racemic compounds4#cfd ,in this case we are no longer dealing with enantiomorphous forms1 and the solubility of the two oppositely active isomerides is no longer the same4 ,the symmetry of the solubility curves therefore disappears1 and a figure is obtained which is identical in its general form with that found in the case of ordinary double salts 7,fig4 #aab74 ,in this case there is a transition interval4 ,illustration3 ,,fig4 #aab4 ,the curves acb belong to a temperature at which the partially racemic compound cannot be formed2 a'dfb'1 to the temperature at which the compound just begins to be stable in contact with water1 and aed'f'b belongs to a temperature at which the partially racemic compound is quite stable in contact with water4 ,suppose now solubility determinations1 made in the first case with the original material alone1 and then with the original body plus each of the two compounds1 formed from the enantiomorphous substances separately1 then if the original body was a mixture1 identical solutions will be obtained in all three cases 7point c72 if it was a partially racemic compound1 three different solutions 7e1 d'1 and f'7 will be obtained if the temperature was outside the transition interval1 and two solutions1 d and f1 if the temperature belonged to the transition interval4 #bhd ,representation in ,space4 ,space ,model for ,carnallite4--,interesting and important as the isothermal solubility curves are1 they are insufficient for the purpose of obtaining a clear insight into the complete behaviour of the systems of two salts and water4 ,a short description will1 therefore1 be given here of the representation in space of the solubility relations of potassium and magnesium chlorides1 and of the double salt which they form1 carnallite4#cfe ,illustration3 ,,fig4 #aac4 ,fig4 #aac is a diagrammatic sketch of the model for carnallite looked at sideways from above4 ,along the ,x-axis is measured the concentration of magnesium chloride in the #bhe solution2 along the ,y-axis1 the concentration of potassium chloride2 while along the ,t-axis is measured the temperature4 ,the three axes are at right angles to one another4 ,the ,,xt-plane1 therefore1 contains the solubility curve of magnesium chloride2 the ,,yt-plane1 the solubility curve of potassium chloride1 and in the space between the two planes1 there are represented the composition of solutions containing both magnesium and potassium chlorides4 ,any surface between the two planes will represent the various solutions in equilibrium with only one solid phase1 and will therefore indicate the area or field of existence of bivariant ternary systems4 ,a line or curve formed by the intersection of two surfaces will represent solutions in equilibrium with two solid phases 7viz4 those belonging to the intersecting surfaces71 and will show the conditions for the existence of univariant systems4 ,lastly1 points formed by the intersection of three surfaces will represent invariant systems1 in which a solution can exist in equilibrium with three solid phases 7viz4 those belonging to the three surfaces74 ,we shall first consider the solubility relations of the single salts4 ,the complete equilibrium curve for magnesium chloride and water is represented in ,fig4 #aac by the series of curves ,,abf#a ,g#a ,h#a ,j#a ,l#a ,n#a4 ,,ab is the freezing-point curve of ice in contact with solutions containing magnesium chloride1 and ,b is the cryohydric point at which the solid phases ice and ,mg,cl#b1ab;,h#b,o can co-exist with solution4 ,,bfg is the solubility curve of magnesium chloride dodecahydrate4 ,this curve shows a point of maximum temperature at ,f#a1 and a retroflex portion ,f#a;,g#a4 ,the curve is therefore of the form exhibited by calcium chloride hexahydrate1 or the hydrates of ferric chloride 7,chapter ,,viii474 ,g#a is a transition point at which the solid phase changes from dodecahydrate to octahydrate1 the solubility of which is represented by the curve ,g#a;,h#a4 ,at ,h#a the octahydrate gives place to the hexahydrate1 which is the solid phase in equilibrium with the solutions represented by the curve ,h#a;,j#a4 ,j#a and ,l#a are also transition points at which the solid phase undergoes change1 in the former case from hexahydrate to tetrahydrate2 and in the latter case1 #bhf from tetrahydrate to dihydrate4 ,the complete curve of equilibrium for magnesium chloride and water is1 therefore1 somewhat complicated1 and is a good example of the solubility curves obtained with salts capable of forming several hydrates4 ,the solubility curve of potassium chloride is of the simplest form1 consisting only of the two branches ,,ac1 the freezing-point curve of ice1 and ,,co1 the solubility curve of the salt4 ,c is the cryohydric point4 ,this point and the two curves lie in the ,,yt-plane4 ,on passing to the ternary systems1 the composition of the solutions must be represented by points or curves situated between the two planes4 ,we shall now turn to the consideration of these4 ,,bd and ,,cd are ternary eutectic curves 7p4 #bhd74 ,they give the composition of solutions in equilibrium with ice and magnesium chloride dodecahydrate 7,,bd71 and with ice and potassium chloride 7,,cd74 ,d is a ternary cryohydric point4 ,if the temperature is raised and the ice allowed to disappear1 we shall pass to the solubility curve for ,mg,cl#b1ab;,h#b,o ,k,cl 7curve ,,de74 ,at ,e carnallite is formed and the potassium chloride disappears2 ,,efg is then the solubility curve for ,mg,cl#b1ab;,h#b,o carnallite 7,k,mg,cl#c1f;,h#b,o74 ,this curve also shows a point of maximum temperature 7,f7 and a retroflex portion4 ,,gh and ,,hj represent the solubility curves of carnallite ,mg,cl#b1h;,h#b,o and carnallite ,mg,cl#b1f;,h#b,o1 ,g and ,h being transition points4 ,,jk is the solubility curve for carnallite ,mg,cl#b1d;,h#b,o4 ,at the point ,k we have the highest temperature at which carnallite can exist with magnesium chloride in contact with solution4 ,above this temperature decomposition takes place and potassium chloride separates out4 ,if at the point ,e1 at which the two single salts and the double salt are present1 excess of potassium chloride is added1 the magnesium chloride will all disappear owing to the formation of carnallite1 and there will be left carnallite and potassium chloride4 ,the solubility curve for a mixture of these two salts is represented by ,,emk2 a simple curve exhibiting1 however1 a temperature maximum at ,m4 ,this maximum point corresponds with the fact that dry carnallite melts at this temperature with separation of potassium chloride4 ,at all temperatures #bhg above this point1 the formation of double salt is impossible4 ,the retroflex portion of the curve represents solutions in equilibrium with carnallite and potassium chloride1 but in which the ratio ,mg,cl#b 3 ,k,cl is greater than in the double salt4 ,throughout its whole course1 the curve ,,emk represents solutions in which the ratio of ,mg,cl#b 3 ,k,cl is greater than in the double salt4 ,as this is a point of some importance1 it will be well1 perhaps1 to make it clearer by giving one of the isothermal curves1 e4g4 the curve for #aj;deg1 which is represented diagrammatically in ,fig4 #aad4 ,e and ,f here represent solutions saturated for carnallite plus magnesium chloride hydrate1 and for carnallite plus potassium chloride4 ,as is evident1 the point ,f lies above the line representing equimolecular proportions of the salts 7,,od74 ,illustration3 ,,fig4 #aad4 ,summary and ,numerical ,data4--,we may now sum up the different systems which can be formed1 and give the numerical data from which the model is constructed4#cff ,i4 ,bivariant ,systems4 -------------------------------------- ,solid phase4 ,area of existence4 -------------------------------------- ,ice ,,abdc ,k,cl ,,cdemklno ,carnallite ,,efghjkm ,mg,cl#b1ab;,h#b,o ,,bf#a;,g#a;,,gfed ,mg,cl#b1h;,h#b,o ,g#a;,h#a;,,hg ,mg,cl#b1f;,h#b,o ,h#a;,i#a;,,ih ,mg,cl#b1d;,h#b,o ,i#a,l#a,,lki ,mg,cl#b1b;,h#b,o ,l#a,n#a,,nl -------------------------------------- ,,ii4 ,univariant ,systems4--,the different univariant systems have already been described4 ,the course of the curves will be sufficiently indicated if the temperature and composition of the solutions for the different invariant systems are given4 #bhh ,,iii4--,invariant ,systems--,binary and ,ternary4 ---------------------------------------- --------------------------------- ,composition of solution4 ,point4 ,solid ,phases4 ,temper- ,gram-molecules of salt ature4 per #ajjj gram-mol4 water4 ---------------------------------------- --------------------------------- ,a ,ice #j;deg -- ,b ,ice2 ,mg,cl#b1ab;,h#b,o -#cc4f;deg #di4b ,mg,cl#b ,c ,ice2 ,k,cl -#aa4a;deg #ei4d ,k,cl ,d ,ice2 ,mg,cl#b1ab;,h#b,o2 -#cd4c;deg #dc ,mg,cl#b2 #c ,k,cl ,k,cl ,e ,mg,cl#b1ab;,h#b,o2 ,k,cl2 -#ba;deg #ff4a ,mg,cl#b2 #d4i ,k,cl carnallite ,f#a ,mg,cl#b1ab;,h#b,o -#af4d;deg #hc4cc ,mg,cl#b ,f ,mg,cl#b1ab;,h#b,o2 -#af4f;deg ,almost same as ,f#a2 carnallite contains small amount of ,k,cl ,g#a ,mg,cl#b1ab;,h#b,o2 -#af4h;deg #hg4e ,mg,cl#b ,mg,cl#b1h;,h#b,o ,g ,mg,cl#b1ab;,h#b,o2 -#af4i;deg ,almost same as ,g#a1 ,mg,cl#b1h;,h#b,o2 but contains small carnallite quantity of ,k,cl ,h#a ,mg,cl#b1h;,h#b,o2 -#c4d;deg #ii ,mg,cl#b ,mg,cl#b1f;,h#b,o ,h ,mg,cl#b1h;,h#b,o2 ca4-#c4d;deg ,almost same as ,h#a1 ,mg,cl#b1f;,h#b,o2 but contains small carnallite amount of ,k,cl ,j#a ,mg,cl#b1f;,h#b,o2 #aaf4fg;deg #afa4h ,mg,cl#b ,mg,cl#b1d;,h#b,o ,j ,mg,cl#b1f;,h#b,o2 #aae4g;deg #afb ,mg,cl#b2 #d ,k,cl ,mg,cl#b1d;,h#b,o2 carnallite ,k ,mg,cl#b1d;,h#b,o2 ,k,cl2 #aeb4e;deg #bjj ,mg,cl#b2 #bd ,k,cl carnallite ,l#a ,mg,cl#b1d;,h#b,o2 #aha;deg #bch4a ,mg,cl#b ,mg,cl#b1b;,h#b,o ,l ,mg,cl#b1d;,h#b,o2 #agf;deg #bdj ,mg,cl#b2 #da ,k,cl ,mg,cl#b1b;,h#b,o2 ,k,cl ,m ,carnallite2 ,k,cl #afg4e;deg #aff4g ,mg,cl#b2 #da4g ,k,cl ,n#a ,mg,cl#b1b;,h#b,o #ahf;deg ca4 #bda ,mg,cl#b ,n ,mg,cl#b1b;,h#b,o2 ,k,cl #ahf;deg #bdj ,mg,cl#b2 #fc ,k,cl ,o ,k,cl #ahf;deg #aie4f ,k,cl ---------------------------------------- --------------------------------- ,with the help of the data in the preceding table and of the solid model it will be possible to state in any given case what will be the behaviour of a system composed of magnesium chloride1 potassium chloride and water4 ,one or two different cases will be very briefly described2 and the reader should have no difficulty in working out the behaviour under other conditions with the help of the model and the numerical data just given4 #bhi ,in the first place it may be again noted that at a temperature above #afg4e;deg 7point ,m7 carnallite cannot exist4 ,if1 therefore1 a solution of magnesium and potassium chlorides is evaporated at a temperature above this point1 the result will be a mixture of potassium chloride and either magnesium chloride tetrahydrate or magnesium chloride dihydrate1 according as the temperature is below or above #agf;deg4 ,the isothermal curve here consists of only two branches4 ,further1 reference has already been made to the fact that all points of the carnallite area correspond to solutions in equilibrium with carnallite1 but in which the ratio of ,mg,cl#b to ,k,cl is greater than in the double salt4 ,a solution which is saturated with respect to double salt alone will be supersaturated with respect to potassium chloride4 ,at all temperatures1 therefore1 carnallite is decomposed by water with separation of potassium chloride2 hence all solutions obtained by adding excess of carnallite to water will lie on the curve ,,em4 ,a pure saturated solution of carnallite cannot be obtained4 ,if an unsaturated solution of the two salts in equimolecular amounts is evaporated1 potassium chloride will first be deposited1 because the plane bisecting the right angle formed by the ,x and ,y axes cuts the area for that salt4 ,deposition of potassium chloride will lead to a relative increase in the concentration of magnesium chloride in the solution2 and on continued evaporation a point 7on the curve ,,em7 will be reached at which carnallite will separate out4 ,so long as the two solid phases are present1 the composition of the solution must remain unchanged4 ,since the separation of carnallite causes a decrease in the relative concentration of the potassium chloride in the solution1 the portion of this salt which was deposited at the commencement must redissolve1 and carnallite will be left on evaporating to dryness4 7,incongruently saturated solution47 ,although carnallite is decomposed by pure water1 it will be possible to crystallize it from a solution having a composition represented by any point in the carnallite area4 ,since during the separation of the double salt the relative amount of magnesium chloride increases1 it is most advantageous to #bij commence with a solution the composition of which is represented by a point lying just above the curve ,,em 7cf4 p4 #bha74 ,from the above description of the behaviour of carnallite in solution1 the processes usually employed for obtaining potassium chloride will be readily intelligible4#cfg ,ferric ,chloride--,hydrogen ,chloride--,water4--,in the case of another system of three components which we shall now describe1 the relationships are considerably more complicated than in those already discussed4 ,they deserve discussion1 however1 on account of the fact that they exhibit a number of new phenomena4 ,in the system formed by the three components1 ferric chloride1 hydrogen chloride1 and water1 not only can various compounds of ferric chloride and water 7p4 #aeb71 and of hydrogen chloride and water be formed1 each of which possesses a definite melting point1 but various ternary compounds are also known4 ,thus we have the following solid phases3-- #b;,fe,cl#c1ab;,h#b,o ,h,cl1#c;,h#b,o #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o #b;,fe,cl#c1g;,h#b,o ,h,cl1#b;,h#b,o #b;,fe,cl#c1b;,h,cl1#h;,h#b,o #b;,fe,cl#c1e;,h#b,o ,h,cl1,h#b,o #b;,fe,cl#c1b;,h,cl1#d;,h#b,o #b;,fe,cl#c1d;,h#b,o ,fe,cl#c ,from this it will be readily understood that the complete study of the conditions of temperature and concentration under which solutions can exist1 either with one solid phase or with two or three solid phases1 are exceedingly complicated2 and1 as a matter of fact1 only a few of the possible equilibria have been investigated4 ,we shall attempt here only a brief description of the most important of these4#cfh ,if we again employ rectangular co-ordinates for the graphic #bia representation of the results1 we have the two planes ,,xot and ,,yot 7,fig4 #aae73 the concentration of ferric chloride being measured along the ,x-axis1 the concentration of hydrogen chloride along the ,y-axis1 and the temperature along the ,t-axis4 ,the curve ,,abcdefghjk is1 therefore1 the solubility curve of ferric chloride in water 7p4 #aeb71 and the curve ,a',b',c',d',e',f' the solubility curve of hydrogen chloride and its hydrates4 ,b' and ,d' are the melting points of the hydrates ,h,cl1#c;,h#b,o and ,h,cl1#b;,h#b,o4 ,in the space between these two planes are represented those systems in which all three components are present4 ,as already stated1 only a few of the possible ternary systems have been investigated1 and these are represented in ,fig4 #aaf4 ,the figure shows the model resting on the ,,xot-plane1 so that the lower edge represents the solubility curve of ferric chloride1 the concentration increasing from right to left4 ,the concentration of hydrogen chloride is measured upwards1 and the temperature forwards4 ,the further end of the model represents the isothermal surface for -#cj;deg4 ,the surface of the model on the left does not correspond with the plane ,,yot in ,fig4 #aae1 but with a parallel plane which cuts the concentration axis for ferric chloride at a point representing #fe gm4-molecules ,fe,cl#c in #ajj gm4-molecules of water4 ,the upper surface corresponds with a plane parallel to the axis ,,xot1 at a distance corresponding with the concentration of #ej gm4-molecules ,h,cl in #ajj gm4-molecules of water4 ,illustration3 ,,fig4 #aae4 ,ternary ,systems4--,we pass over the binary system ,fe,cl#c--;,h#b,o1 which has already been discussed 7p4 #aeb71 and the similar system ,h,cl--,h#b,o 7see ,fig4 #aae71 and turn to the discussion of some of the ternary systems represented by #bib points on the surface of the model between the planes ,,xot and ,,yot4 ,as in the case of carnallite1 a plane represents the conditions of concentration of solution and temperature under which a ternary solution can be in equilibrium with a single solid phase 7bivariant systems71 a line represents the conditions for the coexistence of a solution with two solid phases 7univariant systems71 and a point the conditions for equilibrium with three solid phases 7invariant systems74 ,illustration3 ,,fig4 #aaf4 ,in the case of a binary system1 in which #b;,fe,cl#c1ab;,h#b,o is in equilibrium with a solution of the same composition1 addition of hydrogen chloride must evidently lower the temperature at which equilibrium can exist2 and the same holds1 of course1 #bic for all other binary solutions in equilibrium with this solid phase4 ,in this way we obtain the surface ,i41 which represents the temperatures and concentrations of solutions in which #b;,fe,cl#c1ab;,h#b,o can be in equilibrium with a ternary solution containing ferric chloride1 hydrogen chloride1 and water4 ,this surface is analogous to the curved surface ,k#a,k#bk#dk#c in ,fig4 #ig 7p4 #bef74 ,similarly1 the surfaces ,,ii41 ,,iii41 ,,iv41 and ,v4 represent the conditions for equilibrium between the solid phases #b;,fe,cl#c1g;,h#b,o2 #b;,fe,cl#c1e;,h#b,o2 #b;,fe,cl#c1d;,h#b,o2 ,fe,cl#c and ternary solutions respectively4 ,the lines ,,cl1 ,,em1 ,,gn1 and ,,io on the model represent univariant systems in which a ternary solution is in equilibrium with two solid phases1 viz4 with those represented by the adjoining fields4 ,these lines correspond with the ternary eutectic curves k#c,k#a and k#d,k#b in ,fig4 #ig4 ,besides the surfaces already mentioned1 there are still three others1 ,,vi41 ,,vii41 and ,,viii41 which also represent the conditions for equilibrium between one solid phase and a ternary solution2 but in these cases1 the solid phase is not a binary compound or an anhydrous salt1 but a ternary compound containing all three components4 ,the solid phases which are in equilibrium with the ternary solutions represented by the surfaces ,,vi41 ,,vii41 and ,,viii41 are #b;,fe,cl#c1b;,h,cl1#d;,h#b,o2 #b;,fe,cl#c1b;,h,cl1#h;,h#b,o2 and #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o respectively4 ,the model for ,fe,cl#c--;,h,cl--,h#b,o exhibits certain other peculiarities not found in the case of ,mg,cl#b--,k,cl--,h#b,o4 ,on examining the model more closely1 it is found that the field of the ternary compound #b;,fe,cl#c1b;,h,cl1#h;,h#b,o 7,,vii47 resembles the surface of a sugar cone1 and has a projecting point1 the end of which corresponds with a higher temperature than does any other point of the surface4 ,at the point of maximum temperature the composition of the liquid phase is the same as that of the solid4 ,this point1 therefore1 represents the melting point of the double salt of the above composition4 ,the curves representing univariant systems are of two kinds4 ,in the one case1 the two solid phases present are both binary compounds2 or one is a binary compound and the other is one of the components4 ,in the other case1 either one or both solid phases are ternary compounds4 ,curves belonging #bid to the former class 7so-called border curves7 start from binary eutectic points1 and their course is always towards lower temperatures1 e4g4 ,,cl1 ,,em1 ,,gn1 ,,io4 ,curves belonging to the latter class 7so-called medial curves7 would1 in a triangular diagram1 lie entirely within the triangle4 ,such curves are ,,yv1 ,,wv1 ,,vl1 ,,lm1 ,,mv1 ,,ns1 ,,st1 ,,so1 ,,oz4 ,these curves do not always run from higher to lower temperatures1 but may even exhibit a point of maximum temperature4 ,such maxima are found1 for example1 at ,u 7,fig4 #aaf71 and also on the curves ,,st and ,,lv4 ,finally1 whereas all the other ternary univariant curves run in valleys between the adjoining surfaces1 we find at the point ,x a similar appearance to that found in the case of carnallite1 as the univariant curve here rises above the surrounding surface4 ,the point ,x1 therefore1 does not correspond with a eutectic point1 but with a transition point4 ,at this point the ternary compound #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o melts with separation of #b;,fe,cl#c1ab;,h#b,o1 just as carnallite melts at #afh;deg with separation of potassium chloride4 ,the ,isothermal ,curves4--,a deeper insight into the behaviour of the system ,fe,cl#c--;,h,cl--,h#b,o is obtained from a study of the isothermal curves1 the complete series of which1 so far as they have been studied1 is given in ,fig4 #aag4cfi ,in this figure the lightly drawn curves represent isothermal solubility curves1 the particular temperature being printed beside the curve4#cgj ,the dark lines give the composition of the univariant systems at different temperatures4 ,the point of intersection of a dark with a light curve gives the composition of the univariant solution at the temperature represented by the light curve2 and the point of intersection of two dark lines gives the composition of the invariant solution in equilibrium with three solid phases4 ,the dotted lines represent metastable systems1 and the points ,p1 ,q1 and ,r represent solutions of #bie the composition of the ternary salts1 #b;,fe,cl#c1b;,h,cl1#d;,h#b,o2 #b;,fe,cl#c1b;,h,cl1#h;,h#b,o2 and #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o4 ,illustration3 ,,fig4 #aag4 ,the farther end of the model 7,fig4 #aaf7 corresponds1 as already mentioned1 to the temperature -#cj;deg1 so that the outline evidently represents the isothermal curve for that temperature4 ,fig4 #aag does not show this4 ,we can1 however1 follow the isothermal for -#bj;deg1 which is the extreme curve on the right in ,fig4 #aag4 ,point ,a represents the solubility of #b;,fe,cl#c1ab;,h#b,o in water4 ,if hydrogen chloride is added1 the concentration of ferric chloride in the solution first decreases and then increases1 until at point #cd the ternary double salt #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o is formed4 ,if the addition of hydrogen chloride is continued1 the ferric chloride disappears ultimately1 and only the ternary double salt remains4 ,this salt can coexist with solutions of the composition represented by the curve which passes through the points #agc1 #agd1 #age4 ,at the last-mentioned point1 the ternary salt with #h;,h#b,o is formed4 ,the composition of the solutions with which this salt is in equilibrium at -#bj;deg is represented by the curve which passes through a point of maximal concentration with respect to ,h,cl1 and cuts the curve ,,sn at the point #aab1 at which the solution is in equilibrium with the two solid phases #b;,fe,cl#c1d;,h#b,o and #b;,fe,cl#c1b;,h,cl1#h;,h#b,o4 ,the succeeding portion of the isotherm represents the solubility curve at -#bj;deg of #b;,fe,cl#c1d;,h#b,o1 which cuts the dark line ,,os at point #aac1 at which the solution is in equilibrium with the two solid phases #b;,fe,cl#c1d;,h#b,o and #b;,fe,cl#c1b;,h,cl1#d;,h#b,o4 ,thereafter comes the solubility curve of the latter compound4 ,the other isothermal curves can be followed in a similar manner4 ,if the temperature is raised1 the region of existence of the ternary double salts becomes smaller and smaller1 and at temperatures above #cj;deg the ternary salts with #ab;,h#b,o and #h;,h#b,o are no longer capable of existing4 ,if the temperature is raised above #df;deg1 only the binary compounds of ferric chloride and water and the anhydrous salt can exist as solid phases4 ,the isothermal curve for #j;deg represents the solubility curve for #b;,fe,cl#c1ab;,h#b,o2 #b;,fe,cl#c1g;,h#b,o2 #b;,fe,cl#c1e;,h#b,o2 and #b;,fe,cl#c1d;,h#b,o4 #bif ,finally1 in the case of the system ,fe,cl#c--;,h,cl--,h#b,o1 we find closed isothermal curves4 ,since1 as already stated1 the salt #b;,fe,cl#c1b;,h,cl1#h;,h#b,o has a definite melting point1 the temperature of which is therefore higher than that at which this compound is in equilibrium with solutions of other composition1 it follows that the line of intersection of an isothermal plane corresponding with a temperature immediately below the melting point of the salt with the cone-shaped surface of its region of existence1 will form a closed curve4 ,this is shown by the isotherm for -#d4e;deg1 which surrounds the point ,q1 the melting point of the ternary salt4 ,the following table gives some of the numerical data from which the curves and the model have been constructed3-- ---------------------------------------- --------------------------------- ,composition of the sol- ution in gm4-mols4 salt ,point4 ,solid phases4 ,temper- to #ajj gm4-mols4 water4 ature4 ------------------------ ,h,cl ,fe,cl#c ---------------------------------------- --------------------------------- ,a #b;,fe,cl#c1ab;,h#b,o -#bj;deg -- #f4ef ,c #b;,fe,cl#c1ab;,h#b,o2 #bg4d;deg -- #bd4cj #b;,fe,cl#c1g;,h#b,o ,e #b;,fe,cl#c1g;,h#b,o2 #cj;deg -- #cj4bd #b;,fe,cl#c1e;,h#b,o ,g #b;,fe,cl#c1e;,h#b,o2 #ee;deg -- #dj4fd #b;,fe,cl#c1d;,h#b,o ,j #b;,fe,cl#c1d;,h#b,o2 ,fe,cl#c #ff;deg -- #eh4dj #b;,fe,cl#c1ab;,h#b,o2 ,l #b;,fe,cl#c1g;,h#b,o2 -#g4e;deg #ai4bb #bc4gb #b;,fe,cl#c1b;,h,cl1#h;,h#b,o #b;,fe,cl#c1g;,h#b,o2 ,m #b;,fe,cl#c1e;,h#b,o2 -#g4c;deg #bc4jh #bh4ee #b;,fe,cl#c1b;,h,cl1#h;,h#b,o #b;,fe,cl#c1e;,h#b,o2 ,n #b;,fe,cl#c1d;,h#b,o2 -#af;deg #bh4dj #ca4hi #b;,fe,cl#c1b;,h,cl1#h;,h#b,o #b;,fe,cl#c1d;,h#b,o2 ,s #b;,fe,cl#c1b;,h,cl1#h;,h#b,o2 -#bg4e;deg #cb4cc #cd4ba #b;,fe,cl#c1b;,h,cl1#d;,h#b,o #b;,fe,cl#c1d;,h#b,o2 ,o ,fe,cl#c2 #bi;deg #cc4ga #di4hd #b;,fe,cl#c1b;,h,cl1#d;,h#b,o ,u #b;,fe,cl#c1g;,h#b,o2 -#d4e;deg #bj4ff #be4gd #b;,fe,cl#c1b;,h,cl1#h;,h#b,o #b;,fe,cl#c1ab;,h#b,o2 ,v #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o2 -#ac;deg #bb4dj #ah4jj #b;,fe,cl#c1b;,h,cl1#h;,h#b,o ,x #b;,fe,cl#c1ab;,h#b,o2 -#ab4e;deg #bb4ad #af4fi #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o ,q #b;,fe,cl#c1b;,h,cl1#h;,h#b,o -#c;deg 7melting point7 ---------------------------------------- --------------------------------- ,basic ,salts4--,another class of systems in the study of #big which the ,phase ,rule has performed exceptional service1 is that of the basic salts4 ,in many cases it is impossible1 by the ordinary methods of analysis1 to decide whether one is dealing with a definite chemical individual or with a mixture4 ,the question whether a solid phase is a chemical individual can1 however1 be answered1 in most cases1 with the help of the principles which we have already learnt4 ,let us consider1 for example1 the formation of basic salts from bismuth nitrate1 and water4 ,in this case we can choose as components ,bi#b,o#c1 ,n#b,o#e1 and ,h#b,o2 since all the systems consist of these in varying amounts4 ,if we are dealing with a condition of equilibrium at constant temperature between liquid and solid phases1 three cases can be distinguished1#cga viz4-- #a4 ,the solutions in different experiments have the same composition1 but the composition of the precipitate alters4 ,in this case there must be two solid phases4 #b4 ,the solutions in different experiments can have varying composition1 while the composition of the precipitate remains unchanged4 ,in this case only one solid phase exists1 a definite compound4 #c4 ,the composition both of the solution and of the precipitate varies4 ,in this case the solid phase is a solid solution or a mixed crystal4 ,in order1 therefore1 to decide what is the nature of a precipitate produced by the hydrolysis of a normal salt1 it is only necessary to ascertain whether and how the composition of the precipitate alters with alteration in the composition of the solution4 ,if the composition of the solution is represented by abscissae1 and the composition of the precipitate by ordinates1 the form of the curves obtained would enable us to answer our question2 for vertical lines would indicate the presence of two solid phases 7#ast case71 horizontal lines the presence of only one solid phase 7#bnd case71 and slanting lines the presence of mixed crystals 7#crd case74 ,this method of representation cannot1 however1 be carried out in most cases4 ,it is1 however1 #bih generally possible to find one pair or several pairs of components1 the relative amounts of which in the solution or in the precipitate undergo change when1 and only when1 the composition of the solution or of the precipitate changes4 ,thus1 in the case of bismuth1 nitrate1 and water1 we can represent the ratio of ,bi#b,o#c 3 ,n#b,o#e in the precipitate as ordinates1 and ,n#b,o#e 3 ,h#b,o in the solution as abscissae4 ,a horizontal line then indicates a single solid phase1 and a vertical line two solid phases4 ,an example of this is given in ,fig4 #aah4cgb ,illustration3 ,,fig4 #aah4 ,bi#b,o#c--,n#b,o#e--;,h#b,o4--,although various systems have been studied in which there is formation of basic salts1#cgc we shall content ourselves here with the description of some of the conditions for the formation of basic salts of bismuth nitrate1 and for their equilibrium in contact with solutions4#cgd ,three normal salts of bismuth oxide and nitric acid are known1 viz4 ,bi#b,o#c1c,n#b,o#e1aj;,h#b,o7,s#aj72 ,bi#b,o#c1c,n#b,o#e1d;,h#b,o7,s#d72 and ,bi#b,o#c1c,n#b,o#e1c;,h#b,o7,s#c74 ,besides these normal salts1 there are the following basic salts3-- #bii ,bi#b,o#c1,n#b,o#e1b;,h#b,o 7represented by ,b#a-a-b7 ,bi#b,o#c1,n#b,o#e1;,h#b,o 7 ,b#a-a-a7 #f;,bi#b,o#c1e,n#b,o#e1i;,h#b,o 7 ,b#f-e-i7 #b;,bi#b,o#c1,n#b,o#e1;,h#b,o 7 ,b#b-a-a7 ,probably some others also exist4 ,the problem now is to find the conditions under which these different normal and basic salts can be in equilibrium with solutions of varying concentration of the three components4 ,having determined the equilibrium conditions for the different salts1 it is then possible to construct a model similar to that for ,mg,cl#b--,k,cl--,h#b,o or for ,fe,cl#c--;,h,cl--,h#b,o1 from which it will be possible to determine the limits of stability of the different salts1 and to predict what will occur when we bring the salts in contact with solutions of nitric acid of different concentrations and at different temperatures4 ,for our present purpose it is sufficient to pick out only some of the equilibria which have been studied1 and which are represented in the model 7,fig4 #aai74 ,in this case use has been made of the triangular method of representation1 so that the surface of the model lies within the prism4 ,illustration3 ,,fig4 #aai4 ,this model shows the three surfaces1 ,a1 ,b1 and ,c1 which represent the conditions for the stable existence of the salts ,b#a-a-a1 ,s#aj1 and ,s#c in contact with solution at different #cjj temperatures4 ,the front surface of the model represents the temperature #i;deg1 and the farther end the temperature #ge4e;deg4 ,the dotted curve represents the isotherm for #bj;deg4 ,the prominences between the surfaces represent1 of course1 solutions which are saturated in respect of two solid phases4 ,thus1 for example1 pabc represents solutions in equilibrium with ,b#a-a-a and ,s#aj2 and the ridge qdc1 solutions in equilibrium with ,s#aj and ,s#c4 ,the point b1 which lies at #ge4e;deg1 is the point of maximum temperature for ,s#aj4 ,if the temperature is raised above this point1 ,s#aj decomposes into the basic salt ,b#a-a-a and solution4 ,this point is therefore analogous to the point ,m in the carnallite model1 at which this salt decomposes into potassium chloride and solution 7p4 #bhd72 or to the point at which the salt #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o decomposes into #b;,fe,cl#c1ab;,h#b,o and solution 7p4 #bid74 ,the curve pab has been followed to the temperature of #gb;deg 7point c74 ,the end of the model is incomplete1 but it is probable that in the neighbourhood of the point c there exists a quintuple point at which the basic salt ,b#a-b-b appears4 ,in the neighbourhood of e also there probably exists another quintuple point at which ,s#d is formed4 ,these systems have1 however1 not been studied4 ,the following tables give some of the numerical data3-- ,,isotherm ,,for #bj;deg4 ---------------------------------------- ------------------------------ ,composition of the solution4 ,gram-mols4 in #ajjj gm4-mols4 of water4 ,solid phase4 ---------------------------------------- ,bi#b,o#c ,n#b,o#e ---------------------------------------- ---------------------------- ,b#a-a-a #aj4ej #ch4fe -- #bg4bj #hc4hd ,b#a-a-a2 ,s#aj #cj4ae #ig4ig ,s#aj #bi4gj #if4eg -- #ai4fe #ih4gf -- #aj4ea #afb4eh -- #cc4ea #cee4hg ,s#aj2 ,s#c #ea4jj #djc4j ,s#c #ad4ce #dib4j -- #g4de #eib4i ---------------------------------------- ------------------------------ ,,systems ,,in ,,equilibrium ,,with ,b#a-a-a ,,and ,s#aj 7,,curve pabc74 ---------------------------------------- -------------------- ,composition of the solution4 ,gram-mols4 in #ajjj gm4-mols4 of water4 ,temperature4 ---------------------------------------- ,bi#b,o#c ,n#b,o#e ---------------------------------------- ------------------ #i;deg #bf4g #hh4b #bj;deg 7point a7 #cj4ae #ig4ig #cj;deg #cc4f #aab4c #ej;deg #da4h #adh4d #fe;deg #eg4ba #aij4h #ge4e;deg 7point b7 #hg4i #bhh4d #gb;deg 7point c7 #if4j #cbg4j ---------------------------------------- -------------------- ,,systems ,,in ,,equilibrium ,,with ,s#aj ,,and ,s#c 7,,curve qde74 ---------------------------------------- ---------------- ,composition of the solution4 ,gram-mols4 in #ajjj gm4-mols4 of water4 ,temperature4 ---------------------------------------- - ,bi#b,o#c ,n#b,o#e ---------------------------------------- -------------- #aa4e;deg #dd4e #cif #bj;deg #ea4j #dje4d #ej;deg #ff4e #ddd4b #fe;deg #hj4j #ded4d ---------------------------------------- ---------------- ,basic ,mercury ,salts4--,the ,phase ,rule has also been applied by ,a4 ,j4 ,cox#cge in an investigation of the basic salts of mercury1 the result of which has been to show that1 of the salts mentioned in text-books1 quite a number are incorrectly stated to be chemical compounds or chemical individuals 7p4 #ib74 ,the investigation1 which was carried out essentially in the manner described above1 included the salts mentioned in the following table2 and of the basic salts said to be derived from them1 only those mentioned really exist4 ,in the following table1 the numbers in the second column give the minimum values of the concentration of the acid1 expressed in equivalent normality1 necessary for the existence of the #cja corresponding salts in contact with solution at the temperature given in the third column3-- ---------------------------------------- --------------------- ,salt4 ,normality of ,temperature4 acid4 ---------------------------------------- --------------------- ,hg,cr,o#d #a4da #ej;deg #c;,hg,o4,cr,o#c #b4f x #aj-d #ej;deg ,hg7,,no#c7b4;,h#b,o #ah4gb #be;deg #c;,hg,o4,n#b,o#e #j4aei #be;deg ,hg,s,o#d #f4hg #be;deg #c;,hg,o4,,so#c #a4c x #aj-c #be;deg ,hg,f#b #a4ad #be;deg ,hg,n,o#c4;,h#b,o #b4ie #be;deg #e;,hg#b,o4#c,n#b,o#e4b;,h#b,o ca4 #j4bic #be;deg #b;,hg#b,o4,n#b,o#e787 #j4aaj #be;deg #c;,hg#b,o4,n#b,o#e4b;,h#b,o787 #a4g x #aj-c #be;deg ,hg#b,,so#d #d4b x #aj-c #be;deg #b;,hg#b,o4,,so#c4;,h#b,o #e4f x #aj-d #be;deg ---------------------------------------- --------------------- ,mercuric fluoride does not form any basic salt4 ,since two succeeding members of a series can coexist only in contact with a solution of definite concentration1 we can prepare acid solutions of definite concentration by bringing an excess of two such salts in contact with water4 ,indirect ,determination of the ,composition of the ,solid ,phase4--,it has already been shown 7p4 #bbh7 how the composition of the solid phase in a system of two components can be determined without analysis1 and we shall now describe how this can be done in a system of three components4#cgf ,we shall assume that we are dealing with the aqueous solution of two salts which can give rise to a double salt1 in which case we can represent the solubility relations in a system of rectangular co-ordinates4 ,in this case we should obtain1 as before 7,fig4 #abj71 the isotherm adcb1 if we express the #cjb composition of the solution in gram-molecules of ,a or of ,b to #ajj gram-molecules of water4 ,illustration3 ,,fig4 #abj4 ,let us suppose1 now1 that the double salt is in equilibrium with the solution at a definite temperature1 and that the composition of the solution is represented by the point e4 ,the greater part of the solution is now separated from the solid phase1 and the latter1 together with the adhering mother liquor1 is analyzed4 ,the composition 7expressed1 as before1 in gram-molecules of ,a and ,b to #ajj gram molecules of water7 will be represented by a point 7e4g4 f7 on the line e,s1 where ,s represents the composition of the double salt4 ,that this is so will be evident when one considers that the composition of the whole mass must lie between the composition of the solution and that of the double salt1 no matter what the relative amounts of the solid phase and the mother liquor4 ,if1 in a similar manner1 we analyze a solution of a different composition in equilibrium with the same double salt 7not necessarily at the same temperature as before71 and also the mixture of solid phase and solution1 we shall obtain two other points1 as1 for example1 g and h1 and the line joining these must likewise pass through ,s4 ,the method of finding the #cjc composition of an unknown double salt consists1 therefore1 in finding1 in the manner just described1 the position of two lines such as ef and gh4 ,the point of intersection of these lines then gives the composition of the double salt4 ,if the double salt is anhydrous1 the point ,s lies at infinity1 and the lines ef and gh are parallel to each other4 ,the same result is arrived at by means of the triangular method of representation4#cgg ,if we start with the three components in known amounts1 and represent the initial composition of the whole by a point in the triangle1 and then ascertain the final composition of the solution in equilibrium with the solid phase at a definite temperature1 the line joining the points representing the initial and end concentration passes through the point representing the composition of the solid phase4 ,if two determinations are made with solutions having different initial and final concentrations in equilibrium with the same solid phase1 then the point of intersection of the two lines so obtained gives the composition of the solid phase4 99 99 99 99 99 #cjd ,,chapter ,,xvii ,,absence ,,of ,a ,,liquid ,,phase ,in the preceding chapters dealing with equilibria in three-component systems1 our attention was directed only to those cases in which liquid solutions formed one or more phases4 ,mention must1 however1 be made of certain systems which contain no liquid phase1 and in which only solids and gases are in equilibrium4 ,since1 in all cases1 there can be but one gas phase1 four solid phases will be necessary in order to form an invariant system4 ,when only three solid phases are present1 the system is univariant2 and when only two solid phases coexist with gas1 it is bivariant4 ,if1 however1 we make the restriction that the gas pressure is constant1 we diminish the variability by one4 ,on account of their great industrial importance1 we shall describe briefly some of the systems belonging to this class4 ,iron1 ,carbon ,monoxide1 ,carbon ,dioxide4--,some of the most important systems of three components in which equilibrium exists between solid and gas phases are those formed by the three components--iron1 carbon monoxide1 and carbon dioxide--and they are of importance especially for the study of the processes occurring in the blast furnace4 ,if carbon monoxide is passed over reduced iron powder at a temperature of about #fjj;deg1 the iron is oxidized and the carbon monoxide reduced with separation of carbon in accordance with the equation ,fe ,,co ,fe,o ,c ,this reaction is succeeded by the two reactions ,fe,o ,,co ,fe ,,co#b ,,co#b ,c #b;,,co #cje ,illustration3 ,,fig4 #aba4 ,the former of these reactions is not complete1 but leads to a definite equilibrium4 ,the result of the different reactions is therefore an equilibrium between the three solid phases1 carbon1 iron1 and ferrous oxide1 and the gas phase consisting of carbon monoxide and dioxide4 ,we have here four phases2 and if the total pressure is maintained constant1 equilibrium can occur only at a definite temperature4 ,since1 under certain conditions1 we can also have the reaction ,fe#c,o#d ,,co #c;,fe,o ,,co#b #cjf a second series of equilibria can be obtained of a character similar to the former4 ,these various equilibria have been investigated by ,baur and ,glaessner1#cgh and the following is a short account of the results of their work4 ,mixtures of the solid phases in equilibrium with carbon monoxide and dioxide were heated in a porcelain tube at a definite temperature until equilibrium was produced1 and the gas was then pumped off and analyzed4 ,the results which were obtained are given in the following tables1 and represented graphically in ,fig4 #aba4 ,,solid ,,phases3 ,fe#c,o#d2 ,fe,o4 ---------------------------------------- ------------------------- ,duration of ,percentage of ,no4 ,tube filled the experiment ,temperature4 with in hours4 ,,co#b ,,co ---------------------------------------- ------------------------- #a ,,co #ad #fjj;deg #ei4c #dj4g #b ,,co #ae #eij;deg #ed4g #de4c #c ,,co#b #af #eij;deg #fd4f #ce4d #d ,,co #bd #eij;deg #eh4d #da4f #e ,,co #bb #gcj;deg #fg4g #cb4c #f ,,co#b #bb #gcj;deg #hf4a #ca4i #g ,,co #bb #gej;deg #fh4d #ca4f #h ,,co#b #bb #faj;deg #fd4i #ce4a #i ,,co #bc #dbj;deg #ef4j #dd4j #aj ,,co #dg #cej;deg #fe4f #cd4d #aa ,,co#b #df #cej;deg #gb4h #bg4b #ab ,,co #ec #cej;deg #fd4j #cf4j #ac ,,co #ah #egj;deg #ec4d #df4f #ad ,,co #ai #fhj;deg #fj4e #ci4e #ae ,,co#b #bd #edj;deg #ee4e #dd4e #af ,,co #ba #fcj;deg #eg4e #db4e #ag ,,co#b #ag #fij;deg #fe4e #cd4e #ah ,,co#b #ag #fgj;deg #fg4j #cc4j #ai ,,co#b #bd #daj;deg #eh4e #da4e #bj ,,co #bd #dij;deg #ea4g #dh4h #ba ,,co#b #bc #eij;deg #ed4d #de4f #bb ,,co#b #d #iej;deg #gg4j #bc4j #bc ,,co#b #ae #hej;deg #gc4d #bf4f #bd ,,co #h #hjj;deg #ga4b #bh4h #be ,,co#b #bd #edj;deg #ef4g #dc4c ---------------------------------------- ------------------------- #cjg ,,solid ,,phases3 ,fe,o2 ,fe4 ---------------------------------------- --------------------- ,duration of ,percentage of ,no4 ,tube filled experiment ,temperature4 with in hours4 ,,co#b ,,co ---------------------------------------- -------------------- ,i4 ,,co #ae #hjj;deg #ce4b #fd4h ,,ii4 ,,co #ah #ecj;deg #bi4a #gj4i ,,iii4 ,,co #ac #hhj;deg #cj4b #fi4f ,,iv4 ,,co#b #bd #hgj;deg #cb4c #fg4g ,v4 ,,co #ah #gfj;deg #cf4i #fc4a ,,vi4 ,,co#b #af #hbj;deg #cd4g #fe4c ,,vii4 ,,co#b #ah #gcj;deg #da4a #eh4i ,,viii4 ,,co #ah #fcj;deg #cd4i #fe4a ,,ix4 ,,co#b #ag #fcj;deg #fa4f #eh4d ,x4 ,,co #ah #edj;deg #be4j #ge4j ,,xi4 ,,co#b #be #edj;deg #cf4e #fc4e ---------------------------------------- -------------------- ,as is evident from the above tables and from the curves in ,fig4 #aba1 the curve of equilibrium in the case of the reaction ,fe#c,o#d ,,co #c;,fe,o ,,co#b exhibits a maximum for the ratio ,,co 3 ,,co#b1 at #dij;deg1 while1 for the reaction ,fe,o ,,co ,fe ,,co#b this ratio has a minimum value at #fhj;deg4 ,from these curves can be derived the conditions under which the different solid phases can exist in contact with gas4 ,thus1 for example1 at a temperature of #fij;deg1 ,fe,o and ,fe#c,o#d can coexist with a mixture of #fe4e per cent4 of ,,co#b and #cd4e per cent4 of ,,co4 ,if the partial pressure of ,,co#b is increased1 there occurs the reaction #c;,fe,o ,,co#b ,fe#c,o#d ,,co and if carbon dioxide is added in sufficient amount1 the ferrous oxide finally disappears completely4 ,if1 on the other hand1 the partial pressure of ,,co is increased1 there occurs the reaction ,fe#c,o#d ,,co #c;,fe,o ,,co#b and all the ferric oxide can be made to disappear4 ,we see1 therefore1 that ,fe#c,o#d can only exist at temperatures and in #cjh contact with mixtures of carbon monoxide and dioxide1 represented by the area which lies below the under curve in ,fig4 #aba4 ,similarly1 the region of existence of ,fe,o is that represented by the area between the two curves2 while metallic iron can exist under the conditions of temperature and composition of gas phase represented by the area above the upper curve in ,fig4 #aba4 ,if1 therefore1 ferric oxide or metallic iron is heated for a sufficiently long time at temperatures above #gjj;deg 7to the right of the dotted line2 vide infra71 complete transformation to ferrous oxide finally occurs4 ,in another series of equilibria which can be obtained1 carbon is one of the solid phases4 ,in ,fig4 #aba the equilibria between carbon1 carbon monoxide1 and carbon dioxide under pressures of one and of a quarter atmosphere1 are represented by dotted lines4#cgi ,if we consider only the dotted line on the right1 representing the equilibria under atmospheric pressure1 we see that the points in which the dotted line cuts the other two curves must represent systems in which carbon monoxide and carbon dioxide are in equilibrium with ,fe,o ,fe#c,o#d ,c1 on the one hand1 and with ,fe ,fe,o ,c on the other4 ,these systems can only exist at one definite temperature1 if we make the restriction that the pressure is maintained constant 7atmospheric pressure74 ,starting1 therefore1 with the equilibrium ,fe,o ,fe#c,o#d ,,co ,,co#b at a temperature of about #fgj;deg1 and then add carbon to the system1 the reaction ,c ,,co#b #b;,,co will occur1 because the concentration of ,,co#b is greater than what corresponds with the system ,fe,o ,fe#c,o#d ,c in equilibrium with carbon monoxide and dioxide4 ,in consequence of this reaction1 the equilibrium between ,fe,o ,fe#c,o#d and the gas phase is disturbed1 and the change in the composition of the gas phase is opposed by the reaction ,fe#c,o#d ,,co #c;,fe,o ,,co#b1 which continues until either all the carbon #cji or all the ferric oxide is used up4 ,if the ferric oxide first disappears1 the equilibrium corresponds with a point on the dotted line in the middle area of ,fig4 #aba1 which represents equilibria between ,fe,o ,c as solid phases1 and a mixture of carbon monoxide and dioxide as gas phase4 ,if the temperature is higher than #fhe;deg1 at which temperature the curve for ,c--,,co--,,co#b cuts that for ,fe--,fe,o--,,co--,,co#b2 then1 when all the ferric oxide has disappeared1 the concentration of ,,co#b is still too great for the coexistence of ,fe,o and ,c4 ,consequently1 there occurs the reaction ,c ,,co#b #b;,,co1 and the composition of the gas phase alters until a point on the upper curve is reached4 ,a further increase in the concentration of ,,co is opposed by the reaction ,fe,o ,,co ,fe ,,co#b1 and the pressure remains constant until all the ferrous oxide is reduced and only iron and carbon remain in equilibrium with gas4 ,if the quantities of the substances have been rightly chosen1 we ultimately reach a point on the dotted curve in the upper part of ,fig4 #aba4 ,fig4 #aba shows us1 also1 what are the conditions under which the reduction of ferric to ferrous oxide by carbon can occur4 ,let us suppose1 for example1 that we start with a mixture of carbon monoxide and dioxide at about #fjj;deg 7the lowest point on the dotted line71 and maintain the total pressure constant and equal to one atmosphere4 ,if the temperature is increased1 the concentration of the carbon dioxide will diminish1 owing to the reaction ,c ,,co#b #b;,,co1 but the ferric oxide will undergo no change until the temperature reaches #fdg;deg1 the point of intersection of the dotted curve with the curve for ,fe,o and ,fe#c,o#d4 ,at this point further increase in the concentration of carbon monoxide is opposed by the reduction of ferric oxide in accordance with the equation ,fe#c,o#d ,,co #c;,fe,o ,,co#b4 ,the pressure1 therefore1 remains constant until all the ferric oxide has disappeared4 ,if the temperature is still further raised1 we again obtain a univariant system1 ,fe,o ,c1 in equilibrium with gas 7univariant because the total pressure is constant72 and if the temperature is raised the composition of the gas must undergo change4 ,this is effected by the reaction ,c ,,co#b #b;,,co4 ,when the #caj temperature rises to #fhe;deg1 at which the dotted curve cuts the curve for ,fe--,fe,o1 further change is prevented by the reaction ,fe,o ,,co ,fe ,,co#b4 ,when all the ferrous oxide is used up1 we obtain the system ,fe ,c in equilibrium with gas4 ,if the temperature is now raised1 the composition of the gas undergoes change1 as shown by the dotted line4 ,the two temperatures1 #fdg;deg and #fhe;deg1 give1 evidently1 the limits within which ferric or ferrous oxide can be reduced directly by carbon4 ,it is further evident that at any temperature to the right of the dotted line1 carbon is unstable in presence of iron or its oxides2 while at temperatures lower than those represented by the dotted line1 it is stable4 ,in the blast furnace1 therefore1 separation of carbon can occur only at lower temperatures1 and the carbon must disappear on raising the temperature4 ,finally1 it may be remarked that the equilibrium curves show that ferrous oxide is most easily reduced at #fhj;deg1 since the concentration of the carbon monoxide required at this temperature is a minimum4 ,on the other hand1 ferric oxide is reduced with greatest difficulty at #dij;deg1 since at this temperature the requisite concentration of carbon monoxide is a maximum4 ,other equilibria between solid and gas phases are3 ,equilibrium between iron1 ferric oxide1 water vapour1 and hydrogen1#chj and the equilibria between carbon1 carbon monoxide1 carbon dioxide1 water vapour1 and hydrogen1#cha which is of importance for the manufacture of water gas4 99 99 99 99 99 #caa ,,chapter ,,xviii ,,systems ,,of ,,four ,,components ,in the systems which have so far been studied1 we have met with cases where two or three components could enter into combination2 but in no case did we find double decomposition occurring4 ,the reason of this is that in the systems previously studied1 in which double decomposition might have been possible1 namely in those systems in which two salts acted as components1 the restriction was imposed that either the basic or the acid constituent of these salts must be the same2 a restriction imposed1 indeed1 for the very purpose of excluding double decomposition4 ,now1 however1 we shall allow this restriction to fall1 thereby extending the range of study4 ,hitherto1 in connection with four-component systems1 the attention has been directed solely to the study of aqueous solutions of salts1 and more especially of the salts which occur in sea-water1 i4e4 chiefly1 the sulphates and chlorides of magnesium1 potassium1 and sodium4 ,the importance of these investigations will be recognized when one recollects that by the evaporation of sea-water there have been formed the enormous salt-beds at ,stassfurt1 which constitute at present the chief source of the sulphates and chlorides of magnesium and potassium4 ,the investigations1 therefore1 are not only of great geological interest as tending to elucidate the conditions under which these salt-beds have been formed1 but are of no less importance for the industrial working of the deposits4 ,it is1 however1 not the intention to enter here into any detailed description of the different systems which have so far been studied1 and of the sometimes very complex relationships #cab met with1 but merely to refer briefly to some points of more general import in connection with these systems4#chb ,reciprocal ,salt-,pairs4 ,choice of ,components4--,when two salts undergo double decomposition1 the interaction can be expressed by an equation such as ,,nh#d;,cl ,na,n,o#c ,na,cl ,,nh#d,,no#c ,since one pair of salts--,na,cl ,,nh#d,,no#c--;is formed from the other pair--,,nh#d;,cl ,na,n,o#c--;by double decomposition1 the two pairs of salts are known as reciprocal salt-pairs4#chc ,it is with systems in which the component salts form reciprocal salt-pairs that we have to deal here4 ,it must be noted1 however1 that the four salts formed by two reciprocal salt-pairs do not constitute a system of four1 but only of three components4 ,this will be understood if it is recalled that only so many constituents are taken as components as are necessary to express the composition of all the phases present 7p4 #ab74 ,it will be seen1 now1 that the composition of each of the four salts which can be present together can be expressed in terms of three of them4 ,thus1 for example1 in the case of ,,nh#d;,cl1 ,na,n,o#c1 ,,nh#d,,no#c1 ,na,cl1 we can express the composition of ,,nh#d;,cl by ,,nh#d,,no#c ,na,cl - ,na,n,o#c2 or of ,na,n,o#c by ,,nh#d,,no#c ,na,cl - ,,nh#d;,cl4 ,in all these cases it will be seen that negative quantities of one of the components must be employed2 but that we have seen to be quite permissible 7p4 #ab74 ,the number of components is1 therefore1 three2 but any three of the four salts can be chosen4 ,since1 then1 two reciprocal salt-pairs constitute only three #cac components or independently variable constituents1 another component is necessary in order to obtain a four-component system4 ,as such1 we shall choose water4 ,transition ,point4--,in the case of the formation of double salts from two single salts1 we saw that there was a point--the quintuple point--at which five phases could coexist4 ,this point we also saw to be a transition point1 on one side of which the double salt1 on the other side the two single salts in contact with solution1 were found to be the stable system4 ,a similar behaviour is found in the case of reciprocal salt-pairs4 ,the four-component system1 two reciprocal salt-pairs and water1 can give rise to an invariant system in which the six phases1 four salts1 solution1 vapour1 can coexist2 the temperature at which this is possible constitutes a sextuple point4 ,now1 this sextuple point is also a transition point1 on the one side of which the one salt-pair1 on the other side the reciprocal salt-pair1 is stable in contact with solution4 ,the sextuple point is the point of intersection of the curves of six univariant systems1 viz4 four solubility curves with three solid phases each1 a vapour-pressure curve for the system3 two reciprocal salt-pairs--vapour2 and a transition curve for the condensed system3 two reciprocal salt-pairs--solution4 ,if we omit the vapour phase and work under atmospheric pressure 7in open vessels71 we find that the transition point is the point of intersection of four solubility curves4 ,just as in the case of three-component systems we saw that the presence of one of the single salts along with the double salt was necessary in order to give a univariant system1 so in the four-component systems the presence of a third salt is necessary as solid phase along with one of the salt-pairs4 ,in the case of the reciprocal salt-pairs mentioned above1 the transition point would be the point of intersection of the solubility curves of the systems with the following groups of salts as solid phases3 ,below the transition point3 ,,nh#d;,cl ,na,n,o#c ,na,cl2 ,,nh#d;,cl ,na,n,o#c ,,nh#d,,no#c2 above the transition point3 ,na,cl ,,nh#d,,no#c ,na,n,o#c2 ,na,cl ,,nh#d,,no#c ,,nh#d;,cl4 ,from this we see that the two salts ,,nh#d;,cl and ,na,n,o#c would be able to exist together with solution below the transition point1 but not above it4 ,this transition point has not been determined4 #cad ,formation of ,double ,salts4--,in all cases of four-component systems so far studied1 the transition points have not been points at which one salt-pair passed into its reciprocal1 but at which a double salt was formed4 ,thus1 at #d4d;deg ,glauber's salt and potassium chloride form glaserite and sodium chloride1 according to the equation #b,na#b,,so#d1aj;,h#b,o #c,k,cl ,k#c,na7,,so#d7b #c,na,cl #bj;,h#b,o ,above the transition point1 therefore1 there would be ,k#c,na7,,so#d7b1 ,na,cl and ,k,cl2 and it may be considered that at a higher temperature the double salt would interact with the potassium chloride according to the equation ,k#c,na7,,so#d7b ,k,cl #b,k#b,,so#d ,na,cl thus giving the reciprocal of the original salt-pair4 ,this point has1 however1 not been experimentally realized4#chd ,transition ,interval4--,a double salt1 we learned 7p4 #bgg71 when brought in contact with water at the transition point undergoes partial decomposition with separation of one of the constituent salts2 and only after a certain range of temperature 7transition interval7 has been passed1 can a pure saturated solution be obtained4 ,a similar behaviour is also found in the case of reciprocal salt-pairs4 ,if one of the salt-pairs is brought in contact with water at the transition point1 interaction will occur and one of the salts of the reciprocal salt-pair will be deposited2 and this will be the case throughout a certain range of temperature1 after which it will be possible to prepare a solution saturated only for the one salt-pair4 ,in the case of ammonium chloride and sodium nitrate the lower limit of the transition interval is #e4e;deg1 so that above this temperature and up to that of the transition point 7unknown71 ammonium chloride and sodium nitrate in contact with water would give rise to a third salt by double decomposition1 in this case to sodium chloride4#che #cae ,graphic ,representation4--,for the graphic representation of systems of four components1 four axes may be chosen intersecting at a point like the edges of a regular octahedron 7,fig4 #abb74chf ,along these different axes the equivalent molecular amounts of the different salts are measured4 ,illustration3 ,,fig4 #abb4 ,illustration3 ,,fig4 #abc4 ,to represent a given system consisting of x,b1 y,c1 and z,d in a given amount of water 7where ,b1 ,c1 and ,d represent equivalent molecular amounts of the salts71 measure off on ,,ob and ,,oc lengths equal to x and y respectively4 ,the point of intersection a 7,fig4 #abb7 represents a solution containing x,b and y,c 7ab x2 ac y74 ,from a a line a,p is drawn parallel to ,,od and equal to z4 ,p then represents the solution of the above composition4 ,it is usual1 however1 not to employ the three-dimensional figure1 but its horizontal and vertical projections4 ,fig4 #abb1 if projected on the base of the octahedron1 would yield a diagram such as is shown in ,fig4 #abc4 ,the projection of the edges of the octahedron form two axes at right angles and give rise to four quadrants similar to those employed for the representation of ternary solutions 7p4 #bgc74 ,here1 the point a represents a ternary solution saturated with respect to ,b and ,c2 and a,p1 quaternary solutions in equilibrium with the same two salts as solid phases4 ,such a diagram represents the conditions of equilibrium only for one definite temperature1 and corresponds1 therefore1 to the isothermal diagrams for ternary systems 7p4 #bgc74 ,in such a diagram1 since the temperature and #caf pressure are constant 7vessels open to the air71 a surface will represent a solution in equilibrium with only one solid phase2 a line1 a solution with two solid phases1 and a point1 one in equilibrium with three solid phases4 ,illustration3 ,,fig4 #abd4 ,example4--,as an example of the complete isothermal diagram1 there may be given one representing the equilibria in the system composed of water and the reciprocal salt-pair sodium sulphate--potassium chloride for the temperature #j;deg 7,fig4 #abd74chg ,the amounts of the different salts are measured along the four axes1 and the composition of the solution is #cag expressed in equivalent gram-molecules per #ajjj gram-molecules of water4#chh ,the outline of this figure represents four ternary solutions in which the component salts have a common acid or basic constituent2 viz4 sodium chloride--sodium sulphate1 sodium sulphate--potassium sulphate1 potassium sulphate--potassium chloride1 potassium chloride--sodium chloride4 ,these four sets of curves are therefore similar to those discussed in the previous chapter4 ,in the case of sodium and potassium sulphate1 a double salt1 glaserite ,k#c,na7,,so#d7b is formed4 ,whether glaserite is really a definite compound or not is still a matter of doubt1 since isomorphic mixtures of ,na#b,,so#d and ,k#b,,so#d have been obtained4 ,according to van't ,hoff and ,barscholl1#chi glaserite is an isomorphous mixture2 but ,gossner#cij considers it to be a definite compound having the formula ,k#c,na7,,so#d7b4 ,points ,,viii4 and ,,ix4 represent solutions saturated with respect to glaserite and sodium sulphate1 and glaserite and potassium sulphate respectively4 ,the lines which pass inwards from these boundary curves represent solutions containing three salts1 but in contact with only two solid phases2 and the points where three lines meet1 or where three fields meet1 represent solutions in equilibrium with three solid phases2 with the phases1 namely1 belonging to the three concurrent fields4 ,if it is desired to represent a solution containing the salts say in the proportions1 #ea,na#b;,cl#b1 #i4e,k#b;,cl#b1 #c4e,k#b,,so#d1 the difficulty is met with that two of the salts1 sodium chloride and potassium sulphate1 lie on opposite axes4 ,to overcome this difficulty the difference #ea - #c4e #dg4e is taken and measured off along the sodium chloride axis2 and the solution is therefore represented by the point #dg4e,na#b;,cl#b1 #i4e,k#b;,cl#b4 ,in order1 therefore1 to find the amount of potassium sulphate present #cah from such a diagram1 it is necessary to know the total number of salt molecules in the solution4 ,when this is known1 it is only necessary to subtract from it the sum of the molecules of sodium and potassium chloride1 and the result is equal to twice the number of potassium sulphate molecules4 ,thus1 in the above example1 the total number of salt molecules is #fd4 ,the number of molecules of sodium and potassium chloride is #eg2 #fd - #eg #g1 and therefore the number of potassium sulphate molecules is #c4e4 ,another method of representation employed is to indicate the amounts of only two of the salts in a plane diagram1 and to measure off the total number of molecules along a vertical axis4 ,in this way a solid model is obtained4 ,the numerical data from which ,fig4 #abd was constructed are contained in the following table1 which gives the composition of the different solutions at #j;deg3--#cia ---------------------------------------- ,point4 ,solid phases4 ---------------------------------------- ,i4 ,na,cl ,,ii4 ,k,cl ,,iii4 ,na#b,,so#d1aj;,h#b,o ,,iv4 ,k#b,,so#d ,v4 ,na,cl2 ,k,cl ,,vi4 ,na,cl2 ,na#b,,so#d1aj;,h#b,o ,,vii4 ,k,cl2 ,k#b,,so#d ,,viii4 ,glaserite2 ,na#b,,so#d1aj;,h#b,o ,,ix4 ,glaserite2 ,k#b,,so#d ,x4 ,na#b,,so#d1aj;,h#b,o2 ,k,cl2 ,na,cl ,,xi4 ,na#b,,so#d1aj;,h#b,o2 ,k,cl2 glaserite ,,xii4 ,k#b,,so#d2 ,k,cl2 glaserite ---------------------------------------- ,transcriber's note3 table continued below444 ---------------------------------------- --------------------------------- ,composition of solution in gram-mols4 ,total per #ajjj gram-mols4 water4 number ---------------------------------------- --------------------- of salt ,na#b;,cl#b4 ,k#b;,cl#b4 ,na#b,,so#d4 ,k#b,,so#d4 molecules4 ---------------------------------------- --------------------------------- #ee -- -- -- #ee -- #cd4e -- -- #cd4e -- -- #f -- #f -- -- -- #i #i #df4e #ab4e -- -- #ei #dg4e -- #h -- #ee4e -- #cd4e -- #a #ce4e -- -- #aj #aj #bj -- -- #g4e #aj #ag4e #ea #i4e -- #c4e #fd #dj4e #ac -- #c4e #eg #ah #bc -- #c #dd ---------------------------------------- --------------------------------- ,from the aspect of these diagrams the conditions under which the salts can coexist can be read at a glance4 ,thus1 #cai for example1 ,fig4 #abd shows that at #j;deg ,glauber's salt and potassium chloride can exist together with solution2 namely1 in contact with solutions having the composition ,x--,,xi4 ,this temperature must therefore be below the transition point of this salt-pair 7p4 #cad74 ,on raising the temperature to #d4d;deg1 it is found that the curve ,,viii4--,,xi4 moves so that the point ,,xi4 coincides with point ,x4 ,at this point1 therefore1 there will be four concurrent fields1 viz4 ,glauber's salt1 potassium chloride1 glaserite1 and sodium chloride4 ,but these four salts can coexist with solution only at the transition point2 so that #d4d;deg is the transition temperature of the salt-pair3 ,glauber's salt--potassium chloride4 ,at higher temperatures the line ,,viii4--,,xi4 moves still further to the left1 so that the field for ,glauber's salt becomes entirely separated from the field for potassium chloride4 ,this shows that at temperatures above the transition point the salt-pair ,glauber's salt--potassium chloride cannot coexist in presence of solution4 ,illustration3 ,,fig4 #abe4 ,if it is only desired to indicate the mutual relationships of the different components and the conditions for their coexistence 7paragenesis71 a simpler diagram than ,fig4 #abd can be employed4 ,thus if the boundary curves of ,fig4 #abd are so drawn that they cut one another at right angles1 a figure such as ,fig4 #abe is obtained1 the ,roman numerals here corresponding with those in ,fig4 #abd4 ,ammonia-,soda ,process4--,one of the most important applications of the ,phase ,rule to systems of four components with reciprocal salt-pairs has recently been made by ,fedotieff#cib in his investigations of the conditions for the formation of sodium carbonate by the so-called ammonia-soda 7,solvay7 #cbj process4#cic ,this process consists1 as is well known1 in passing carbon dioxide through a solution of common salt saturated with ammonia4 ,whatever differences of detail there may be in the process as carried out in different manufactories1 the reaction which forms the basis of the process is that represented by the equation ,na,cl ,,nh#d;,,hco#c ,na,h,c,o#c ,,nh#d;,cl ,we are dealing here1 therefore1 with reciprocal salt-pairs1 the behaviour of which has just been discussed in the preceding pages4 ,the present case is1 however1 simpler than that of the salt-pair ,na#b,,so#d4aj;,h#b,o ,k,cl1 inasmuch as under the conditions of experiment neither hydrates nor double salts are formed4 ,since the study of the reaction is rendered more difficult on account of the fact that ammonium bicarbonate in solution1 when under atmospheric pressure1 undergoes decomposition at temperatures above #ae;deg1 this temperature was the one chosen for the detailed investigation of the conditions of equilibrium4 ,since1 further1 it has been shown by ,bodlaender#cid that the bicarbonates possess a definite solubility only when the pressure of carbon dioxide in the solution has a definite value1 the measurements were carried out in solutions saturated with this gas4 ,this1 however1 does not constitute another component1 because we have made the restriction that the sum of the partial pressures of carbon dioxide and water vapour is equal to #a atmosphere4 ,the concentration of the carbon dioxide is1 therefore1 not independently variable 7p4 #aj74 ,illustration3 ,,fig4 #abf4 ,in order to obtain the data necessary for a discussion of the conditions of soda formation by the ammonia-soda process1 solubility determinations with the four salts1 ,na,cl1 ,,nh#d;,cl1 ,,nh#d;,,hco#c1 and ,na,h,c,o#c were made1 first with the single salts and then #cba with the salts in pairs4 ,the results obtained are represented graphically in ,fig4 #abf1 which is an isothermal diagram similar to that given by ,fig4 #abd4 ,the points ,i41 ,,ii41 ,,iii41 ,,iv41 represent the composition of solutions in equilibrium with two solid salts4 ,we have1 however1 seen 7p4 #cad7 that the transition point1 when the experiment is carried out under constant pressure 7atmospheric pressure71 is the point of intersection of four solubility curves1 each of which represents the composition of solutions in equilibrium with three salts1 viz4 one of the reciprocal salt-pairs along with a third salt4 ,since1 now1 it was found that the stable salt-pair at temperatures between #j;deg and #cj;deg is sodium bicarbonate and ammonium chloride1 determinations were made of the composition of solutions in equilibrium with ,na,h,c,o#c ,,nh#d;,cl ,,nh#d;,,hco#c and with ,na,h,c,o#c ,,nh#d;,cl ,na,cl as solid phases4 ,under the #cbb conditions of experiment 7temperature #ae;deg7 sodium chloride and ammonium bicarbonate cannot coexist in contact with solution4 ,these determinations gave the data necessary for the construction of the complete isothermal diagram 7,fig4 #abg74 ,the most important of these data are given in the following table 7temperature1 #ae;deg73-- ---------------------------------------- --------------------------------- ,composition of the solution in gram-molecules to #ajjj gram-molecules ,point4 ,solid phases4 of water4 ---------------------------------------- ------ ,na,h,c,o#c ,na,cl ,,nh#d;,,hco#c ,,nh#d;,cl ---------------------------------------- --------------------------------- -- ,na,h,c,o#c #a4jh -- -- -- -- ,na,cl -- #f4ab -- -- -- ,,nh#d;,,hco#c -- -- #b4cf -- -- ,,nh#d;,cl -- -- -- #f4fd ,i4 ,na,h,c,o#c2 ,na,cl #j4ab #f4jf -- -- ,,ii4 ,na,cl2 ,,nh#d;,cl -- #d4ee -- #c4gb ,,iii4 ,,nh#d;,cl2 -- -- #j4ha #f4dj ,,nh#d;,,hco#c ,,iv4 ,na,h,c,o#c2 #j4ga -- #b4af -- ,,nh#d;,,hco#c ,p#a ,na,h,c,o#c2 #j4ic #j4ea -- #f4bh ,,nh#d;,,hco#c2 ,,nh#d;,cl ,p#b ,na,h,c,o#c2 #j4ah #d4dd -- #c4gc ,na,cl2 ,,nh#d;,cl ---------------------------------------- --------------------------------- ,with reference to the solution represented by the point ,p#a1 it may be remarked that it is an incongruently saturated solution 7p4 #bgi74 ,if sodium chloride is added to this solution1 the composition of the latter undergoes change2 and if a sufficient amount of the salt is added1 the solution ,p#b is obtained4 ,turning now to the practical application of the data so obtained1 consider first what is the influence of concentration on the yield of soda4 ,since the reaction consists essentially in a double decomposition between sodium chloride and ammonium bicarbonate1 then1 after the deposition of the sodium bicarbonate1 we obtain a solution containing sodium chloride1 ammonium chloride1 and sodium bicarbonate4 ,in order to ascertain to what extent the sodium chloride has been converted into solid sodium bicarbonate1 it is necessary to examine the composition of the solution which is obtained #cbc with definite amounts of sodium chloride and ammonium bicarbonate4 ,illustration3 ,,fig4 #abg4 ,consider1 in the first place1 the solutions represented by the curve ,p#b,p#a4 ,with the help of this curve we can state the conditions under which a solution1 saturated for ammonium chloride1 is obtained1 after deposition of sodium bicarbonate4 ,in the following table the composition of the solutions is given which are obtained with different initial amounts of sodium chloride and ammonium bicarbonate4 ,the last two columns give the percentage amount of the sodium used1 which is deposited as solid sodium bicarbonate 7,u,na72 and likewise the percentage amount of ammonium bicarbonate which is usefully converted into sodium bicarbonate1 that is to say1 the amount of the radical ,,hco#c deposited 7,u,,nh#d73-- #cbd --------------------------- ,initial composition of the solutions3 grams of salt to #ajjj ,point4grams of water4 -------------------- ,na,cl ,,nh#d;,,hco#c -------------------------- ,p#b #dgi #bie -- #ddh #cfj -- #dag #dca ,p#a #cig #dif -------------------------- ,transcriber's note3 table continued below444 ---------------------------------------- ------------- ,composition of solutions obtained3 gram-equivalents per #ajjj grams ,u,na ,u,,nh#d of water4 per cent4per cent4 ------------------------------- ,,hco#c ,cl ,na ,,nh#d ---------------------------------------- ---------- #j4ah #h4ag #d4fb #c4gc #dc4d #ie4a #j4ca #g4fe #c4ci #d4ef #ee4g #ic4d #j4ea #g4ac #b4ai #e4de #fi4b #ij4e #j4ib #f4gi #a4dd #f4bh #gh4h #he4a ---------------------------------------- ---------- ,this table shows that the greater the excess of sodium chloride1 the greater is the percentage utilization of ammonia 7,point ,p#b72 and the more the amount of sodium chloride decreases1 the greater is the percentage amount of sodium chloride converted into bicarbonate4 ,in the latter case1 however1 the percentage utilization of the ammonium bicarbonate decreases2 that is to say1 less sodium bicarbonate is deposited1 or more of it remains in solution4 ,consider1 in the same manner1 the relations for solutions represented by the curve ,p#b;,,iv1 which gives the composition of solutions saturated with respect to sodium bicarbonate and ammonium bicarbonate4 ,in this case we obtain the following results3-- --------------------------- ,initial composition of the solutions3 grams of salt to #ajjj ,point4grams of water4 -------------------- ,na,cl ,,nh#d;,,hco#c -------------------------- ,p#a #cig #dif -- #cea #ddf -- #caf #dab -- #bid #chi -- #bcd #cbg -------------------------- ,transcriber's note3 table continued below444 ---------------------------------------- ---------- ,composition of solutions obtained3 in gram-equivalents per #ajjj grams,u,na,u,,nh#d of water4 ------------------------------- ,,hco#c ,cl ,na ,,nh#d ---------------------------------------- ------- #j4ib #f4gi #a4dd #f4bh #gh4h #he4a #j4ii #f4jj #a4cd #e4fe #gg4g #hb4e #a4jg #e4da #a4bg #e4ba #gf4d #gi4e #a4ab #e4jc #a4bc #d4ib #ge4e #ge4a #a4cj #d4jj #a4af #d4ad #ga4j #fh4f ---------------------------------------- ------- ,as is evident from this table1 diminution in the relative amount of sodium chloride exercises only a slight influence #cbe on the utilization of this salt1 but is accompanied by a rapid diminution of the effective transformation of the ammonium bicarbonate4 ,so far as the efficient conversion of the sodium is concerned1 we see that it reaches its maximum at the point ,p#a1 and that it decreases both with increase and with decrease of the relative amount of sodium chloride employed2 and faster1 indeed1 in the former than in the latter case4 ,on the other hand1 the effective transformation of the ammonium bicarbonate reaches its maximum at the point ,p#b1 and diminishes with increase in the relative amount of ammonium bicarbonate employed4 ,since sodium chloride is1 in comparison with ammonia--even when this is regenerated--a cheap material1 it is evidently more advantageous to work with solutions which are relatively rich in sodium chloride 7solutions represented by the curve ,p#a,p#b74 ,this fact has also been established empirically4 ,when1 as is the case in industrial practice1 we are dealing with solutions which are saturated not for two salts but only for sodium bicarbonate1 it is evident that we have then to do with solutions the composition of which is represented by points in the area ,p#a,p#b;,i1,,iv4 ,since in the commercial manufacture1 the aim must be to obtain as complete a utilization of the materials as possible1 the solutions employed industrially must lie in the neighbourhood of the curves ,p#b,p#a;,,iv1 as is indicated by the shaded portion in ,fig4 #abg4 ,the best results1 from the manufacturer's standpoint1 will be obtained1 as already stated1 when the composition of the solutions approaches that given by a point on the curve ,p#b,p#a4 ,considered from the chemical standpoint1 the results of the experiments lead to the conclusion that the ,solvay process1 i4e4 passage of carbon dioxide through a solution of sodium chloride saturated with ammonia1 is not so good as the newer method of ,schloesing1 which consists in bringing together sodium chloride and ammonium bicarbonate with water4#cie #cbf ,preparation of ,barium ,nitrite4--,mention may also be made here of the preparation of barium nitrite by double decomposition of barium chloride and sodium nitrite4#cif ,the reaction with which we are dealing here is represented by the equation ,ba,cl#b #b,na,n,o#b #b,na,cl ,ba7,,no#b7b ,it was found that at the ordinary temperature ,na,cl and ,ba7,,no#b7b form the stable salt-pair4 ,if1 therefore1 barium chloride and sodium nitrite are brought together with an amount of water insufficient for complete solution1 transformation to the stable salt-pair occurs1 and sodium chloride and barium nitrite are deposited4 ,when1 however1 a stable salt-pair is in its transition interval 7p4 #cae71 a third salt--in this case barium chloride--will be deposited1 as we have already learned4 ,on bringing barium chloride and sodium nitrite together with water1 therefore1 three solid phases are obtained1 viz4 ,ba,cl#b1 ,na,cl1 ,ba7,,no#b7b4 ,these three phases1 together with solution and vapour1 constitute a univariant system1 so that at each temperature the composition of the solution must be constant4 ,witt and ,ludwig found that the presence of solid barium chloride can be prevented by adding an excess of sodium nitrite1 as can be readily foreseen from what has been said4 ,since the solution in presence of the three solid phases must have a definite composition at a definite temperature1 the addition of sodium nitrite to the solution must have1 as its consequence1 the solution of an equivalent amount of barium chloride1 and the deposition of an equivalent amount of sodium chloride and barium nitrite4 ,by sufficient addition of sodium nitrite1 the complete disappearance of the solid barium chloride can be effected1 and there will remain only the stable salt-pair sodium chloride and barium nitrite4 ,as was pointed out by ,meyerhoffer1 however1 the disappearance of the barium chloride is effected1 not by a change in the #cbg composition of the solution1 but by the necessity for the composition of the solution remaining constant4 ,illustration3 ,,fig4 #abh4 ,barium ,carbonate and ,potassium ,sulphate4--,as has been found by ,meyerhoffer1#cig these two salts form the stable pair1 not only at the ordinary temperature1 but also at the melting point4 ,for the ordinary temperatures this was proved in the following manner3 ,a solution with the solid phases ,k#b,,so#d and ,k#b;,,co#c4b;,h#b,o in excess can only coexist in contact either with ,ba,c,o#c or with ,ba,s,o#d1 since1 evidently1 in one of the two groups the stable system must be present4 ,two solutions were prepared1 each with excess of ,k#b,,so#d ,k#b;,,co#c4b;,h#b,o1 #cbh and to one was added ,ba,c,o#c and to the other ,ba,s,o#d4 ,after stirring for a few days1 the barium sulphate was completely transformed to ,ba,c,o#c1 whereas the barium carbonate remained unchanged4 ,consequently1 ,ba,c,o#c ,k#b,,so#d ,k#b;,,co#c4b;,h#b,o is stable1 and1 therefore1 so also is ,ba,c,o#c ,k#b,,so#d4 ,that ,ba,c,o#c ,k#b,,so#d is the stable pair also at the melting point was proved by a special analytical method which allows of the detection of ,k#b;,,co#c in a mixture of the four solid salts4 ,this analysis showed that a mixture of ,ba,c,o#c ,k#b,,so#d1 after being fused and allowed to solidify1 contains only small amounts of ,k#b;,,co#c2 and this is due entirely to the fact that ,ba,c,o#c ,k#b,,so#d on fusion deposits a little ,ba,s,o#d1 thereby giving rise at the same time to the separation of an equivalent amount of ,k#b;,,co#c4 ,the different solubilities are shown in ,fig4 #abh4 ,in this diagram the solubility of the two barium salts has been neglected4 ,a is the solubility of ,k#b;,,co#c4b;,h#b,o2 addition of ,ba,c,o#c does not alter this4 ,b is the solubility of ,k#b;,,co#c4b;,h#b,o ,k#b,,so#d ,ba,c,o#c4 ,a and ,b almost coincide1 since the potassium sulphate is very slightly soluble in the concentrated solution of potassium carbonate4 ,d gives the concentration of the solution in equilibrium with ,k#b,,so#d ,ba,s,o#d4 ,the most interesting point is ,c4 ,this solution is obtained by adding a small quantity of water to ,ba,c,o#c ,k#b,,so#d1 whereupon1 being in the transition interval1 ,ba,s,o#d separates out and an equivalent amount of ,k#b;,,co#c goes into solution4 ,c is the end point of the curve ,,co1 which is called the ,guldberg-,waage curve1 because these investigators determined several points on it4 ,in their experiments1 ,guldberg and ,waage found the ratio ,k#b;,,co#c 3 ,k#b,,so#d in solution to be constant and equal to #d4 ,this result is1 however1 not exact1 for the curve ,,co is not a straight line1 as it should be if the above ratio were constant2 but it is concave to the abscissa axis1 and more so at lower than at higher temperatures4 ,the following table refers to the temperature of #be;deg4 ,the ,roman numbers in the first column refer to the points in ,fig4 #abh4 ,the numbers in the column ,sigmak#b give the amount1 #cbi in gram-molecules1 of ,k#b;,,co#c ,k#b,,so#d contained in #ajjj gram-molecules of water3-- ,,solubility ,,determinations ,,at #be;deg4 ---------------------------------------- ------------------------- #ajj gms4 of the solution contain1 ,no4 ,solid phases4 in grams1 ,k#b;,,co#c,k#b,,so#d ---------------------------------------- ------------------------ ,i4 ,k#b;,,co#c4b;,h#b,o ,ba,c,o#c #ec4b -- ,,ii4 ,k#b;,,co#c4b;,h#b,o ,k#b,,so#d #ec4j #j4jbc ,ba,c,o#c ,,iii4 ,k#b,,so#d ,ba,c,o#c #bh4e #j4hhf ,,iv4 #bb4a #a4gb ,v4 ,ba,c,o#c ,k#b,,so#d ,ba,s,o#d #ag4ha #b4dhe ,,vi4 ,k#b,,so#d ,ba,s,o#d #ab4f #c4ib ,,vii4 #e4he #f4gf ,,viii4 ,k#b,,so#d -- #aj4gf ,,ix4 ,ba,c,o#c ,ba,s,o#d #g4ce #j4fjb ,x4 #b4he #j4agc ---------------------------------------- ------------------------ ,transcriber's note3 table continued below444 ---------------------------------------- ---------------- #ajjj moles of water contain1 ,k#b;,,co#c ,no4 in moles1 ,sigmak#b ----------- ,k#b,,so#d ,k#b;,,co#c,k#b,,so#d ---------------------------------------- --------------- ,i4 #adg4i -- -- -- ,,ii4 #adg4h #j4jea -- -- ,,iii4 #eb4eh #a4bif -- -- ,,iv4 #cg4gi #b4ccc -- -- ,v4 #bi4aa #c4bbj #cb4cb #i4jc ,,vi4 #ai4ff #d4hec -- -- ,,vii4 #h4gbd #g4iie -- -- ,,viii4 -- #ab4dg -- -- ,,ix4 #aj4dc #j4fgf #aa4aa #ae4j ,x4 #c4hbh #j4ahd #d4j #ba4j ---------------------------------------- --------------- ,the ,guldberg-,waage curve at #ajj;deg was also determined1 and it was found that the ratio ,k#b;,,co#c3 ,k#b,,so#d is also not constant1 although the variations are not so great as at #be;deg4 ,,guldberg-,,waage ,,curve ,,at #ajj;deg4 ---------------------------------------- ----------------------------- #ajj moles of water ,k#b;,,co#c ,solid phases4 contain1 in moles1 ,sigmak#b ----- ,k#b,,so#d ,k#b;,,co#c,k#b,,so#d ---------------------------------------- ---------------------------- ,ba,c,o#c ,k#b,,so#d #bc4i #ab4fe #ce4fe #a4hb ,ba,s,o#d ,ba,c,o#c ,ba,s,o#d #f4bh #b4jb #h4c #c4a #c4ag #j4hea #d4jbe #c4g ---------------------------------------- ---------------------------- 99 99 99 99 99 #ccj ,,appendix ,,experimental ,,determination ,,of ,,the ,,transition ,,point ,for the purpose of determining the transition temperature1 a number of methods have been employed1 and the most important of these will be briefly described here4 ,in any given case it is sometimes possible to employ more than one method1 but all are not equally suitable1 and the values of the transition point obtained by the different methods are not always identical4 ,indeed1 a difference of several degrees in the value found may quite well occur4#cih ,in each case1 therefore1 some care must be taken to select the method most suitable for the purpose4 ,i4 ,the ,dilatometric ,method4--,since1 in the majority of cases1 transformation at the transition point is accompanied by an appreciable change of volume1 it is only necessary to ascertain the temperature at which this change of volume occurs1 in order to determine the transition point4 ,for this purpose the dilatometer is employed1 an apparatus which consists of a bulb with capillary tube attached1 and which constitutes a sort of large thermometer 7,fig4 #abi74 ,some of the substance to be examined is passed into the bulb ,a through the tube ,b1 which is then sealed off4 ,the rest of the bulb and a small portion of the capillary tube is then filled with some liquid1 which1 of course1 must be without chemical action on the substance under investigation4 ,a liquid1 however1 may be employed which dissolves the substance1 for1 as we have seen 7p4 #gj71 the transformation at the transition point is1 as a rule1 accelerated by the presence of a solvent4 ,on the other hand1 the liquid must not dissolve in the substance under examination1 for the temperature of transformation would be thereby altered4 #cca ,in using the dilatometer1 two methods of procedure may be followed4 ,according to the first method1 the dilatometer containing the form stable at lower temperatures is placed in a thermostat1 maintained at a constant temperature1 until it has taken the temperature of the bath4 ,the height of the meniscus is then read on a millimetre scale attached to the capillary4 ,the temperature of the thermostat is then raised degree by degree1 and the height of the meniscus at each point ascertained4 ,if1 now1 no change takes place in the solid1 the expansion will be practically uniform1 or the rise in the level of the meniscus per degree of temperature will be practically the same at the different temperatures1 as represented diagrammatically by the line ,,ab in ,fig4 #acj4 ,on passing through the transition point1 however1 there will be a more or less sudden increase in the rise of the meniscus per degree 7line ,,bc7 if the specific volume of the form stable at higher temperatures is greater than that of the original modification2 thereafter1 the expansion will again be uniform 7line ,,cd74 ,similarly1 on cooling1 contraction will at first be uniform and then at the transition point there will be a relatively large diminution of volume4 ,illustration3 ,,fig4 #abi4 ,illustration3 ,,fig4 #acj4 ,if1 now1 transformation occurred immediately the transition point was reached1 the sudden expansion and contraction would take place at the same temperature4 ,it is1 however1 generally found that there is a lag1 and that with rising temperature the relatively large expansion does not take place until a temperature somewhat higher than the transition point2 and with falling temperature the contraction occurs at a temperature somewhat below the transition point4 ,this is represented in ,fig4 #acj by the lines ,,bc and ,,ef4 ,the amount of lag will vary from case to case1 and will #ccb also depend on the length of time during which the dilatometer is maintained at constant temperature4 ,as an example1 there may be given the results obtained in the determination of the transition point at which sodium sulphate and magnesium sulphate form astracanite 7p4 #bfh74cii ,the dilatometer was charged with a mixture of the two sulphates4 ---------------------------------------- ---------------- ,temperature4 ,level of oil in capillary4 ,rise per #a;deg4 ---------------------------------------- ---------------- #ae4f;deg #acd #af4f;deg #ada #g #ag4f;deg #adh #g #ah4f;deg #aed #f #ai4f;deg #afa #g #bj4f;deg #afh #g #ba4f;deg #bda #gc #bb4f;deg #bdc #b #bc4f;deg #bea #h #bd4f;deg #bei #h ---------------------------------------- ---------------- ,the transition point1 therefore1 lies about #ba4f;deg 7p4 #bfh74 ,the second method of manipulation depends on the fact that1 while above or below the transition point transformation of one form into the other can take place1 at the transition point the two forms undergo no change4 ,the bulb of the dilatometer is1 therefore1 charged with a mixture of the stable and metastable forms and a suitable liquid1 and is then immersed in a bath at constant temperature4 ,after the temperature of the bath has been acquired1 readings of the height of the meniscus are made from time to time to ascertain whether expansion or contraction occurs4 ,if expansion is found1 the temperature of the thermostat is altered until a temperature is obtained at which a gradual contraction takes place4 ,the transition point must then lie between these two temperatures2 and by repeating the determinations it will be possible to reduce the difference between the temperatures at which expansion and contraction take place to1 say1 #a;deg1 and to fix the temperature of the transition point1 therefore1 to within half a degree4 ,by this method the transition point1 for example1 of sulphur was found to be #ie4f;deg under a pressure of #d atm4#djj ,the following are the figures obtained by ,reicher1 who used a mixture #ccc of #a part of carbon disulphide 7solvent for sulphur7 and #e parts of turpentine as the measuring liquid4 ,,temperature #ie4a;deg4 ----------------------------------- ,time in minutes4 ,level of liquid4 ----------------------------------- #e #cdc4e #cj #cdj4e #ee #cce4ge #fe #ccc ----------------------------------- ,,temperature #if4a;deg4 ----------------------------------- ,time in minutes4 ,level of liquid4 ----------------------------------- #e #cdb4ge #cj #ced4ge #ee #cfj4e #fj #cfa4e ----------------------------------- ,,temperature #ie4f;deg4 ----------------------------------- ,time in minutes4 ,level of liquid4 ----------------------------------- #e #cfh4ge #ajj #cfh #aaj #cfh4ge ----------------------------------- ,at a temperature of #ie4a;deg there is a contraction1 i4e4 monoclinic sulphur passes into the rhombic1 the specific volume of the former being greater than that of the latter4 ,at #if4a;deg1 however1 there is expansion1 showing that at this temperature rhombic sulphur passes into monoclinic2 while at #ie4f;deg there is neither expansion nor contraction4 ,this is1 therefore1 the transition temperature2 and since the dilatometer was sealed up to prevent evaporation of the liquid1 the pressure within it was #d atm4 ,,ii4 ,measurement of the ,vapour ,pressure4--,in the preceding pages it has been seen repeatedly that the vapour pressures of the two systems undergoing reciprocal transformation become identical at the transition point 7more strictly1 at the triple or #ccd multiple point71 and the latter can therefore be determined by ascertaining the temperature at which this identity of vapour pressure is established4 ,the apparatus usually employed for this purpose is the ,bremer-,frowein tensimeter 7p4 #ia74 ,although this method has not as yet been applied to systems of one component1 it has been used to a considerable extent in the case of systems containing water or other volatile component4 ,an example of this has already been given in ,glauber's salt 7p4 #aci74 ,,iii4 ,solubility ,measurements4--,the temperature of the transition point can also be fixed by means of solubility measurements1 for at that point the solubility of the two systems becomes identical4 ,reference has already been made to several cases in which this method was employed1 e4g4 ammonium nitrate 7p4 #aab71 ,glauber's salt 7p4 #acd71 astracanite and sodium and magnesium sulphates 7p4 #bfh74 ,the determinations of the solubility can be carried out in various ways4 ,one of the simplest methods1 which also gives sufficiently accurate results when the temperature is not high or when the solvent is not very volatile1 can be carried out in the following manner4 ,the solid substance is finely powdered 7in order to accelerate the process of solution71 and placed in sufficient quantity along with the solvent in a tube carefully closed by a glass stopper2 the latter is protected by a rubber cap1 such as a rubber finger-stall4 ,the tube is then rotated in a thermostat1 the temperature of which does not vary more than one or two tenths of a degree1 until saturation is produced4 ,the solution is withdrawn by means of a pipette to which a small glass tube1 filled with cotton wool to act as a filter1 is attached4 ,the solution is then run into a weighing bottle1 and weighed2 after which the amount of solid in solution is determined in a suitable manner4 ,for more accurate determinations of the solubility1 especially when the solvent is appreciably volatile at the temperature of experiment1 other methods are preferable4 ,in ,fig4 #aca is shown the apparatus employed by ,h4 ,goldschmidt1#dja and used to a considerable extent in the laboratory of van't ,hoff4 ,this consists essentially of three parts3 a1 a tube in which the solvent and salt are placed2 this is closed at the foot by an india-rubber stopper4 ,through this stopper there passes the bent tube cb1 which connects the tube a with the weighing-tube d4 ,at c there is a plug of cotton wool4 ,tube e is open to the air4 ,the wider portion of the tube cb1 which passes through the rubber stopper in a1 can be closed by a plug #cce attached to a glass rod ff1 which passes up through a hollow ,witt stirrer1 g4 ,after being fitted together1 the whole apparatus is immersed in the thermostat4 ,after the solution has become saturated1 the stopper of the bent tube is raised by means of the rod ff and a suction-pump attached to the end of e4 ,the solution is thereby drawn into the weighing-tube d1 the undissolved salt being retained by the plug at c4 ,the apparatus is then removed from the thermostat1 tube d detached and immediately closed by a ground stopper4 ,it is then carefully dried and weighed4 ,illustration3 ,,fig4 #aca4 ,another form of solubility vessel1 due to ,meyerhoffer and ,saunders1 is shown in ,fig4 #acb4djb ,this consists of a single tube1 and the stirring is effected by means of a glass screw4 ,illustration3 ,,fig4 #acb4 ,the progress of the solution towards saturation can be very well tested by determining the density of the solution from time to #ccf time4 ,this is most conveniently carried out by means of the pipette shown in ,fig4 #acc4djc ,with this pipette the solution can not only be removed for weighing1 but the volume can be determined at the same time4 ,it consists of the wide tube a1 to which the graduated capillary b1 furnished with a cap c1 is attached4 ,to the lower end of the pipette the tube e1 with plug of cotton wool1 can be fixed4 ,after the pipette has been filled by sucking at the end of b1 the stop-cock d is closed and the cap c placed on the capillary4 ,the apparatus can then be weighed1 and the volume of the solution be ascertained by means of the graduations4 ,as has already been insisted1 particular care must be paid to the characterization of the solid in contact with the solution4 ,illustration3 ,,fig4 #acc4 ,,iv4 ,thermometric ,method4--,if a substance is heated1 its temperature will gradually rise until the melting point is reached1 and the temperature will then remain constant until all the solid has passed into liquid4 ,similarly1 if a substance which can undergo transformation is heated1 the temperature will rise until the transition point is reached1 and will then remain constant until complete transformation has taken place4 ,this method1 it will be remembered1 was employed by ,richards for the determination of the transition point of sodium sulphate decahydrate 7p4 #acf74 ,the following figures give the results obtained by ,meyerhoffer in the case of the transformation3-- ,cu,k#b;,cl#d1b;,h#b,o -- ,cu,k,cl#c ,k,cl #b;,h#b,o the temperature being noted from minute to minute3 #ie;deg1 #ic;deg1 #ia4h;deg1 #ia4g;deg1 #ib;deg1 #ib4c;deg1 #ib4d;deg1 #ib4b;deg1 #ib4b;deg1 #ib;deg1 #ij4e;deg1 #hi;deg1 and then a rapid fall in the temperature4 ,from this we see that the transition point is about #ib4b;deg4 ,it is also evident that a slight supercooling took place 7#ia4g;deg71 owing to a delay in the transformation1 but that then the temperature rose to the transition point4 ,this is analogous to the supercooling of a liquid4 ,a similar halt in the temperature would be observed on passing from lower to higher temperatures2 but owing to a lag in the transformation1 the same temperature is not always obtained4 #ccg ,v4 ,optical ,method4--,the transition point can sometimes be determined by noting the temperature at which some alteration in the appearance of the substance occurs1 such as a change of colour or of the crystalline form4 ,thus mercuric iodide changes colour from red to yellow1 and the blue quadratic crystals of copper calcium acetate change1 on passing the transition point1 into green rhombs of copper acetate and white needles of calcium acetate 7p4 #bfj74 ,or again1 changes in the double refraction of the crystals may be also employed to ascertain the temperature of the transition point4 ,these changes are best observed by means of a microscope4 ,for the purpose of regulating the temperature of the substance a small copper air-bath is employed4#djd ,,vi4 ,electrical ,methods4--,electrical methods for the determination of the transition point are of two kinds1 based on measurements of conductivity or of electromotive force4 ,both methods are restricted in their application1 but where applicable give very exact results4 ,the former method1 which has been employed in several cases1 need not be described here4 ,the second method1 however1 is of considerable interest and importance1 and calls for special reference4#dje ,if two pieces1 say1 of zinc1 connected together by a conducting wire1 are placed in a solution of a zinc salt1 e4g4 zinc sulphate1 the potential of the two electrodes will be the same1 and no current will be produced in the connecting wire4 ,if1 however1 the zinc electrodes are immersed in two solutions of different concentration contained in separate vessels1 but placed in connection with one another by means of a bent tube filled with a conducting solution1 the potentials at the electrodes will no longer be the same1 and a current will now flow through the connecting wire4 ,the direction of this current in the cell will be from the weaker to the more concentrated solution4 ,the greater the difference in the concentration of the solutions with respect to zinc1 the greater will be the difference of the potential at the two electrodes1 or the greater will be the ,e4,m4,f4 of the cell4 ,when the concentration of the two solutions becomes the same1 the ,e4,m4,f4 will become zero1 and no current will pass4 ,it will be understood now how this method can be made use of #cch for determining the transition point of a salt1 when we bear in mind that at the transition point the solubility of the two forms becomes identical4 ,thus1 for example1 the transition point of zinc sulphate heptahydrate into hexahydrate could be determined in the following manner4 ,tube ,a 7,fig4 #acd7 contains1 say1 a saturated solution of the heptahydrate along with some of the solid salt2 tube ,b1 a saturated solution of the hexahydrate along with the solid salt4 ,the tube ,c is a connecting tube bent downwards so as to prevent the mixing of the solutions by convection currents4 ,,zz are two zinc electrodes immersed in the solution2 the cell is placed in a thermostat and the zinc electrodes connected with a galvanometer4 ,since1 now1 at temperatures below the transition point the solubility of the hexahydrate 7the metastable form7 is greater than that of the heptahydrate1 a current will be produced1 flowing in the cell from heptahydrate to hexahydrate4 ,as the temperature is raised towards the transition point1 the solubilities of the two hydrates also approach1 and the current produced will therefore become weaker1 because the ,e4,m4,f4 of the cell becomes less2 and when the transition point is attained1 the ,e4,m4,f4 becomes zero1 and the current ceases4 ,if the temperature is raised above this1 the solubility of the heptahydrate becomes greater than that of the hexahydrate1 and a current will again be produced1 but in the opposite direction4 ,by noting the temperature1 therefore1 at which the current ceases1 or the ,e4,m4,f4 becomes zero1 the transition temperature can be ascertained4#djf ,illustration3 ,,fig4 #acd4 ,in the case just described1 the electrodes consisted of the same metal as was contained in the salt4 ,but in some cases1 e4g4 sodium sulphate1 electrodes of the metal contained in the salt cannot be employed4 ,nevertheless1 the above electrical method can be used #cci even in those cases1 if a suitable non-polarizable mercury electrode is employed4#djg ,although1 as we saw1 no current was produced when two pieces of zinc were immersed in the same solution of zinc salt1 a current will be obtained if two different metals1 or even two different modifications of the same metal1 are employed4 ,thus an ,e4,m4,f4 will be established when electrodes of grey and of white tin are immersed in the same solution of zinc salt1 but at the transition point this ,e4,m4,f4 will become zero4 ,by this method ,cohen determined the transition point of grey and white tin 7p4 #db74 99 99 99 99 99 #cdj ,,name ,,index ,a ,abegg1 #eb ,adriani1 #ahf1 #bag1 #bbj ,alexejeff1 #ig1 #abe ,allan1 #bih ,allen1 ,l4 ,e41 #aji ,allen1 ,r4 ,w41 #fc ,ampolla1 #bac ,andreae1 #aji ,aristotle1 #da ,armstrong1 ,e4 ,f41 #cac ,armstrong1 ,h4 ,e41 #aif ,arzruni1 #cc ,aten1 #adg1 #afc ,auerbach1 #cbf ,b ,babo1 #abf ,bancroft1 #ajb1 #ajd1 #afa1 #agf1 #aif1 #bjb1 #bbi1 #bdf1 #bfj1 #bfa1 #bgb1 #bha1 #cjb ,barnes1 #cca1 #cci ,barschall1 #cah ,barus1 #fg ,battelli1 #bc ,baur1 #bcc1 #cjg ,beckmann1 #di ,bell1 #bbi ,berthollet1 #g ,bodlaender1 #aha1 #bdg1 #caa1 #cba ,bogojawlenski1 #gb ,boudouard1 #cji1 #caa ,braun1 #ajg ,brauns1 #dj1 #ea1 #gd ,bredig1 #eb ,bremer1 #ia ,brodie1 #cd1 #dg ,bruner1 #abf ,bruni1 #aha1 #ahb1 #bef1 #beg ,bunsen1 #fg ,c ,cady1 #aib ,calvert1 #acj ,cameron1 #bjc ,carnelley1 #dg ,carpenter1 #bbe ,carveth1 #bjd1 #bee ,centnerszwer1 #aeh ,chapman1 #dg ,chappuis1 #ea1 #agf ,charpy1 #bee ,churchill1 #adj ,coehn1 #eb ,cohen1 #da1 #gb1 #acf1 #aci1 #adj ,cooke1 #cca1 #cci ,cox1 #cja ,d ,dawson1 #bfc ,debray1 #gd1 #ha1 #aci ,deville1 #di1 #gd ,dewar1 #bf1 #ea1 #agh ,dietz1 #aeg #cda ,doelter1 #bcc ,donnan1 #h1 #ah ,dreyer1 #gc ,duhem1 #ef1 #aea ,dutoit1 #bjd ,e ,etard1 #aae1 #ace ,f ,fahrenheit1 #cj ,faraday1 #hb1 #hi ,fath1 #bjd ,fedotieff1 #cae1 #cbj ,findlay1 #aaa1 #bjd1 #bjf1 #bai ,foote1 #fi ,friedlaender1 #gb ,fritsche1 #da ,frowein1 #ia ,fuechtbauer1 #ge ,fyffe1 #adc ,g ,gattermann1 #ea1 #eb ,gautier1 #bbb1 #bbc ,gay-,lussac1 #ace ,gernez1 #gb ,gibbs1 #g1 #h1 #aea1 #bcf ,glaessner1 #cjg ,goldschmidt1 ,e41 #da ,goldschmidt1 ,h41 #cce ,goldschmidt1 ,v41 #cb ,goossens1 #bf ,gossner1 #cah ,graham1 #agh ,guertler1 #gc ,guldberg1 #g ,guthrie1 #ig1 #ajd1 #aag1 #aah1 #aai1 #bcc ,h ,haber1 #caa ,hahn1 #cji1 #caa ,hallock1 #ce ,hammerl1 #ade ,hautefeuille1 #df1 #di1 #ej1 #ea1 #agh ,heller1 #caa ,henry1 #id ,herold1 #cba ,hertz1 #di ,heycock1 #aid1 #bba1 #bbc ,heyn1 #bbe1 #bbh ,hickmans1 #bai ,hiorns1 #bbh ,hissink1 #aae1 #aij ,hoitsema1 #ad1 #ij1 #agg1 #agh1 #bih ,hollmann1 #bjd ,holsboer1 #aaj ,horstmann1 #h1 #hc1 #hi ,hudson1 #ajb ,hulett1 #aj1 #dh1 #eb1 #ed1 #fg1 #aji ,i ,isaac1 #aad ,isambert1 #hj1 #hb1 #hd ,j ,jaffe1 #gd1 #aad ,joulin1 #agf ,juhlin1 #bc1 #bd1 #cj von ,jueptner1 #bbe ,k ,kastle1 #ga ,kaufler1 #di ,kaufmann1 #aab ,kayser1 #agf ,keeling1 #bbe ,kelvin1 #be ,kenrick1 #bfc1 #big ,kipping1 #bai ,kirchhoff1 #cb ,knorr1 #bjc de ,kock1 #ec1 #ahb1 #aid ,konowaloff1 #ajb1 #ajc1 #ajd ,krasnicki1 #add ,kremann1 #adg1 #bab ,kuenen1 #aje ,kultascheff1 #bcc #cdb ,kuriloff1 #baf ,kurnakoff1 #bba1 #bbb1 #bcj ,kuester1 #gb1 #aha1 #ahc ,l ,laar1 #aie ,labenburg1 #baf ,lattey1 #aja ,le ,chatelier1 #eh1 #ha1 #bcc ,lehfeldt1 #cch1 #cdj ,lehmann1 #cc1 #eb1 #ec ,lidbury1 #adg ,loewel1 #acd1 #ace ,loewenherz1 #acd1 #caf ,lowry1 #aif1 #aih ,ludwig1 #cbg ,lumsden1 #hj1 #aji1 #aaj ,lussana1 #fh ,luther1 #bb ,m ,mack1 #fg ,magnus1 #bb ,mathews1 #bba ,mellor1 #hj ,meusser1 #adb ,meyer1 ,j41 #ga ,meyer1 ,v41 #dg ,meyerhoffer1 #aeh1 #bcc1 #bei1 #bfh1 #bga1 #bgh1 #bgi1 #bhj1 #bhd1 #cac1 #cae1 #cag1 #cai1 #cbg1 #cbh1 #ccf1 #ccg ,middelberg1 #aaf ,miers1 #aad ,miller1 #big ,mitscherlich1 #cc1 #di ,mond1 #agh ,moore1 #gb ,moss1 #ff ,mueller1 #aab1 #bfe ,mylius1 #aji1 #adb1 #aeg ,n ,naumann1 #di ,neville1 #aid1 #bba1 #bbc ,o ,offer1 #aai ,ostwald1 #h1 #aj1 #ac1 #af1 #bb1 #dd1 #eh1 #fh1 #gj1 #gd1 #he1 #hh1 #ib1 #ajb1 #aaj1 #aag1 #abe1 #abg1 #acj1 #ada1 #aih ,p ,padoa1 #gc1 #aha ,parsons1 #bih ,pasteur1 #bff ,paterno1 #bac ,payen1 #gd ,pedler1 #dg ,pfaundler1 #aai ,philip1 #bac1 #bad von ,pickardt1 #gc ,planck1 #fh ,pope1 #bai ,poynting1 #fh ,preuner1 #caa ,puschin1 #bbb ,q ,quincke1 #eb ,r ,rabe1 #aac ,ramsay1 #c1 #bb1 #bc1 #bd1 #cj1 #cb1 #fc1 #fd1 #ff1 #gi1 #ij1 #afe1 #agh ,raoult1 #ahj ,reed1 #ga ,regnault1 #bb ,reicher1 #cf1 #cg1 #aaj1 #bfj1 #ccc ,reinders1 #ga1 #ahe1 #ahh ,reinitzer1 #ea1 #eb ,richards1 #acf1 #adj ,riddle1 #dg ,riecke1 #dh1 #ee ,roberts-,austen1 #fc1 #aid1 #bba1 #bbc1 #bbe ,roloff1 #aag ,roozeboom1 #aj1 #ch1 #de1 #dg1 #di1 #ej1 #ea1 #ed1 #ef1 #eg1 #fb1 #fc1 #fh1 #hh1 #ajc1 #abf1 #ade1 #adg1 #aej1 #aea1 #aeg1 #afb1 #agj1 #agd1 #agh1 #ahb1 #aif1 #bja1 #baa1 #bag1 #bbj1 #bbe1 #bcf1 #bch1 #bfb1 #bfd1 #bfi1 #bgb1 #bgc1 #bha1 #bhb1 #bij1 #cca #cdc ,rose1 #bbc ,rotarski1 #eb ,rothmund1 #ig1 #ih1 #ajj ,rutten1 #bih ,s ,saposchnikoff1 #bab ,saunders1 #cac1 #cag1 #cai1 #ccf1 #ccg ,saurel1 #aea ,schaum1 #di1 #ge ,scheel1 #bb1 #bc1 #cj ,schenck1 #di1 #eb1 #ed1 #caa ,schneider1 #eb ,schoenbeck1 #ge ,schreinemakers1 #abb1 #abf1 #bdf1 #bdh1 #bej1 #beb1 #bij1 #cjb ,schroetter1 #df ,schukowsky1 #eb ,schwarz1 #cca ,seitz1 #eb ,shenstone1 #aji1 #aae1 #ace ,shepherd1 #bba1 #bee ,shields1 #agh ,skirrow1 #acj ,spring1 #fc von ,stackelberg1 #ajg1 #aaj ,staedel1 #bfg ,stansfield1 #aid1 #bba ,stokes1 #bcf ,stortenbeker1 #dd1 #adg1 #afa1 #afd1 #bha ,t ,taber1 #bbi ,tammann1 #bf1 #cb1 #cc1 #cg1 #ch1 #ci1 #dh1 #eb1 #fe1 #fg1 #fh1 #gb1 #gc1 #adj1 #aea1 #agf1 #bba1 #bcj ,thiesen1 #bb1 #bc1 #cj ,thomson1 ,j41 #be1 #bh1 #cb ,thomson1 ,w41 #be ,tilden1 #aji1 #aae1 #ace ,trevor1 #af ,troost1 #df1 #di1 #ej1 #ea ,tumlirz1 #gb ,v ,van ,bemmelen1 #ahj ,van ,deventer1 #aaj1 #aci1 #bff1 #bfg1 #ccc ,van ,eyk1 #da1 #fc1 #aib1 #cch ,van't ,hoff1 #cf1 #ch1 #eh1 #gj1 #ij1 #ib1 #ajh1 #abg1 #aci1 #adj1 #afe1 #age1 #bbe1 #beh1 #bfj1 #bfc1 #bfe1 #bff1 #bfg1 #bgb1 #bhd1 #bij1 #cac1 #cah1 #ccc1 #cdj ,van ,leeuwen1 #bei ,van ,wyk1 #ahe ,vogt1 #e1 #bcc ,w ,waage1 #g ,wald1 #ib ,walden1 #aeh ,walker1 #hj1 #aje1 #abb1 #abf1 #adc ,wegscheider1 #aj1 #di1 #bjb ,wells1 #acf ,wenzel1 #g ,wiebe1 #bb ,witt1 #cbg ,wright1 #bda1 #bdf1 #bdg von ,wrochem1 #aji1 #adb ,y ,young1 #c1 #bb1 #bc1 #bd1 #cj1 #cb1 #fc1 #fd1 #ff1 #gi1 #aje1 #afe ,z ,zacharias1 #ahj ,zawidski1 #fc ,zenghelis1 #ce ,zimmermann1 #caa ,zincke1 #dd ,ziz1 #ada 99 99 99 99 99 #cdd ,,subject ,,index ,a ,acetaldehyde and paraldehyde1 #bjd ,acetic acid1 chloroform1 water1 #bda ,acetone1 phenol1 water1 #bdh ,adsorption1 #agf ,alcohol1 chloroform1 water1 #bdf ----1 ether1 water1 #bdf ,alloys1 equilibrium curves of1 #bba ---- of copper and tin1 liquefaction of1 by cooling1 #aid ---- of iron and carbon1 #bbc ---- of thallium and mercury1 #bbb ----1 ternary1 #bdf ,ammonia compounds of metal chlorides1 #hb ,ammonia silver chlorides1 #hb ---- ---- ----1 dissociation pressures of1 #hd ,ammonia-soda process1 #cbj ,ammonium chloride1 dissociation of1 #c1 #gi ---- cyanide1 dissociation of1 #hj ---- hydrosulphide1 dissociation of1 #hj ---- nitrate1 solubility of1 #aac ,aniline1 phenol1 water1 #bej ,astracanite1 #bfj1 #bfa1 #bfh1 #bgd ,b ,babo1 law of1 #abf ,barium acetate1 solubility of1 #adc ,barium carbonate and potassium sulphate1 #cbh ---- nitrite1 preparation of1 #cbg ,basic salts1 #bif ,benzaldoximes1 #bjc ,benzene and picric acid1 #baf ,bismuth1 effect of pressure on the melting point of1 #fg ----1 lead1 tin1 #bee ---- nitrates1 basic1 #bih ,bivariant systems1 #af ,bromocinnamic aldehyde and chlorocinnamic aldehyde1 #ahc ,c ,calcium carbonate1 dissociation of1 #c1 #aa1 #ha ---- chloride hexahydrate1 solubility of1 #adf ---- ----1 solubility of hydrates of1 #adh ---- ----1 vapour-pressure of hydrates of1 #hh ,camphor oximes1 #bai1 #beg ,carnallite1 #bhd ,carvoximes1 #ahf1 #bai ,cementite1 #bbd ,chlorine and iodine1 #afa ,chlorocinnamic aldehyde and bromocinnamic aldehyde1 #ahc ,chloroform1 acetic acid1 water1 #bda ----1 alcohol1 water1 #bdf #cde ,classification of systems1 #ag ,component1 #h1 #aj1 #ab ----1 systems of one1 #ba1 #ee ,components1 choice of1 #ab1 #ac1 #ad1 #gf1 #cac ----1 determination of number of1 #ac ----1 systems of four1 #cab ----1 ---- of three1 #bcd ----1 ---- of two1 #gf1 #bjg ----1 variation in number of1 #aa1 #ad ,composition1 determination of1 without analysis1 #bbh1 #cjb ,concentration-temperature curve for two liquids1 #aja ,condensed systems1 #cf ,constituent1 #aj ,cooling curve1 #bcj ,copper calcium acetate1 #bfj ---- chloride1 heat of solution of1 #aaj ---- dipotassium chloride1 #bei ---- sulphate1 #he ,critical concentration1 #ih1 #bdb ---- pressure of water1 #bc ---- solution temperature1 #ih ---- temperature of water1 #bc ,cryohydrates1 #aag1 #aah ,cryohydric point1 #aag ---- ----1 changes at the1 #aai ---- ---- for silver nitrate and ice1 #aaf ,crystals1 liquid1 #ea ----1 ----1 equilibria of1 #ec ----1 ----1 list of1 #ed ----1 ----1 nature of1 #eb ----1 mixed1 #ahj ,crystallization1 velocity of1 #gb1 #gd ----1 spontaneous1 #aad ,d ,deliquescence1 #acj ,devitrification1 #gc ,diethylamine and water1 solubility of1 #aja ,dilatometer1 determination of transition points by1 #cca ,dineric surface1 #bdg ,dissociation equilibrium1 effect of addition of dissociation products on1 #d ---- of ammonia compounds of metal chlorides1 #hb1 #hd ---- of ammonium chloride1 #c1 #gi ---- ---- cyanide1 #hj ---- ---- hydrosulphide1 #hj ---- of calcium carbonate1 #c1 #ha ---- of compounds1 degree of1 #adg ---- of phosphonium bromide1 #hj ---- of salt hydrates1 #he ----1 phenomena of1 #gi ,dissociation pressure1 #ha ,distillation of supercooled liquid to solid1 #cb1 #ej ,double salt interval1 #bgh ---- salts1 crystallization from solution1 #bhj ---- ----1 decomposition by water1 #bfg ---- ----1 formation of1 #beh1 #bgc1 #cae ,e ,efflorescence1 #hf ,electrical methods of determining transition points1 #cch ,enantiotropy1 #dd1 #ea ,equilibria1 ,gibbs's theory of1 #h ----1 metastable1 #fi ,equilibrium apparent 7false71 #e1 #f ---- between ice and solution1 #aaf ---- between ice and water1 #be ---- between ice1 water1 vapour1 #bg ---- between water and vapour1 #ba ----1 chemical1 #c1 #af ----1 heterogeneous1 #e ----1 homogeneous1 #e ----1 independence of1 on amounts of phases1 #i ----1 law of movable1 #eh #cdf ----1 physical1 #c1 #af ---- real 7true71 #e1 #f ,ether1 alcohol1 water1 #bdf ----1 succinic nitrile1 water1 #beb ,ethylene bromide1 picric acid1 beta-naphthol1 #bef ,eutectic mixtures1 #aag1 #aia1 #bji1 #bee1 #beg ---- point1 #aag1 #bji1 #bac1 #bec ,f ,ferric chloride1 evaporation of solutions of1 #aee ---- ----1 hydrates of1 #aea1 #aec ---- ----1 hydrogen chloride and water1 systems of1 #bij ,ferrite1 modifications of1 #bbd ,freedom1 degree of1 #ad ,freezing mixtures1 #abj ---- point1 natural1 #aih ,fusion curve1 #ff ---- ---- of ice1 #be ---- of ice1 influence of pressure on1 #bf ----1 partial1 #aci ,g ,glaserite1 #cae1 #cag ,glasses1 #agf ,glauber's salt1 #ac1 #acd ---- ----1 transition curve of1 #fh1 #adj ,graphic representation in space1 #gg1 #bhd ,h ,hydrates1 range of existence of1 #hi ---- chloride and water1 #agd ,hydrogen bromide and water1 #agd ,hylotropic substances1 #aih ,i ,ice ,i41 #cb ---- ,,ii41 #cb ---- ,,iii41 #cb ----1 equilibrium between water and1 #be ----1 influence of pressure on melting point of1 #be1 #bf ----1 sublimation curve of1 #bd ----1 vapour pressure of1 #be1 #ca ,indifferent point1 #aej ,individual1 chemical1 #ib ,inversion temperature1 #cf ,iodine and chlorine1 #afa ,iron--carbon alloys1 #bbc ----1 carbon monoxide and carbon dioxide1 #cje ,isomerides1 dynamic1 #aie1 #aif ----1 ----1 equilibrium between1 #aie1 #aif ----1 ----1 equilibrium point of1 #aih ----1 transformation of unstable into stable1 #bja ,isomerism1 dynamic1 #aif ,isothermal evaporation1 #bgh ---- solubility curves1 #bgb ,l ,lead1 bismuth1 tin1 #bee ----1 desilverization of1 #bdg ----1 silver1 zinc1 #bdf ,le ,chatelier1 theorem of1 #eg ,lime1 burning of1 #c ,liquidus curve1 #ahb ,m ,mandelic acid1 #bag ,martensite1 #bbd ,mass action1 law of1 #g ,melting point1 influence of pressure on1 #ff #cdg ---- ----1 congruent1 #adf ---- ----1 incongruent1 #aci ---- under the solvent1 #abb ,menthyl mandelates1 #bai ,mercuric bromide and iodide1 #ahh ,mercury salts1 basic1 #cja ,metastable equilibria1 #fi ---- region1 #cj ---- state1 #cj ,methylethyl ketone and water1 #ajj ,minerals1 formation of1 #bcb ,miscibility of liquids1 complete1 #ie1 #ajd1 #aad ---- ----1 partial1 #ie1 #if1 #aba ,mixed crystals1 #ahj1 #bha ---- ----1 changes in1 with temperature1 #aib ---- ----1 examples of1 #ahc1 #ahf1 #ahg1 #aij1 #aib1 #bai1 #bbc ---- ----1 formation of1 #aha1 #ahb ---- ----1 fractional crystallization of1 #ahh ---- ----1 freezing points of1 #ahb ---- ----1 melting points of1 #ahb1 #ahd ---- ----1 pseudoracemic1 #bai ,mixtures1 isomorphous1 #aha ---- of constant boiling point1 #aje ---- of constant melting point1 #aag1 #ahf1 #ahg1 #aib1 #bji1 #bee1 #beg ,monotropy1 #dd1 #ea ,multivariant systems1 #af ,n ,naphthalene and monochloracetic acid1 #aib ---- and beta-naphthol1 mixed crystals of1 #ahc beta-,naphthol1 ethylene bromide1 picric acid1 #bef alpha-,naphthylamine and phenol1 #bac ,nickel iodate1 solubility of1 #adb o-,nitrophenol and p-toluidine1 #bac ,o ,occlusion of gases1 #agf ,optical method of determining transition points1 #cch ,optically active substances1 freezing-point curves of1 #baf ,order of a system1 #ac ,organic compounds1 application of ,phase ,rule to1 #bab ,p ,palladium and hydrogen1 #ij1 #agh ,paragenesis1 #cbj ,paraldehyde and acetaldehyde1 #bjd ,partial pressures of two components1 #ajb ,pearlite1 #bbd ,phase1 #h ---- ,rule1 #h1 #af ---- ----1 deduction of1 #ah ---- ----1 scope of1 #a ,phases1 formation of new1 #fi ----1 number of1 #i ,phenol1 acetone1 water1 #bdh ----1 aniline1 water1 #bej ---- and alpha-naphthylamine1 #bac ---- and p-toluidine1 #bad ---- and water1 solubility of1 #ig ,phosphonium bromide1 dissociation of1 #hj ---- chloride1 #fe ,phosphorus1 #df ----1 distillation of white to red1 #ej ----1 melting point of red1 #dg ----1 ---- ---- of white1 #dh ----1 solubility of white and red1 #dg ----1 vapour pressure of white and red1 #df ,picric acid and benzene1 #baf ---- ----1 ethylene bromide1 and beta-naphthol1 #bef ,polymorphic forms1 solubility of1 #aab #cdh ---- substances1 list of1 #fc ,polymorphism1 #cc ,potassium nitrate and thallium nitrate1 #aib ,potential1 chemical1 #ai ,pressure-concentration diagram for two liquids1 #ajb ,pressure-temperature diagram for solutions1 #abf ,pseudomonotropy1 #de ,pseudo-racemic mixed crystals1 #ba ,pyridine and methyl iodide1 #adg ,pyrometer1 registering1 #bcj ,q ,quadruple point1 #aaf ,quintuple point1 #bcd1 #bfa ,r ,racemates1 characterization of1 #bag1 #bhb ,reactions1 law of successive1 #gc ,reciprocal salt-pairs1 #cac ---- ----1 transition point of1 #cad ,rubidium tartrates1 #bfe ,s ,salt hydrates1 #he ---- ----1 indefiniteness of vapour pressure of1 #hg ---- ---- with definite melting point1 #ade ,separation of salt on evaporation1 #acj ,silicates1 hydrated1 #agf ,silver1 lead1 zinc1 #bdf ,silver nitrate1 solubility of1 #aad ---- ---- and sodium nitrate1 #aij ,single salt interval1 #bgh ,sodium ammonium tartrates1 #bff ---- nitrate and silver nitrate1 #aij ---- sulphate and water1 equilibria between1 #acd ,sodium sulphate and water1 vapour pressures of1 #ach1 #adj ---- ----1 anhydrous1 dehydration by1 #ach ---- ----1 solubility of1 #ace ---- ---- decahydrate1 solubility of1 #acd ---- ---- ----1 transition point of1 #acf1 #aci ---- ---- heptahydrate1 solubility of1 #acf ---- ---- ----1 transition point of1 #acg ,solidus curve1 #ahb ,solubility curve at higher temperatures1 #aad ---- ----1 form of1 #ajh ---- ---- of anhydrous salts1 #aaa ---- ----1 retroflex1 #adf1 #aea1 #afb ---- curves1 interpolation and extrapolation of1 #aaa ---- ---- of three component systems1 #bfd ----1 determination of transition points by1 #cce ----1 influence of pressure on1 #ajg ----1 ---- of subdivision on1 #aj ----1 ---- of temperature on1 #aji ---- of metastable forms1 #dg1 #aab1 #acg ,solubility of polymorphic forms1 #aab ---- of salt hydrates1 #acc1 #ade ---- of supercooled liquids1 #abe ----1 retrograde1 #bde ,solute1 #ic ,solution1 definition of1 #ib ----1 heat of1 #aji1 #aaj ----1 saturated1 #ajf1 #ajh ----1 supersaturated1 #ajh ---- temperature1 critical1 #ih ----1 unsaturated1 #ajh ,solutions1 bivariant systems1 #abi ----1 congruently saturated1 #bgi ---- conjugate1 #ig1 #bda #cdi ----1 incongruently saturated1 #bgi1 #bhi ----1 inevaporable1 #aeg ---- of gases in liquids1 #ic ---- ---- in solids1 #agf ---- of liquids in liquids 7binary71 #ie ---- ---- ---- 7ternary71 #bdj ---- ----1 influence of temperature on1 #bdg ---- of solids in liquids1 #ajf ---- ---- in solids1 #ahj ----1 solid1 #age1 #ahj ----1 univariant systems1 #abg ,space model for carnallite1 #bhd ,stability limit1 #bjb ,steel1 formation of1 #bbc ,sublimation curve1 #fc ---- ---- of ice1 #bd ---- without fusion1 #fe ,succinic nitrile and water1 #abb ---- ether1 water1 #beb ,sulphur1 #cc1 #cd ---- dioxide and water1 #afi ---- ---- and potassium iodide1 #aeh ----1 transition point of rhombic and monoclinic1 #cf ,supersaturation1 #aac1 #aad1 #abd ----1 limits of1 #aad ,systems1 condensed1 #cf ---- of one component1 #ba ---- of two components1 #gf1 #gg1 #bjg ,t ,tachydrite1 influence of pressure on the transition point of1 #bfc ,tartrate1 dimethyl1 #bag ----1 sodium potassium1 #bei ,tautomeric substances1 #aie ,tensimeter1 #ia ,thallium nitrate and potassium nitrate1 #aib ,theorem of van't ,hoff and ,le ,chatelier1 #eg ,thermometric determination of transition point1 #ccg ,tin1 #da ----1 lead1 bismuth1 #bee ---- plague1 #dc ----1 transition point of white and grey1 #da p-,toluidine and o-nitrophenol1 #bac ---- and phenol1 #bad ,transformation of optically active substances1 #bbj ----1 suspended1 #cg1 #fi1 #hi1 #aac1 #acg1 #aee ----1 velocity of1 #gj ,transition curve1 #ff ---- ---- of ,glauber's salt1 #fh1 #adj ---- ---- of rhombic and monoclinic sulphur1 #cg ---- interval1 #bgj1 #bgg1 #cae ---- point1 #cd ---- ---- for double salts1 #beh ---- ----1 influence of pressure on the1 #fh ---- points1 as fixed points in thermometry1 #adj ---- ----1 methods of determining1 #cca ---- ---- of polymorphic substances1 #fc ,triangle1 graphic representation by1 #bce ,triethylamine and water1 #aja ,triple point1 #bg1 #ee ---- ----1 arrangement of curves round1 #ef ---- ----1 changes at1 #eh ---- ----1 ice1 water1 vapour1 #bg ---- ----1 ice ,,ii41 ice ,,iii41 and water1 #cc ---- ----1 metastable1 #ch ---- ----1 monoclinic sulphur1 liquid1 vapour1 #ch ---- ----1 monoclinic and rhombic sulphur1 liquid1 #ch ---- ----1 monoclinic and rhombic sulphur1 vapour1 #cd #cej ---- ----1 red phosphorus1 liquid1 vapour1 #dg ---- ----1 rhombic sulphur1 liquid1 vapour1 #ch ---- ---- solid1 solid1 vapour1 #fb ---- ----1 white phosphorus1 liquid1 vapour1 #dh ,u ,univariant systems1 #af ,v ,van't ,hoff1 theorem of1 #eg ,vaporization curve1 #fc ---- ----1 interpolation and extrapolation of1 #ff ---- ---- of water1 #ba1 #bc ,vapour pressure1 constancy of1 and formation of compounds1 #ij ---- ----1 dependence of1 on solid phase1 #hh ---- ----1 influence of surface tension on1 #b ---- ---- in three-component systems1 #bfa ---- ----1 measurement of1 #ia1 #ccd ---- ---- of calcium chloride solutions1 #aej ---- ---- of ice1 #be1 #ca ---- ---- of small drops1 #aj ---- ---- of sodium sulphate and water1 #ach ,vapour pressure of solid1 solution1 vapour1 #abf ---- ---- of water1 #ba1 #ca ,variability of a system1 #ad1 #af ,variance of a system1 #af ,volatile components1 two1 #afa ,w ,water1 #ba ----1 acetic acid1 chloroform1 #bda ----1 acetone1 phenol1 #bdh ----1 alcohol1 ether1 #bdf ----1 ----1 chloroform1 #bdf ----1 aniline1 phenol1 #bej ----1 bivariant systems of1 #bi ----1 critical pressure of1 #bc ----1 critical temperature of1 #bc ----1 equilibrium between ice and1 #be ----1 ---- between vapour and1 #ba ----1 ether1 succinic nitrile1 #beb ----1 supercooled1 #cj ----1 ----1 vapour pressure of1 #ca ----1 vaporization curve of1 #ba ----1 vapour pressure of1 #bc ,z ,zeolites1 #agf ,zinc1 lead1 silver1 #bdf ---- chloride in water1 solubility of1 #aeg ,,the ,,end ,,printed ,,by ,,william ,,clowes ,,and ,,sons1 ,,limited1 ,,london ,,and ,,beccles4 99 99 99 99 99 ,,notes #a ,except when the volume of the liquid becomes exceedingly small1 in which case the surface tension exerts an influence on the vapour pressure4 #b ,for reasons which will appear later 7,chap4 ,,iv471 the volume of the vapour is supposed to be large in comparison with that of the solid and liquid4 #c ,ramsay and ,young1 ,phil4 ,trans41 #ahhf1 #agg4 #hg4 #d ,see1 more especially1 ,vogt1 ,die ,silikatschmelzloesungen4 7,christiania1 #aijc1 #aijd47 #e ,trans4 ,connecticut ,acad41 #ahgd-ahgh4 #f ,lehre von der chemischen ,verwandtschaft der ,koerper1 #aggg4 #g ,see ,ostwald's ,klassiker1 ,no4 #gd4 #h ,etudes sur les affinites chimiques1 #ahfg2 ,ostwald's ,klassiker1 ,no4 #ajd4 #i ,died ,april1 #aijc4 #aj ,for a mathematical treatment of the ,phase ,rule the reader is referred to the volume in this series on ,thermodynamics1 by ,f4 ,g4 ,donnan4 #aa ,liebig's ,annalen1 #ahgc1 #agj1 #aib2 ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #aaa4 #ab ,the action of gravity and other forces being excluded 7see p4 #e74 #ac ,it may seem as if this were a contradiction to what was said on p4 #d as to the effect of the addition of ammonia or hydrogen chloride to the system constituted by solid ammonium chloride in contact with its products of dissociation4 ,there is1 however1 no contradiction1 because in the case of ammonium chloride the gaseous phase consists of ammonia and hydrogen chloride in equal proportions1 and in adding ammonia or hydrogen chloride alone we are not adding the gaseous phase1 but only a constituent of it4 ,addition of ammonia and hydrogen chloride together in the proportions in which they are combined to form ammonium chloride would cause no change in the equilibrium4 #ad ,the vapour pressure of water in small drops is greater than that of water in mass1 and the solubility of a solid is greater when in a state of fine subdivision than when in large pieces 7cf4 ,hulett1 ,zeitschr4 physikal4 ,chem41 #aija1 #cg4 #che74 #ae ,see ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #dgf1 #icd2 ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahid1 #ae4 #aej2 ,heterogene ,gleichgewichte1 ,i4 p4 #af2 ,wegscheider1 ,zeitschr4 physikal4 ,chem41 #aijc1 #dc4 #hi4 #af ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #dgh4 #ag ,see also ,hoitsema1 ,zeitschr4 physikal4 ,chem4 #ahie1 #ag4 #fea4 #ah ,the term degree of freedom employed here must not be confused with the same term used to denote the various movements of a gas molecule according to the kinetic theory4 #ai ,trevor1 ,jour4 ,physical ,chem41 #aijb1 #f4 #acf4 #bj ,ostwald1 ,principles of ,inorganic ,chemistry1 translated by ,a4 ,findlay1 #bnd edit41 p4 #g4 7,macmillan1 #aijd47 #ba ,see the volume in this series on ,thermodynamics by ,f4 ,g4 ,donnan4 #bb ,pogg4 ,annalen1 #ahdd1 #fa4 #bbe4 #bc ,memoires de l',acad41 #bf4 #gea4 #bd ,phil4 ,trans4 #ahhd1 #age4 #dfa2 #ahib1 ,a1 #ahc4 #ajg4 #be ,bihang ,svenska ,akad4 ,handl4 #ahia1 #ag4 ,i4 #a4 #bf ,abhandl4 physikal4-tech4 ,reichsanstalt1 #aijj1 #c4 #ga4 #bg ,ostwald-,luther1 ,physiko-chemische ,messungen1 #bnd edit41 p4 #aef4 #bh ,annales chim4 et phys41 #ahib #f1 #bf4 #dbe4 #bi ,the vapour pressure of water at #j;deg has recently been very accurately determined by ,thiesen and ,scheel 7loc4 cit471 and found to be #d4egi _/- #j4jja mm4 of mercury 7at #j;deg71 or equal to #j4jjfjbe atm4 #cj ,juhlin1 ,bihang ,svenska ,akad4 ,handl41 #ahia1 #ag4 ,i4 #eh4 ,see also ,ramsay and ,young1 loc4 cit4 #ca ,trans4 ,roy4 ,soc4 ,edin41 #ahdi1 #af4 #ege4 #cb ,proc4 ,roy4 ,soc4 ,edin41 #ahej1 #b1 #bfg4 #cc ,annalen der ,physik1 #ahii #c1 #fh4 #efd2 #aijj #d1 #b4 #a1 #dbd4 ,see also ,dewar1 ,proc4 ,roy4 ,soc41 #ahhj1 #cj4 #ecc4 #cd ,the pressure of #a atmosphere is equal to #a4jcc kilogm4 per sq4 cm42 or the pressure of #a kilogm4 per sq4 cm4 is equal to #j4ifh atm4 #ce ,tammann1 loc4 cit41 #aijj1 #b4 #a1 #dbd2 cf4 ,goossens1 ,arch4 neerland1 #ahhf1 #bj4 #ddi4 #cf ,j4 ,thomson1 ,proc4 ,roy4 ,soc41 #ahgd1 #bb4 #bh4 #cg ,a field is enclosed by two curves when these cut at an angle less than two right angles4 ,it may be useful to remember that an invariant system is represented by a point1 a univariant system by a line1 and a bivariant system by an area4 #ch ,phil4 ,trans41 #agbd1 #ci4 #gh4 #ci ,juhlin1 loc4 cit41 p4 #fa2 cf4 ,ramsay and ,young1 loc4 cit43 ,thiesen and ,scheel1 loc4 cit4 #dj ,this small difference is due to experimental errors in the determination of the vapour pressures2 a differential method betrayed no difference between the vapour pressure of ice and of water at #j;deg4 #da ,phil4 ,mag41 #ahgd #d1 #dg4 #ddg2 ,proc4 ,roy4 ,soc41 #ahgc1 #bb4 #bg4 #db ,pogg4 ,annalen1 #aheh1 #ajc1 #bjf4 #dc ,see ,phil4 ,trans41 #ahhd1 #age1 #dfa4 #dd ,this phenomenon of distillation from the supercooled liquid to the solid has been very clearly observed in the case of furfuraldoxime 7,v4 ,goldschmidt1 ,zeitschr4 f4 ,krystallographie1 #ahig1 #bh4 #afi74 #de ,annalen der ,physik1 #aijj #d1 #b4 #a1 #dbd4 #df ,a similar triple point has been determined by ,tammann in the case of phenol 7,annalen der ,physik1 #aijb #d1 #i4 #bdi74 #dg ,annales chim4 et phys41 #ahba1 #ai4 #dad4 #dh ,lehmann1 ,molekularphysik1 ,i4 #aec42 ,arzruni1 ,physikalische ,chemie der ,krystalle4 7,graham-,otto1 ,lehrbuch der ,chemie1 ,i4 #c47 #di ,brodie1 ,proc4 ,roy4 ,soc41 #ahee1 #g4 #bd4 #ej ,that solid sulphur does possess a certain vapour pressure has been shown by ,hallock1 who observed the formation at the ordinary temperature of copper sulphide in a tube containing copper and sulphur 7,amer4 ,jour4 ,sci41 #ahhi #c1 #cg4 #dje74 ,see also ,zenghelis1 ,zeitschr4 physikal4 ,chem41 #aijd1 #ej4 #bai4 #ea ,zeitschr4 fuer ,krystallographie1 #ahhd1 #h4 #eic4 #eb ,van't ,hoff1 ,studies on ,chemical ,dynamics1 p4 #afc4 #ec ,reicher1 loc4 cit4 ,see also ,tammann1 ,annalen der ,physik1 #ahii #c1 #fh4 #ffc4 #ed ,tammann1 ,annalen der ,physik1 #ahii #c1 #fh4 #fcc4 #ee ,rec4 ,trav4 ,chim4 ,pays-,bas1 #ahhg1 #f4 #cad4 #ef ,cf4 van't ,hoff1 ,lectures on ,physical ,chemistry1 ,i41 p4 #bg 7,arnold74 #eg ,annalen der ,physik1 #ahii #c1 #fh4 #ffc4 #eh ,brauns1 ,jahrbuch fuer ,mineralogie1 #ahii-aija1 #ac4 ,beilage1 p4 #ci4 #ei ,fritsche1 ,ber41 #ahfi1 #b4 #aab1 #edj4 #fj ,de mirabilibus ,auscultationibus1 ,cap4 #ea 7v4 ,cohen1 ,zeitschr4 physikal4 ,chem41 #aija1 #cf4 #eac74 #fa ,e4 ,cohen and ,c4 van ,eyk1 ,zeitschr4 physikal4 ,chem41 #ahii1 #cj4 #fja2 ,cohen1 ibid41 #aijj1 #cc4 #ei2 #ce4 #ehh2 #aija1 #cf4 #eac2 ,cohen and ,e4 ,goldschmidt1 ibid41 #aijd1 #ej4 #bbe4 #fb ,zeitschr4 physikal4 ,chem41 #aijj1 #cc1 #eh4 #fc ,stortenbeker1 ,zeitschr4 physikal4 ,chem41 #ahhi1 #c4 #aa2 ,rec4 ,trav4 ,chim4 ,pays-,bas1 #ahhh1 #g4 #aeb4 #fd ,zincke1 ,ber41 #ahga1 #d4 #egf4 #fe ,ostwald1 ,zeitschr4 physikal4 ,chem41 #ahig1 #bb4 #cac4 #ff ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #agg4 #fg ,roozeboom1 ibid41 p4 #agi4 #fh ,schroetter1 ,pogg4 ,annalen1 #ahej1 #ha4 #bgf2 ,troost and ,hautefeuille1 ,annales de ,chim4 et ,phys4 #ahgd #e1 #b4 #aec2 ,ann4 ,scient4 ,ecole ,norm4 #ahfh #b1 ,,ii4 #bff4 #fi ,pedler1 ,trans4 ,chem4 ,soc41 #ahij1 #eg4 #eii4 #gj ,brodie1 ,trans4 ,chem4 ,soc41 #ahec1 #e1 #bhi4 #ga ,this is a familiar fact in the case of the solubility in carbon disulphide4 #gb ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #agj4 #gc ,trans4 ,chem4 ,soc41 #ahii1 #eg4 #gcd4 #gd ,carnelley1 ,trans4 ,chem4 ,soc41 #ahgf1 #bi4 #dhi2 #ahgh1 #cc4 #bge4 ,v4 ,meyer and ,riddle1 ,ber41 #ahic1 #bf4 #bddc4 #ge ,riecke1 ,zeitschr4 physikal4 ,chem41 #ahij1 #f4 #daa4 #gf ,annalen der ,physik41 #ahih #c1 #ff4 #dib4 #gg ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #fff4 #gh ,see ,naumann1 ,ber41 #ahgb1 #d4 #fdf2 ,troost and ,hautefeuille1 ,compt4 rend41 #ahfh1 #ff4 #gie2 #ahfh1 #fg4 #acde2 ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 pp4 #fb1 #aga4 #gi ,mitscherlich1 ,lieb4 ,annalen1 #ahcd1 #ab4 #acg2 ,deville and ,troost1 ,compt4 rend41 #ahfc1 #ef4 #hia4 #hj ,beckmann1 ,zeitschr4 physikal4 ,chem41 #ahij1 #e4 #gi2 ,hertz1 ibid41 #f4 #ceh4 #ha ,ber41 #aijb1 #ce4 #cea4 ,cf4 also1 ,k4 ,schaum1 ,annalen der ,chem41 #ahih1 #cjj4 #bba2 ,r4 ,wegscheider and ,kaufler1 ,sitzungsber4 kaiserl4 ,akad4 ,wissensch4 in ,wien1 #aija1 #aaj1 ,,ii4 #fjf4 #hb ,see also ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #agg4 #hc ,annales de ,chim4 et ,phys41 #ahgd #e1 #b4 #aed4 #hd ,compt4 rend41 #ahhg1 #ajd4 #aeje4 #he ,compt4 rend41 #ahfh1 #ff4 #gie4 #hf ,phil4 ,mag41 #ahhd #e1 #ah4 #baj4 ,see also ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #agg4 #hg ,brauns1 ,neues ,jahrbuch fuer ,mineralogie1 #aijj1 #ac4 ,beilage-,band1 p4 #ci2 ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #aha4 #hh ,monatshefte1 #ahhh1 #i4 #dce4 #hi ,gattermann1 ,ber41 #ahij1 #ec4 #agch4 #ij ,zeitschr4 physikal4 ,chem41 #ahhi1 #d4 #dfh2 ,annalen der ,physik1 #aijj #d1 #b4 #fdi4 #ia ,quincke1 ,annalen der ,physik1 #ahid #c1 #ec4 #fac2 ,tammann1 ,annalen der ,physik1 #aija #d1 #d4 #ebd2 #aijb1 #h4 #ajc2 ,rotarski1 ibid41 #d4 #ebh4 #ib ,annalen der ,physik1 #aijj #d1 #b4 #fdi4 #ic ,annalen der ,physik1 #aijb #d1 #h4 #iaa4 #id ,see1 more especially1 ,o4 ,lehmann1 ,annalen der ,physik1 #aijj #d1 #b4 #fdi2 ,reinitzer1 ,sitzungsber4 kaiserl4 ,akad4 zu ,wien41 #ahhh1 #id4 7#b71 #gai2 #ig4 7#a71 #afg2 ,gattermann1 loc4 cit42 ,schenck1 ,zeitschr4 physikal4 ,chem41 #ahig1 #bc4 #gjc2 #ahih1 #be4 #ccg2 #bg4 #agj2 #ahii1 #bh4 #bhj2 ,schenck and ,schneider1 ibid41 #ahii1 #bi4 #edf2 ,abegg and ,seitz1 ibid41 #ahii1 #bi4 #dia2 ,hulett1 ibid41 #ahii1 #bh4 #fbi2 ,coehn1 ,zeitschr4 ,elektrochem41 #aijd1 #aj4 #hef3 ,bredig and ,schukowsky1 ibid41 #cdai4 ,for a full account of the subject1 the reader is referred to the work by ,lehmann1 ,fluessige ,kristalle 7,engelmann1 #aijd71 or the smaller monograph by ,schenck1 ,kristallinische ,fluessigkeiten und fluessige ,kristalle 7,engelmann1 #aije74 #ie ,a4 ,c4 de ,kock1 ,zeitschr4 physikal4 ,chem41 #aijd1 #dh4 #abi4 #if ,on account of the fact that all grades of rigidity have been realized between the ordinary solid and the liquid state1 in the case both of crystalline and amorphous substances1 it has been proposed to abandon the terms solid and liquid1 and to class bodies as crystalline or amorphous1 the passage from the one condition to the other being discontinuous2 crystalline bodies possess a certain regular orientation of their molecules and a directive force1 while in amorphous bodies these are wanting 7see ,lehmann1 ,annalen der ,physik1 #aijj #d1 #b4 #fif74 #ig ,hulett1 loc4 cit4 #ih ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #add4 ,see also ,schenck1 ,kristallinische ,fluessigkeiten und fluessige ,kristalle1 p4 #h 7,engelmann1 #aijd74 #ii ,the possible number of triple points in a one-component system is given by the expression 7n7n - #a77n - #b77_/a4b4c1 where n is the number of phases 7,riecke1 ,zeitschr4 physikal4 ,chem41 #ahij1 #f1 #daa74 ,the number of triple points1 therefore1 increases very rapidly as the number of possible phases increases4 #ajj ,duhem1 ,zeitschr4 physikal4 ,chem41 #ahia1 #h4 #cga4 ,cf4 ,roozeboom1 ,das ,heterogene ,gleichgewicht1 p4 #id ff4 #aja ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #ii4 #ajb ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahhh1 #b4 #dgd4 #ajc ,these changes can be predicted quantitatively by means of the thermodynamic equation1 dp_/dt ,q_/7,t7v#b - v#a771 provided the specific volumes of the phases are known1 and the heat effect which accompanies the transformation of one phase into the other4 #ajd ,studies on ,chemical ,dynamics1 translated by ,ewan1 p4 #bah4 #aje ,le ,chatelier1 ,compt4 rend41 #ahhd1 #ii4 #ghf4 #ajf ,see ,principles of ,inorganic ,chemistry1 translated by ,findlay1 #bnd edit41 p4 #acc4 7,macmillan1 #aijd47 #ajg ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahhh1 #b4 #dgd4 #ajh ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #ahi4 #aji ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #abe4 ,see also ,zawidski1 ,zeitschr4 physikal4 ,chem41 #aijd1 #dg4 #gbg2 van ,eyk1 ibid41 #aije1 #ea4 #gbj4 #aaj ,roberts-,austen1 ,proc4 ,roy4 ,soc41 #fc4 #ded2 ,spring1 ,zeitschr4 physikal4 ,chem41 #ahid1 #ae4 #fe4 ,see also p4 #ce4 #aaa ,ramsay and ,young1 ,phil4 ,trans41 #ahhd1 #age4 #dfa2 ,allen1 ,trans4 ,chem4 ,soc41 #aijj1 #gg4 #dac4 #aab ,ramsay and ,young1 ,phil4 ,trans4 #ahhf1 #agg4 #hg4 #aac ,this is exemplified in the well-known experiment with the cryophorus4 #aad ,tammann has1 however1 found that the fusion curve 7solid in contact with liquid7 of phosphonium chloride can be followed up to temperatures above the critical point 7,arch4 neer41 #aija #b1 #f4 #bdd74 #aae ,phil4 ,mag41 #ahhf1 #ba4 #cc4 ,see also ,s4 ,a4 ,moss1 ,physical ,review1 #aijc1 #af4 #cef4 #aaf ,this is found also in the case of bismuth4 ,see ,tammann1 ,zeitschr4 anorgan4 ,chem41 #aijd1 #dj4 #ed4 #aag ,see p4 #eg1 footnote4 #aah ,pogg4 ,annalen1 #ahej1 #ha4 #efb4 #aai ,barus1 ,amer4 ,jour4 ,sci41 #ahib1 #db4 #abe2 ,mack1 ,compt4 rend41 #ahih1 #abg4 #cfa2 ,hulett1 ,zeitschr4 physikal4 ,chem41 #ahii1 #ch4 #fbi4 #abj ,annalen der ,physik1 #ahii #c1 #fh4 #eec1 #fbi2 #aijj #d1 #a4 #bge2 #b4 #a2 #c4 #afa4 ,see also ,tammann1 ,kristallisieren und ,schmelzen 7,leipzig1 #aijc74 #aba ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #cgc2 ,poynting1 ,phil4 ,mag41 #ahha #e1 #ab4 #b2 ,planck1 ,wied4 ,annalen1 #ahhb1 #ae4 #ddf4 #abb ,bakhuis ,roozeboom1 ,das ,heterogene ,gleichgewicht1 ,i4 p4 #ia4 #abc ,lussana1 ,il nuovo ,cimento1 #ahie #d1 #a4 #aje4 #abd ,tammann1 ,zeitschr4 physikal4 ,chem41 #aijc1 #df4 #hah4 #abe ,foote1 ,zeitschr4 physikal4 ,chem41 #aijj1 #cc4 #gdj4 #abf ,ostwald1 ,zeitschr4 physikal4 ,chem41 #ahig1 #bb4 #bhi4 #abg ,van't ,hoff1 ,arch1 neer41 #aija1 #f4 #dga4 #abh ,see1 for example1 the determinations of the solubility of rhombic and monoclinic sulphur1 by ,j4 ,meyer1 ,zeitschr4 anorg4 ,chem41 #aijb1 #cc4 #adj4 #abi ,zeitschr4 physikal4 ,chem41 #ahii1 #cb4 #ejf4 #acj ,kastle and ,reed1 ,amer4 ,chem4 ,jour41 #aijb1 #bg4 #bji4 #aca ,zeitschr4 physikal4 ,chem41 #aijj1 #ce4 #eha4 #acb ,compt4 rend41 #ahhb1 #ie4 #abgh2 #ahhd1 #ig4 #abih1 #acff1 #adcc4 #acc ,zeitschr4 physikal4 ,chem41 #ahic1 #ab4 #ede4 #acd ,sitzungsber4 ,wiener ,akad41 #ahid1 #ajc4 ,i,ia4 #bbf4 #ace ,zeitschr4 physikal4 ,chem41 #bc-bi4 ,see also ,kuester1 ibid41 #be-bh4 #acf ,zeitschr4 physikal4 ,chem41 #ahig1 #bd4 #aeb4 #acg ,ibid41 #ahih1 #bg4 #ehe4 #ach ,see ,w4 ,guertler1 ,zeitschr4 anorgan4 ,chem41 #aijd1 #dj4 #bfh2 ,tammann1 ,zeitschr4 ,elektrochem41 #aijd1 #aj4 #ecb4 #aci ,e4 von ,pickardt1 ,zeitschr4 physikal4 ,chem41 #aijb1 #db4 #ag4 #adj ,zeitschr4 physikal4 ,chem41 #aijd1 #dh4 #dfg4 #ada ,m4 ,padoa1 ,accad4 ,lincei1 ,atti1 #aijd1 #ac4 #cbi4 #adb ,deville1 ,compt4 rend41 #aheb1 #cd4 #efa2 ,payen1 ibid41 #aheb1 #cd4 #ejh2 ,debray1 ibid41 #aheh1 #df4 #egf4 ,it has also been found by ,jaffe 7,zeitschr4 physikal4 ,chem41 #aijc1 #dc4 #dfe7 that when spontaneous crystallization from solution occurs1 the less stable form always separates first when purification has been carried sufficiently far4 #adc ,brauns1 ,neues ,jahrbuch fuer ,mineralogie1 #ahii1 #ac4 7,beilage ,band7 #hd4 #add ,lehrbuch1 ,,ii4 #b4 #dde4 ,see also ,principles of ,inorganic ,chemistry1 #bnd edit41 p4 #baj ff4 #ade ,schaum and ,schoenbeck1 ,annalen der ,physik1 #aijb #d1 #h4 #feb4 ,see also ,chr4 ,fuechtbauer1 ,zeitschr4 physikal4 ,chem41 #aijd1 #dh4 #edi4 #adf ,ramsay and ,young1 ,phil4 ,trans41 #ahhf1 #agg4 #hg4 #adg ,see volume in this series on ,chemical ,dynamics1 by ,dr4 ,j4 ,w4 ,mellor4 #adh ,isambert1 ,compt4 rend41 #ahha1 #ib4 #iai2 #ahhb1 #id4 #ieh2 #ahhc1 #if4 #fdc4 ,walker and ,lumsden1 ,jour4 ,chem4 ,soc41 #ahig1 #ga4 #dbh4 #adi ,compt4 rend41 #ahfg1 #fd4 #fjc4 #aej ,compt4 rend41 #ahhc1 #ajb4 #abdc4 #aea ,compt4 rend41 #ahfh1 #ff1 #abei4 #aeb ,horstmann1 ,ber41 #ahgf1 #i4 #gdi4 #aec ,loc4 cit4 #aed ,for the reasons for choosing anhydrous salt and water instead of salt hydrate and water as components1 see p4 #ad4 #aee ,see ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #ebg4 #aef ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #ech4 #aeg ,zeitschr4 physikal4 ,chem41 #ahhi1 #d4 #dc4 #aeh ,ber41 #ahgf1 #i4 #gdi4 #aei ,see1 for example1 van't ,hoff1 ,lectures on ,theoretical and ,physical ,chemistry1 ,i4 p4 #fb 7,arnold74 #afj ,jour4 ,chem4 ,soc41 #ahgg1 #cb4 #cie4 #afa ,hoitsema1 ,zeitschr4 physikal4 ,chem41 #ahie1 #ag4 #a4 #afb ,zeitschr4 physikal4 ,chem41 #ahhg1 #a4 #e2 #ahie1 #ag4 #eb4 #afc ,it is important to powder the salt1 since otherwise the dehydration of the hydrate and the production of equilibrium occurs with comparatively great tardiness4 #afd ,a chemical individual is a substance which persists as a phase of constant composition when the conditions of temperature1 pressure1 and composition of the other phases present1 undergo continuous alteration within certain limits--the limits of existence of the substance 7,wald1 ,zeitschr4 physikal4 ,chem41 #ahig1 #bd4 #fdh74 #afe ,van't ,hoff1 ,zeitschr4 physikal4 ,chem41 #ahij1 #e4 #cbc2 ,ostwald1 ,lehrbuch1 ,i4 #fjf4 #aff ,that mercury does dissolve in water can be argued from analogy1 say1 with mercury and bromonaphthalene4 ,at the ordinary temperature these two liquids appear to be quite insoluble in one another1 but at a temperature of #bhj;deg the mercury dissolves in appreciable quantity2 for on heating a tube containing bromonaphthalene over mercury the latter sublimes through the liquid bromonaphthalene and condenses on the upper surface of the tube4 #afg ,phil4 ,mag41 #ahhd1 #e1 #ah4 #bb2 #die4 #afh ,wied4 ,annalen1 #ahhf1 #bh4 #cje4 #afi ,zeitschr4 physikal4 ,chem41 #ahih1 #bf4 #dcc4 #agj ,rothmund1 loc4 cit4 #aga ,rothmund1 loc4 cit4 #agb ,a similar behaviour is found in the case of diethylamine and water 7,r4 ,t4 ,lattey1 ,phil4 ,mag41 #aije1 #f1 #aj1 #cig74 #agc ,c4 ,s4 ,hudson1 ,zeitschr4 physikal4 ,chem41 #aijd1 #dg4 #aac4 #agd ,konowaloff1 ,wied4 ,annalen1 #ahha1 #ad4 #bai4 ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #fhg4 ,bancroft1 ,phase ,rule1 p4 #if4 #age ,konowaloff1 loc4 cit4 #agf ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahia1 #h4 #ebf2 ,rec4 ,trav4 ,chim4 ,pays-,bas1 #ahhd1 #c4 #ch4 #agg ,konowaloff1 loc4 cit4 ,cf4 ,bancroft1 ,phase ,rule1 p4 #ajj4 #agh ,phil4 ,mag41 #ahhd #e1 #ah4 #ejc4 #agi ,see1 for example1 ,walker1 ,introduction to ,physical ,chemistry1 #crd edit41 p4 #hf 7,macmillan1 #aijc74 ,consult also ,young1 ,fractional ,distillation 7,macmillan1 #aijc71 or ,kuenen1 ,verdampfung und ,verfluessigung von ,gemischen 7,barth1 #aijf71 where the subject is fully treated4 #ahj ,since this is the only phase of variable composition present4 #aha ,e4 von ,stackelberg1 ,zeitschr4 physikal4 ,chem41 #ahif1 #bj4 #ccg4 ,if the change of volume which accompanies solution1 and the heat effect are known1 the quantitative change of the solubility with the pressure can be calculated 7,braun1 ,zeitschr4 physikal4 ,chem41 #ahhg1 #a4 #bei74 #ahb ,van't ,hoff1 ,arch4 neerland4 #aija #b1 #f4 #dga4 #ahc ,tilden and ,shenstone1 ,phil4 ,trans4 #ahhd1 #age4 #bc2 ,hulett and ,allen1 ,jour4 ,amer4 ,chem4 ,soc4 #aijb1 #bd4 #ffg2 ,andreae1 ,jour4 prak4 ,chem4 #acg4 #dgd2 ,lumsden1 ,jour4 ,chem4 ,soc41 #aijb1 #ha4 #cej2 ,mylius and v4 ,wrochem1 ,ber4 #aijj1 #cc4 #cfhi4 #ahd ,e4 von ,stackelberg1 ,zeitschr4 physikal4 ,chem4 #ahif1 #bj4 #aei2 #ahih1 #bf4 #ecc2 ,lumsden1 ,jour4 ,chem4 ,soc41 #aijb1 #ha4 #cej2 ,holsboer1 ,zeitschr4 physikal4 ,chem41 #aijb1 #ci4 #fia4 #ahe ,reicher and van ,deventer1 ,zeitschr4 physikal4 ,chem4 #ahij1 #e4 #eei2 cf4 ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #hjc4 #ahf ,it has been shown that the formula of ,ramsay and ,young 7p4 #ff7 can be applied 7with certain restrictions7 to the interpolation and extrapolation of the solubility curve of a substance provided two 7or three7 points on the curve are known4 ,in this case ,t1 ,t#a1 etc41 refer to the temperatures at which the two substances--one the solubility curve of which is known1 the other the solubility curve of which is to be calculated--have equal solubilities1 instead of1 as in the previous case1 equal vapour pressures4 7,findlay1 ,proc4 ,roy4 ,soc41 #aijb1 #fi4 #dga2 ,zeitschr4 physikal4 ,chem41 #aijc1 #db4 #aaj47 #ahg ,w4 ,mueller and ,p4 ,kaufmann1 ,zeitschr4 physikal4 ,chem4 #aijc1 #db4 #dig4 #ahh ,w4 ,o4 ,rabe1 ,zeitschr4 physikal4 ,chem41 #aija1 #ch4 #age4 #ahi ,with regard to the limits of supersaturation and the spontaneous crystallization of the solute from supersaturated solutions1 see ,jaffe1 ,zeitschr4 physikal4 ,chem41 #aijc1 #dc4 #efe1 and the very interesting paper by ,miers and ,isaac1 ,trans4 ,chem4 ,soc41 #aijf1 #hi4 #dac4 #aij ,annales chim4 phys41 #ahid #g1 #b4 #ebd4 #aia ,phil4 ,trans41 #ahhd1 #age4 #bc4 #aib ,hissink1 ,zeitschr4 physikal4 ,chem41 #aijj1 #cb4 #edc4 #aic ,zeitschr4 physikal4 ,chem41 #aijc1 #dc4 #cac4 #aid ,guthrie1 ,phil4 ,mag41 #ahge1 #d1 #di4 #a2 #ahhd1 #e1 #ag4 #dfb4 #aie ,see ,roloff1 ,zeitschr4 physikal4 ,chem41 #ahie1 #ag4 #cbe2 ,guthrie1 loc4 cit4 #aif ,guthrie1 ,phil4 ,mag41 loc4 cit4 ,cf4 ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #hdc4 #aig ,guthrie1 ,phil4 ,mag41 #ahge #d1 #di4 #bfi4 #aih ,ber41 #ahgg1 #bj4 #bbbc4 #aii ,silz-,ber4 ,wien4 ,akad41 #ahhj1 #ha4 ,,ii4 #ajeh4 #bjj ,guthrie1 ,phil4 ,mag41 #ahge #d1 #di4 #bjf4 #bja ,if in the neighbourhood of the cryohydric point solution should be accompanied by an evolution of heat1 then as the solubility would in that case increase with fall of temperature1 salt would pass into solution4 #bjb ,walker1 ,zeitschr4 physikal4 ,chem41 #ahij1 #e4 #aic4 #bjc ,zeitschr4 physikal4 ,chem41 #ahig1 #bc4 #dah4 #bjd ,provided the solid nitrile is not present in too great excess4 #bje ,wied4 ,annalen1 #ahhf1 #bh4 #cbh4 ,cf4 ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #hgb4 #bjf ,walker1 ,zeitschr4 physikal4 ,chem41 #ahij1 #e4 #aic4 ,schreinemakers1 ibid41 #ahig1 #bc4 #dag4 ,roozeboom1 ,rec4 trav4 chim4 ,pays-,bays1 #ahhi1 #h4 #beg4 ,bruner1 ,zeitschr4 physikal4 ,chem41 #ahig1 #bc4 #edb4 #bjg ,van't ,hoff1 ,lectures on ,theoretical ,chemistry1 ,i4 p4 #db4 ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #hbd4 #bjh ,ostwald1 ,principles of ,inorganic ,chemistry1 translated by ,a4 ,findlay1 #bnd edit41 p4 #dec 7,macmillan1 #aijd72 ,skirrow and ,calvert1 ,zeitschr4 physikal4 ,chem41 #aija1 #cg4 #bag4 #bji ,vide ,loewel1 ,annales chim4 phys41 #aheg #c1 #di4 #cb4 ,cf4 ,loewenherz1 ,zeitschr4 physikal4 ,chem41 #ahie1 #ah4 #hb4 #baj ,loewel1 loc4 cit4 ,gay-,lussac1 ,annales chim4 phys41 #ahai1 #aa4 #bif4 ,for the solubility at higher temperatures1 see ,tilden and ,shenstone1 ,phil4 ,trans41 #ahhd1 #age4 #bc4 ,etard1 ,annales chim4 phys41 #ahid #g1 #b4 #edh4 #baa ,richards1 ,zeitschr4 physikal4 ,chem41 #ahih1 #bf4 #fij2 ,richards and ,wells1 ibid41 #aijc1 #dc4 #dfe4 ,this temperature is not quite the same as that of the quadruple point anhydrous salt--hydrated salt--solution--vapour1 because the latter is the temperature at which the system is under the pressure of its own vapour4 ,since1 however1 the influence of pressure on the solubility is very slight 7p4 #ajg71 the position of the two points will not be greatly different4 ,the quadruple point was found by ,cohen 7,zeitschr4 physikal4 ,chem41 #ahid1 #ad4 #ij7 to be #cb4f;deg and #cj4h mm4 of mercury4 #bab ,van't ,hoff and van ,deventer1 ,zeitschr4 physikal4 ,chem41 #ahhg1 #a4 #ahe4 ,cf4 ,cohen1 ibid41 #ahid1 #ad4 #hh4 #bac ,debray1 ,compt4 rend41 #ahfh1 #ff4 #aid4 #bad ,richards1 ,zeitschr4 physikal4 ,chem41 #ahih1 #bf4 #fij4 ,a number of other salt hydrates1 having transition-points ranging from #bj;deg to #gh;deg1 which might be used for the same purpose1 have been given by ,richards and ,churchill1 ibid41 #ahii1 #bh4 #cac4 #bae ,zeitschr4 physikal4 ,chem41 #aijc1 #df4 #hah4 #baf ,van't ,hoff1 ,lectures on ,physical ,chemistry1 ,i4 p4 #fg4 #bag ,cohen1 ,zeitschr4 physikal4 ,chem41 #ahid1 #ad4 #ij4 #bah ,ziz1 ,schweigger's ,journal1 #ahae1 #ae4 #aff4 ,see ,ostwald1 ,lehrbuch1 ,,ii4 #b4 #gag4 #bai ,see1 for example1 the solubility determinations published in ,wissenschaftliche ,abhandl4 der physikalisch-technischen ,reichsanstalt1 ,vol4 ,,iii41 or in the ,berichte1 for the years #ahig-aija4 #bbj ,meusser1 ,ber41 #aija1 #cd4 #bddj4 #bba ,mylius and von ,wrochem1 ,ber41 #aijj1 #cc4 #cfic4 #bbb ,walker and ,fyffe1 ,jour4 ,chem4 ,soc41 #aijc1 #hc4 #ahj4 #bbc ,monatshefte1 #ahhg1 #h4 #fja4 #bbd ,the equilibria between calcium chloride and water have been most completely studied by ,roozeboom 7,zeitschr4 physikal4 ,chem41 #ahhi1 #d4 #ca74 #bbe ,hammerl1 ,sitzungsber4 ,wien4 ,akad41 #bte ,abteil1 #ahgh1 #gh4 #ei4 ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahhi1 #d4 #ca4 #bbf ,lidbury1 ,zeitschr4 physikal4 ,chem41 #aijb1 #ci4 #dec4 ,the curvature at the melting point is all the greater the more the compound is dissociated into its components in the liquid state4 ,if the compound is completely undissociated1 even in the vapour phase1 the two branches of the curve will intersect1 7e4g4 pyridine and methyl iodide2 ,aten1 ,versl4 ,konink4 ,akad4 ,wetensch4 ,amsterdam1 #aije1 #ac4 #dfb74 ,the smaller the degree of dissociation1 therefore1 the sharper will be the bend4 7,see ,stortenbeker1 ,zeitschr4 physikal4 ,chem41 #ahib1 #aj4 #aid47 ,from the extent of flattening of the curve1 it is also possible1 with some degree of approximation1 to calculate the degree of dissociation of the substance in the fused state4 7,see ,roozeboom and ,aten1 ,zeitschr4 physikal4 ,chem41 #aije1 #ec4 #dfc2 ,kremann1 ,zeitschr4 ,elektrochem41 #aijf1 #ab4 #bei47 #bbg ,see ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahhi1 #d4 #ca4 #bbh ,tammann1 ,wied4 ,annalen1 #ahii1 #fh4 #egg4 #bbi ,duhem1 ,journ4 ,physical ,chem41 #ahih1 #b4 #ca4 #bcj ,gibbs1 ,trans4 ,conn4 ,acad41 #c4 #aee2 ,saurel1 ,journ4 ,phys4 ,chem41 #aija1 #e4 #ce4 #bca ,in the case of the fusion of a compound of two components with formation of a liquid phase of the same composition1 the temperature is a maximum2 in the case of liquid mixtures of constant boiling-point1 the temperature may be a minimum 7p4 #aje74 #bcb ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahib1 #aj4 #dgg4 ,the formula of ferric chloride has been doubled1 in order to avoid fractions in the expression of the water of crystallization4 #bcc ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahib1 #aj4 #dgg4 #bcd ,a similar series of hydrates is formed by zinc chloride and water 7,dietz and ,mylius1 ,zeitschr4 anorg4 ,chem41 #aije1 #dd4 #bji74 #bce ,meyerhoffer1 ,ber41 #ahig1 #cj4 #ahaj4 #bcf ,walden1 ,ber41 #ahii1 #cb4 #bhfc4 #bcg ,zeitschr4 physikal4 ,chem41 #aijc1 #db4 #dcb4 #bch ,this composition was also confirmed by measurements of the vapour pressure 7cf4 p4 #ij74 #bci ,since all substances are no doubt volatile to a certain extent at some temperature1 it is to be understood here that the substances are appreciably volatile at the temperature of the experiment4 #bdj ,for a general discussion of the partial pressures in a system of two components1 see ,bancroft1 ,journ4 ,physical ,chem41 #ahii1 #c4 #a4 #bda ,zeitschr4 physikal4 ,chem41 #ahhi1 #c4 #aa2 ,rec4 trav4 chim4 ,pays-,bas1 #ahhh1 #g4 #aeb4 #bdb ,the composition of a solution is represented symbolically by placing a double wavy line between the symbols of the components1 and indicating the number of atoms present in the ordinary manner3 thus1 ,i wavy ,clx represents a solution containing x atoms of chlorine to one atom of iodine 7,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahhh1 #b4 #dej74 #bdc ,since iodine monochloride in the liquid state is only very slightly dissociated1 the bend at ,c is very sharp 7see p4 #adg1 footnote74 ,see also the investigation of the system pyridine and methyl iodide 7,aten1 ,versl4 ,konink4 ,akad4 ,wetensch4 ,amsterdam1 #aije1 #ac4 #dfb74 #bdd ,this upper branch of the curve is not shown in the figure1 as the ordinate corresponding to #cj;deg would be very great4 #bde ,stortenbeker1 ,zeitschr4 physikal4 ,chem41 #ahhi1 #c4 #bb4 #bdf ,ramsay and ,young1 ,journ4 ,chem4 ,soc41 #ahhf1 #di4 #deh4 #bdg ,van't ,hoff1 ,lectures on ,physical ,chemistry1 ,i4 p4 #gg 7,arnold74 #bdh ,this is different from what we found in the case of non-volatile solutes 7p4 #abf74 ,in the present case1 the partial pressure of the iodine in the vapour will be lowered by addition of chlorine1 but the total pressure is increased4 #bdi ,the diminution of volume is supposed to be carried out at constant temperature4 ,the pressure and the composition of the phases must1 therefore1 remain unchanged1 and only the relative amounts of these can undergo alteration4 #bej ,at point b the ratio of chlorine to iodine in the solution is less than in the monochloride1 so that by the separation of this the excess of chlorine yielded by the condensation of the vapour is removed4 #bea ,roozeboom1 ,rec4 trav4 chim4 ,pays-,bas1 #ahhd1 #c4 #bi2 #ahhe1 #d4 #fe2 ,zeitschr4 physikal4 ,chem41 #ahhh1 #b4 #dej4 #beb ,two curves enclose a field when they form with one another an angle less than two right angles4 #bec ,roozeboom1 ,zeitschr4 physikal4 ,chem41 loc4 cit4 #bed ,van't ,hoff1 ,zeitschr4 physikal4 ,chem41 #ahij1 #e4 #cbc4 #bee ,bancroft has proposed to restrict the term occlusion to the formation of solid solutions1 and to apply adsorption only to effects which are primarily due to surface tension4 ,such a distinction1 however1 would probably be very difficult to carry through1 for although adsorption may1 in large measure1 be due to surface tension1 the behaviour of adsorbed substances is similar to that of substances existing in solid solutions4 #bef ,tammann1 ,wied4 ,annalen1 #ahig1 #fc4 #af2 ,zeitschr4 physikal4 ,chem41 #ahih1 #bg4 #cbc4 #beg ,see1 for example1 ,chappuis1 ,wied4 ,annalen1 #ahha1 #ab4 #afa2 ,joulin1 ,annal4 chim4 phys41 #ahha1 #e1 #bb4 #cih2 ,kayser1 ,wied4 ,annalen1 #ahha1 #ab4 #ebf4 #beh ,hoitsema1 ,zeitschr4 physikal4 ,chem41 #ahie1 #ag4 #a4 #bei ,annales chim4 phys41 #ahgd1 #e1 #b4 #bgi4 #bfj ,hoitsema1 ,zeitschr4 physikal4 ,chem41 #ahie1 #ag4 #a2 ,dewar1 ,phil4 ,mag41 #ahgd1 #d1 #dg1 #cbd1 #cdb2 ,mond1 ,ramsay and ,shields1 ,proc4 ,royal ,soc41 #ahig1 #fb4 #bij4 #bfa ,loc4 cit4 #bfb ,it is noteworthy that the form of curve obtained for hydrogen and palladium bears a striking resemblance to that for the dehydration of colloids containing absorbed water1 e4g4 silicic acid 7vide van ,bemmelen1 ,zeitschr4 anorg4 ,chem41 #ahig-aijj4 ,cf4 ,zacharias1 ,zeitschr4 physikal4 ,chem41 #aijb1 #ci4 #dhj74 #bfc ,zeitschr4 physikal4 ,chem41 #ahij1 #e4 #cbb4 #bfd ,kuester1 ,zeitschr4 physikal4 ,chem41 #ahie1 #ag4 #cfg4 ,bodlaender1 ,neues ,jahrbuch f4 ,mineralogie1 #ahih-ii1 ,beilage ,band1 #ab4 #ib4 #bfe ,bruni and ,padoa1 ,atti ,accad4 ,lincei1 #aijb #e1 #aa4 #a2 #efe4 #bff ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahii1 #cj4 #che2 ,bruni1 ,rend4 ,accad4 ,lincei1 #ahih1 #b4 #ach1 #cdg4 ,for a general account of solid solutions the reader is referred to ,bruni1 ,ueber feste ,loesungen 7,ahrens'sche ,sammlung71 and to ,bodlaender1 loc4 cit4 ,for the formation and transformation of liquid mixed crystals1 see ,a4 ,c4 de ,kock1 ,zeitschr4 physikal4 ,chem41 #aijd1 #dh4 #abi4 #bfg ,in discussing the various systems which may be obtained here1 ,roozeboom 7loc4 cit47 made use of the variation of the thermodynamic potential 7p4 #bi7 with the concentration4 ,in spite of the advantages which such a treatment affords1 the temperature-concentration diagram has been adopted as being more readily understood and as more suitable for an elementary discussion of the subject4 #bfh ,these curves are also called the liquidus and the solidus curve respectively4 #bfi ,kuester1 ,zeitschr4 physikal4 ,chem41 #ahie1 #ag4 #cfj4 #bgj ,kuester1 ibid41 #ahia1 #h4 #ehi4 #bga ,it should be remarked that the behaviour described here will hold strictly only when the solid mixed crystals undergo change sufficiently rapidly to be always in equilibrium with the liquid4 ,this1 however1 is not always the case 7see ,reinders1 ,zeitschr4 physikal4 ,chem41 #aijj1 #cb4 #did2 van ,wyk1 ,zeitschr4 anorg4 ,chem41 #aije1 #dh4 #be71 and complete solidification will not in this case take place at the temperature corresponding with the line dc in ,fig4 #ej1 but only at a lower temperature4 #bgb ,adriani1 ,zeitschr4 physikal4 ,chem41 #aijj1 #cc4 #dfi4 #bgc ,reinders1 ,zeitschr4 physikal4 ,chem41 #aijj1 #cb4 #did4 #bgd ,hissink1 ,zeitschr4 physikal4 ,chem41 #aijj1 #cb4 #edb4 #bge ,van ,eyk1 ,zeitschr4 physikal4 ,chem41 #ahii1 #cj4 #dcj4 #bgf ,cady1 ,journ4 ,physical4 ,chem41 #ahii1 #c4 #abg4 #bgg ,see ,roberts-,austen and ,stansfield1 ,rapports du congres international de physique1 #aijj1 ,i4 #cfc4 #bgh ,heycock and ,neville1 ,proc4 ,roy4 ,soc41 #aijc1 #ga4 #dji4 ,for the partial liquefaction of mixed crystals on cooling1 see also ,a4 ,c4 de ,kock 7,zeitschr4 physikal4 ,chem41 #aijd1 #dh4 #abi74 #bgi ,armstrong1 ,watt's ,dictionary of ,chemistry 7,morley and ,muir71 ,,iii41 p4 #hh4 ,see also ,lowry1 ,jour4 ,chem4 ,soc41 #ahii1 #ge4 #baa4 #bhj ,see ,bancroft1 ,journ4 ,physical ,chem41 #ahih1 #b4 #adc2 ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #bhh4 #bha ,hylotropic substances are such as can undergo transformation into other substances of the same composition 7,ostwald1 ,lehrbuch1 ,,ii4 #b4 #bih74 #bhb ,also called ,equilibrium ,point 7,lowry74 #bhc ,for a discussion of these systems1 see ,roozeboom1 ,zeitschr4 physikal4 ,chem41 loc4 cit4 #bhd ,see ,bancroft1 loc4 cit41 p4 #adg2 ,wegscheider1 ,sitzungsber4 ,wiener ,akad41 #aijb1 #aaj4 #ijh4 #bhe ,reference may be made here to the term stability limit1 introduced by ,knorr 7,annalen1 #ahif1 #bic4 #hh7 to indicate that temperature above which liquefaction and isomeric change takes place4 ,as employed by ,knorr and others1 the term does not appear to have a very precise meaning1 since it is used to denote1 not the temperature at which these changes can occur1 but the temperature at which the change is rapid 7vide ,annalen1 #ahif1 #bic4 #ia2 #ahii1 #cjf4 #ccd72 and the introduction of an indefinite velocity of change renders the temperature of the stability limit also somewhat indefinite4 ,the definiteness of the term is also not a little diminished by the fact that the limit can be altered by means of catalytic agents4 ,since1 as we have seen1 the stable modification can always undergo isomeric change and liquefy at temperatures above the natural freezing point1 but not below that point2 and1 further1 the less stable modification can undergo isomeric transformation and liquefy at temperatures above the eutectic point1 but will not liquefy at temperatures below that2 it seems to the author that it would be more precise to identify these two points--the natural freezing point and the eutectic point--which are not altered by catalytic agents1 with the stability limits of the stable and unstable modification respectively4 ,a perfectly definite meaning would thereby be given to the term4 ,in the case of those substances which do not undergo appreciable isomeric change at the temperature of the melting point1 the stability limits would be the points ,g and ,h1 ,fig4 #fj4 #bhf ,cameron1 ,journ4 ,physical ,chem41 #ahih1 #b4 #dji4 #bhg ,carveth1 ,journ4 ,phys4 ,chem41 #ahih1 #b4 #aei4 ,see also ,dutoit and ,fath1 ,journ4 chim4 phys41 #aijc1 #a4 #ceh2 ,findlay1 ,trans4 ,chem4 ,soc41 #aijd1 #he4 #djc4 #bhh ,hollmann1 ,zeitschr4 physikal4 ,chem41 #aijc1 #dc4 #abi4 #bhi ,for other examples of the application of the ,phase ,rule to isomeric substances1 see ,journ4 ,physical ,chem41 vols4 #b4 et seq42 ,findlay1 ,trans4 ,chem4 ,soc41 #aijd1 #he4 #djc4 #bij ,see ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahii1 #cj4 #daj4 #bia ,see also ,saposchnikoff1 ,zeitschr4 physikal4 ,chem41 #di4 #fhh2 ,kremann1 ,monatshefte1 #aijd1 #be4 #abae1 #abga1 #acaa4 #bib ,j4 ,c4 ,philip1 ,journ4 ,chem4 ,soc41 #aijc1 #hc4 #hba4 #bic ,cf4 also ,paterno and ,ampolla1 ,gazzetta chim4 ital41 #ahig1 #bg4 #dha4 #bid ,philip1 loc4 cit41 p4 #hbf4 #bie ,philip1 loc4 cit41 p4 #hbi4 ,compare curves for iodine monochloride1 ,fig4 #db1 p4 #afb4 #bif ,kuriloff1 ,zeitschr4 physikal4 ,chem41 #ahig1 #bc4 #fgf4 #big ,ladenburg1 ,ber41 #ahie1 #bh4 #afc2 #aiia4 #bih ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #did2 ,adriani1 ibid41 #aijj1 #cc4 #dec4 #bii ,adriani1 ,zeitschr4 physikal4 ,chem41 #aijj1 #cc4 #dec4 #cjj ,a4 ,findlay and ,miss ,e4 ,hickmans4 #cja ,kipping and ,pope1 ,journ4 ,chem4 ,soc41 #ahig1 #ga4 #iic4 #cjb ,see ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #eab2 ,adriani1 ibid41 #aijj1 #cc4 #dgc2 #aija1 #cf4 #afh4 #cjc ,in this connection reference should be made more especially to the paper by ,roberts-,austen and ,stansfield1 ,sur la constitution des alliages metalliques1 in the ,rapports du congres international de physique1 #aijj1 ,i4 #cfc2 ,j4 ,a4 ,mathews1 ,journ4 of the ,franklin ,inst41 #aijb2 ,gautier1 ,compt4 rend41 #ahif1 #abc4 #aji2 ,roberts-,austen1 ,reports of the ,alloys ,research ,committee1 in ,journ4 ,inst4 ,mechan4 ,engineers1 from #ahia to #aijd2 and the papers by ,heycock and ,neville1 published in the ,journ4 ,chem4 ,soc41 and the ,trans4 ,roy4 ,soc4 since #ahig2 also ,neville1 ,reports of the ,british ,association1 #aijj1 p4 #aca4 ,reference must also be made to the important metallographic investigations by ,tammann and his pupils1 and of ,kurnakoff 7,zeitschr4 anorgan4 ,chem41 vol4 #dj and onwards71 and also to those of ,shepherd1 ,journ4 ,physical ,chem41 #h4 ,a bibliography of the alloys is given in ,zeitschr4 anorgan4 ,chem41 #aijc1 #ce4 #bdi4 #cjd ,kurnakoff and ,puschin1 ,zeitschr4 anorgan4 ,chem41 #aijb1 #cj4 #ajd4 #cje ,gautier1 ,bull4 ,soc4 d',encouragement1 #ahif #e1 #a4 #acab4 #cjf ,heycock and ,neville1 ,phil4 ,trans41 #aijj1 #aid4 #bja4 #cjg ,gautier1 loc4 cit4 ,see also ,roberts-,austen and ,rose1 ,proc4 ,roy4 ,soc41 #aijc1 #ga4 #afa4 #cjh ,heycock and ,neville1 ,journ4 ,chem4 ,soc41 #ahig1 #ga4 #dad4 #cji ,see ,roberts-,austen1 ,introduction to ,metallurgy1 #eth edit41 p4 #ajb2 ,bakhuis ,roozeboom1 ,journ4 ,iron and ,steel ,inst41 #aijj1 ,,ii4 #caa2 ,zeitschr4 physikal4 ,chem41 #aijj1 #cd4 #dcg2 von ,jueptner1 ,siderology1 p4 #bbc 7translation by ,c4 ,salter72 van't ,hoff1 ,zinn1 ,gips1 und ,stahl1 p4 #bd1 or ,acht ,vortraege ueber physikalische ,chemie1 p4 #cg4 ,further1 ,roozeboom1 ,zeitschr4 ,elektrochem41 #aijd1 #aj4 #dhi2 ,e4 ,heyn1 ibid41 p4 #dia2 ,carpenter and ,keeling1 ,journ4 ,iron and ,steel ,inst41 #aijd1 #fe4 #bbd4 #caj ,the melting point of pure iron is given by ,carpenter and ,keeling 7,journ4 ,iron and ,steel ,inst41 #aijd1 #fe4 #bbd7 as #aeje;deg4 #caa ,zeitschr4 fuer ,elektrochem41 #aijd1 #aj4 #dia4 #cab ,see also ,hiorns1 ,journ4 ,soc4 ,chem4 ,ind41 #aijf1 #be4 #ej4 #cac ,bancroft1 ,jour4 ,physical ,chem41 #aijb1 #f4 #agh2 ,bell and ,taber1 ibid41 #aijf1 #aj4 #abj4 #cad ,the method to be followed when the third component enters into the solid phase will be explained later4 #cae ,tammann1 ,zeitschr4 anorg4 ,chem41 #aijc1 #cg4 #cjc2 #aije1 #de4 #bd4 ,reference may be made here to the registering pyrometer of ,kurnakoff1 ,zeitschr4 anorg4 ,chem41 #aijd1 #db4 #ahd4 #caf ,in this connection1 see ,doelter1 ,physikalisch-chemisch ,mineralogie 7,barth1 #aija72 ,meyerhoffer1 ,zeitschr4 f4 ,kristallographie1 #aijb1 #cf4 #eic2 ,guthrie1 ,phil4 ,mag41 #ahhd #e1 #ag4 #dgi2 ,le ,chatelier1 ,compt4 rend41 #aijj1 #acj4 #he2 and especially ,e4 ,baur1 ,zeitschr4 physikal4 ,chem41 #aijc1 #db4 #efg2 ,j4 ,h4 ,l4 ,vogt1 ,zeitschr4 ,elektrochem41 #aijc1 #i4 #heb1 and ,die ,silikatschmelzloesungen1 ,parts ,i4 and ,,ii4 7,christiania1 #aijc1 #aijd74 ,see also ,n4 ,v4 ,kultascheff1 ,zeitschr4 anorg4 ,chem41 #aijc1 #ce4 #ahg4 #cag ,g4 ,g4 ,stokes1 ,proc4 ,roy4 ,soc41 #ahia1 #di4 #agd2 ,gibbs1 ,trans4 ,conn4 ,acad41 #ahgf1 #c4 #agf2 ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahid1 #ae4 #adg4 #cah ,this figure has been taken from ,ostwald's ,lehrbuch1 ,,ii4 #b4 #ihd4 #cai ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahic1 #ab4 #cfi4 #cbj ,c4 ,r4 ,a4 ,wright1 ,proc4 ,roy4 ,soc41 #ahia1 #di4 #agd2 #ahib1 #ej4 #cge4 #cba ,the distribution coefficient will not remain constant because1 apart from other reasons1 the mutual solubility of chloroform and water is altered by the addition of the acid4 #cbb ,bancroft1 ,physical ,review1 #ahie1 #c4 #ba2 ,schreinemakers1 ,zeitschr4 physikal4 ,chem41 #ahig1 #bc4 #feb1 and subsequent volumes4 #cbc ,c4 ,r4 ,a4 ,wright1 ,proc4 ,roy4 ,soc41 #ahhi-ahic4 #cbd ,c4 ,r4 ,a4 ,wright1 ,proc4 ,roy4 ,soc41 #ahib1 #ej4 #cij4 #cbe ,bodlaender1 ,berg- und ,huettenmaenn4 ,ztg41 #ahig1 #ef4 #cca4 #cbf ,c4 ,r4 ,a4 ,wright1 ,proc4 ,roy4 ,soc41 loc4 cit4 #cbg ,schreinemakers1 ,zeitschr4 physikal4 ,chem41 #aijj1 #cc4 #gh4 #cbh ,schreinemakers1 ,zeitschr4 physikal4 ,chem41 #ahih1 #bg4 #ie4 #cbi ,schreinemakers1 ,zeitschr4 physikal4 ,chem41 #ahii1 #bi4 #egg4 #ccj ,schreinemakers1 ,zeitschr4 physikal4 ,chem41 #ahih1 #be4 #edc4 #cca ,charpy1 ,compt4 rend41 #ahih1 #abf4 #aefi4 ,compare the curves for the system ,,kno#c--,na,n,o#c--,li,n,o#c 7,h4 ,r4 ,carveth1 ,journ4 ,physical ,chem41 #ahih1 #b4 #bji74 ,also alloys of ,pb--,sn--,bi 7,e4 ,s4 ,shepherd1 ,journ4 ,physical ,chem41 #aijb1 #f4 #ebg74 #ccb ,it should be remembered that in the triangular diagram a line parallel to one of the sides indicates1 at a given temperature1 a constant amount of the component represented by the opposite corner of the triangle2 and1 hence1 points in a plane1 parallel to one face of a right prism1 will indicate for different temperatures1 variation in the amounts of two components1 but constancy in the amount of the third4 #ccc ,gazzetta chim4 ital41 #ahih1 #bh4 ,,ii4 #ebj4 #ccd ,bruni1 ,gazzetta chim4 ital41 #ahih1 #bh4 ,,ii4 #ejh2 #aijj1 #cj4 ,i4 #ce4 #cce ,zeitschr4 physikal4 ,chem41 #aijj1 #cf4 #afh4 #ccf ,for a discussion of these systems1 see van't ,hoff1 ,bildung und ,spaltung von ,doppelsalzen 7,leipzig1 #ahig74 #ccg ,van ,leeuwen1 ,zeitschr4 physikal4 ,chem41 #ahig1 #bc4 #ce4 #cch ,meyerhoffer1 ,zeitschr4 physikal4 ,chem41 #ahhi1 #c4 #ccf2 #ahij1 #e4 #ig4 #cci ,reicher1 ,zeitschr4 physikal4 ,chem41 #ahhg1 #a4 #bbj4 #cdj ,for other examples of the formation and decomposition of double salts at a transition point1 the reader is referred to the work by van't ,hoff1 already cited1 on the ,bildung und ,spaltung von ,doppelsalzen2 or to ,bancroft1 ,phase ,rule1 p4 #ahj4 #cda ,bancroft1 ,phase ,rule1 p4 #ahc4 #cdb ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahhh1 #b4 #ead4 #cdc ,the influence of pressure on the transition point in the case of tachydrite has been determined by van't ,hoff1 ,kenrick1 and ,dawson 7,zeitschr4 physikal4 ,chem41 #aija1 #ci4 #bg1 #cd2 van't ,hoff1 ,zur ,bildung der ozeanischen ,salzablagerungen1 ,i4 p4 #ff--;,brunswick1 #aije74 ,this salt is formed from magnesium chloride and calcium chloride at #bb;deg1 in accordance with the equation-- #b,mg,cl#b4f;,h#b,o ,ca,cl#b4f;,h#b,o ,mg#b;,ca,cl#f4ab;,h#b,o #f;,h#b,o ,increase of pressure raises the transition point1 because the formation of tachydrite is accompanied by increase of volume2 the elevation being #j4jaf;deg for an increase of pressure of #a atm4 ,the number calculated from the theoretical formula 7p4 #eg7 is #j4jac;deg for #a atm4 ,if one calculates the influence of the pressure of sea-water on the temperature of formation of tachydrite 7which is of interest on account of the natural occurrence of this salt71 it is found that a depth of water of #aejj metres1 exerting a pressure of #ahj atm41 would alter the temperature of formation of tachydrite by only #c;deg4 ,the effect is1 therefore1 comparatively unimportant4 #cdd ,roozeboom1 ,zeitschr4 physical4 ,chem41 #ahhg1 #a4 #bbg4 #cde ,zeitschr4 physical4 ,chem41 #ahhg1 #a4 #bbg4 #cdf ,van't ,hoff and ,mueller1 ,ber41 #ahih1 #ca4 #bbjf4 #cdg ,van't ,hoff and van ,deventer1 ,zeitschr4 physikal4 ,chem41 #ahhg1 #a4 #afe4 #cdh ,for a full discussion of the solubility relations of sodium ammonium racemate1 see van't ,hoff1 ,bildung und ,spaltung von ,doppelsalzen1 p4 #ha4 #cdi ,annales chim4 phys41 #ahdh #c1 #bd4 #ddb4 #cej ,see ,van't ,hoff and van ,deventer1 ,zeitschr4 phys4 ,chem41 #ahhg1 #a4 #afe4 #cea ,meyerhoffer1 ,zeitschr4 physikal4 ,chem41 #ahij1 #e4 #aba4 #ceb ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahhh1 #b4 #eah4 #cec ,meyerhoffer1 ,zeitschr4 physikal4 ,chem41 #ahij1 #e4 #aji4 ,on the importance of the transition interval in the case of optically active substances1 see ,meyerhoffer1 ,ber41 #aijd1 #cg4 #bfjd4 #ced ,in connection with this chapter1 see1 more especially1 van't ,hoff1 ,bildung und ,spaltung von ,doppelsalzen1 p4 #c1 ff42 ,roozeboom1 ,zeitschr4 physikal ,chem41 #ahib1 #aj4 #aeh2 ,bancroft1 ,phase ,rule1 p4 #bja2 #bji4 #cee ,the same restriction must be made here as was imposed in the preceding chapter1 namely1 that the two salts in solution give a common ion4 #cef ,for example1 addition of ammonium chloride to solutions of ferric chloride 7,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahib1 #aj4 #adi74 #ceg ,it must1 of course1 be understood that the temperature is on that side of the transition point on which the double salt is stable4 #ceh ,excess of the double salt must be taken1 because otherwise an unsaturated solution might be formed1 and this would1 of course1 not deposit any salt4 #cei ,meyerhoffer1 ,ber41 #aijd1 #cg4 #bfje4 #cfj ,meyerhoffer1 ,ber41 #ahig1 #cj4 #ahji4 #cfa ,meyerhoffer1 ,ber41 #aijd1 #cg4 #bfjd4 #cfb ,bancroft1 ,phase ,rule1 p4 #bjc2 ,roozeboom1 ,zeitschr4 physikal4 ,chem41 #ahia1 #h4 #ejd1 #eca2 ,stortenbeker1 ibid41 #ahie1 #ag4 #fdc2 #ahig1 #bb4 #fj2 #aijj1 #cd4 #ajh4 #cfc ,roozeboom1 ,zeitschr4 phys4 ,chem41 #ahii1 #bh4 #did2 ,ber41 #ahii1 #cb4 #ecg4 #cfd ,as1 for instance1 strychnine racemate1 a compound of racemic acid with the optically active strychnine4 ,this would be resolved into strychnine d-tartrate and strychnine l-tartrate1 which are not enantiomorphous forms4 #cfe ,van't ,hoff and ,meyerhoffer1 ,zeitschr4 physikal ,chem41 #ahih1 #bg4 #ge2 #ahii1 #cj4 #hf4 ,fig4 #aac is taken from the latter paper4 #cff ,solid models constructed of plaster of ,paris can be obtained from ,max ,kaehler and ,martini1 ,berlin4 #cfg ,instead of the present method of obtaining potassium chloride by decomposing carnallite with water1 advantage might be taken of the fact that carnallite when heated to #afh;deg undergoes decomposition with separation of three-fourths of the potassium chloride 7van't ,hoff1 ,acht ,vortraege ueber physikalische ,chemie1 #aijb1 p4 #cb74 #cfh ,roozeboom and ,schreinemakers1 ,zeitschr4 physikal4 ,chem41 #ahid1 #ae4 #ehh4 #cfi ,these curves represent only portions of the isotherms1 since the systems in which a ternary solution is in equilibrium with solid hydrogen chloride or a hydrate1 have not been investigated4 #cgj ,the numbers printed beside the points on the curves refer to the number of the experiment in the original paper4 #cga ,lash1 ,miller and ,kenrick1 ,journ4 ,physical4 ,chem41 #aijc1 #g4 #bei2 ,allan1 ,amer4 ,chem4 ,journ41 #aija1 #be4 #cjg4 #cgb ,allan1 ,amer4 ,chem4 ,journ41 #aija1 #be4 #cjg4 #cgc ,hoitsema1 ,zeitschr4 physikal4 ,chem41 #ahie1 #ag4 #fea2 ,allan1 loc4 cit4 #cgd ,rutten1 ,zeitschr4 anorgan4 ,chem41 #aijb1 #cj4 #cdb4 ,compare the system ,be,o--,,so#c--;,h#b,o2 ,parsons1 ,zeitschr4 anorgan4 ,chem41 #aijd1 #db4 #bej4 #cge ,zeitschr4 anorgan4 ,chem41 #aijd1 #dj4 #adf4 #cgf ,schreinemakers1 ,zeitschr4 physikal4 ,chem41 #ahic1 #aa4 #gf2 ,bancroft1 ,journ4 ,physical ,chem41 #aijb1 #f4 #agi4 #cgg ,zeitschr4 anorgan4 ,chem41 #aijd1 #dj4 #adh4 #cgh ,zeitschr4 physikal4 ,chem41 #aijc1 #dc4 #ced4 #cgi ,these equilibria were obtained by ,boudouard1 ,annales chim4 phys41 #aija #g1 #bd4 #e4 ,see also ,hahn1 ,zeitschr4 physikal4 ,chem41 #aijc1 #db4 #gje2 #dd4 #eac4 #chj ,g4 ,preuner1 ,zeitschr4 physikal4 ,chem41 #aijc1 #dg4 #che4 #cha ,see ,hahn1 ,zeitschr4 physikal4 ,chem41 #aijc1 #db4 #gje2 #dd4 #eac2 ,boudouard1 ,bull4 ,soc4 chim41 #c1 #be4 #dhd2 ,bodlaender1 ,zeitschr4 f4 ,elektrochem41 #aijb1 #h4 #hcc2 ,r4 ,schenck and ,zimmermann1 ,ber41 #aijc1 #cf4 #abca1 #cffc2 ,schenck and ,heller1 ibid41 #aije1 #ch4 #bacb2 ,zeitschr4 f4 ,elektrochem41 #aijc1 #i4 #fia2 ,haber1 ,thermodynamik technischer ,gasreaktionen1 p4 #bic 7,munich1 #aijc74 #chb ,a very useful summary of the investigations carried out by van't ,hoff and his pupils on the formation of the ,stassfurt salt-beds is given by ,e4 ,f4 ,armstrong1 in the ,reports of the ,british ,association for #aija1 p4 #bfb4 ,see also van't ,hoff1 ,zur ,bildung der ozeanischen ,salzablagerungen 7,brunswick1 #aije74 #chc ,see especially ,meyerhoffer1 ,silzungsber4 ,wien4 ,akad41 #ahie1 #ajd4 ,,ii4 b1 #hdj2 ,meyerhoffer and ,saunders1 ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #dec2 #ca4 #cgj4 ,the investigation of the equilibria between reciprocal salt-pairs alone 7three-component systems7 is of great importance for the artificial preparations of minerals1 as also in analytical chemistry for the proper understanding of the methods of conversion of insoluble systems into soluble by fusion 7see ,meyerhoffer1 ,zeitschr4 physikal4 ,chem41 #aija1 #ch4 #cjg74 #chd ,see ,meyerhoffer1 ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #dei4 #che ,compare the reciprocal salt-pair ,na,cl--,,nh#d;,,hco#c 7p4 #cba74 ,in this case the upper limit of the transition interval was found by extrapolation of the solubility curve for ,na,h,c,o#c ,,nh#d;,cl ,,nh#d;,,hco#c and ,na,h,c,o#c ,,nh#d;,cl ,na,cl to be #cb;deg 7,fedotieff1 ,zeitschr4 phys4 ,chem41 #aijd1 #di4 #agi74 #chf ,loewenherz1 ,zeitschr4 physikal4 ,chem41 #ahid1 #ac4 #dfd4 #chg ,meyerhoffer and ,saunders1 ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #dgi4 #chh ,as the quantities of the salts are expressed in equivalent gram-molecules1 the molecule of sodium and potassium chloride must be doubled in order to be equivalent to sodium sulphate and potassium sulphate4 #chi ,sitz-,ber4 der kgl4 preuss4 ,akad4 der ,wiss41 #aijc1 p4 #cei4 ,van't ,hoff1 ,zur ,bildung der ozeanischen ,salzablagerungen1 ,i4 p4 #cd 7,brunswick1 #aije74 #cij ,zeitschr4 fuer ,kristallographie1 #aijd1 #ci4 #aee4 #cia ,meyerhoffer and ,saunders1 ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #dgi4 #cib ,zeitschr4 physikal4 ,chem41 #aijd1 #di4 #afb4 #cic ,another commercial process1 in the study of which good service is done by the ,phase ,rule1 is the caustification of the alkali salts 7,g4 ,bodlaender1 ,zeitschr4 fuer ,elektrochem41 #aije1 #aa4 #ahf2 ,j4 ,herold1 ibid41 #dah74 #cid ,zeitschr4 physikal4 ,chem41 #aijj1 #ce4 #cb4 #cie ,mention may also be made here of the equilibria between magnesium carbonate and potassium carbonate1 although these do not form a reciprocal salt-pair 7,auerbach1 ,zeitschr4 fuer ,elektrochem41 #aijd1 #aj4 #afa74 #cif ,o4 ,n4 ,witt and ,k4 ,ludwig1 ,ber41 #aijc1 #cf4 #dchd2 ,meyerhoffer1 ibid41 #aijd1 #cg4 #bfa1 #aaaf4 #cig ,zeitschr4 physikal4 ,chem41 #aije1 #ec4 #eac4 ,compare also1 ibid41 #aijc1 #ch4 #cjg4 #cih ,see ,schwarz1 ,beitraege zur ,kenntnis der umkehrbaren ,umwandlungen polymorpher ,korper 7,goettingen1 #ahib72 or1 ,roozeboom1 ,heterogen4 ,gleichgewicht1 ,i4 p4 #abe4 ,also ,barnes and ,cooke1 ,journ4 ,physical ,chem41 #aijb1 #f4 #agb4 #cii ,van't ,hoff and van ,deventer1 ,zeitschr4 physikal4 ,chem41 #ahhg1 #a4 #agc4 #djj ,reicher1 ,zeitschr4 fuer ,krystallographie1 #ahhd1 #h4 #eic4 #dja ,zeitschr4 physikal4 ,chem41 #ahie1 #ag4 #aec4 #djb ,zeitschr4 physikal4 ,chem41 #ahii1 #bh4 #dfd4 #djc ,meyerhoffer and ,saunders1 ibid41 p4 #dff4 #djd ,see ,van ,eyk1 ,zeitschr4 physikal4 ,chem41 #ahii1 #cj4 #ddf4 #dje ,see in this connection the volume in this series on ,electro-chemistry1 by ,dr4 ,r4 ,a4 ,lehfeldt4 #djf ,barnes and ,cooke1 ,journ4 ,physical ,chem41 #aijb1 #f4 #agb4 #djg ,for a description and explanation of these1 the reader should consult the volume in this series by ,dr4 ,lehfeldt on ,electro-chemistry2 and van't ,hoff1 ,bildung und ,spaltung von ,doppelsalzen1 p4 #dh ff4 99 99 99 99 99 ,changes made to the printed original4 ,pages #cj-ca4 ,fig4 #c1 p4 #bg43 'p4 #be4 in original4 ,so also page #cc1 ,fig4 #b1 p4 #bg4 ,page #eg4 pp4 #bi and #ce3 'pp4 #be and #ch in original4 ,page #fe4 p4 #eg43 'p4 #fj in original 7twice74 ,page #aff4 there is the point ,c#a3 ,c' in original4 ,page #bbe4 ,c is an eutectic point3 'eutetic' in original4 ,page #bbh4 ,although this view put forward by ,heyn3 ',athough' in original4 ,page #bcb4 the period of constant temperature for the eutectic point c3 'the eutectic point e' in original4 ,page #bdi4 two liquid layers between #ac;deg and #ca;deg3 'betwen' in original4 ,page #beg4 ,tables entries #d and #g4 naphthol3 'napthol' in original4 ,page #bhg4 from which the model is constructed3 'he model' in original4