file :i* includes ! orig9al illu/rations4 ,see #cddeg-;h4htm or #cddeg-;h4zip3 7https3_/_/www4gut5b]g4org_/ca*e_/epub_/ #cddeg_/pg#cddeg-;images4html7 or 7https3_/_/www4gut5b]g4org_/files_/#cdde g_/cddeg-;h4zip7 ,transcrib]'s note3 ,page numb]s enclos$ by curly braces 7example3 #be7 h be5 incorporat$ to facilitate ! use ( ! ,table ( ,cont5ts4 ,9 *emical =mulas an und]score is us$ to indicate t ! foll[+ numb] enclos$ by curly braces is a subscript4 ,= example1 ! =mula ( wat] is indicat$ by ,h#b,o4 ,a c>at "* foll[$ by a numb] enclos$ by curly braces indicate an expon5t4 ,= example1 t5 rais$ to ! m9us #g? p[] is indicat$ by #aj-g4 ,a few typographical errors h be5 correct$ & are li/$ at ! end ( ! text4 ,,! ,,phase ,,rule ,,& ,,its ,,applications by ,,alex4 ,,f9dlay1 ,m4,a41 ,,ph4,d41 ,d4,,sc4 99 99 99 99 99 ,,text-,,books ,,( ,,physical ,,*emi/ry4 ,,edit$ ,,by ,,sir ,,william ,,ramsay1 ,k4,c4,b41 ,f4,r4,s41 ,d4,,sc4 99 99 99 99 99 ,,/oi*iometry4 ,by ,,sydney ,,"y1 ,d4,sc41 ,f4,r4,s41 ,pr(essor ( ,*emi/ry 9 ! ,univ]sity ( ,dubl92 toge!r ) an ,,introduction ,,to ,,! ,,/udy ,,( ,,physical ,,*emi/ry by ,sir ,,william ,,ramsay1 ,k4,c4,b41 ,f4,r4,s41 ,editor ( ! ,s]ies4 ,cr[n #hvo4 #gs4 #f;d4 ,,an ,,introduction ,,to ,,! ,,/udy ,,( ,,physical ,,*emi/ry4 ,be+ a ,g5]al ,introduction to ! ,s]ies by ,sir ,,william ,,ramsay1 ,k4,c4,b41 ,f4,r4,s41 ,d4,sc4 ,cr[n #hvo4 #as4 net4 ,,*emical ,,/atics ,,& ,,dynamics1 includ+ ,,! ,,!ories ,,( ,,*emical ,,*ange1 ,,catalysis ,,& ,,explosions4 ,,by ,j4 ,w4 ,,mellor1 ,d4,sc4 7,n4,z471 ,b4,sc4 7,vict47 ,cr[n #hvo4 #gs4 #f;d4 ,,! ,,phase ,,rule ,,& ,,its ,,applications4 ,by ,,alex4 ,,f9dlay1 ,m4,a41 ,ph4,d41 ,d4,sc41 ,lectur] & ,demon/rator 9 ,*emi/ry1 ,univ]sity ( ,birm+ham4 ,) #acd ,figures 9 ! ,text4 ,cr[n #hvo4 #es4 ,,spectroscopy4 ,by ,e4 ,c4 ,c4 ,,baly1 ,f4,i4,c41 ,lectur] on ,spectroscopy & ,assi/ant ,pr(essor ( ,*emi/ry1 ,univ]sity ,college1 ,london4 ,) #afc ,illu/rations4 ,cr[n #hvo4 #ajs4 #f;d4 ,,!rmo*emi/ry4 ,by ,,julius ,,?oms51 ,em]itus ,pr(essor ( ,*emi/ry 9 ! ,univ]sity ( ,cop5hag54 ,translat$ by ,,ka?>9e ,a4 ,,burke1 ,b4,sc4 7,lond471 ,assi/ant 9 ! ,dep>tm5t ( ,*emi/ry1 ,univ]sity ,college1 ,london4 ,cr[n #hvo4 #is4 ,,electro-,,*emi/ry4 ,,"p ,i4--,,g5]al ,,!ory4 ,by ,r4 ,a4 ,,lehfeldt1 ,d4,sc41 ,pr(essor ( ,physics at ! ,ea/ ,london ,te*nical ,college4 ,includ+ a ,*apt] on ! ,relation ( ,*emical ,con/itution to ,conductivity1 by ,t4 ,s4 ,,moore1 ,b4,a41 ,b4,sc41 ,lectur] 9 ! ,univ]sity ( ,birm+ham4 ,cr[n #hvo4 #es4 ,,"p ,,ii4--,,applications ,,to ,,electrolysis1 ,,prim>y ,,& ,,second>y ,,batt]ies1 etc4 ,by ,n4 ,t4 ,m4 ,,wilsmore1 ,d4,sc4 ,9 ! press4 ,,/]eo*emi/ry4 ,by ,a4 ,w4 ,,/ew>t1 ,d4,sc41 ,c>negie ,rese>* ,fell[1 ,lectur] on ,/]eo*emi/ry 9 ,univ]sity ,college1 ,london4 ,) #hg ,illu/rations4 ,cr[n #hvo4 #ajs4 #f;d4 ,,relations ,,betwe5 ,,*emical ,,con/itution ,,& ,,physical ,,prop]ties4 ,by ,,samuel ,,smiles1 ,d4,sc4 ,9 prep>ation4 ,,!rmodynamics4 ,by ,f4 ,g4 ,,donnan1 ,m4,a41 ,ph4,d4 ,9 prep>ation4 ,,act9o*emi/ry4 ,by ,c4 ,e4 ,k4 ,,mees1 ,d4,sc41 & ,s4 ,e4 ,,%epp>d1 ,d4,sc4 ,9 prep>ation4 ,,practical ,,spectrographic ,,analysis4 ,by ,j4 ,h4 ,,pollok1 ,d4,sc4 ,9 prep>ation4 ,,longmans1 ,,gre51 ,,& ,,co4 #ci ,,pat]no/] ,,r[1 ,,london ,,new ,,york1 ,,bombay1 ,,& ,,calcutta 99 99 99 99 99 ,,! ,,phase ,,rule ,,& ,,its ,,applications ,,by ,,alex4 ,,f9dlay1 ,m4,a41 ,,ph4,d41 ,d4,,sc4 ,lectur] on ,physical ,*emi/ry1 ,univ]sity ( ,birm+ham ,) ,"o ,hundr$ & ,?irty-,f\r ,figures 9 ! ,text ,?ird ,impression ,longmans1 ,gre51 & ,co4 #ci ,pat]no/] ,r[1 ,london ,new ,york1 ,bombay1 & ,calcutta #aijh ,all rights res]v$ ,,d$icat$ ,,to ,,francis ,,rob]t ,,japp1 ,,ll4,d41 ,f4,r4,s4 ,,pr(essor ,,( ,,*emi/ry1 ,,univ]sity ,,( ,,ab]de51 ,,9 ,,gratitude ,,= ,,e>ly ,,tra9+ ,,& ,,advice vii ,,preface ,,to ,,! ,,second ,,edition4 ,dur+ ! two ye>s :i* h elaps$ s9ce ! fir/ edition ( ?is book appe>$1 ! /udy ( *emical equilibria has be5 prosecut$ ) consid]able activity1 & valuable additions h be5 made to our k 9 sev]al dep>tm5ts ( ?is subject4 ,9 view ( ! scope ( ! pres5t "w1 x has be51 ( c\rse1 impossible to incorporate all t has be5 done2 b sev]al new sections h be5 ins]t$1 notably ^? on ! /udy ( basic salts2 ! int]pretation ( cool+ curves1 & ! det]m9ation ( ! composition ( solid phases )\t analysis2 ! equilibria betwe5 iron1 c>bon monoxide1 & c>bon dioxide1 :i* are ( importance 9 connection ) ! processes occurr+ 9 ! bla/ furnace2 & ! ,phase ,rule /udy ( ! ammonia-soda process4 ,i h also incorporat$ a %ort section on ! reciprocal salt-pair b>ium c>bonate--potassium sulphate1 :i* _h be5 writt5 = ! ,g]man edition ( ?is book by ! late ,pr(essor ,w4 ,mey]h(f]4 ,! section on ! iron-c>bon alloys1 :i* 9 ! fir/ edition 0 some:at unsatisfactory1 has be5 rewritt54 ,a4 ,f4 ,septemb]1 #aijf4 viii ,,preface ,al?\gh we are indebt$ to ! late ,pr(essor ,will>d ,gibbs = ! fir/ enunciation ( ! ,phase ,rule1 x 0 n till #ahhg t its practical applicability to ! /udy ( ,*emical ,equilibria 0 made app>5t4 ,9 t ye> ,roozeboom disclos$ ! great g5]alization1 :i* = upw>ds ( t5 ye>s _h rema9$ hidd5 & unkn[n save to a v few1 by /ripp+ f x ! g>b ( ab/ract ,ma!matics 9 :i* x _h be5 clo!d by its fir/ discov]]4 ,! ,phase ,rule 0 ?us made g5]ally accessible2 & its adoption by ,roozeboom z ! basis ( classification ( ! diff]5t cases ( *emical equilibrium !n kn[n e/abli%$ its value1 n only z a means ( co-ord9at+ ! l>ge numb] ( isolat$ cases ( equilibrium & ( giv+ a deep] insight into ! relation%ips exi/+ betwe5 ! diff]5t sy/ems1 b also z a guide 9 ! inve/igation ( unkn[n sy/ems4 ,:ile ! revelation ( ! pr9ciple emb$d$ 9 ! ,phase ,rule is prim>ily due to ,roozeboom1 x %\ld n be =gott5 t1 "s ye>s previ\sly1 van't ,h(f1 9 ignorance ( ! "w ( ,will>d ,gibbs1 _h enunciat$ 8 law ( ! incompatibility ( cond5s$ sy/ems1 :i* 9 "s respects co9cides ) ! ,phase ,rule2 & x is only ow+ to ! m g5]al applicability ( ! latt] t ! v ix important g5]alization ( van't ,h(f has be5 some:at lo/ sight (4 ,! exposition ( ! ,phase ,rule & its applications giv5 9 ! foll[+ pages has be5 made entirely non-ma!matical1 ! desire hav+ be5 to expla9 z cle>ly z possible ! pr9ciples und]ly+ ! ,phase ,rule1 & to illu/rate _! application to ! classification & inve/igation ( equilibria1 by means ( a numb] ( cases actually /udi$4 ,:ile x has be5 s\ght to make ! treatm5t suffici5tly elem5t>y to be und]/ood by ! /ud5t j comm5c+ ! /udy ( *emical equilibria1 an attempt has be5 made to advance 8 k to su* a /age z to enable him to /udy ) pr(it ! l>g] works on ! subject1 & to foll[ ) intellig5ce ! c\rse ( inve/igation 9 ?is dep>tm5t ( ,physical ,*emi/ry4 ,x is also hop$ t ! volume may be ( use1 n only to ! /ud5t ( ,physical ,*emi/ry1 or ( ! o!r bran*es ( t sci5ce1 b also to ! /ud5t ( ,metallurgy & ( ,geology1 = :om an acqua9tance ) at lea/ ! pr9ciples ( ! ,phase ,rule is becom+ increas+ly important4 ,9 writ+ ! foll[+ acc\nt ( ! ,phase ,rule1 x is sc>cely necess>y to say t ,i h be5 greatly indebt$ to ! l>g] works on ,*emical ,equilibria by ,o/wald 7,lehrbu*71 ,roozeboom 7,die ,het]og55 ,glei*gewi*te71 & ,bancr(t 7,! ,phase ,rule72 & 9 ! case ( ! fir/-nam$1 to ! inspiration also ( p]sonal tea*+4 ,my indebt$ness to ^! & o!r au?ors ,i h indicat$ 9 ! foll[+ pages4 ,9 conclusion1 ,i w\ld express my ?anks to ,sir ,william ,ramsay1 ^: guidance & c\nsel h be5 con/antly x at my disposal2 & to my colleagues1 ,dr4 ,t4 ,slat] ,price & ,dr4 ,a4 ,mc,kenzie1 = _! fri5dly criticism & advice4 ,to ,messrs4 ,j4 ,n4 ,fri5d1 ,m4,sc41 & ,w4 ,e4 ,s4 ,turn]1 ,b4,sc41 ,i am also indebt$ = _! assi/ance 9 read+ ! pro(-%eets4 ,a4 ,f4 ,novemb]1 #aijc4 xi ,,cont5ts ,,page ,,*apt] ,i ,,introduction #a ,g5]al1 ,i4 ,homog5e\s & het]og5e\s equilibrium1 #e4 ,real & app>5t equilibrium1 #e4 ,,*apt] ,,ii ,,! ,,phase ,,rule #g ,phases1 #h4 ,compon5ts1 #aj4 ,degree ( fre$om4 ,v>iability ( a sy/em1 #ad4 ,! ,phase ,rule1 #af4 ,classification ( sy/ems accord+ to ! ,phase ,rule1 #ag4 ,d$uction ( ! ,phase ,rule1 #ah4 ,,*apt] ,,iii ,,typical ,,sy/ems ,,( ,,"o ,,compon5t #ba ,a4 ,wat]4 ,equilibrium betwe5 liquid & vap\r4 ,vaporization curve1 #ba4 ,upp] limit ( vaporization curve1 #bc4 ,sublimation curve ( ice1 #bd4 ,equilibrium betwe5 ice & wat]4 ,curve ( fusion1 #be4 ,equilibrium betwe5 ice1 wat]1 & vap\r4 ,! triple po9t1 #bg4 ,biv>iant sy/ems ( wat]1 #bi4 ,sup]cool$ wat]4 ,meta/able /ate1 #cj4 ,o!r sy/ems ( ! sub/ance wat]1 #cb4 ,b4 ,sulphur1 #cc4 ,polymorphism1 #cc4 ,sulphur1 #cd4 ,triple po9t--,rhombic & monocl9ic sulphur & vap\r4 ,transition po9t1 #cd4 ,cond5s$ sy/ems1 #cf4 ,susp5d$ trans=mation1 #cg4 ,transition curve--,rhombic & monocl9ic sulphur1 #cg4 ,triple po9t--,monocl9ic sulphur1 liquid1 & vap\r4 ,melt+ po9t ( monocl9ic sulphur1 #ch4 ,triple po9t--,rhombic & monocl9ic sulphur & liquid1 #ch4 ,triple po9t--,rhombic sulphur1 liquid1 & vap\r4 ,meta/able triple po9t1 #ch4 ,fusion curve ( rhombic sulphur1 #ci4 ,biv>iant sy/ems1 #ci4 ,c4 ,t91 #da4 ,transition po9t1 #da4 xii ,enantiotropy & monotropy1 #dd4 ,d4 ,phosphorus1 #df4 ,enantiotropy comb9$ ) monotropy1 #ea4 ,e4 ,liquid ,cry/als1 #ea4 ,ph5om5a obs]v$1 #ea4 ,nature ( liquid cry/als1 #eb4 ,equilibrium relations 9 ! case ( liquid cry/als1 #ec4 ,,*apt] ,,iv ,,g5]al ,,summ>y #ee ,triple po9t1 #ee4 ,!orems ( van't ,h(f & ( ,le ,*ateli]1 #eg4 ,*anges at ! triple po9t1 #eh4 ,triple po9t solid--solid--vap\r1 #fb4 ,sublimation & vaporization curves1 #fc4 ,fusion curve--,transition curve1 #ff4 ,susp5d$ trans=mation4 ,meta/able equilibria1 #fi4 ,velocity ( trans=mation1 #gj4 ,law ( successive reactions1 #gc4 ,,*apt] ,v ,,sy/ems ,,( ,,two ,,compon5ts--,,ph5om5a ,,( ,,dissociation #gf ,diff]5t sy/ems ( two compon5ts1 #gg4 ,,ph5om5a ,,( ,,dissociation4 ,biv>iant sy/ems1 #gi4 ,univ>iant sy/ems1 #hj4 ,ammonia comp\nds ( metal *lorides1 #hb4 ,salts ) wat] ( cry/allization1 #he4 ,effloresc5ce1 #hf4 ,indef9it5ess ( ! vap\r pressure ( a hydrate1 #hg4 ,susp5d$ trans=mation1 #hi4 ,range ( exi/5ce ( hydrates1 #ij4 ,con/ancy ( vap\r pressure & ! =mation ( comp\nds1 #ij4 ,measurem5t ( ! vap\r pressure ( hydrates1 #ia4 ,,*apt] ,,vi ,,solutions #ib ,def9ition1 #ib4 ,,solutions ,,( ,,gases ,,9 ,,liquids1 #ic4 ,,solutions ,,( ,,liquids ,,9 ,,liquids1 #ie4 ,p>tial or limit$ miscibility1 #if4 ,ph5ol & wat]1 #ig4 ,me?yle?ylketone & wat]1 #ajj4 ,trie?ylam9e & wat]1 #aja4 ,g5]al =m ( conc5tration-temp]ature curve1 #aja4 ,pressure-conc5tration diagram1 #ajb4 ,complete miscibility1 #ajd4 ,pressure-conc5tration diagram1 #ajd4 ,,*apt] ,,vii ,,solutions ,,( ,,solids ,,9 ,,liquids1 ,,only ,,"o ,,( ,,! ,,compon5ts ,,be+ ,,volatile #ajf ,g5]al1 #ajf4 ,! saturat$ solution1 #ajh4 ,=m ( ! solubility curve1 #ajh4 ,a4 ,,anhydr\s ,,salt ,,& ,,wat]4 xiii ,! solubility curve1 #aaa4 ,susp5d$ trans=mation & sup]saturation1 #aac4 ,solubility curve at high] temp]atures1 #aad4 7#a7 ,complete miscibility ( ! fus$ compon5ts4 ,ice z solid phase1 #aaf4 ,cryohydrates1 #aag4 ,*anges at ! quadruple po9t1 #aai4 ,freez+ mixtures1 #abj4 7#b7 ,p>tial miscibility ( ! fus$ compon5ts4 ,sup]saturation1 #abd4 ,pressure-temp]ature diagram1 #abf4 ,vap\r pressure ( solid--solution--vap\r1 #abf4 ,o!r univ>iant sy/ems1 #abg4 ,biv>iant sy/ems1 #abi4 ,deliquesc5ce1 #acj4 ,sep>ation ( salt on evaporation1 #acj4 ,g5]al summ>y1 #aca4 ,,*apt] ,,viii ,,solutions ,,( ,,solids ,,9 ,,liquids1 ,,only ,,"o ,,( ,,! ,,compon5ts ,,be+ ,,volatile #acc ,b4 ,,hydrat$ ,,salt ,,& ,,wat]1 7#a7 ,! comp\nds =m$ d n h a def9ite melt+ po9t4 ,conc5tration-temp]ature diagram1 #acc4 ,sodium sulphate & wat]1 #acd4 ,susp5d$ trans=mation1 #acg4 ,dehydration by means ( anhydr\s sodium sulphate1 #ach4 ,pressure-temp]ature diagram1 #ach4 7#b7 ,! comp\nds =m$ h a def9ite melt+ po9t4 ,solubility curve ( calcium *loride hexahydrate1 #ade4 ,pressure-temp]ature diagram1 #adi4 ,! indiff]5t po9t1 #aej4 ,! hydrates ( f]ric *loride1 #aea4 ,susp5d$ trans=mation1 #aee4 ,evaporation ( solutions at con/ant temp]ature1 #aee4 ,inevaporable solutions1 #aeg4 ,illu/ration1 #aeh4 ,,*apt] ,,ix ,,equilibria ,,betwe5 ,,two ,,volatile ,,compon5ts #afa ,g5]al1 #afa4 ,iod9e & *lor9e1 #afa4 ,conc5tration-temp]ature diagram1 #afb4 ,pressure-temp]ature diagram1 #afe4 ,biv>iant sy/ems1 #afg4 ,sulphur dioxide & wat]1 #afi4 ,pressure-temp]ature diagram1 #agj4 ,biv>iant sy/ems1 #agc4 ,,*apt] ,x ,,solid ,,solutions4 ,,mix$ ,,cry/als #age ,g5]al1 #age4 ,solution ( gases 9 solids1 #agf4 ,palladium & hydrog51 #agh4 ,solutions ( solids 9 solids4 ,mix$ cry/als1 #ahj4 ,=mation ( mix$ cry/als ( isomorph\s sub/ances1 #ahb4 ,i4 ,! two compon5ts c =m an unbrok5 s]ies ( mix$ cry/als4 7a7 ,! freez+ po9ts ( all mixtures lie betwe5 ! freez+ po9ts ( ! pure compon5ts4 ,examples1 #ahc4 ,melt+-po9t curve1 #ahc4 7b7 ,! freez+-po9t curve passes ?r\gh a maximum4 ,example1 #ahf4 7c7 ,! freez+-po9t curve passes ?r\gh a m9imum4 ,example1 #ahh4 ,fractional xiv cry/allization ( mix$ cry/als1 #ahh4 ,,ii4 ,! two compon5ts d n =m a cont9u\s s]ies ( mix$ cry/als4 7a7 ,! freez+-po9t curve exhibits a transition po9t1 #aij4 ,example1 #aij4 7b7 ,! freez+-po9t curve exhibits a eutectic po9t1 #aia4 ,examples1 #aib4 ,*anges 9 mix$ cry/als ) ! temp]ature1 #aib4 ,,*apt] ,,xi ,,equilibrium ,,betwe5 ,,dynamic ,,isom]ides #aie ,temp]ature-conc5tration diagram1 #aif4 ,trans=mation ( ! un/able into ! /able =m1 #bja4 ,examples1 #bjc4 ,b5zaldoximes1 #bjc4 ,acetaldehyde & p>aldehyde1 #bjd4 ,,*apt] ,,xii ,,summ>y4--,,application ,,( ,,! ,,phase ,,rule ,,to ,,! ,,/udy ,,( ,,sy/ems ,,( ,,two ,,compon5ts #bjg ,summ>y ( ! diff]5t sy/ems ( two compon5ts1 #bjh4 7#a7 ,organic comp\nds1 #bab4 7#b7 ,optically active sub/ances1 #bac4 ,examples1 #baf4 ,trans=mations1 #bag4 7#c7 ,alloys1 #bbj4 ,iron--c>bon alloys1 #bbc4 ,det]m9ation ( ! composition ( comp\nds )\t analysis1 #bbh4 ,=mation ( m9]als1 #bcb4 ,,*apt] ,,xiii ,,sy/ems ,,( ,,?ree ,,compon5ts #bcd ,g5]al1 #bcd4 ,graphic repres5tation1 #bce4 ,,*apt] ,,xiv ,,solutions ,,( ,,liquids ,,9 ,,liquids #bdj #a4 ,! ?ree compon5ts =m only "o pair ( p>tially miscible liquids1 #bdj4 ,retrograde solubility1 #bde4 ,! influ5ce ( temp]ature1 #bdg4 #b4 ,! ?ree compon5ts c =m two pairs ( p>tially miscible liquids1 #bdi4 #c4 ,! ?ree compon5ts =m ?ree pairs ( p>tially miscible liquids1 #bea4 ,,*apt] ,,xv ,,pres5ce ,,( ,,solid ,,phases #bec ,a4 ,! t]n>y eutectic po9t1 #bec4 ,=mation ( comp\nds1 #bee4 ,b4 ,equilibria at high] temp]atures4 ,=mation ( d\ble salts1 #beh4 ,transition po9t1 #beh4 ,vap\r pressure4 xv ,qu9tuple po9t1 #bfa4 ,solubility curves at ! transition po9t1 #bfd4 ,decomposition ( ! d\ble salt by wat]1 #bfg4 ,transition int]val1 #bgj4 ,summ>y1 #bga4 ,,*apt] ,,xvi ,,iso!rmal ,,curves ,,& ,,! ,,space ,,model #bgb ,non-=mation ( d\ble salts1 #bgb4 ,=mation ( d\ble salt1 #bgc4 ,transition int]val1 #bgg4 ,iso!rmal evaporation1 #bgh4 ,cry/allization ( d\ble salt f solutions conta9+ excess ( "o compon5t1 #bhj4 ,=mation ( mix$ cry/als1 #bha4 ,application to ! *>act]ization ( racemates1 #bhb4 ,repres5tation 9 space4 ,space model = c>nallite1 #bhd4 ,summ>y & num]ical data1 #bhg4 ,f]ric *loride--hydrog5 *loride--wat]1 #bij4 ,t]n>y sy/ems1 #bia4 ,! iso!rmal curves1 #bid4 ,basic ,salts1 #bif4 ,bi#b,o#c--,n#b,o#e--;,h#b,o1 #bih4 ,basic m]cury salts1 #cja4 ,indirect det]m9ation ( ! composition ( ! solid phase1 #cjb4 ,,*apt] ,,xvii ,,abs5ce ,,( ,,liquid ,,phase #cje ,iron1 c>bon monoxide1 c>bon dioxide1 #cje4 ,,*apt] ,,xviii ,,sy/ems ,,( ,,f\r ,,compon5ts #cab ,reciprocal salt-pairs4 ,*oice ( compon5ts1 #cac4 ,transition po9t1 #cad4 ,=mation ( d\ble salts1 #cae4 ,transition int]val1 #cae4 ,graphic repres5tation1 #caf4 ,example1 #cag4 ,ammonia-soda process1 #cbj4 ,prep>ation ( b>ium nitrite1 #cbg4 ,b>ium c>bonate & potassium sulphate1 #cbh4 ,,app5dix ,,exp]im5tal ,,det]m9ation ,,( ,,! ,,transition ,,po9t #cca ,i4 ,! dilatometric me?od1 #cca4 ,,ii4 ,measurem5t ( ! vap\r pressure1 #ccd4 ,,iii4 ,solubility measurem5ts1 #cce4 ,,iv4 ,!rmometric me?od1 #ccg4 ,v4 ,optical me?od1 #cch4 ,,vi4 ,electrical me?ods1 #cch4 ,,"n ,,index #cda ,,subject ,,index #cde 99 99 99 99 99 #a ,,! ,,phase ,,rule ,,*apt] ,i ,,introduction ,g5]al4--,be=e proce$+ to ! m sy/ematic treatm5t ( ! ,phase ,rule1 x may1 p]haps1 be n amiss to give fir/ a brief =eca/ ( ! nature ( ! subject we are ab\t to /udy1 9 ord] t we may ga9 "s idea ( :at ! ,phase ,rule is1 ( ! k9d ( problem :i* x enables u to solve1 & ( ! scope ( its application4 ,x has long be5 kn[n t if wat] is plac$ 9 a clos$1 exhau/$ space1 vap\r is giv5 (f & a c]ta9 pressure is creat$ 9 ! enclos+ vessel4 ,?us1 :5 wat] is plac$ 9 ! ,torricellian vacuum ( ! b>omet]1 ! m]cury is depress$1 & ! am\nt ( depression increases z ! temp]ature is rais$4 ,b1 al?\gh ! pressure ( ! vap\r increases z ! temp]ature rises1 its value at any giv5 temp]ature is con/ant1 no matt] :e!r ! am\nt ( wat] pres5t or ! volume ( ! vap\r is great or small2 if ! pressure on ! vap\r is alt]$ :ile ! temp]ature is ma9ta9$ con/ant1 ei!r ! wat] or ! vap\r w ultimately disappe>2 ! =m] by evaporation1 ! latt] by cond5sation4 ,at any giv5 temp]ature )9 c]ta9 limits1 !re=e1 wat] & vap\r c exi/ p]man5tly 9 contact ) "o ano!r--or1 z x is said1 be 9 equilibrium ) "o ano!r--only :5 ! pressure has a c]ta9 def9ite value4 ,! same law ( con/ancy ( vap\r pressure at a giv5 #b temp]ature1 q irrespective ( ! volumes ( liquid & vap\r1#a holds good also 9 ! case ( alcohol1 e!r1 b5z5e1 & o!r pure liquids4 ,x is1 !re=e1 n unnatural to ask ! "q1 ,does x hold good = all liquids8 ,is x valid1 = example1 9 ! case ( solutions8 ,we c f9d ! answ] to ^! que/ions by /udy+ ! behavi\r ( a solution--say1 a solution ( common salt 9 wat]--:5 plac$ 9 ! ,torricellian vacuum4 ,9 ?is case1 also1 x is obs]v$ t ! pressure ( ! vap\r increases z ! temp]ature is rais$1 b ! pressure is no long] indep5d5t ( ! volume2 z ! volume increases1 ! pressure sl[ly dim9i%es4 ,if1 h[ev]1 solid salt is pres5t 9 contact ) ! solution1 !n ! pressure aga9 becomes con/ant at con/ant temp]ature1 ev5 :5 ! volume ( ! vap\r is alt]$4 ,z we see1 !re=e1 solutions d n behave 9 ! same way z pure liquids4 ,moreov]1 on l[]+ ! temp]ature ( wat]1 a po9t is rea*$ at :i* ice beg9s to sep>ate out2 & if heat be n[ add$ to ! sy/em or )drawn f x1 no *ange w take place 9 ! temp]ature or vap\r pressure ( ! latt] until ei!r ! ice or ! wat] has disappe>$4#b ,ice1 wat]1 & vap\r1 !re=e1 c be 9 equilibrium ) "o ano!r only at "o def9ite temp]ature & "o def9ite pressure4 ,9 ! case ( a solution ( common salt1 h[ev]1 we may h ice 9 contact ) ! solution at diff]5t temp]atures & pressures4 ,fur!r1 x is possible to h a solution 9 equilibrium n only ) anhydr\s salt 7,na,cl71 b also ) ! hydrat$ salt 7,na,cl1 #b;,h#b,o71 z well z ) ice1 & ! "q1 !re=e1 arises3 ,is x possible to /ate 9 a g5]al mann] ! conditions "u :i* su* diff]5t sy/ems c exi/ 9 equilibrium2 or to obta9 "s insight #c into ! relations :i* exi/ betwe5 pure liquids & solutions8 ,z we %all le>n1 ! ,phase ,rule enables u to give an answ] to ?is "q4 ,! prec$+ examples belong to ! class ( s-call$ physical equilibria1 or equilibria dep5d+ on *anges 9 ! physical /ate4 ,m ?an a hundr$ ye>s ago1 h[ev]1 x 0 %[n by ,w5zel & ,b]?ollet t *emical equilibria c also exi/2 t *emical reactions d n always take place completely 9 "o direction z indicat$ by ! usual *emical equation1 b t be=e ! react+ sub/ances are all us$ up ! reaction ceases1 & !re is a condition ( equilibrium betwe5 ! react+ sub/ances & ! products ( reaction4 ,z an example ( ?is1 !re may be tak5 ! process ( lime-burn+1 :i* dep5ds on ! fact t :5 calcium c>bonate is heat$1 c>bon dioxide is giv5 (f & quicklime is produc$4 ,if ! c>bonate is heat$ 9 a clos$ vessel x w be f\nd1 h[ev]1 n to und]go entire decomposition4 ,:5 ! pressure ( ! c>bon dioxide rea*es a c]ta9 value 7:i* is f\nd to dep5d on ! temp]ature71 decomposition ceases1 & calcium c>bonate exi/s side by side ) calcium oxide & c>bon dioxide4 ,moreov]1 at any giv5 temp]ature ! pressure is con/ant & indep5d5t ( ! am\nt ( c>bonate or oxide pres5t1 or ( ! volume ( ! gas2 nor does ! addition ( ei!r ( ! products ( dissociation1 c>bon dioxide or calcium oxide1 cause any *ange 9 ! equilibrium4 ,"h1 !n1 we see t1 al?\gh !re are ?ree diff]5t sub/ances pres5t1 & al?\gh ! equilibrium is no long] due to physical1 b to *emical *ange1 x nev]!less obeys ! same law z ! vap\r pressure ( a pure volatile liquid1 su* z wat]4 ,x might be suppos$1 n[1 t ?is behavi\r w\ld be %[n by o!r dissociat+ sub/ances1 e4g4 ammonium *loride4 ,:5 ?is sub/ance is heat$ x dissociates into ammonia & hydrog5 *loride1 & at any giv5 temp]ature ! pressure ( ^! gases is con/ant1#c & is indep5d5t ( ! am\nts ( solid & gas pres5t4 ,s f>1 !re=e1 ammonium *loride behaves l calcium c>bonate4 ,if1 h[ev]1 "o ( ! #d products ( dissociation be add$ to ! sy/em1 x is f\nd t ! pressure is no long] con/ant at a giv5 temp]ature1 b v>ies ) ! am\nt ( gas1 ammonia or hydrog5 *loride1 :i* is add$4 ,9 ! case ( c]ta9 dissociat+ sub/ances1 !re=e1 addition ( "o ( ! products ( dissociation alt]s ! equilibrium1 :ile 9 o!r cases x does n4 ,) ! help ( ! ,phase ,rule1 h[ev]1 a g5]al int]pretation ( ?is diff]5ce ( behavi\r c be giv5--an int]pretation :i* c be appli$ n only to ! two cases cit$1 b to all cases ( dissociation4 ,aga91 x is well kn[n t sulphur exi/s 9 two diff]5t cry/all9e =ms1 octah$ral & prismatic1 ea* ( :i* melts at a diff]5t temp]ature4 ,! problem "h is1 !re=e1 m complicat$ ?an 9 ! case ( ice1 = !re is n[ a possibility n only ( "o solid =m1 b ( two diff]5t =ms ( ! same sub/ance exi/+ 9 contact ) liquid4 ,:at are ! conditions "u :i* ^! two =ms c exi/ 9 contact ) liquid1 ei!r s+ly or toge!r1 & "u :at conditions c ! two solid =ms exi/ toge!r )\t ! pres5ce ( liquid sulphur8 ,to ^! que/ions an answ] c also be giv5 ) ! help ( ! ,phase ,rule4 ,^! cases are1 h[ev]1 comp>atively simple2 b :5 we come1 = in/ance1 to /udy ! conditions "u :i* solutions are =m$1 & especially :5 we inquire into ! solubility relations ( salts capable ( =m+1 p]haps1 a s]ies ( cry/all9e hydrates2 & :5 we seek to det]m9e ! conditions "u :i* ^! diff]5t =ms c exi/ 9 contact ) ! solution1 ! problem becomes m complicat$1 & ! necessity ( "s g5]al guide to ! elucidation ( ! behavi\r ( ^! diff]5t sy/ems becomes m urg5t4 ,x is1 n[1 to ! /udy ( su* physical & *emical equilibria z ^? above-m5tion$ t ! ,phase ,rule f9ds application2 to ! /udy1 also1 ( ! conditions regulat+1 = example1 ! =mation ( alloys f mixtures ( ! fus$ metals1 or ( ! v>i\s salts ( ! ,/assfurt deposits2 ! behavi\r ( iron & c>bon 9 ! =mation ( /eel & ! #e sep>ation ( diff]5t m9]als f a fus$ rock-mass4#d ,) ! help ( ! ,phase ,rule we c gr\p toge!r into classes ! l>ge numb] ( diff]5t isolat$ cases ( sy/ems 9 equilibrium2 ) its aid we are able to /ate1 9 a g5]al mann] at lea/1 ! conditions "u :i* a sy/em c be 9 equilibrium1 & by its means we c ga9 "s insight into ! relations exi/+ betwe5 diff]5t k9ds ( sy/ems4 ,homog5e\s & ,het]og5e\s ,equilibrium4--,be=e pass+ to ! consid]ation ( ?is g5]alization1 x w be well to fir/ make m5tion ( c]ta9 re/rictions :i* mu/ be plac$ on its treatm5t1 & also ( ! limitations to :i* x is subject4 ,if a sy/em is uni=m ?r\gh\t its :ole ext5t1 & possesses 9 e "p id5tical physical prop]ties & *emical composition1 x is call$ homog5e\s4 ,su* is1 = example1 a solution ( sodium *loride 9 wat]4 ,an equilibrium occurr+ 9 su* a homog5e\s sy/em 7su* z ! equilibrium occurr+ 9 ! =mation ( an e/] 9 alcoholic solution7 is call$ homog5e\s equilibrium4 ,if1 h[ev]1 ! sy/em consi/s ( p>ts :i* h diff]5t physical prop]ties1 p]haps also diff]5t *emical prop]ties1 & :i* are m>k$ (f & sep>at$ f "o ano!r by b\nd+ surfaces1 ! sy/em is said to be het]og5e\s4 ,su* a sy/em is =m$ by ice1 wat]1 & vap\r1 9 :i* ! ?ree portions1 ea* 9 itself homog5e\s1 c be me*anically sep>at$ f "o ano!r4 ,:5 equilibrium exi/s betwe5 diff]5t1 physically di/9ct p>ts1 x is kn[n z het]og5e\s equilibrium4 ,x is1 n[1 ) het]og5e\s equilibria1 ) ! conditions "u :i* a het]og5e\s sy/em c exi/1 t we %all deal "h4 ,fur!r1 we %all n take into acc\nt *anges ( equilibrium due to ! action ( electrical1 magnetic1 or capill>y =ces1 or ( gravity2 b %all discuss only ^? :i* are due to *anges ( pressure1 temp]ature1 & volume 7or conc5tration74 ,real & ,app>5t ,equilibrium4--,9 discuss+ equilibria1 also1 a di/9ction mu/ be drawn betwe5 real & #f app>5t equilibria4 ,9 ! =m] case !re is a /ate ( re/ :i* und]goes cont9u\s *ange ) *ange ( ! conditions 7e4g4 *ange ( temp]ature or ( pressure71 & = :i* ! *ief crit]ion is t ! same condition ( equilibrium is rea*$ f :i*ev] side x is approa*$4 ,?us 9 ! case ( a solution1 if ! temp]ature is ma9ta9$ con/ant1 ! same conc5tration w be obta9$1 no matt] :e!r we />t ) an unsaturat$ solution to :i* we add m solid1 or ) a sup]saturat$ solution f :i* we all[ solid to cry/allize out2 or1 9 ! case ( wat] 9 contact ) vap\r1 ! same vap\r pressure w be obta9$1 no matt] :e!r we heat ! wat] up to ! giv5 temp]ature or cool x d[n f a high] temp]ature4 ,9 ?is case1 wat] & vap\r are 9 real equilibrium4 ,on ! o!r h&1 wat] 9 contact ) hydrog5 & oxyg5 at ! ord9>y temp]ature is a case only ( app>5t equilibrium2 on *ang+ ! pressure & temp]ature cont9u\sly )9 c]ta9 limits !re is no cont9u\s *ange obs]v$ 9 ! relative am\nts ( ! two gases4 ,on heat+ beyond ^! limits !re is a sudd5 & n a cont9u\s *ange1 & ! sy/em no long] rega9s its =m] condition on be+ cool$ to ! ord9>y temp]ature4 ,9 all su* cases ! sy/em may be reg>d$ z und]go+ *ange & z t5d+ t[>ds a /ate ( true or real equilibrium1 b ) su* sl[ness t no *ange is obs]v$4 ,al?\gh ! case ( wat] 9 contact ) hydrog5 & oxyg5 is an extreme "o1 x mu/ be borne 9 m9d t ! condition ( true equilibrium may n be rea*$ in/antane\sly or ev5 ) measurable velocity1 & 9 all cases x is necess>y to be on "o's gu>d aga9/ mi/ak+ app>5t 7or false7 = real 7or true7 equilibrium4 ,! importance ( ?is w be fully illu/rat$ 9 ! sequel4 99 99 99 99 99 #g ,,*apt] ,,ii ,,! ,,phase ,,rule ,al?\gh ! fact t *emical reactions d n take place completely 9 "o direction1 b proce$ only to a c]ta9 po9t & !re make a halt1 0 kn[n 9 ! la/ qu>t] ( ! eighte5? c5tury 7,w5zel1 #aggg2 ,b]?ollet1 #agii72 & al?\gh ! op5+ & subsequ5t decades ( ! foll[+ c5tury br\ght _m fur!r examples ( su* equilibria to our k1 x 0 n until ! la/ qu>t] ( ! n9ete5? c5tury t a !orem1 g5]al 9 its application & ) f\ndations weak5$ by no hypo!tical assumptions z to ! nature or con/itution ( matt]1 0 put =w>d by ,will>d ,gibbs2#e a g5]alization :i* s]ves at once z a gold5 rule by :i* ! condition ( equilibrium ( a sy/em c be te/$1 & z a guide to ! simil>ities & dissimil>ities exi/+ 9 diff]5t sy/ems4 ,be=e t "t1 c]ta9ly1 attempts _h be5 made to br+ ! diff]5t kn[n cases ( equilibria--*emical & physical--"u g5]al laws4 ,f ! v fir/1 bo? ,w5zel#f & ,b]?ollet#g recogniz$ ! influ5ce ex]cis$ by ! mass ( ! sub/ances on ! equilibrium ( ! sy/em4 ,x 0 res]v$1 h[ev]1 = ,guldb]g & ,waage1 by _! m g5]al /atem5t & ma!matical treatm5t ( ! ,law ( ,mass ,action1#h to inaugurate ! p]iod ( quantitative /udy ( equilibria4 ,! law :i* ^! inve/igators enunciat$ #h s]v$ satisfactorily to summ>ize ! conditions ( equilibrium 9 _m cases bo? ( homog5e\s &1 ) ! help ( c]ta9 assumptions & additions1 ( het]og5e\s equilibrium4 ,by reason1 h[ev]1 ( ! fact t x 0 develop$ on ! basis ( ! k9etic & molecul> !ories1 & involv$1 !re=e1 c]ta9 hypo!tical assumptions z to ! nature & condition ( ! sub/ances tak+ "p 9 ! equilibrium1 ! law ( mass action fail$1 z x necess>ily mu/1 :5 appli$ to ^? sy/ems 9 :i* nei!r ! numb] ( diff]5t molecul> aggregates nor ! degree ( _! molecul> complexity 0 kn[n4 ,t5 ye>s aft] ! law ( mass action 0 prop\nd$ by ,guldb]g & ,waage1 ,will>d ,gibbs1#i ,pr(essor ( ,physics 9 ,yale ,univ]sity1 %[$ h[1 9 a p]fectly g5]al mann]1 free f all hypo!tical assumptions z to ! molecul> condition ( ! p>ticipat+ sub/ances1 all cases ( equilibrium c\ld be survey$ & gr\p$ into classes1 & h[ simil>ities 9 ! behavi\r ( app>5tly diff]5t k9ds ( sy/ems1 & diff]5ces 9 app>5tly simil> sy/ems1 c\ld be expla9$4 ,z ! basis ( 8 !ory ( equilibria1 ,gibbs adopt$ ! laws ( !rmodynamics1#aj a me?od ( treatm5t :i* _h fir/ be5 employ$ by ,hor/mann4#aa ,9 d$uc+ ! law ( equilibrium1 ,gibbs reg>d$ a sy/em z possess+ only ?ree indep5d5tly v>iable factors#ab--temp]ature1 pressure1 & ! conc5tration ( ! compon5ts ( ! sy/em--& he enunciat$ ! g5]al !orem n[ usually kn[n z ! ,phase ,rule1 by :i* he def9$ ! conditions ( equilibrium z a relation%ip betwe5 ! numb] ( :at are call$ ! phases & ! compon5ts ( ! sy/em4 ,phases4--,be=e proce$+ f>!r we %all fir/ consid] :at exactly is meant by ! t]ms phase & compon5t4 ,we h already se5 7p4 #e7 t a het]og5e\s sy/em is made #i up ( diff]5t portions1 ea* 9 itself homog5e\s1 b m>k$ (f 9 space & sep>at$ f ! o!r portions by b\nd+ surfaces4 ,^! homog5e\s1 physically di/9ct & me*anically sep>able portions are call$ phases4 ,?us ice1 wat]1 & vap\r1 are ?ree phases ( ! same *emical sub/ance--wat]4 ,a phase1 h[ev]1 :il/ x mu/ be physically & *emically homog5e\s1 ne$ n necess>ily be *emically simple4 ,?us1 a gase\s mixture or a solution may =m a phase2 b a het]og5e\s mixture ( solid sub/ances con/itutes z _m phases z !re are sub/ances pres5t4 ,?us :5 calcium c>bonate dissociates "u ! influ5ce ( heat1 calcium oxide & c>bon dioxide are =m$4 ,!re are !n two solid phases pres5t1 viz4 calcium c>bonate & oxide1 & "o gas phase1 c>bon dioxide4 ,! numb] ( phases :i* c exi/ side by side may v>y greatly 9 diff]5t sy/ems4 ,9 all cases1 h[ev]1 !re c be b "o gas or vap\r phase on ! acc\nt ( ! fact t all gases are miscible ) "o ano!r 9 all proportions4 ,9 ! case ( liquid & solid phases ! numb] is indef9ite1 s9ce ! above prop]ty does n apply to !m4 ,! numb] ( phases :i* c be =m$ by any giv5 sub/ance or gr\p ( sub/ances also diff]s greatly1 & 9 g5]al increases ) ! numb] ( p>ticipat+ sub/ances4 ,ev5 9 ! case ( a s+le sub/ance1 h[ev]1 ! numb] may be consid]able2 9 ! case ( sulphur1 = example1 at lea/ eight diff]5t solid phases are kn[n 7v4 ,*ap4 ,,iii474 ,x is ( importance to be> 9 m9d t equilibrium is indep5d5t ( ! am\nts ( ! phases pres5t4#ac ,?us x is a famili> fact t ! pressure ( a vap\r 9 contact ) a #aj liquid 7i4e4 ! pressure ( ! saturat$ vap\r7 is unaffect$ by ! am\nts1 :e!r relative or absolute1 ( ! liquid & vap\r2 also ! am\nt ( a sub/ance dissolv$ by a liquid is indep5d5t ( ! am\nt ( solid 9 contact ) ! solution4 ,x is true t deviations f ?is g5]al law occur :5 ! am\nt ( liquid or ! size ( ! solid p>ticles is r$uc$ beyond a c]ta9 po9t1#ad ow+ to ! influ5ce ( surface en]gy2 b we h already 7p4 #e7 exclud$ su* cases f consid]ation4 ,compon5ts4--,al?\gh ! conception ( phases is "o :i* is readily und]/ood1 some:at great] difficulty is exp]i5c$ :5 we come to consid] :at is meant by ! t]m compon5t2 = ! compon5ts ( a sy/em are n synonym\s ) ! *emical elem5ts or comp\nds pres5t1 i4e4 ) ! con/itu5ts ( ! sy/em1 al?\gh bo? elem5ts & comp\nds may be compon5ts4 ,by ! latt] t]m !re are meant only ^? con/itu5ts ! conc5tration ( :i* c und]go indep5d5t v>iation 9 ! diff]5t phases1 & x is only ) ^! t we are conc]n$ "h4#ae ,to und]/& ! mean+ ( ?is t]m we %all consid] briefly "s cases ) :i* ! read] w be famili>1 & at ! outset x mu/ be emphasiz$ t ! ,phase ,rule is conc]n$ m]ely ) ^? con/itu5ts :i* take "p 9 ! /ate ( real equilibrium 7p4 #e72 = x is only to ! f9al /ate1 n to ! processes by :i* t /ate is rea*$1 t ! ,phase ,rule applies4 ,consid] n[ ! case ( ! sy/em wat]--vap\r or ice--wat]--vap\r4 ,! numb] ( con/itu5ts tak+ "p 9 ! equilibrium "h is only "o1 viz4 ! *emical sub/ance1 wat]4 ,hydrog5 & oxyg51 ! con/itu5ts ( wat]1 are n to be reg>d$ z compon5ts1 because1 9 ! fir/ place1 !y are #aa n pres5t 9 ! sy/em 9 a /ate ( real equilibrium 7p4 #f72 9 ! second place1 !y are comb9$ 9 def9ite proportions to =m wat]1 & _! am\nts1 !re=e1 _c be v>i$ indep5d5tly4 ,a v>iation 9 ! am\nt ( hydrog5 necessitates a def9ite v>iation 9 ! am\nt ( oxyg54 ,9 ! case1 already ref]r$ to1 9 :i* hydrog5 & oxyg5 are pres5t along ) wat] at ! ord9>y temp]ature1 we are n deal+ ) a condition ( true equilibrium4 ,if1 h[ev]1 ! temp]ature is rais$ to a c]ta9 po9t1 a /ate ( true equilibrium betwe5 hydrog51 oxyg51 & wat]-vap\r w be possible4 ,9 ?is case hydrog5 & oxyg5 w be compon5ts1 because n[ !y d take "p 9 ! equilibrium2 also1 !y ne$ no long] be pres5t 9 def9ite proportions1 b excess ( "o or ! o!r may be add$4 ,( c\rse1 if ! re/riction be arbitr>ily made t ! free hydrog5 & oxyg5 %all be pres5t always & only 9 ! proportions 9 :i* !y are comb9$ to =m wat]1 !re w be1 z be=e1 only "o compon5t1 wat]4 ,f ?is1 !n1 we see t a *ange 9 ! conditions ( ! exp]im5t 79 ! pres5t case a rise ( temp]ature7 may necessitate a *ange 9 ! numb] ( ! compon5ts4 ,x is1 h[ev]1 only 9 ! case ( sy/ems ( m ?an "o compon5t t any difficulty w be f\nd2 = only 9 ?is case w a *oice ( compon5ts be possible4 ,take1 = in/ance1 ! dissociation ( calcium c>bonate into calcium oxide & c>bon dioxide4 ,at ea* temp]ature1 z we h se51 !re is a def9ite /ate ( equilibrium4 ,:5 equilibrium has be5 e/abli%$1 !re are ?ree diff]5t sub/ances pres5t--calcium c>bonate1 calcium oxide1 & c>bon dioxide2 & ^! are ! con/itu5ts ( ! sy/em betwe5 :i* equilibrium exi/s4 ,n[1 al?\gh ^! con/itu5ts take "p 9 ! equilibrium1 !y are n all to be reg>d$ z compon5ts1 = !y are n mutually indep5d5t4 ,on ! contr>y1 ! diff]5t phases are relat$ to "o ano!r1 & if two ( ^! are tak51 ! composition ( ! ?ird is def9$ by ! equation ,ca,c,o#c ,ca,o ,,co#b #ab ,n[1 9 decid+ ! numb] ( compon5ts 9 any giv5 sy/em1 n only mu/ ! con/itu5ts *os5 be capable ( indep5d5t v>iation1 b a fur!r re/riction is impos$1 & we obta9 ! foll[+ rule3 ,z ! compon5ts ( a sy/em !re are to be *os5 ! smalle/ numb] ( indep5d5tly v>iable con/itu5ts by means ( :i* ! composition ( ea* phase p>ticipat+ 9 ! /ate ( equilibrium c be express$ 9 ! =m ( a *emical equation4 ,apply+ ?is rule to ! case "u consid]ation1 we see t ( ! ?ree con/itu5ts pres5t :5 ! sy/em is 9 a /ate ( equilibrium1 only two1 z already /at$1 are indep5d5tly v>iable4 ,x w fur!r be se5 t 9 ord] to express ! composition ( ea* phase pres5t1 two ( ^! con/itu5ts are necess>y4 ,! sy/em is1 !re=e1 "o ( two compon5ts1 or a sy/em ( ! second ord]4 ,:51 n[1 we proce$ to ! actual *oice ( compon5ts1 x is evid5t t any two ( ! con/itu5ts c be select$4 ,?us1 if we *oose z compon5ts ,ca,c,o#c & ,ca,o1 ! composition ( ea* phase c be express$ by ! foll[+ 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 ,z we see1 !n1 bo? z]o & negative quantities ( ! compon5ts h be5 introduc$2 & simil> expressions w\ld be obta9$ if ,ca,c,o#c & ,,co#b 7 *os5 z compon5ts4 ,! matt] c1 h[ev]1 be simplifi$ & ! use ( negative quantities avoid$ if ,ca,o & ,,co#b are *os52 & x is1 !re=e1 cu/om>y to select ^! z ! compon5ts4 ,:ile x is possible 9 ! case ( sy/ems ( ! second ord] to *oose ! two compon5ts 9 su* a way t ! composition ( ea* phase c be express$ by positive quantities ( ^!1 su* a *oice is n always possible :5 deal+ ) sy/ems ( a high] ord] 7conta9+ ?ree or f\r compon5ts74 ,f ! example :i* has j be5 discuss$1 x might #ac appe> z if ! *oice ( ! compon5ts 0 r arbitr>y4 ,on exam9+ ! po9t1 h[ev]1 x w be se5 t ! arbitr>9ess affects only ! nature1 n ! numb]1 ( ! compon5ts2 a *oice c\ld be made ) respect to :i*1 n to h[ _m1 con/itu5ts 7 to be reg>d$ z compon5ts4 ,z we %all see pres5tly1 h[ev]1 x is only ! numb]1 n ! nature ( ! compon5ts t is ( importance4 ,aft] ! discussion ( ! conditions :i* ! sub/ances *os5 z compon5ts mu/ satisfy1 ano!r me?od may be giv5 by :i* ! numb] ( compon5ts pres5t 9 a sy/em c be det]m9$4 ,suppose a sy/em consi/+ ( sev]al phases 9 equilibrium1 & ! composition ( ea* phase det]m9$ by analysis4 ,if ea* phase pres5t1 reg>d$ z a :ole1 has ! same composition1 ! sy/em conta9s only "o compon5t1 or is ( ! fir/ ord]4 ,if two phases mu/ be mix$ 9 suitable quantities 9 ord] t ! composition ( a ?ird phase may be obta9$1 ! sy/em is "o ( two compon5ts or ( ! second ord]2 & if ?ree phases are necess>y to give ! composition ( a f\r? coexi/+ phase1 ! sy/em is "o ( ?ree compon5ts1 or ( ! ?ird ord]4#af ,al?\gh ! examples to be consid]$ 9 ! sequel w af=d suffici5t illu/ration ( ! application ( ! rules giv5 above1 "o case may p]haps be discuss$ to %[ ! application ( ! me?od j giv5 = det]m9+ ! numb] ( compon5ts4 ,consid] ! sy/em consi/+ ( ,glaub]'s salt 9 equilibrium ) solution & vap\r4 ,if ^! ?ree phases are analyz$1 ! composition ( ! solid w be express$ by ,na#b,,s#d1 #aj;,h#b,o2 t ( ! solution by ,na#b,,s#d x,h#b,o1 :ile ! vap\r phase w be ,h#b,o4 ,! sy/em evid5tly _c be a "o-compon5t sy/em1 = ! phases h n all ! same composition4 ,by v>y+ ! am\nts ( two phases1 h[ev] 7e4g4 ,na#b,,s#d1 #aj;,h#b,o & ,h#b,o71 ! composition ( ! ?ird phase--! solution--c be obta9$4 ,! sy/em is1 !re=e1 "o ( two compon5ts4 ,b sodium sulphate c also exi/ 9 ! anhydr\s =m & z ! hydrate ,na#b,,s#d1 #g;,h#b,o4 ,9 ^! cases !re may #ad be *os5 z compon5ts ,na#b,,s#d & ,h#b,o1 & ,na#b,,s#d1 #g;,h#b,o & ,h#b,o respectively4 ,9 bo? cases1 !re=e1 !re are two compon5ts4 ,b ! two sy/ems 7,na#b,,s#d1 #aj;,h#b,o--,h#b,o1 & ,na#b,,s#d1 #g;,h#b,o--,h#b,o7 c be reg>d$ z special cases ( ! sy/em ,na#b,,s#d--;,h#b,o1 & ^! two compon5ts w apply to all sy/ems made up ( sodium sulphate & wat]1 no matt] :e!r ! solid phase is anhydr\s salt or "o ( ! hydrates4 ,9 all ?ree cases1 ( c\rse1 ! numb] ( compon5ts is ! same2 b by *oos+ ,na#b,,s#d & ,h#b,o z compon5ts1 ! possible occurr5ce ( negative quantities ( compon5ts 9 express+ ! composition ( ! phases is avoid$2 &1 fur!r1 ^! compon5ts apply ov] a mu* l>g] range ( exp]im5tal conditions4 ,aga91 !re=e1 we see t1 al?\gh ! numb] ( ! compon5ts ( a sy/em is def9ite1 a c]ta9 am\nt ( lib]ty is all[$ 9 ! *oice ( ! sub/ances2 & we also see t ! *oice w be influ5c$ by ! conditions ( exp]im5t4 ,summ+ up1 n[1 we may say-- 7#a7 ,! compon5ts are to be *os5 f among ! con/itu5ts :i* are pres5t :5 ! sy/em is 9 a /ate ( true equilibrium1 & :i* take "p 9 t equilibrium4 7#b7 ,z compon5ts are to be *os5 ! smalle/ numb] ( su* con/itu5ts necess>y to express ! composition ( ea* phase p>ticipat+ 9 ! equilibrium1 z]o & negative quantities ( ! compon5ts be+ p]missible4 7#c7 ,9 any giv5 sy/em ! numb] ( ! compon5ts is def9ite1 b may alt] ) alt]ation ( ! conditions ( exp]im5t4 ,a c]ta9 fre$om ( *oice1 h[ev]1 is all[$ 9 ! 7qualitative1 n quantitative7 selection ( ! compon5ts1 ! *oice be+ influ5c$ by consid]ations ( simplicity1 suitability1 or g5]ality ( application4#ag ,degree ( ,fre$om4 ,v>iability ( a ,sy/em4--,x is well kn[n t 9 deal+ ) a c]ta9 mass ( gas or vap\r1 e4g4 wat] vap\r1 if only "o ( ! indep5d5tly v>iable factors--temp]ature1 pressure1 & conc5tration 7or volume7--is fix$1 ! /ate ( ! gas or vap\r is undef9$2 :ile occupy+ ! same volume 7! conc5tration1 !re=e1 rema9+ #ae un*ang$71 ! temp]ature & ! pressure may be alt]$2 at a giv5 temp]ature1 a gas c exi/ "u diff]5t pressures & occupy diff]5t volumes1 & "u any giv5 pressure ! temp]ature & volume may v>y4 ,if1 h[ev]1 two ( ! factors are arbitr>ily fix$1 !n ! ?ird factor c only h a c]ta9 def9ite value2 at any giv5 values ( temp]ature & pressure a giv5 mass ( gas c occupy only a def9ite volume4 ,suppose1 h[ev]1 t ! sy/em consi/s ( wat] 9 contact ) vap\r4 ,! condition ( ! sy/em !n becomes p]fectly def9$ on arbitr>ily giv+ "o ( ! v>iables a c]ta9 value4 ,if ! temp]ature is fix$1 ! pressure "u :i* wat] & wat] vap\r c coexi/ is also det]m9$2 & conv]sely1 if a def9ite pressure is *os51 ! temp]ature is also def9$4 ,wat] & vap\r c coexi/ "u a giv5 pressure only at a def9ite temp]ature4 ,f9ally1 let ! wat] & vap\r be cool$ d[n until ice beg9s to sep>ate out4 ,s soon z ! ?ird phase1 ice1 appe>s1 ! /ate ( ! sy/em z reg>ds temp]ature & pressure ( ! vap\r is p]fectly def9$1 & none ( ! v>iables c be arbitr>ily *ang$ )\t caus+ ! disappe>ance ( "o ( ! phases1 ice1 wat]1 or vap\r4 ,we see1 !re=e1 t 9 ! case ( "s sy/ems two1 9 o!r cases1 only "o ( ! indep5d5t v>iables 7temp]ature1 pressure1 conc5tration7 c be alt]$ )\t de/roy+ ! nature ( ! sy/em2 :ile 9 o!r sy/ems1 aga91 ^! v>iables h all fix$ & def9ite values4 ,we %all !re=e def9e ! numb] ( degrees ( fre$om#ah ( a sy/em z ! numb] ( ! v>iable factors1 temp]ature1 pressure1 & conc5tration ( ! compon5ts1 :i* mu/ be arbitr>ily fix$ 9 ord] t ! condition ( ! sy/em may be p]fectly def9$4 ,f :at has be5 said1 !re=e1 we %all describe a gas or vap\r z hav+ two degrees ( fre$om2 ! sy/em wat]--vap\r z hav+ only "o2 & ! sy/em ice--wat]--vap\r z hav+ no degrees ( fre$om4 ,we may also speak ( ! #af v>iability or v>iance ( a sy/em1 & describe a sy/em z be+ inv>iant1 univ>iant1 biv>iant1 multiv>iant1#ai accord+ z ! numb] ( degrees ( fre$om is n\ght1 "o1 two1 or m ?an two4 ,a k ( its v>iability is1 !re=e1 ( ess5tial importance 9 /udy+ ! condition & behavi\r ( a sy/em1 & x is ! great m]it ( ! ,phase ,rule t ! /ate ( a sy/em is def9$ entirely by ! relation exi/+ betwe5 ! numb] ( ! compon5ts & ! phases pres5t1 no acc\nt be+ tak5 ( ! molecul> complexity ( ! p>ticipat+ sub/ances1 nor any assumption made ) reg>d to ! con/itution ( matt]4 ,x is1 fur!r1 z we see1 q immat]ial :e!r we are deal+ ) physical or *emical equilibrium2 9 pr9ciple1 inde$1 no di/9ction ne$ be drawn betwe5 ! two classes1 al?\gh x is nev]!less (t5 conv5i5t to make use ( ! t]ms1 9 spite ( a c]ta9 am\nt ( indef9it5ess :i* atta*es to !m--an indef9it5ess1 inde$1 :i* atta*es equally to ! t]ms physical & *emical process4#bj ,! ,phase ,rule4--,! ,phase ,rule ( ,gibbs1 :i* def9es ! condition ( equilibrium by ! relation betwe5 ! numb] ( coexi/+ phases & ! compon5ts1 may be /at$ z foll[s3 ,a sy/em consi/+ ( n compon5ts c exi/ 9 n #b phases only :5 ! temp]ature1 pressure1 & conc5tration h fix$ & def9ite values2 if !re are n compon5ts 9 n #a phases1 equilibrium c exi/ :ile "o ( ! factors v>ies1 & if !re are only n phases1 two ( ! v>y+ factors may be arbitr>ily fix$4 ,?is rule1 ! application ( :i*1 x is hop$1 w become cle> 9 ! sequel1 may be v concisely & conv5i5tly summ>iz$ 9 ! =m ( ! equation-- ,p ,f ,c #b1 or ,f ,c #b - ,p :]e ,p d5otes ! numb] ( ! phases1 ,f ! degrees ( fre$om1 & ,c ! numb] ( compon5ts4 ,f ! second =m ( ! equation x c be readily se5 t ! great] ! numb] ( ! phases1 ! few] are ! degrees ( fre$om4 ,) increase 9 ! numb] ( ! phases1 !re=e1 ! #ag condition ( ! sy/em becomes m & m def9$1 or less & less v>iable4 ,classification ( ,sy/ems accord+ to ! ,phase ,rule4--,we h already le>n$ 9 ! introductory *apt] t sy/ems :i* are app>5tly q diff]5t 9 "* may behave 9 a v simil> mann]4 ,?us x 0 /at$ t ! laws :i* gov]n ! equilibrium betwe5 wat] & its vap\r are q analog\s to ^? :i* are obey$ by ! dissociation ( calcium c>bonate into c>bon dioxide & calcium oxide2 9 ea* case a c]ta9 temp]ature is associat$ ) a def9ite pressure1 no matt] :at ! relative or absolute am\nts ( ! respective sub/ances are4 ,& o!r examples 7 giv5 ( sy/ems :i* 7 app>5tly simil> 9 "*1 b :i* nev]!less behav$ 9 a diff]5t mann]4 ,! relations betwe5 ! v>i\s sy/ems1 h[ev]1 become p]fectly cle> & intelligible 9 ! light ( ! ,phase ,rule4 ,9 ! case fir/ m5tion$1 t ( wat] 9 equilibrium ) its vap\r1 we h "o compon5t--wat]--pres5t 9 two phases1 i4e4 9 two physically di/9ct =ms1 viz4 liquid & vap\r4 ,accord+ to ! ,phase ,rule1 !re=e1 s9ce ,c #a1 & ,p #b1 ! degree ( fre$om ,f is equal to #a #b - #b #a2 ! sy/em possesses "o degree ( fre$om1 z has already be5 /at$4 ,b 9 ! case ( ! second sy/em m5tion$ above !re are two compon5ts1 viz4 calcium oxide & c>bon dioxide 7p4 #ab71 & ?ree phases1 viz4 two solid phases1 ,ca,o & ,ca,c,o#c1 & ! gase\s phase1 ,,co#b4 ,! numb] ( degrees ( fre$om ( ! sy/em1 !re=e1 is #b #b - #c #a2 ?is sy/em1 !re=e1 also possesses "o degree ( fre$om4 ,we c n[ und]/& :y ^! two sy/ems behave 9 a simil> mann]2 bo? are univ>iant1 or possess only "o degree ( fre$om4 ,we %all !re=e expect a simil> behavi\r 9 ! case ( all univ>iant sy/ems1 no matt] h[ dissimil> ! sy/ems may outw>dly appe>4 ,simil>ly1 all biv>iant sy/ems w exhibit analog\s behavi\r2 & g5]ally1 sy/ems possess+ ! same degree ( fre$om w %[ a l behavi\r4 ,9 accordance ) ! ,phase ,rule1 !re=e1 we may classify ! diff]5t sy/ems :i* may be f\nd into inv>iant1 univ>iant1 biv>iant1 multiv>iant1 #ah accord+ to ! relation :i* obta9s betwe5 ! numb] ( ! compon5ts & ! numb] ( coexi/+ phases2 & we %all expect t 9 ea* case ! memb]s ( any p>ticul> gr\p w exhibit a uni=m behavi\r4 ,by ?is means we are enabl$ to obta9 an insight into ! g5]al behavi\r ( any sy/em1 s soon z we h det]m9$ ! numb] ( ! compon5ts & ! numb] ( ! coexi/+ phases4 ,! adoption ( ! ,phase ,rule = ! purposes ( classification has be5 ( great importance 9 /udy+ *anges 9 ! equilibrium exi/+ betwe5 diff]5t sub/ances2 = n only does x r5d] possible ! gr\p+ toge!r ( a l>ge numb] ( isolat$ ph5om5a1 b ! guidance x af=ds has l$ to ! discov]y ( new sub/ances1 has giv5 ! clue to ! conditions "u :i* ^! sub/ances c exi/1 & has l$ to ! recognition ( o!rwise unobs]v$ resemblances exi/+ betwe5 diff]5t sy/ems4 ,d$uction ( ! ,phase ,rule4--,9 ! prec$+ pages we h re/rict$ ourselves to ! /atem5t ( ! ,phase ,rule1 )\t giv+ any indication ( h[ x has be5 d$uc$4 ,at ! close ( ?is *apt]1 !re=e1 ! ma!matical d$uction ( ! g5]alization w be giv51 b 9 brief outl9e only1 ! read] be+ ref]r$ to works on ,!rmodynamics = a full] treatm5t ( ! subject4#ba ,all =ms ( en]gy c be resolv$ into two factors1 ! capacity factor & ! int5sity factor2 b = ! production ( equilibrium1 only ! int5sity factor is ( importance4 ,?us1 if two bodies hav+ ! same temp]ature are br\ght 9 contact ) ea* o!r1 !y w be 9 equilibrium z reg>ds heat en]gy1 no matt] :at may be ! am\nts ( heat 7capacity factor7 conta9$ 9 ei!r1 because ! int5sity factor--! temp]ature--is ! same4 ,b if ! temp]ature ( ! two bodies is diff]5t1 i4e4 if ! int5sity factor ( heat en]gy is diff]5t1 ! two bodies w no long] be 9 equilibrium2 b heat w pass f ! hott] to ! cold] until bo? h ! same temp]ature4 ,z ) heat en]gy1 s ) *emical en]gy4 ,if we h a sub/ance exi/+ 9 two diff]5t /ates1 or 9 two diff]5t #ai phases ( a sy/em1 equilibrium c occur only :5 ! int5sity factor ( *emical en]gy is ! same4 ,?is int5sity factor may be call$ ! *emical pot5tial2 & we c !re=e say t a sy/em w be 9 equilibrium :5 ! *emical pot5tial ( ea* compon5t is ! same 9 all ! phases 9 :i* ! compon5t occurs4 ,?us1 = example1 ice1 wat]1 & vap\r h1 at ! triple po9t1 ! same *emical pot5tial4 ,! pot5tial ( a compon5t 9 any phase dep5ds n only on ! composition ( ! phase1 b also on ! temp]ature & ! pressure 7or volume74 ,if1 !re=e1 we h a sy/em ( ,c compon5ts exi/+ 9 ,p phases1 !n1 9 ord] to fix ! composition ( unit mass ( ea* phase1 x is necess>y to "k ! masses ( 7,c - #a7 compon5ts 9 ea* ( ! phases4 ,z reg>ds ! composition1 !re=e1 ea* phase possesses 7,c - #a7 v>iables4 ,s9ce !re are ,p phases1 x foll[s t1 z reg>ds composition1 ! :ole sy/em possesses ,p7,c - #a7 v>iables4 ,besides ^! !re are1 h[ev]1 two o!r v>iables1 viz4 temp]ature & pressure1 s t altoge!r a sy/em ( ,c compon5ts 9 ,p phases possesses ,p7,c - #a7 #b v>iables4 ,9 ord] to def9e ! /ate ( ! sy/em completely1 x w be necess>y to h z _m equations z !re are v>iables4 ,if1 !re=e1 !re are few] equations ?an !re are v>iables1 !n1 accord+ to ! defici5cy 9 ! numb] ( ! equations1 "o or m ( ! v>iables w h an undef9$ value2 & values mu/ be assign$ to ^! v>iables be=e ! sy/em is entirely def9$4 ,! numb] ( ^! undef9$ values gives u ! v>iability or ! degree ( fre$om ( ! sy/em4 ,! equations by :i* ! sy/em is to be def9$ are obta9$ f ! relation%ip betwe5 ! pot5tial ( a compon5t & ! composition ( ! phase1 ! temp]ature & ! pressure4 ,fur!r1 z has already be5 /at$1 equilibrium occurs :5 ! pot5tial ( ea* compon5t is ! same 9 ! diff]5t phases 9 :i* x is pres5t4 ,if1 !re=e1 we *oose z /&>d "o ( ! phases 9 :i* all ! compon5ts occur1 !n 9 any o!r phase 9 equilibrium ) #bj x1 ! pot5tial ( ea* compon5t mu/ be ! same z 9 ! /&>d phase4 ,= ea* phase 9 equilibrium ) ! /&>d phase1 !re=e1 !re w be a def9ite equation ( /ate = ea* compon5t 9 ! phase2 s t1 if !re are ,p phases1 we obta9 = ea* compon5t 7,p - #a7 equations2 & = ,c compon5ts1 !re=e1 we obta9 ,c7,p - #a7 equations4 ,b we h se5 above t !re are ,p7,c - #a7 #b v>iables1 & z we h only ,c7,p - #a7 equations1 !re mu/ be ,p7,c - #a7 #b - ,c7,p - #a7 ,c #b - ,p v>iables undef9$4 ,t is to say1 ! degree ( fre$om 7,f7 ( a sy/em consi/+ ( ,c compon5ts 9 ,p phases is-- ,f ,c #b - ,p 99 99 99 99 99 #ba ,,*apt] ,,iii ,,typical ,,sy/ems ,,( ,,"o ,,compon5t ,a4 ,wat]4 ,= ! sake ( r5d]+ ! ,phase ,rule m readily intelligible1 & at ! same "t also = ! purpose ( obta9+ examples by :i* we may illu/rate ! g5]al behavi\r ( sy/ems1 we %all 9 ?is *apt] exam9e 9 detail ! behavi\r ( sev]al well-kn[n sy/ems consi/+ ( only "o compon5t4 ,! mo/ famili> examples ( equilibria 9 a "o-compon5t sy/em are ^? furni%$ by ! ?ree phases ( wat]1 viz4 ice1 wat]1 wat] vap\r4 ,! sy/em consi/s ( "o compon5t1 because all ?ree phases h ! same *emical composition1 repres5t$ by ! =mula ,h#b,o4 ,z ! crit]ion ( equilibrium we %all *oose a def9ite pressure1 & %all /udy ! v>iation ( ! pressure ) ! temp]ature2 & = ! purpose ( repres5t+ ! relation%ips :i* we obta9 we %all employ a temp]ature-pressure diagram1 9 :i* ! temp]atures are measur$ z abscissae & ! pressures z ord9ates4 ,9 su* a diagram inv>iant sy/ems w be repres5t$ by po9ts2 univ>iant sy/ems by l9es1 & biv>iant sy/ems by areas4 ,equilibrium betwe5 ,liquid & ,vap\r4 ,vaporization ,curve4--,consid] 9 ! fir/ place ! conditions = ! coexi/5ce ( liquid & vap\r4 ,accord+ to ! ,phase ,rule 7p4 #af71 a sy/em consi/+ ( "o compon5t 9 two phases has "o degree ( fre$om1 or is univ>iant4 ,we %\ld !re=e expect t x w be possible = liquid wat] to coexi/ ) wat] vap\r at diff]5t values ( temp]ature & #bb pressure1 b t if we arbitr>ily fix "o ( ! v>iable factors1 pressure1 temp]ature1 or volume 79 ! case ( a giv5 mass ( sub/ance71 ! /ate ( ! sy/em w !n be def9$4 ,if we fix1 say1 ! temp]ature1 !n ! pressure w h a def9ite value2 or if we adopt a c]ta9 pressure1 ! liquid & vap\r c coexi/ only at a c]ta9 def9ite temp]ature4 ,ea* temp]ature1 !re=e1 w correspond to a def9ite pressure2 & if 9 our diagram we jo9 by a cont9u\s l9e all ! po9ts indicat+ ! values ( ! pressure correspond+ to ! diff]5t temp]atures1 we %all obta9 a curve 7,fig4 #a7 repres5t+ ! v>iation ( ! pressure ) ! temp]ature4 ,?is is ! curve ( vap\r pressure1 or ! vaporization curve ( wat]4 ,illu/ration3 ,,fig4 #a4 ,n[1 ! results ( exp]im5t are q 9 agreem5t ) ! requirem5ts ( ! ,phase ,rule1 & at any giv5 temp]ature ! sy/em wat]--vap\r c exi/ 9 equilibrium only "u a def9ite pressure4 ,! vap\r pressure ( wat] at diff]5t temp]atures has be5 subject$ to c>eful measurem5t by ,magnus1#bb ,regnault1#bc ,ramsay & ,"y1#bd ,juhl91#be ,?ies5 & ,s*eel1#bf & o!rs4 ,9 ! foll[+ table ! values ( ! vap\r pressure f -#aj;deg to #ajj;deg are ^? calculat$ f ! measurem5ts ( ,regnault1 correct$ by ! measurem5ts ( ,wiebe & ,?ies5 & ,s*eel2#bg ^? f #abj;deg to #bgj;deg 7 det]m9$ #bc by ,ramsay & ,"y1 :ile ! values ( ! critical pressure & temp]ature are ^? det]m9$ by ,battelli4#bh ,,vap\r ,,pressure ,,( ,,wat]4 ---------------------------------------- ------------------------ ,temp]ature4 ,pressure 9 cm4 ,temp]ature4 ,pressure 9 cm4 m]cury4 m]cury4 ---------------------------------------- ------------------------ -#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 temp]ature7 ---------------------------------------- ------------------------ ,! pressure is1 ( c\rse1 indep5d5t ( ! relative or absolute volumes ( ! liquid & vap\r2 on increas+ ! volume at con/ant temp]ature1 a c]ta9 am\nt ( ! liquid w pass into vap\r1 & ! pressure w rega9 its =m] value4 ,if1 h[ev]1 ! pressure be p]man5tly ma9ta9$ at a value diff]5t f t correspond+ to ! temp]ature employ$1 !n ei!r all ! liquid w pass into vap\r1 or all ! vap\r w pass into liquid1 & we %all h ei!r vap\r alone or liquid alone4 ,upp] ,limit ( ,vaporization ,curve4--,on cont9u+ to add heat to wat] conta9$ 9 a clos$ vessel1 ! pressure ( ! vap\r w gradually increase4 ,s9ce ) increase ( pressure ! d5sity ( ! vap\r mu/ increase1 & s9ce ) rise ( temp]ature ! d5sity ( ! liquid mu/ decrease1 a po9t w be rea*$ at :i* ! d5sity ( liquid & vap\r become id5tical2 ! sy/em ceases to be het]og5e\s1 & passes into "o homog5e\s phase4 ,! temp]ature at :i* ?is occurs is call$ ! critical temp]ature4 ,to ?is temp]ature !re w1 ( c\rse1 correspond a c]ta9 def9ite pressure1 call$ ! critical pressure4 ,! curve repres5t+ ! #bd equilibrium betwe5 liquid & vap\r mu/1 !re=e1 end abruptly at ! critical po9t4 ,at temp]atures above ?is po9t no pressure1 h[ev] great1 c cause ! =mation ( ! liquid phase2 at temp]atures above ! critical po9t ! vap\r becomes a gas4 ,9 ! case ( wat]1 ! critical temp]ature is #cfd4c;deg1 & ! critical pressure #aid4f atm42 at ! po9t repres5t+ ^! conditions ! vap\r-pressure curve ( wat] mu/ cease4 ,sublimation ,curve ( ,ice4--,vap\r is giv5 (f n only by liquid wat]1 b also by solid wat]1 or ice4 ,t ?is is s is famili> to e "o ?r\gh ! fact t ice or sn[1 ev5 at temp]atures bel[ ! melt+ po9t1 gradually disappe>s 9 ! =m ( vap\r4 ,ev5 at temp]atures consid]ably l[] ?an #j;deg1 ! vap\r pressure ( ice1 al?\gh small1 is q appreciable2 & x is possible1 !re=e1 to h ice & vap\r coexi/+ 9 equilibrium4 ,:5 we inquire into ! conditions "u :i* su* a sy/em c exi/1 we see aga9 t we are deal+ ) a univ>iant sy/em--"o compon5t exi/+ 9 two phases--& t1 !re=e1 j z 9 ! case ( ! sy/em wat] & vap\r1 !re w be = ea* temp]ature a c]ta9 def9ite pressure ( ! vap\r1 & ?is pressure w be indep5d5t ( ! relative or absolute am\nts ( ! solid or vap\r pres5t1 & w dep5d solely on ! temp]ature4 ,fur!r1 j z 9 ! case ( ! vap\r pressure ( wat]1 ! condition ( equilibrium betwe5 ice & wat] vap\r w be repres5t$ by a l9e or curve %[+ ! *ange ( pressure ) ! temp]ature4 ,su* a curve1 repres5t+ ! conditions ( equilibrium betwe5 a solid & its vap\r1 is call$ a sublimation curve4 ,at temp]atures repres5t$ by any po9t on ?is curve1 ! solid 7ice7 w sublime or pass into vap\r )\t previ\sly fus+4 ,s9ce ice melts at #j;deg 7vide infra71 ! sublimation curve mu/ end at t temp]ature4 ,! foll[+ are ! values ( ! vap\r pressure ( ice betwe5 #j;deg & -#ej;deg4#cj #be ,,vap\r ,,pressure ,,( ,,ice4 ---------------------------------------- ----------------------- ,temp]ature4 ,pressure 9 mm4 ,temp]ature4 ,pressure 9 mm4 m]cury4 m]cury4 ---------------------------------------- -------------------- -#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 betwe5 ,ice & ,wat]4 ,curve ( ,fusion4--,!re is /ill ano!r univ>iant sy/em ( ! "o compon5t wat]1 ! exi/5ce ( :i*1 at def9ite values ( temp]ature & pressure1 ! ,phase ,rule all[s u to pr$ict4 ,?is is ! sy/em solid--liquid4 ,ice on be+ heat$ to a c]ta9 temp]ature melts & passes into ! liquid /ate2 & s9ce ?is sy/em solid--liquid is univ>iant1 !re w be = ea* temp]ature a c]ta9 def9ite pressure at :i* ice & wat] c coexi/ or be 9 equilibrium1 indep5d5tly ( ! am\nts ( ! two phases pres5t4 ,s9ce n[ ! temp]ature at :i* ! solid phase is 9 equilibrium ) ! liquid phase is kn[n z ! melt+ po9t or po9t ( fusion ( ! solid1 ! curve repres5t+ ! temp]atures & pressures at :i* ! solid & liquid are 9 equilibrium w repres5t ! *ange ( ! melt+ po9t ) ! pressure4 ,su* a curve is call$ ! curve ( fusion1 or ! melt+-po9t curve4 ,x 0 n until ! middle ( ! n9ete5? c5tury t ?is connection betwe5 ! pressure & ! melt+ po9t1 or ! *ange ( ! melt+ po9t ) ! pressure1 0 obs]v$4 ,! fir/ to recognize ! exi/5ce ( su* a relation%ip 0 ,james ,?omson1#ca :o 9 #ahdi %[$ t f !oretical consid]ations su* a relation%ip mu/ exi/1 & pr$ict$ t 9 ! case ( ice ! melt+ po9t w\ld be l[]$ by pressure4 ,?is pr$iction 0 fully confirm$ by 8 bro!r1 ,w4 ,?omson#cb 7,"l ,kelv971 :o f\nd t "u a pressure #bf ( #h4a atm4 ! melt+ po9t ( ice 0 -#j4jei;deg2 "u a pressure ( #af4h atm4 ! melt+ po9t 0 -#j4abi;deg4 ,! exp]im5ts :i* 7 fir/ made 9 ?is connection 7 m ( a qualitative nature1 b 9 rec5t ye>s c>eful measurem5ts ( ! influ5ce ( pressure on ! melt+ po9t ( ice h be5 made m especially by ,tammann1#cc & ! results obta9$ by him are giv5 9 ! foll[+ table & repres5t$ graphically 9 ,fig4 #b4 ,,fusion ,,pressure ,,( ,,ice4 ---------------------------------------- ----------------------------- ,pressure 9 kilogms4 p] ,*ange ( melt+ po9t = ,temp]ature4 sq4 cm4#cd an increase ( pressure ( #a kilogm4 p] 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 ---------------------------------------- ----------------------------- ,f ! numb]s 9 ! table & f ! figure we see t z ! pressure is increas$ ! melt+ po9t ( ice is l[]$2 b we also obs]ve t a v l>ge *ange ( pressure is requir$ 9 ord] to produce a v small *ange 9 ! melt+ po9t4 ,! curve1 !re=e1 is v /eep4 ,increase ( pressure by "o atmosph]e l[]s ! melt+ po9t by only #j4jjgf;deg1#ce or an increase ( pressure ( #ace atm4 is requir$ to produce a l[]+ ( ! melt+ po9t ( #a;deg4 ,we see fur!r t ! fusion curve b5ds slightly z ! pressure is increas$1 :i* signifies t ! v>iation ( #bg ! melt+ po9t ) ! pressure *anges2 at -#ae;deg1 :5 ! pressure is #afbe kilogm4 p] sq4 cm41 increase ( pressure by #a kilogm4 p] sq4 cm4 l[]s ! melt+ po9t by #j4jab;deg4 ,?is curvature ( ! fusion curve we %all lat] 7,*ap4 ,,iv47 see to be an almo/ univ]sal ph5om5on4 ,illu/ration3 ,,fig4 #b4 ,illu/ration3 ,,fig4 #c4 ,equilibrium betwe5 ,ice1 ,wat]1 & ,vap\r4 ,! ,triple ,po9t4--,on exam9+ ! vap\r-pressure curves ( ice & wat] 7,fig4 #c71 we see t at a temp]ature ( ab\t #j;deg & "u a pressure ( ab\t #d4f mm4 m]cury1 ! two curves cut4 ,at ?is po9t liquid wat] & solid ice are ea* 9 equilibrium ) vap\r at ! same pressure4 ,s9ce ?is is s1 !y mu/1 ( c\rse1 be 9 equilibrium #bh ) "o ano!r1 z exp]im5t also %[s4 ,at ?is po9t1 !re=e1 ice1 wat]1 & vap\r c be 9 equilibrium1 & z !re are ?ree phases pres5t1 ! po9t is call$ a triple po9t4#cf ,! triple po9t1 h[ev]1 does n lie exactly at #j;deg ,c41 = ?is temp]ature is def9$ z ! melt+ po9t ( ice "u atmosph]ic pressure4 ,at ! triple po9t1 h[ev]1 ! pressure is equal to ! vap\r pressure ( ice & wat]1 & ?is pressure1 z we see f ! tables on pp4 #ba & #bc1 is v ne>ly #d4f mm41 or almo/ #a atm4 less ?an 9 ! previ\s case4 ,n[1 we h j se5 t a *ange ( pressure ( #a atm4 corresponds to a *ange ( ! melt+ po9t ( #j4jjgf;deg2 ! melt+ po9t ( ice1 !re=e1 :5 "u ! pressure ( its own vap\r1 w be v ne>ly #j4jjgf;deg1 & ! pressure ( ! vap\r w be v slightly great] ?an #d4egi mm41 :i* is ! pressure at #j;deg 7p4 #ba74 ,! diff]5ce is1 h[ev]1 slight1 & may be neglect$ "h4 ,at ! temp]ature1 !n1 ( #j4jjgf;deg1 & "u a pressure ( #d4f mm4 ( m]cury1 ice1 wat]1 & vap\r w be 9 equilibrium2 ! po9t 9 our diagram repres5t+ ?is p>ticul> temp]ature & pressure is1 !re=e1 ! triple po9t ( ! sy/em ice--wat]--vap\r4 ,s9ce at ! triple po9t we h ?ree phases ( "o compon5t1 ! sy/em at ?is po9t is inv>iant--x possesses no degrees ( fre$om4 ,if ! temp]ature is *ang$1 ! sy/em w und]go alt]ation 9 su* a way t "o ( ! phases w disappe>1 & a univ>iant sy/em w result2 if heat be add$1 ice w melt1 & we %all h left wat] & vap\r2 if heat be ab/ract$1 wat] w freeze1 & we %all h left ice & vap\r2 if1 :5 ! temp]ature is alt]$1 ! pressure is kept con/ant1 !n we %all ultimately obta9 only "o phase 7see ,*ap4 ,,iv474 ,! triple po9t is n only ! po9t ( int]section ( ! vaporization & sublimation curves1 b x is also ! end-po9t ( ! fusion curve4 ,! fusion curve1 z we h se51 is ! curve ( equilibrium betwe5 ice & wat]2 & s9ce at ! triple po9t ice & wat] are ea* 9 equilibrium ) #bi vap\r ( ! same pressure1 !y mu/1 ( c\rse1 also be 9 equilibrium ) "o ano!r4 ,illu/ration3 ,,fig4 #d4 ,biv>iant ,sy/ems ( ,wat]4--,if we exam9e ,fig4 #d1 we see t ! curves ,,oa1 ,,ob1 ,,oc1 :i* repres5t diagrammatically ! conditions "u :i* wat] & vap\r1 ice & vap\r1 & wat] & ice are 9 equilibrium1 =m ! b\nd>ies ( ?ree fields1 or areas1 ,i41 ,,ii41 ,,iii4 ,^! areas1 n[1 repres5t ! conditions = ! exi/5ce ( ! s+le phases1 solid1 liquid1 & vap\r respectively4 ,at temp]atures & pressures repres5t$ by any po9t 9 ! field ,i41 solid only c exi/ z a /able phase4 ,s9ce we h "h "o compon5t 9 only "o phase1 ! sy/em is biv>iant1 & at any giv5 temp]ature1 !re=e1 ice c exi/ "u a s]ies ( pressures2 & "u any giv5 pressure1 at a s]ies ( temp]atures1 ^! pressures & temp]atures be+ limit$ only by ! curves ,,ob1 ,,oc4 ,simil>ly also ) ! areas ,,ii4 & ,,iii4 ,we see1 fur!r1 t ! diff]5t areas are ! regions ( /ability ( ! phase common to ! two curves by :i* ! area is enclos$4#cg ,?us1 ! phase common to ! two sy/ems #cj repres5t$ by ,,bo 7ice & vap\r71 & ,,oa 7wat] & vap\r7 is ! vap\r phase2 & ! area ,,boa is !re=e ! area ( ! vap\r phase4 ,simil>ly1 ,,boc is ! area ( ! ice phase1 & ,,coa ! area ( ! wat] phase4 ,sup]cool$ ,wat]4 ,meta/able ,/ate4--,:5 heat$ "u ! ord9>y atmosph]ic pressure1 ice melts :5 ! temp]ature rea*es #j;deg1 & x has s f> n be5 f\nd possible to raise ! temp]ature ( ice above ?is po9t )\t liquefaction tak+ place4 ,on ! o!r h&1 x has long be5 kn[n t wat] c be cool$ bel[ z]o )\t solidification occurr+4 ,?is 0 fir/ discov]$ 9 #agbd by ,fahr5heit1#ch :o f\nd t wat] c\ld be expos$ to a temp]ature ( -#i4d;deg )\t solidify+2 s soon1 h[ev]1 z a small p>ticle ( ice 0 br\ght 9 contact ) ! wat]1 cry/allization comm5c$4 ,sup]fus$ or sup]cool$ wat]--i4e4 wat] cool$ bel[ #j;deg--is un/able only 9 respect ( ! solid phase2 s long z ! pres5ce ( ! solid phase is c>efully avoid$1 ! wat] c be kept = any l5g? ( "t )\t solidify+1 & ! sy/em sup]cool$ wat] & vap\r behaves 9 e way l a /able sy/em4 ,a sy/em1 n[1 :i* 9 itself is /able1 & :i* becomes in/able only 9 contact ) a p>ticul> phase1 is said to be meta/able1 & ! region ?r\gh\t :i* ?is condition exi/s is call$ ! meta/able region4 ,sup]cool$ wat]1 !re=e1 is 9 a meta/able condition4 ,if ! sup]cool+ be c>ri$ bel[ a c]ta9 temp]ature1 solidification takes place spontane\sly )\t ! addition ( ! solid phase2 ! sy/em !n ceases to be meta/able1 & becomes in/able4 ,n only has wat] be5 cool$ to temp]atures consid]ably bel[ ! melt+ po9t ( ice1 b ! vap\r pressure ( ! sup]cool$ wat] has be5 measur$4 ,x is ( int]e/ & importance1 n[1 to see :at relation%ip exi/s betwe5 ! vap\r pressure ( ice & t ( sup]cool$ wat] at ! same temp]ature4 ,?is relation%ip is cle>ly %[n by ! numb]s 9 ! foll[+ table1#ci & is repres5t$ 9 ,fig4 #c1 #ca p4 #bg41 & diagrammatically 9 ,fig4 #d1 ! vap\r pressures ( sup]cool$ wat] be+ repres5t$ by ! curve ,,oa'1 :i* is ! unbrok5 cont9uation ( ,,ao4 ,,vap\r ,,pressure ,,( ,,ice ,,& ,,( ,,sup]cool$ ,,wat]4 ---------------------------------------- ----------------------------- ,pressure 9 mm4 m]cury4 ---------------------------------------- -------------- ,temp]ature4 ,wat]4 ,ice4 ,diff]5ce4 ---------------------------------------- ----------------------------- #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 temp]atures bel[ #j;deg 7m correctly #j4jjgf;deg71 at :i* temp]ature wat] & ice h ! same vap\r pressure1 ! vap\r pressure ( sup]cool$ wat] is great] ?an t ( ice at ! same temp]ature4 ,f ! relative positions ( ! curves ,,ob & ,,oa 7,fig4 #d7 we see t at all temp]atures above #j;deg1 ! 7meta/able7 sublimation curve ( ice1 if x c\ld be obta9$1 w\ld be high] ?an ! vaporization curve ( wat]4 ,?is %[s1 !re=e1 t at #j;deg a break mu/ occur 9 ! curve ( /ates1 & t 9 ! neighb\rhood ( ?is break ! curve above t po9t mu/ asc5d less rapidly ?an ! curve bel[ ! break4 ,s9ce1 h[ev]1 ! diff]5ces 9 ! vap\r pressures ( sup]cool$ wat] & ( ice are v small1 ! *ange 9 ! direction ( ! vap\r-pressure curve on pass+ f ice to wat] 0 at fir/ n obs]v$1 & ,regnault reg>d$ ! sublimation curve z pass+ cont9u\sly into #cb ! vaporization curve4 ,! exi/5ce ( a break 01 h[ev]1 %[n by ,james ,?omson#da & by ,kir*h(f#db to be dem&$ by !rmo-dynamical consid]ations1 & ! pr$iction ( !ory 0 aft]w>ds realiz$ exp]im5tally by ,ramsay & ,"y 9 _! det]m9ations ( ! vap\r pressure ( wat] & ice1 z well z 9 ! case ( o!r sub/ances4#dc ,f :at has j be5 said1 we c readily und]/& :y ice & wat] _c exi/ 9 equilibrium bel[ #j;deg4 ,=1 suppose we h ice & wat] 9 ! same clos$ space1 b n 9 contact ) "o ano!r1 !n s9ce ! vap\r pressure ( ! sup]cool$ wat] is high] ?an t ( ice1 ! vap\r ( ! =m] mu/ be sup]saturat$ 9 contact ) ! latt]2 vap\r mu/1 !re=e1 cond5se on ! ice2 & 9 ?is way !re w be a sl[ di/illation f ! wat] to ! ice1 until at la/ all ! wat] w h disappe>$1 & only ice & vap\r rema94#dd ,o!r ,sy/ems ( ! ,sub/ance ,wat]4--,we h ?us f> discuss$ only ^? sy/ems :i* are con/itut$ by ! ?ree phases--ice1 wat]1 & wat] vap\r4 ,x has1 h[ev]1 be5 rec5tly f\nd t at a l[ temp]ature & "u a high pressure ord9>y ice c pass into two o!r cry/all9e v>ieties1 call$ by ,tammann#de ice ,,ii4 & ice ,,iii41 ord9>y ice be+ ice ,i4 ,accord+ to ! ,phase ,rule1 n[1 s9ce ea* ( ^! solid =ms con/itutes a sep>ate phase 7p4 #i71 x w be possible to h ! foll[+ 7& m7 sy/ems ( wat]1 9 addition to ^? already /udi$1 viz4 wat]1 ice ,i41 ice ,,ii42 wat]1 ice ,i41 ice ,,iii42 wat]1 ice ,,ii41 ice ,,iii41 =m+ inv>iant sy/ems & exi/+ 9 equilibrium only at a def9ite triple po9t2 fur!r1 wat]1 ice ,,ii42 wat]1 ice ,,iii42 ice ,i41 ice ,,ii42 ice ,i41 ice ,,iii42 ice ,,ii41 ice ,,iii41 =m+ univ>iant sy/ems1 exi/+1 !re=e1 at def9ite correspond+ values ( #cc temp]ature & pressure2 & la/ly1 ! biv>iant sy/ems1 ice ,,ii4 & ice ,,iii4 ,sev]al ( ^! sy/ems h be5 inve/igat$ by ,tammann4 ,! triple po9t = wat]1 ice ,i41 ice ,,iii41 lies at -#bb;deg1 & a pressure ( #bbjj kilogms4 p] sq4 cm4 7#bacj atm471 z indicat$ 9 ,fig4 #b1 p4 #bg4df ,9 contra/ ) ! behavi\r ( ord9>y ice1 ! temp]ature ( equilibrium 9 ! case ( wat]--ice ,,ii41 & wat]--ice ,,iii41 is rais$ by increase ( pressure4 ,b4 ,sulphur4 ,polymorphism4--,ref]5ce has j be5 made to ! fact t ice c exi/ n only 9 ! ord9>y =m1 b 9 at lea/ two o!r cry/all9e v>ieties4 ,?is ph5om5on1 ! exi/5ce ( a sub/ance 9 two or m diff]5t cry/all9e =ms1 is call$ polymorphism4 ,polymorphism 0 fir/ obs]v$ by ,mits*]li*#dg 9 ! case ( sodium phosphate1 & lat] 9 ! case ( sulphur4 ,to ^! two cases o!rs 7 soon add$1 at fir/ ( inorganic1 & lat] ( organic sub/ances1 s t polymorphism is n[ recogniz$ z ( v frequ5t occurr5ce inde$4#dh ,^! v>i\s =ms ( a sub/ance diff] n only 9 cry/all9e %ape1 b also 9 melt+ po9t1 specific gravity1 & o!r physical prop]ties4 ,9 ! liquid /ate1 h[ev]1 ! diff]5ces d n exi/4 ,accord+ to our def9ition ( phases 7p4 #i71 ea* ( ^! polymorphic =ms con/itutes a sep>ate phase ( ! p>ticul> sub/ance4 ,z is readily app>5t1 ! numb] ( possible sy/ems =m$ ( "o compon5t may be consid]ably increas$ :5 t compon5t is capable ( exi/+ 9 diff]5t cry/all9e =ms4 ,we h1 !re=e1 to inquire :at are ! conditions "u :i* diff]5t polymorphic =ms c coexi/1 ei!r alone or 9 pres5ce ( ! liquid & vap\r phase4 ,= ! purpose ( illu/rat+ ! g5]al behavi\r ( su* sy/ems1 we %all /udy ! sy/ems =m$ by ! diff]5t cry/all9e =ms ( sulphur1 t91 & b5zoph5one4 #cd ,sulphur exi/s 9 two well-kn[n cry/all9e =ms--rhombic1 or octah$ral1 & monocl9ic1 or prismatic sulphur4 ,( ^!1 ! =m] melts at #aad4e;deg2 ! latt] at #abj;deg4#di ,fur!r1 at ! ord9>y temp]ature1 rhombic sulphur c exi/ un*ang$1 :]eas1 on be+ heat$ to temp]atures some:at bel[ ! melt+ po9t1 x passes into ! prismatic v>iety4 ,on ! o!r h&1 at temp]atures above #if;deg1 prismatic sulphur c rema9 un*ang$1 :]eas at ! ord9>y temp]ature x passes sl[ly into ! rhombic =m4 ,if1 n[1 we exam9e ! case ( sulphur ) ! help ( ! ,phase ,rule1 we see t ! foll[+ sy/ems are !oretically possible3-- ,i4 ,biv>iant ,sy/ems3 ,"o compon5t 9 "o phase4 7a7 ,rhombic sulphur4 7b7 ,monocl9ic sulphur4 7c7 ,sulphur vap\r4 7d7 ,liquid sulphur4 ,,ii4 ,univ>iant ,sy/ems3 ,"o compon5t 9 two phases4 7a7 ,rhombic sulphur & vap\r4 7b7 ,monocl9ic sulphur & vap\r4 7c7 ,rhombic sulphur & liquid4 7d7 ,monocl9ic sulphur & liquid4 7e7 ,rhombic & monocl9ic sulphur4 7f7 ,liquid & vap\r4 ,,iii4 ,inv>iant ,sy/ems3 ,"o compon5t 9 ?ree phases4 7a7 ,rhombic & monocl9ic sulphur & vap\r4 7b7 ,rhombic sulphur1 liquid & vap\r4 7c7 ,monocl9ic sulphur1 liquid & vap\r4 7d7 ,rhombic & monocl9ic sulphur & liquid4 ,illu/ration3 ,,fig4 #e4 ,triple ,po9t--,rhombic & ,monocl9ic ,sulphur & ,vap\r4 ,transition ,po9t4--,9 ! case ( ice1 wat] & vap\r1 we saw t at ! triple po9t ! vap\r pressures ( ice & wat] are equal2 bel[ ?is po9t1 ice is /able2 above ?is po9t1 wat] is /able4 ,we saw1 fur!r1 t bel[ #j;deg ! vap\r pressure ( ! /able sy/em is l[] ?an t ( ! meta/able1 & !re=e t at ! triple po9t !re is a break 9 ! vap\r pressure curve ( su* a k9d t above #ce ! triple po9t ! vap\r-pressure curve asc5ds m sl[ly ?an bel[ x4 ,n[1 al?\gh ! vap\r pressure ( solid sulphur has n be5 det]m9$1 we c nev]!less consid] t x does possess a c]ta91 ev5 if v small1 vap\r pressure1#ej & t at ! temp]ature at :i* ! vap\r pressures ( rhombic & monocl9ic sulphur become equal1 we c h ^! two solid =ms exi/+ 9 equilibrium ) ! vap\r4 ,bel[ t po9t only "o =m1 t ) ! l[] vap\r pressure1 w be /able2 above t po9t only ! o!r =m w be /able4 ,on pass+ ?r\gh ! triple po9t1 !re=e1 !re w be a *ange ( ! "o =m into ! o!r4 ,?is po9t is repres5t$ 9 our diagram 7,fig4 #e7 by ! po9t ,o1 ! two curves ,,ao & ,,ob repres5t+ diagrammatically ! vap\r pressures ( rhombic & monocl9ic sulphur respectively4 ,if ! vap\r phase is abs5t & ! sy/em ma9ta9$ "u a con/ant pressure1 e4g4 #cf atmosph]ic pressure1 !re w also be a def9ite temp]ature at :i* ! two solid =ms are 9 equilibrium1 & on pass+ ?r\gh :i* complete & rev]sible trans=mation ( "o =m into ! o!r occurs4 ,?is temp]ature1 :i* ref]s to equilibrium 9 abs5ce ( ! vap\r phase1 is kn[n z ! transition temp]ature or inv]sion temp]ature4 ,7 we dep5d5t on measurem5ts ( pressure & temp]ature1 ! det]m9ation ( ! transition po9t might be a matt] ( great difficulty4 ,:5 we consid]1 h[ev]1 t ! o!r physical prop]ties ( ! solid phases1 e4g4 ! d5sity1 und]go an abrupt *ange on pass+ ?r\gh ! transition po9t1 ow+ to ! trans=mation ( "o =m into ! o!r1 !n any me?od by :i* ?is abrupt *ange 9 ! physical prop]ties c be detect$ may be employ$ = det]m9+ ! transition po9t4 ,a consid]able numb] ( su* me?ods h be5 devis$1 & a description ( ! mo/ important ( ^! is giv5 9 ! ,app5dix4 ,9 ! case ( sulphur1 ! transition po9t ( rhombic into monocl9ic sulphur 0 f\nd by ,rei*]#ea to lie at #ie4e;deg4 ,bel[ ?is temp]ature ! octah$ral1 above x ! monocl9ic1 is ! /able =m4 ,cond5s$ ,sy/ems4--,we h already se5 t 9 ! *ange ( ! melt+ po9t ( wat] ) ! pressure1 a v great increase ( ! latt] 0 necess>y 9 ord] to produce a comp>atively small *ange 9 ! temp]ature ( equilibrium4 ,?is is a *>act]i/ic ( all sy/ems f :i* ! vap\r phase is abs5t1 & :i* are compos$ only ( solid & liquid phases4 ,su* sy/ems are call$ cond5s$ sy/ems1#eb & 9 det]m9+ ! temp]ature ( equilibrium ( su* sy/ems1 practically ! same po9t w be obta9$ :e!r ! measurem5ts are c>ri$ out "u atmosph]ic pressure or "u ! pressure ( ! vap\r ( ! solid or liquid phases4 ,! transition po9t1 !re=e1 z det]m9$ 9 op5 vessels at atmosph]ic pressure1 w diff] only by a v slight am\nt f ! triple po9t1 or po9t at :i* ! two solid or liquid phases are 9 equilibrium "u ! pressure ( _! vap\r4 #cg ,! det]m9ation ( ! transition po9t is !reby greatly simplifi$4 ,susp5d$ ,trans=mation4--,9 _m respects ! transition po9t ( two solid phases is analog\s to ! melt+ po9t ( a solid1 or po9t at :i* ! solid passes into a liquid4 ,9 bo? cases ! *ange ( phase is associat$ ) a def9ite temp]ature & pressure 9 su* a way t bel[ ! po9t ! "o phase1 above ! po9t ! o!r phase1 is /able4 ,! transition po9t1 h[ev]1 diff]s 9 s f> f a po9t ( fusion1 t :ile x is possible to sup]cool a liquid1 no def9ite case is kn[n :]e ! solid has be5 heat$ above ! triple po9t )\t pass+ into ! liquid /ate4 ,trans=mation1 !re=e1 is susp5d$ only on "o side ( ! melt+ po9t4 ,9 ! case ( two solid phases1 h[ev]1 ! transition po9t c be ov]/epp$ 9 bo? directions1 s t ea* phase c be obta9$ 9 ! meta/able condition4 ,9 ! case ( sup]cool$ wat]1 fur!r1 we saw t ! introduction ( ! /able1 solid phase caus$ ! spe$y trans=mation ( ! meta/able to ! /able condition ( equilibrium2 b 9 ! case ( two solid phases ! *ange f ! meta/able to ! /able modification may occur ) great sl[ness1 ev5 9 pres5ce ( ! /able =m4 ,?is t>d9ess ) :i* ! /able condition ( equilibrium is rea*$ greatly increases 9 _m cases ! difficulty ( accurately det]m9+ ! transition po9t4 ,! ph5om5a ( susp5d$ trans=mation w1 h[ev]1 receive a full] discussion lat] 7p4 #fh74 ,transition ,curve--,rhombic & ,monocl9ic ,sulphur4--,j z we f\nd ! melt+ po9t ( ice to v>y ) ! pressure1 s also d we f9d t *ange ( pressure causes an alt]ation 9 ! transition po9t4 ,9 ! case ( ! transition po9t ( rhombic into monocl9ic sulphur1 increase ( pressure by #a atm4 raises ! transition po9t by #j4jd;deg-#j4je;deg4#ec ,! transition curve1 or curve repres5t+ ! *ange ( ! transition po9t ) pressure1 w !re=e slope to ! "r away f ! pressure axis4 ,?is is curve ,,oc 7,fig4 #e74 #ch ,triple ,po9t--,monocl9ic ,sulphur1 ,liquid1 & ,vap\r4 ,melt+ ,po9t ( ,monocl9ic ,sulphur4--,above #ie4e;deg1 monocl9ic sulphur is1 z we h se51 ! /able =m4 ,on be+ heat$ to #abj;deg1 "u atmosph]ic pressure1 x melts4 ,?is temp]ature is1 !re=e1 ! po9t ( equilibrium betwe5 monocl9ic sulphur & liquid sulphur "u atmosph]ic pressure4 ,s9ce we are deal+ ) a cond5s$ sy/em1 ?is temp]ature may be reg>d$ z v ne>ly t at :i* ! solid & liquid are 9 equilibrium ) _! vap\r1 i4e4 ! triple po9t1 solid 7monocl9ic7--liquid--vap\r4 ,?is po9t is repres5t$ 9 ! diagram by ,b4 ,triple ,po9t--,rhombic & ,monocl9ic ,sulphur & ,liquid4--,9 contra/ ) t ( ice1 ! fusion po9t ( monocl9ic sulphur is rais$ by increase ( pressure1 & ! fusion curve1 !re=e1 slopes to ! "r4 ,! transition curve ( rhombic & monocl9ic sulphur1 z we h se51 also slopes to ! "r1 & m s ?an ! fusion curve ( monocl9ic sulphur4 ,!re w1 !re=e1 be a c]ta9 pressure & temp]ature at :i* ! two curves w cut4 ,?is po9t lies at #aea;deg1 & a pressure ( #acbj kilogm4 p] sq4 cm41 or ab\t #abhh atm4#ed ,x1 !re=e1 =ms ano!r triple po9t1 ! exi/5ce ( :i* _h be5 pr$ict$ by ,roozeboom1#ee at :i* rhombic & monocl9ic sulphur are 9 equilibrium ) liquid sulphur4 ,x is repres5t$ 9 our diagram by ! po9t ,c4 ,beyond ?is po9t monocl9ic sulphur ceases to exi/ 9 a /able condition4 ,at temp]atures & pressures above ?is triple po9t1 rhombic sulphur w be ! /able modification1 & ?is fact is ( m9]alogical int]e/1 because x expla9s ! occurr5ce 9 nature ( well-=m$ rhombic cry/als4 ,"u ord9>y conditions1 prismatic sulphur sep>ates out on cool+ fus$ sulphur1 b at temp]atures above #aea;deg & "u pressures great] ?an #abhh atm41 ! rhombic =m w\ld be produc$4#ef ,triple ,po9t--,rhombic ,sulphur1 ,liquid1 & ,vap\r4 ,meta/able ,triple ,po9t4--,on acc\nt ( ! sl[ness ) #ci :i* trans=mation ( "o =m into ! o!r takes place on pass+ ! transition po9t1 x has be5 f\nd possible to heat rhombic sulphur up to its melt+ po9t 7#aad4e;deg74 ,at ?is temp]ature1 n only is rhombic sulphur 9 a meta/able condition1 b ! liquid is also meta/able1 its vap\r pressure be+ great] ?an t ( solid monocl9ic sulphur4 ,?is po9t is repres5t$ 9 our diagram by ! po9t b4 ,f ! relative positions ( ! meta/able melt+ po9t ( rhombic sulphur & ! /able melt+ po9t ( monocl9ic sulphur at #abj;deg1 we see t1 ( ! two =ms1 ! meta/able =m has ! l[] melt+ po9t4 ,?is1 ( c\rse1 is valid only = ! relative /ability 9 ! neighb\rhood ( ! melt+ po9t2 = we h already le>n$ t at l[] temp]atures rhombic sulphur is ! /able1 monocl9ic sulphur ! meta/able 7or un/able7 =m4 ,fusion ,curve ( ,rhombic ,sulphur4--,l any o!r melt+ po9t1 t ( rhombic sulphur w be displac$ by increase ( pressure2 increase ( pressure raises ! melt+ po9t1 & we c !re=e obta9 a meta/able fusion curve repres5t+ ! conditions "u :i* rhombic sulphur is 9 equilibrium ) liquid sulphur4 ,?is meta/able fusion curve mu/ pass ?r\gh ! triple po9t = rhombic sulphur--monocl9ic sulphur--liquid sulphur1 & on pass+ ?is po9t x becomes a /able fusion curve4 ,! cont9uation ( ?is curve1 !re=e1 above #aea;deg =ms ! /able fusion curve ( rhombic sulphur 7curve ,,cd74 ,^! curves h be5 inve/igat$ at high pressures by ,tammann1 & ! results are repres5t$ accord+ to scale 9 ,fig4 #f1eg a be+ ! curve = monocl9ic sulphur & liquid2 b1 t = rhombic sulphur & liquid2 & c1 t = rhombic & monocl9ic sulphur4 ,biv>iant ,sy/ems4--,j z 9 ! case ( ! diagram ( /ates ( wat]1 ! areas 9 ,fig4 #e repres5t ! conditions = ! /able exi/5ce ( ! s+le phases3 rhombic sulphur 9 ! area to ! left ( ,,aocd2 monocl9ic sulphur 9 ! area ,,obc2 liquid sulphur 9 ! area ,,ebcd2 sulphur vap\r bel[ ! curves ,,aobe4 ,z c be se5 f ! diagram1 #dj ! exi/5ce ( monocl9ic sulphur is limit$ on all sides1 its area be+ b\nd$ by ! curves ,,ob1 ,,oc1 ,,bc4 ,at any po9t outside ?is area1 monocl9ic sulphur c exi/ only 9 a meta/able condition4 ,illu/ration3 ,,fig4 #f4 ,o!r cry/all9e =ms ( sulphur h be5 obta9$1#eh s t ! exi/5ce ( o!r sy/ems ( ! "o-compon5t sulphur besides ^? already describ$ is possible4 ,ref]5ce w be made to ^! lat] 7p4 #ea74 #da ,c4 ,t94 ,ano!r sub/ance capable ( exi/+ 9 m ?an "o cry/all9e =m1 is ! metal t91 & al?\gh ! g5]al behavi\r1 s f> z /udi$1 is analog\s to t ( sulphur1 a %ort acc\nt ( ! two v>ieties ( t9 may be giv5 "h1 n only on acc\nt ( _! metallurgical int]e/1 b also on acc\nt ( ! importance :i* ! ph5om5a possess = ! employm5t ( ?is metal 9 ev]yday life4 ,aft] a w9t] ( extreme sev]ity 9 ,russia 7#ahfg-ahfh71 ! some:at unpleasant discov]y 0 made t a numb] ( blocks ( t91 :i* _h be5 /or$ 9 ! ,cu/oms ,h\se at ,/4 ,pet]sburg1 _h und]gone dis9tegration & crumbl$ to a grey p[d]4#ei ,t t9 und]goes *ange on exposure to extreme cold 0 kn[n1 h[ev]1 be=e t "t1 ev5 z f> back z ! "t ( ,ari/otle1 :o spoke ( ! t9 z melt+4#fj ,ludicr\s z t t]m may n[ appe>1 ,ari/otle nev]!less unconsci\sly employ$ a /rik+ly accurate analogy1 = ! conditions "u :i* ord9>y :ite t9 passes into ! grey modification are1 9 _m ways1 q analog\s to ^? "u :i* a sub/ance passes f ! solid to ! liquid /ate4 ,! k ( ?is 01 h[ev]1 beyond ! wisdom ( ! ,greek philosoph]4 ,= _m ye>s !re exi/$ consid]able confusion bo? z to ! conditions "u :i* ! trans=mation ( :ite t9 into its allotropic modification occurs1 & to ! reason ( ! *ange4 ,"u ! guidance ( ! ,phase ,rule1 h[ev]1 ! confusion :i* obta9$ has be5 cle>$ away1 & ! my/]i\s behavi\r ( t9 br\ght into accord ) o!r ph5om5a ( trans=mation4#fa ,transition ,po9t4--,j z 9 ! case ( sulphur1 s also 9 ! case ( t91 !re is a transition po9t above :i* ! #db "o =m1 ord9>y :ite t91 & bel[ :i* ! o!r =m1 grey t91 is ! /able v>iety4 ,9 ! case ( ?is metal1 ! transition po9t 0 f\nd by ,coh5 & van ,eyk1 :o employ$ bo? ! dilatometric & ! electrical me?ods 7,app5dix7 to be #bj;deg4 ,bel[ ?is temp]ature1 grey t9 is ! /able =m4 ,b1 z we h se5 9 ! case ( sulphur1 ! *ange ( ! meta/able into ! /able solid phase occurs ) consid]able sl[ness1 & ?is behavi\r is f\nd also 9 ! case ( t94 ,7 x n s1 we %\ld n be able to use ?is metal = ! _m purposes to :i* x is appli$ 9 ev]yday life2 =1 ) ! exception ( a comp>atively small numb] ( days 9 ! ye>1 ! temp]ature ( our climate is bel[ #bj;deg1 & :ite t9 is1 !re=e1 at ! ord9>y temp]ature1 9 a meta/able condition4 ,! *ange1 h[ev]1 into ! /able =m at ! ord9>y temp]ature1 al?\gh sl[1 nev]!less takes place1 z is %[n by ! p>tial or entire conv]sion ( articles ( t9 :i* h la9 buri$ = sev]al hundr$s ( ye>s4 ,on l[]+ ! temp]ature1 ! velocity ) :i* ! trans=mation ( ! t9 occurs is increas$1 & ,coh5 & van ,eyk f\nd t ! temp]ature ( maximum velocity is ab\t -#ej;deg4 ,contact ) ! /able =m w1 ( c\rse1 facilitate ! trans=mation4 ,! *ange ( :ite t9 into grey takes place also ) increas$ velocity 9 pres5ce ( a solution ( t9 ammonium *loride 7p9k salt71 :i* is able to dissolve small quantities ( t94 ,9 pres5ce ( su* a solution also1 x 0 f\nd t ! temp]ature at :i* ! velocity ( trans=mation 0 greate/ 0 rais$ to #j;deg4 ,at ?is temp]ature1 :ite t9 9 contact ) a solution ( t9 ammonium *loride1 & ! grey modification1 und]goes trans=mation to an appreciable ext5t 9 ! c\rse ( a few days4 ,fig4 #g is a photograph ( a piece ( :ite t9 und]go+ trans=mation into ! grey v>iety4#fb ,! bright surface ( ! t9 becomes cov]$ ) a numb] ( w>ty masses1 =m$ ( ! less d5se grey =m1 & ! numb] & size ( ^! cont9ue to gr[ until ! :ole ( ! :ite t9 has pass$ #dc into a grey p[d]4 ,on acc\nt ( ! appe>ance :i* is "h se51 ?is trans=mation ( t9 has be5 call$ by ,coh5 ! t9 plague4 ,illu/ration3 ,,fig4 #g4 #dd ,enantiotropy & ,monotropy4--,9 ! case ( sulphur & t91 we h met ) two sub/ances exi/+ 9 polymorphic =ms1 & we h also le>n$ t ^! =ms exhibit a def9ite transition po9t at :i* _! relative /ability is rev]s$4 ,ea* =m1 !re=e1 possesses a def9ite range ( /able exi/5ce1 & is capable ( und]go+ trans=mation into ! o!r1 at temp]atures above or bel[ t ( ! transition po9t4 ,ano!r class ( dimorph\s sub/ances is1 h[ev]1 met ) z1 = in/ance1 9 ! case ( ! well-kn[n comp\nds iod9e mono*loride & b5zoph5one4 ,ea* cry/all9e =m has its own melt+ po9t1 ! dimorph\s =ms ( iod9e mono*loride melt+ at #ac4i;deg & #bg4b;deg1#fc & ^? ( b5zoph5one at #bf;deg & #dh;deg4#fd ,?is class ( sub/ance diff]s f t :i* we h already /udi$ 7e4g4 sulphur & t971 9 t at all temp]atures up to ! melt+ po9t1 only "o ( ! =ms is /able1 ! o!r be+ meta/able4 ,!re is1 !re=e1 no transition po9t1 & trans=mation ( ! cry/all9e =ms c be obs]v$ only 9 "o direction4 ,^! two classes ( ph5om5a are di/+ui%$ by ! names enantiotropy & monotropy2 enantiotropic sub/ances be+ su* t ! *ange ( "o =m into ! o!r is a rev]sible process 7e4g4 rhombic sulphur into monocl9ic1 & monocl9ic sulphur into rhombic71 & monotropic sub/ances1 ^? 9 :i* ! trans=mation ( ! cry/all9e =ms is irrev]sible4 ,illu/ration3 ,,fig4 #h4 ,illu/ration3 ,,fig4 #i4 ,^! diff]5ces 9 ! behavi\r c be expla9$ v well 9 _m cases by suppos+ t 9 ! case ( enantiotropic sub/ances ! transition po9t lies bel[ ! melt+ po9t1 :ile 9 ! case ( monotropic sub/ances1 x lies above ! melt+ po9t4#fe ,^! conditions w\ld be repres5t$ by ! ,figs4 #h & #i4 ,9 ^! two figures1 ,o#c is ! transition po9t1 ,o#a & ,o#b ! melt+ po9ts ( ! meta/able & /able =ms #de respectively4 ,f ,fig4 #i we see t ! cry/all9e =m ,i4 at all temp]atures up to its melt+ po9t is meta/able ) respect to ! =m ,,ii4 ,9 su* cases ! transition po9t c\ld be rea*$ only at high] pressures4 ,al?\gh1 z already /at$1 ?is explanation suffices = _m cases1 x does n prove t 9 all cases ( monotropy ! transition po9t is above ! melt+ po9t ( ! two =ms4 ,x is also q possible t ! transition po9t may lie bel[ ! melt+ po9ts2#ff 9 ?is case we h :at is kn[n z pseudomonotropy4 ,x is possible t graphite & diamond1#fg p]haps also ! two =ms ( phosphorus1 /& 9 ! relation ( pseudomonotropy 7v4 p4 #di74 ,! disposition ( ! curves 9 ,figs4 #h & #i also expla9s ! ph5om5on sometimes met )1 especially 9 organic *emi/ry1 t ! sub/ance fir/ melts1 !n solidifies1 & remelts at a high] temp]ature4 ,on aga9 det]m9+ ! melt+ po9t aft] re-solidification1 only ! high] melt+ po9t is obta9$4 ,! explanation ( su* a behavi\r is1 t if ! det]m9ation ( ! melt+ po9t is c>ri$ out rapidly1 ! po9t ,o#a1 ! melt+ po9t ( ! meta/able solid =m1 may be realiz$4 ,at ?is temp]ature1 h[ev]1 ! liquid is meta/able ) respect to ! /able solid =m1 & if ! temp]ature is #df n all[$ to rise above ! melt+ po9t ( ! latt]1 ! liquid may solidify4 ,! /able solid modification ?us obta9$ w melt only at a high] temp]ature4 ,d4 ,phosphorus4 ,an int]e/+ case ( a monotropic dimorph\s sub/ance is f\nd 9 phosphorus1 :i* occurs 9 two cry/all9e =ms2 :ite phosphorus belong+ to ! regul> sy/em1 & r$ phosphorus belong+ to ! hexagonal sy/em4 ,f det]m9ations ( ! vap\r pressures ( liquid :ite phosphorus1 & ( solid r$ phosphorus1#fh x 0 f\nd t ! vap\r pressure ( r$ phosphorus 0 consid]ably l[] ?an t ( liquid :ite phosphorus at ! same temp]ature1 ! values obta9$ be+ giv5 9 ! foll[+ table4 ,,vap\r ,,pressures ,,( ,,:ite ,,& ,,r$ ,,phosphorus4 ---------------------------------------- --------------------------------- ,vap\r pressure ( liquid :ite phosphorus4 ,vap\r pressure ( r$ phosphorus4 ---------------------------------------- -------------------------------- ,temp]ature4 ,pressure ,temp]ature4 ,pressure ,temp]ature4 ,pressure 9 cm4 9 atm4 9 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 ---------------------------------------- --------------------------------- ,^! values are also repres5t$ graphically 9 ,fig4 #aj4 ,illu/ration3 ,,fig4 #aj4 ,at all temp]atures above ab\t #bfj;deg1 trans=mation ( ! :ite into ! r$ modification takes place ) appreciable velocity1 & ?is velocity increases z ! temp]ature is rais$4 ,ev5 at l[] temp]atures1 e4g4 at ! ord9>y temp]ature1 ! velocity ( trans=mation is increas$ "u ! influ5ce #dg ( light1#fi or by ! pres5ce ( c]ta9 sub/ances1 e4g4 iod9e1#gj j z ! velocity ( trans=mation ( :ite t9 into ! grey modification 0 increas$ by ! pres5ce ( a solution ( t9 ammonium *loride 7p4 #dj74 ,at ! ord9>y temp]ature1 !re=e1 :ite phosphorus mu/ be consid]$ z ! less /able 7meta/able7 =m1 = al?\gh x c exi/ 9 contact ) r$ phosphorus = a long p]iod1 its vap\r pressure1 z we h se51 is great] ?an t ( ! r$ modification1 & also1 its solubility 9 diff]5t solv5ts is great]#ga ?an t ( ! r$ modification2 z we %all f9d lat]1 ! solubility ( ! meta/able =m is always great] ?an t ( ! /able4 ,! relation%ips :i* are met ) 9 ! case ( phosphorus c be be/ repres5t$ by ! diagram1 ,fig4 #aa4gb ,9 ?is figure1 ,,bo#a repres5ts ! conditions ( equilibrium ( ! univ>iant sy/em r$ phosphorus & vap\r1 :i* ends at ,o#a1 ! melt+ po9t ( r$ phosphorus4 ,by heat+ 9 capill>y tubes ( h>d glass1 ,*apman#gc f\nd t r$ phosphorus melts at ! melt+ po9t ( potassium iodide1 i4e4 ab\t #fcj;deg1#gd b ! pressure at ?is temp]ature is unkn[n4 ,at ,o#a1 !n1 we h ! triple po9t1 r$ phosphorus1 liquid1 & vap\r1 & />t+ f x1 we %\ld h ! #dh vaporization curve ( liquid phosphorus1 ,o#a;,a1 & ! fusion curve ( r$ phosphorus1 ,o#a;,f4 ,al?\gh ^! h n be5 det]m9$1 ! latt] curve mu/1 f !oretical consid]ations 7v4 p4 #eh71 slope slightly to ! "r2 i4e4 increase ( pressure raises ! melt+ po9t ( r$ phosphorus4 ,illu/ration3 ,,fig4 #aa4 ,:5 :ite phosphorus is heat$ to #dd;deg1 x melts4 ,at ?is po9t1 !re=e1 we %all h ano!r triple po9t1 :ite phosphorus--liquid--vap\r2 ! pressure at ?is po9t has be5 calculat$ to be #c mm4#ge ,?is po9t is ! int]section ( ?ree curves1 viz4 sublimation curve1 vaporization curve1 & ! fusion curve ( :ite phosphorus4 ,! fusion curve1 ,o#b;,e1 has be5 det]m9$ by ,tammann#gf & by ,g4 ,a4 ,hulett1#gg & x 0 f\nd t increase ( pressure by #a atm4 raises ! melt+ po9t by #j4jbi;deg4 ,! sublimation curve ( :ite phosphorus has n yet be5 det]m9$4 ,z c be se5 f ! table ( vap\r pressures 7p4 #df71 ! vap\r pressure ( :ite phosphorus has be5 det]m9$ up to #ejj;deg2 at temp]atures above ?is1 h[ev]1 ! velocity ) :i* trans=mation into r$ phosphorus takes place is s great z to r5d] ! det]m9ation ( ! vap\r pressure #di at high] temp]atures impossible4 ,s9ce1 h[ev]1 ! diff]5ce betwe5 :ite phosphorus & r$ phosphorus disappe>s 9 ! liquid /ate1 ! vap\r pressure curve ( :ite phosphorus mu/ pass ?r\gh ! po9t ,o#a1 ! melt+ po9t ( r$ phosphorus1 & mu/ be cont9u\s ) ! curve ,o#a;,a1 ! vap\r pressure curve ( liquid phosphorus 7vide infra74 ,s9ce1 z ,fig4 #aj %[s1 ! vap\r pressure curve ( :ite phosphorus asc5ds v rapidly at high] temp]atures1 ! break betwe5 ,,bo#a & ,o#a;,a mu/ be v slight4 ,z comp>$ ) monotropic sub/ances l b5zoph5one1 phosphorus exhibits ! peculi>ity t trans=mation ( ! meta/able into ! /able modification takes place ) great sl[ness2 & fur!r1 ! "t requir$ = ! production ( equilibrium betwe5 r$ phosphorus & phosphorus vap\r is great comp>$ ) t requir$ = e/abli%+ ! same equilibrium 9 ! case ( :ite phosphorus4 ,?is behavi\r c be be/ expla9$ by ! assumption t *ange 9 ! molecul> complexity 7polym]ization7 occurs 9 ! conv]sion ( :ite into r$ phosphorus1 & :5 r$ phosphorus passes into vap\r 7depolym]ization74#gh ,?is is borne out by ! fact t measurem5ts ( ! vap\r d5sity ( phosphorus vap\r at temp]atures ( #ejj;deg & m1 %[ x to h ! molecul> weight repres5t$ by ,p#d1gi & ! same molecul> weight has be5 f\nd = phosphorus 9 solution4#hj ,on ! o!r h&1 x has rec5tly be5 %[n by ,r4 ,s*5ck1#ha t ! molecul> weight ( r$ phosphorus is at lea/ ,p#h1 & v possibly high]4 ,9 ! case ( phosphorus1 !re=e1 x is m ?an possible t we are deal+1 n simply ) two polymorphic #ej =ms ( ! same sub/ance1 b ) polym]ic =ms1 & t !re is no transition po9t at temp]atures above ! absolute z]o1 unless we assume ! molecul> complexity ( ! two =ms to become ! same4 ,! curve = r$ phosphorus w\ld !re=e lie bel[ t ( :ite phosphorus1 = ! vap\r pressure ( ! polym]ic =m1 if produc$ f ! simpl] =m ) evolution ( heat1 mu/ be l[] ?an t ( ! latt]4 ,a transition po9t w\ld1 ( c\rse1 become possible if ! sign ( ! heat effect 9 ! trans=mation ( ! "o modification into ! o!r %\ld *ange4 ,if1 fur!r1 ! liquid :i* is produc$ by ! fusion ( r$ phosphorus at #fcj;deg "u high pressure also exi/s 9 a polym]ic =m1 great] ?an ,p#d1 !n ! meta/able vaporization curve ( :ite phosphorus w\ld n pass ?r\gh ! melt+ po9t ( r$ phosphorus1 z 0 assum$ above4#hb ,we h already se5 9 ! case ( wat] 7p4 #ca7 t ! vap\r pressure ( sup]cool$ wat] is great] ?an t ( ice1 & t !re=e x is possible1 !oretically at lea/1 by a process ( di/illation1 to transf] ! wat] f "o end ( a clos$ tube to ! o!r1 & to !re cond5se x z ice4 ,on acc\nt ( ! v small diff]5ce betwe5 ! vap\r pressure ( sup]cool$ wat] & ice1 ?is di/illation process has n be5 exp]im5tally realiz$4 ,9 ! case ( phosphorus1 h[ev]1 :]e ! diff]5ce 9 ! vap\r pressures is comp>atively great1 x has be5 f\nd possible to di/il :ite phosphorus f "o "p ( a clos$ tube to ano!r1 & to !re cond5se x z r$ phosphorus2 & s9ce ! vap\r pressure ( r$ phosphorus at #cej;deg is less ?an ! vap\r pressure ( :ite phosphorus at #bjj;deg1 x is possible to c>ry out ! di/illation f a cold] "p ( ! tube to a hott]1 by hav+ :ite phosphorus at ! =m] & r$ phosphorus at ! latt]4 ,su* a process ( di/illation has be5 c>ri$ out by ,troo/ & ,hautefeuille betwe5 #cbd;deg & #cej;deg4#hc ,relation%ips simil> to ^? f\nd 9 ! case ( phosphorus are also met ) 9 ! case ( cyanog5 & #ea p>acyanog51 :i* h be5 /udi$ by ,*appuis1#hd ,troo/ & ,hautefeuille1#he & ,dew>1#hf & also 9 ! case ( o!r organic sub/ances4 ,enantiotropy comb9$ ) ,monotropy4--,n only c polymorphic sub/ances exhibit enantiotropy or monotropy1 b1 if ! sub/ance is capable ( exi/+ 9 m ?an two cry/all9e =ms1 bo? relation%ips may be f\nd1 s t "s ( ! =ms may be enantiotropic to "o ano!r1 :ile ! o!r =ms exhibit only monotropy4 ,?is behavi\r is se5 9 ! case ( sulphur1 :i* c exi/ 9 z _m z eight diff]5t cry/all9e v>ieties4 ,( ^! only monocl9ic & rhombic sulphur exhibit ! relation%ip ( enantiotropy1 i4e4 !y possess a def9ite transition po9t1 :ile ! o!r =ms are all meta/able ) respect to rhombic & monocl9ic sulphur1 & rema9 s up to ! melt+ po9t2 t is to say1 !y are monotropic modifications4#hg ,e4 ,liquid ,cry/als4 ,ph5om5a obs]v$4--,9 #ahhh x 0 discov]$ by ,re9itz]#hh t ! two sub/ances1 *ole/]yl acetate & *ole/]yl b5zoate1 possess ! peculi> prop]ty ( melt+ %>ply at a def9ite temp]ature to milky liquids2 & t ! latt]1 on be+ fur!r heat$1 sudd5ly become cle>1 also at a def9ite temp]ature4 ,o!r sub/ances1 m especially p-azoxyanisole & p-azoxyph5etole1 71 lat]1 f\nd to possess ! same prop]ty ( hav+ app>5tly a d\ble melt+ po9t4#hi ,on cool+ ! cle> liquids1 ! rev]se s]ies ( *anges occurr$4 ,! turbid liquids :i* 7 ?us obta9$ 7 f\nd to possess n only ! usual prop]ties ( liquids 7su* z ! #eb prop]ty ( fl[+ & ( assum+ a p]fectly sph]ical %ape :5 susp5d$ 9 a liquid ( ! same d5sity71 b also ^? prop]ties :i* _h hi!rto be5 obs]v$ only 9 ! case ( solid cry/all9e sub/ances1 viz4 ! prop]ty ( d\ble refraction & ( giv+ int]f]5ce col\rs :5 exam9$ by pol>iz$ light2 ! turbid liquids are anisotropic4 ,to su* liquids1 ! optical prop]ties ( :i* 7 discov]$ by ,o4 ,lehmann1#ij ! "n liquid cry/als1 or cry/all9e liquids1 0 giv54 ,nature ( ,liquid ,cry/als4--,dur+ ! pa/ t5 ye>s ! "q z to ! nature ( liquid cry/als has be5 discuss$ by a numb] ( inve/igators1 sev]al ( :om h cont5d$ /rongly aga9/ ! idea ( ! t]m liquid be+ appli$ to ! cry/all9e condition2 & v>i\s attempts h be5 made to prove t ! turbid liquids are 9 reality het]og5e\s & are to be class$ along ) emulsions4#ia ,?is view 0 no d\bt l>gely sugge/$ by ! fact t ! anisotropic liquids 7 turbid1 :]eas ! solid cry/als 7 cle>4 ,lehmann f\nd1 h[ev]1 t1 :5 exam9$ "u ! microscope1 ! simple liquid cry/als 7 also cle>1#ib ! app>5t turbidity be+ due to ! aggregation ( a numb] ( diff]5tly ori5t$ cry/als1 9 ! same way z a piece ( m>ble does n appe> transp>5t al?\gh compos$ ( transp>5t cry/als4#ic ,fur!r1 no pro( ( ! het]og5eity ( liquid cry/als has yet be5 obta9$1 b r all *emical & physical inve/igations indicate t !y are homog5e\s4#id ,no sep>ation #ec ( a solid sub/ance f ! milky1 anisotropic liquids has be5 effect$2 ! anisotropic liquid is 9 "s cases less visc\s ?an ! isotropic liquid =m$ at a high] temp]ature2 & ! temp]ature ( liquefaction is con/ant1 & is affect$ by pressure & admixture ) =eign sub/ances exactly z 9 ! case ( a pure sub/ance4#ie ,illu/ration3 ,,fig4 #ab4 ,equilibrium ,relations 9 ! ,case ( ,liquid ,cry/als4--,s9ce1 n[1 we h se5 t we are deal+ "h ) sub/ances 9 two cry/all9e =ms 7:i* we may call ! solid & liquid#if cry/all9e =m71 :i* possess a def9ite transition po9t1 at :i*1 trans=mation ( ! "o =m into ! o!r occurs 9 bo? directions1 we c repres5t ! conditions ( equilibrium by a diagram 9 all respects simil> to t employ$ 9 ! case ( o!r enantiotropic sub/ances1 e4g4 sulphur 7p4 #ce74 #ed ,9 ,fig4 #ab !re is giv5 a diagrammatic repres5tation ( ! relation%ips f\nd 9 ! case ( p-azoxyanisole4#ig ,al?\gh ! vap\r pressure ( ! sub/ance 9 ! solid1 or liquid /ate1 has n be5 det]m9$1 x w be und]/ood f :at we h already le>n$1 t ! curves ,,ao1 ,,ob1 ,,bc1 repres5t+ ! vap\r pressure ( solid cry/als1 liquid cry/als1 isotropic liquid1 mu/ h ! relative positions %[n 9 ! diagram4 ,po9t ,o1 ! transition po9t ( ! solid into ! liquid cry/als1 lies at #aah4bg;deg1 & ! *ange ( ! transition po9t ) ! pressure is #j4jcb;deg pro #a atm4 ,! transition curve ,,oe slopes1 !re=e1 slightly to ! "r4 ,! po9t ,b1 ! melt+ po9t ( ! liquid cry/als1 lies at #ace4he;deg1 & ! melt+ po9t is rais$ #j4jdhe;deg pro #a atm4 ,! curve ,,bd1 !re=e1 also slopes to ! "r1 & m s ?an ! transition curve4 ,9 ?is respect azoxyanisole is diff]5t f sulphur4 ,! areas b\nd$ by ! curves repres5t ! conditions = ! /able exi/5ce ( ! f\r s+le phases1 solid cry/als1 liquid cry/als1 isotropic liquid & vap\r4 ,! mo/ important sub/ances hi!rto f\nd to =m liquid cry/als are#ih3-- ---------------------------------------- -------------- ,sub/ance4 ,transition ,melt+ po9t4 po9t4 ---------------------------------------- -------------- ,*ole/]yl b5zoate #ade4e;deg #agh4e;deg ,azoxyanisole #aah4c;deg #ace4i;deg ,azoxyph5etole #acd4e;deg #afh4a;deg ,cond5sation product f b5zaldehyde & b5zid9e #bcd;deg #bfj;deg ,az9e ( p-oxye?ylb5zaldehyde #agb;deg #aif;deg ,cond5sation product f p-tolylaldehyde & b5zid9e #bca;deg -- p-,me?oxyc9namic acid #afi;deg #ahe;deg ---------------------------------------- -------------- 99 99 99 99 99 #ee ,,*apt] ,,iv ,,g5]al ,,summ>y ,9 ! prec$+ pages we h le>n$ h[ ! pr9ciples ( ! ,phase ,rule c be appli$ to ! elucidation ( v>i\s sy/ems consi/+ ( "o compon5t4 ,9 ! pres5t *apt] x is propos$ to give a %ort summ>y ( ! relation%ips we h met )1 & also to discuss m g5]ally h[ ! ,phase ,rule applies to o!r "o-compon5t sy/ems4 ,on acc\nt ( ! fact t beg9n]s are sometimes incl9$ to expect too mu* ( ! ,phase ,rule2 to expect1 = example1 t x w in=m !m z to ! exact behavi\r ( a sub/ance1 x may "h be emphasiz$ t ! ,phase ,rule is a g5]al rule2 x in=ms u only z to ! g5]al conditions ( equilibrium1 & leaves ! det]m9ation ( ! def9ite1 num]ical data to exp]im5t4 ,triple ,po9t4--,we h already 7p4 #bh7 def9$ a triple po9t 9 a "o-compon5t sy/em1 z be+ t pressure & temp]ature at :i* ?ree phases coexi/ 9 equilibrium2 x repres5ts1 !re=e1 an inv>iant sy/em 7p4 #af74 ,at ! triple po9t also1 ?ree curves cut1 viz4 ! curves repres5t+ ! conditions ( equilibrium ( ! ?ree univ>iant sy/ems =m$ by ! comb9ation ( ! ?ree phases 9 pairs4 ,! mo/ common triple po9t ( a "o-compon5t sy/em is1 ( c\rse1 ! triple po9t1 solid1 liquid1 vap\r 7,s-,l-,v71 b o!r triple po9ts#ii are also possible :51 z 9 ! case ( #ef sulphur or b5zoph5one1 polymorphic =ms occur4 ,:e!r or n all ! triple po9ts c be exp]im5tally realiz$ w1 ( c\rse1 dep5d on circum/ances4 ,we %all1 9 ! fir/ place1 consid] only ! triple po9t ,s-,l-,v4 ,z to ! g5]al arrangem5t ( ! ?ree univ>iant curves ar\nd ! triple po9t1 ! foll[+ rules may be giv54 7#a7 ,! prolongation ( ea* ( ! curves beyond ! triple po9t mu/ lie betwe5 ! o!r two curves4 7#b7 ,! middle position at "o & ! same temp]ature 9 ! neighb\rhood ( ! triple po9t is tak5 by t curve 7or its meta/able prolongation7 :i* repres5ts ! two phases ( mo/ widely diff]+ specific volume4#ajj ,t is to say1 if a l9e ( con/ant temp]ature is drawn imm$iately above or bel[ ! triple po9t s z to cut ! ?ree curves--two /able curves & ! meta/able prolongation ( ! ?ird--! position ( ! curves at t temp]ature w be su* t ! middle position is occupi$ by t curve 7or its meta/able prolongation7 :i* repres5ts ! two phases ( mo/ widely diff]+ specific volume4 ,n[1 al?\gh ^! rules admit ( a consid]able v>iety ( possible arrangem5ts ( curves ar\nd ! triple po9t1#aja only two ( ^! h be5 exp]im5tally obta9$ 9 ! case ( ! triple po9t solid--liquid--vap\r4 ,at pres5t1 !re=e1 we %all consid] only ^! two cases 7,figs4 #ac & #ad74 ,illu/ration3 ,,fig4 #ac4 ,illu/ration3 ,,fig4 #ad4 ,an exam9ation ( ^! two figures %[s t !y satisfy ! rules laid d[n4 ,ea* ( ! curves on be+ prolong$ passes betwe5 ! o!r two curves4 ,9 ! case ( sub/ances ( ! fir/ type 7,fig4 #ac71 ! specific volume ( ! solid is great] ?an t ( ! liquid 7! sub/ance contracts on fusion72 ! diff]5ce ( specific volume w1 !re=e1 be greate/ betwe5 liquid & vap\r4 ,! curve1 !re=e1 = liquid & vap\r 7or its prolongation7 mu/ lie betwe5 ! o!r two curves2 ?is is se5 f ! figure to be ! case4 ,simil>ly1 ! rule is satisfi$ by ! arrangem5t ( curves 9 ,fig4 #ad1 :]e ! diff]5ce ( specific volumes is #eg greate/ betwe5 ! solid & vap\r4 ,9 ?is case ! curve ,s-,v occupies ! int]m$iate position4 ,z we see1 ! two figures diff] f "o ano!r only 9 t ! fusion curve ,,oc 9 "o case slopes to ! "r away f ! pressure axis1 ?us indicat+ t ! melt+ po9t is rais$ by increase ( pressure2 9 ! o!r case1 to ! left1 indicat+ a l[]+ ( ! melt+ po9t ) ! pressure4 ,^! conditions are f\nd exemplifi$ 9 ! case ( sulphur & ice 7pp4 #bi & #ce74 ,we see fur!r f ! two figures1 t ,o 9 ,fig4 #ac gives ! highe/ temp]ature at :i* ! solid c exi/1 = ! curve = solid--liquid slopes back to regions ( l[] temp]ature2 9 ,fig4 #ad1 ,o gives ! l[e/ temp]ature at :i* ! liquid phase c exi/ z /able phase4#ajb ,!orems ( van't ,h(f & ( ,le ,*ateli]4--,s f> we h /udi$ only ! conditions "u :i* v>i\s sy/ems exi/ 9 equilibrium2 & we n[ pass to a consid]ation ( ! *anges :i* take place 9 a sy/em :5 ! ext]nal conditions ( temp]ature & pressure are alt]$4 ,= all su* *anges !re exi/ two !orems1 bas$ on ! laws ( !rmodynamics1 by means ( :i* ! alt]ations 9 a sy/em c be qualitatively pr$ict$4#ajc ,! fir/ ( ^!1 usually #eh kn[n z van't ,h(f's law ( movable equilibrium1#ajd /ates3 ,:5 ! temp]ature ( a sy/em 9 equilibrium is rais$1 t reaction takes place :i* is accompani$ by absorption ( heat2 &1 conv]sely1 :5 ! temp]ature is l[]$1 t reaction occurs :i* is accompani$ by an evolution ( heat4 ,! second ( ! two !orems ref]s to ! effect ( *ange ( pressure1 & /ates3#aje ,:5 ! pressure on a sy/em 9 equilibrium is increas$1 t reaction takes place :i* is accompani$ by a dim9ution ( volume2 & :5 ! pressure is dim9i%$1 a reaction ensues :i* is accompani$ by an increase ( volume4 ,! demon/ration ( ! univ]sal applicability ( ^! two !orems is due *iefly to ,le ,*ateli]1 :o %[$ t !y may be reg>d$ z consequ5ces ( ! g5]al law ( action & reaction4 ,= ?is reason !y are g5]ally reg>d$ z special cases ( ! m g5]al law1 kn[n z ! !orem ( ,le ,*ateli]1 :i* may be /at$ 9 ! words ( ,o/wald1 z foll[s3#ajf ,if a sy/em 9 equilibrium is subject$ to a con/ra9t by :i* ! equilibrium is %ift$1 a reaction takes place :i* opposes ! con/ra9t1 i4e4 "o by :i* its effect is p>tially de/roy$4 ,?is !orem ( ,le ,*ateli] is ( v great importance1 = x applies to all sy/ems & *anges ( ! condition ( equilibrium1 :e!r physical or *emical2 to vaporization & fusion2 to solution & *emical action4 ,9 all cases1 :5ev] *anges 9 ! ext]nal condition ( a sy/em 9 equilibrium are produc$1 processes also occur )9 ! sy/em :i* t5d to c\nt]act ! effect ( ! ext]nal *anges4 ,*anges at ! ,triple ,po9t4--,if n[ we apply ?is !orem to equilibria at ! triple po9t ,s-,l-,v1 & ask :at *anges w occur 9 su* a sy/em :5 ! ext]nal conditions ( pressure & temp]ature are alt]$1 ! g5]al answ] to ! "q w be3 ,s long z ! ?ree phases are pres5t1 no #ei *ange 9 ! temp]ature or pressure ( ! sy/em c occur1 b only *anges 9 ! relative am\nts ( ! phases2 t is to say1 ! effect on ! sy/em ( *ange 9 ! ext]nal conditions is oppos$ by ! reactions or *anges :i* take place )9 ! sy/em 7accord+ to ! !orems ( van't ,h(f & ,le ,*ateli]74 ,we n[ proce$ to discuss :at ^! *anges are1 & %all consid] fir/ ! effect ( alt]ation ( ! temp]ature at con/ant volume & con/ant pressure1 & !n ! effect ( alt]ation ( ! pressure bo? :5 ! temp]ature rema9s con/ant & :5 x v>ies4 ,:5 ! volume is kept con/ant1 ! effect ( ! addition ( heat to a sy/em at ! triple po9t ,s-,l-,v diff]s some:at accord+ z !re is an increase or dim9ution ( volume :5 ! solid passes into ! liquid /ate4 ,9 ! =m] & mo/ g5]al case 7,fig4 #ad71 addition ( heat w cause a c]ta9 am\nt ( ! solid phase to melt1 :]eby ! heat :i* is add$ becomes lat5t2 ! temp]ature ( ! sy/em !re=e does n rise4 ,s9ce1 h[ev]1 ! melt+ ( ! solid is accompani$ by an increase ( volume1 :]eby an increase ( pressure w\ld result1 a c]ta9 portion ( ! vap\r mu/ cond5se to liquid1 9 ord] t ! pressure may rema9 con/ant4 ,! total effect ( addition ( heat1 !re=e1 is to cause bo? solid & vap\r to pass into liquid1 i4e4 !re occurs ! *ange ,s ,v -- ,l4 ,x w1 !re=e1 dep5d on ! relative quantities ( solid & vap\r1 :i* w disappe> fir/4 ,if ! solid disappe>s fir/1 !n we %all pass to ! sy/em ,l-,v2 if vap\r disappe>s fir/1 we %all obta9 ! sy/em ,s-,l4 ,)drawal ( heat causes ! rev]se *ange1 ,l -- ,s ,v2 at all temp]atures bel[ ! triple po9t ! liquid is un/able or meta/able 7p4 #cj74 ,:5 fusion is accompani$ by a dim9ution ( volume 7e4g4 ice1 ,fig4 #ac71 !n1 s9ce ! melt+ ( ! solid phase w\ld decrease ! total volume1 i4e4 w\ld l[] ! pressure1 a c]ta9 quantity ( ! solid mu/ also pass into vap\r 9 ord] t ! pressure may be ma9ta9$ con/ant4 ,on addition ( heat1 !re=e1 !re occurs ! reaction ,s -- ,l ,v2 )drawal ( heat causes ! rev]se *ange ,l ,v -- ,s4 ,above ! temp]ature ( ! triple po9t ! #fj solid _c exi/2 bel[ ! triple po9t bo? sy/ems1 ,s-,l & ,s-,v1 c exi/1 & x w !re=e dep5d on ! relative am\nts ( liquid & vap\r :i* ( ^! two sy/ems is obta9$ on )draw+ heat f ! sy/em at con/ant volume4 ,! same *anges 9 ! phases occur :5 heat is add$ or )drawn at con/ant pressure1 s long z ! ?ree phases are pres5t4 ,cont9u$ addition ( heat1 h[ev]1 at con/ant pressure w ultimately cause ! =mation ( ! biv>iant sy/em vap\r alone2 cont9u$ )drawal ( heat w ultimately cause ! =mation ( solid alone4 ,?is w be readily und]/ood f ,fig4 #ae4 ,! dott$ l9e ,d',,od is a l9e ( con/ant pressure2 on add+ heat1 ! sy/em passes along ! l9e ,,od into ! region ( vap\r2 on heat be+ )drawn1 ! sy/em passes along ,,od' into ! area ( solid4 ,illu/ration3 ,,fig4 #ae4 ,simil> *anges are produc$ :5 ! volume ( ! sy/em is alt]$4 ,alt]ation ( volume may take place ei!r :ile transf]5ce ( heat to or f ! sy/em is cut (f 7adiabatic *ange71 or :ile su* transf]5ce may occur 7iso!rmal *ange74 ,9 ! latt] case1 ! temp]ature ( ! sy/em w rema9 con/ant2 9 ! =m] case1 s9ce at ! triple po9t ! pressure mu/ be con/ant s long z ! ?ree phases are pres5t1 increase ( volume mu/ be comp5sat$ by ! evaporation ( liquid4 ,?is1 h[ev]1 w\ld cause ! temp]ature to fall 7s9ce communication ( heat f ! outside is suppos$ to be cut (f71 & a portion ( ! liquid mu/ !re=e freeze4 ,9 ?is way ! lat5t heat ( evaporation is c\nt]balanc$ by ! lat5t heat ( fusion4 ,z ! result ( increase ( volume1 !re=e1 ! process occurs ,l -- ,s ,v4 ,dim9ution ( volume1 )\t transf]5ce ( heat1 w br+ ab\t ! opposite *ange1 ,s ,v -- ,l4 ,9 ! =m] case !re is ultimately obta9$ ! univ>iant sy/em ,s-,v2 9 ! latt] case !re w be #fa obta9$ ei!r ,s-,l or ,l-,v accord+ z ! vap\r or solid phase disappe>s fir/4 ,?is argum5t holds good = bo? types ( triple po9t %[n 9 ,figs4 #ac & #ad 7p4 #eg74 ,a glance at ^! figures w %[ t increase ( volume 7dim9ution ( pressure7 w lead ultimately to ! sy/em ,s-,v1 = at pressures l[] ?an t ( ! triple po9t1 ! liquid phase _c exi/4 ,decrease ( volume 7increase ( pressure71 on ! o!r h&1 w lead ei!r to ! sy/em ,s-,l or ,l-,v1 because ^! sy/ems c exi/ at pressures high] ?an t ( ! triple po9t4 ,if ! vap\r phase disappe>s & we pass to ! curve ,s-,l1 cont9u$ dim9ution ( volume w be accompani$ by a fall 9 temp]ature 9 ! case ( sy/ems ( ! fir/ type 7,fig4 #ac71 & by a rise 9 temp]ature 9 ! case ( sy/ems ( ! second type 7,fig4 #ad74 ,illu/ration3 ,,fig4 #af4 ,illu/ration3 ,,fig4 #ag4 ,la/ly1 if ! temp]ature is ma9ta9$ con/ant1 i4e4 if heat c pass into or out ( ! sy/em1 !n on *ang+ ! volume ! same *anges 9 ! phases w take place z describ$ above until "o ( ! phases has disappe>$4 ,cont9u$ increase ( volume 7decrease ( pressure7 w !n cause ! disappe>ance ( a second phase1 ! sy/em pass+ along ! dott$ l9e ,,oe' 7,figs4 #af1 #ag71 s t ultimately !re rema9s only ! vap\r phase4 ,conv]sely1 dim9ution ( volume 7increase ( pressure7 w ultimately lead ei!r to solid 7,fig4 #af7 or to liquid alone 7,fig4 #ag71 ! sy/em pass+ along ! dott$ l9e ,,oe4 #fb ,9 discuss+ ! alt]ations :i* may take place at ! triple po9t ) *ange ( temp]ature & pressure1 we h consid]$ only ! triple po9t ,s-,l-,v4 ,! same reason+1 h[ev]1 applies1 mutatis mut&is1 to all o!r triple po9ts1 s t if ! specific volumes ( ! phases are kn[n1 & ! sign ( ! heat effects :i* accompany ! trans=mation ( "o phase into ! o!r1 x is possible to pr$ict 7by means ( ! !orem ( ,le ,*ateli]7 ! *anges :i* w be produc$ 9 ! sy/em by alt]ation ( ! pressure & temp]ature4 ,9 all cases ( trans=mation at ! triple po9t1 x %\ld be not$ t all ?ree phases are involv$ 9 ! *ange1#ajg & n two only2 ! fact t 9 ! case1 say1 ( ! trans=mation f solid to liquid1 or liquid to solid1 at ! melt+ po9t ) *ange ( temp]ature1 only ^! two phases appe> to be affect$1 is due to !re g5]ally be+ a l>ge excess ( ! vap\r phase pres5t & to ! prior disappe>ance !re=e ( ! solid or liquid phase4 ,9 ! case ( triple po9ts at :i* two solid phases are 9 equilibrium ) liquid1 o!r arrangem5ts ( ! curves ar\nd ! triple po9t are f\nd4 ,x is1 h[ev]1 unnecess>y to give a g5]al treatm5t ( ^! "h1 s9ce ! pr9ciples :i* h be5 appli$ to ! triple po9t ,s-,l-,v c also be appli$ to ! o!r triple po9ts4#ajh ,triple ,po9t ,solid--,solid--,vap\r4--,! triple po9t solid--solid--vap\r is "o :i* is ( consid]able importance4 ,examples ( su* a triple po9t h already be5 giv5 9 sulphur & t91 & a li/ ( o!r sub/ances capable ( yield+ two solid phases is giv5 bel[4 ,! triple po9t ,s-,s-,v is n precisely ! same z ! transition po9t1 b is v ne>ly s4 ,! transition po9t is ! temp]ature at :i* ! relative /ability ( ! two solid phases und]goes *ange1 :5 ! vap\r phase is abs5t & ! pressure is #a atm42 :]eas at ! triple po9t ! pressure is t ( ! sy/em itself4 ,! transition po9t1 !re=e1 be>s ! same relation to ! triple po9t ,s-,s-,v z ! melt+ po9t to ! triple po9t ,s-,l-,v4 #fc ,9 ! foll[+ table is giv5 a li/ ( ! mo/ important polymorph\s sub/ances1 & ! temp]atures ( ! transition po9t4#aji ---------------------------------------- --------- ,sub/ance4 ,transition temp]ature4 ---------------------------------------- --------- ,ammonium nitrate-- beta-rhombic -- alpha-rhombic #ce;deg alpha-rhombic -- rhomboh$ral #hc;deg ,rhomboh$ral -- regul> #abe;deg ,m]curic iodide #abf;deg ,potassium nitrate #abi;deg ,silv] iodide #ade;deg ,silv] nitrate #afj;deg ,sulphur #ie4e;deg ,tetrabromme?ane #df4h;deg ,?allium nitrate-- ,rhombic -- rhomboh$ral #hj;deg ,rhomboh$ral -- regul> #adb4e;deg ,?allium picrate #df;deg ,t9 #bj;deg ---------------------------------------- --------- ,sublimation & ,vaporization ,curves4--,we h already se51 9 ! case ( ice & liquid wat]1 t ! vap\r pressure increases z ! temp]ature rises1 ! increase ( pressure p] degree be+ great] ! high] ! temp]ature4 ,! sublimation & vaporization curves1 !re=e1 are n /raight l9es1 b are b5t1 ! convex side ( ! curve be+ t[>ds ! temp]ature axis 9 ! ord9>y pt-diagram4 ,9 ! case ( sulphur & ( t91 we assum$ vap\r to be giv5 (f by ! solid sub/ance1 al?\gh ! pressure ( ! vap\r has n hi!rto be5 measur$4 ,! assumption1 h[ev]1 is entirely ju/ifi$1 n only on !oretical gr\nds1 b also because ! exi/5ce ( a vap\r pressure has be5 obs]v$ 9 ! case ( _m solid sub/ances at temp]atures mu* bel[ ! melt+ po9t1#aaj & 9 "s cases1 e4g4 camphor1#aaa ! vap\r pressure is consid]able4 #fd ,z ! result ( a l>ge numb] ( det]m9ations1 x has be5 f\nd t all vap\r pressure curves h ! same g5]al =m allud$ to above4 ,attempts h also be5 made to obta9 a g5]al expression = ! quantitative *anges 9 ! vap\r pressure ) *ange ( temp]ature1 b )\t success4 ,nev]!less1 ! qualitative *anges1 or ! g5]al direction ( ! curves1 c be pr$ict$ by means ( ! !orem ( ,le ,*ateli]4 ,z we h already le>n$ 7p4 #af71 ! ,phase ,rule takes no acc\nt ( ! molecul> complexity ( ! sub/ances p>ticipat+ 9 an equilibrium4 ,a dissociat+ sub/ance1 !re=e1 9 contact ) its vapor\s products ( dissociation 7e4g4 ammonium *loride 9 contact ) ammonia & hydrog5 *loride71 w likewise con/itute a univ>iant sy/em ( "o compon5t1 provid$ ! composition ( ! vap\r phase z a :ole is ! same z t ( ! solid or liquid phase 7p4 #ac74 ,= all su* sub/ances1 !re=e1 ! conditions ( equilibrium w be repres5t$ by a curve ( ! same g5]al =m z ! vap\r pressure curve ( a non-dissociat+ sub/ance4#aab ,! same behavi\r is also f\nd 9 ! case ( sub/ances :i* polym]ize on pass+ into ! solid or liquid /ate 7e4g4 r$ phosphorus74 ,:]e su* *anges 9 ! molecul> /ate occur1 h[ev]1 ! "t requir$ = equilibrium to be e/abli%$ is1 z a rule1 great] ?an :5 ! molecul> /ate is ! same 9 bo? phases4 ,f an exam9ation ( ,figs4 #ac & #ad1 x w be easy to pr$ict ! effect ( *ange ( pressure & temp]ature on ! univ>iant sy/ems ,s-,v or ,l-,v4 ,if ! volume is kept con/ant1 addition ( heat w cause an increase ( pressure1 ! sy/em ,s-,v mov+ along ! curve ,,ao until at ! triple po9t ! liquid phase is =m$1 & ! sy/em ,l-,v mov+ along ! curve ,,ob2 s long z two phases are pres5t1 ! condition ( ! sy/em mu/ be repres5t$ by ^! two curves4 ,conv]sely1 )drawal ( heat w cause cond5sation ( vap\r1 & !re=e dim9ution ( pressure2 ! sy/em w !re=e move along ! vaporization or sublimation curve to l[] temp]atures & pressures1 s long z ! sy/em rema9s univ>iant4 #fe ,if transf]5ce ( heat to or f ! sy/em is prev5t$1 increase ( volume 7dim9ution ( pressure7 w cause ! sy/em ,l-,v to pass along ! curve ,,bo2 liquid w pass into vap\r & ! temp]ature w fall4#aac ,at ,o solid may appe>1 & ! temp]ature ( ! sy/em w !n rema9 con/ant until ! liquid phase has disappe>$ 7p4 #eg72 ! sy/em w !n foll[ ! curve ,,oa until ! solid phase disappe>s1 & we are ultimately left ) vap\r4 ,on ! o!r h&1 dim9ution ( volume 7increase ( pressure7 w cause cond5sation ( vap\r1 & ! sy/em ,s-,v w pass along ! curve ,,ao to high] temp]atures & pressures2 at ,o ! solid w melt1 & ! sy/em w ultimately pass to ! curve ,,ob or to ,,oc 7p4 #eg74 ,addition or )drawal ( heat at con/ant pressure1 & increase or dim9ution ( ! pressure at con/ant temp]ature1 w cause ! sy/em to pass along l9es p>allel to ! temp]ature & ! pressure axis respectively2 ! work+ out ( ^! *anges may be left to ! read]1 guid$ by :at has be5 said on pp4 #fj & #fa4 ,! sublimation curve ( all sub/ances1 s f> z yet f\nd1 has its upp] limit at ! melt+ po9t 7triple po9t71 al?\gh ! possibility ( ! exi/5ce ( a sup]heat$ solid is n exclud$4 ,! l[] limit is1 !oretically at lea/1 at ! absolute z]o1 provid$ no new phase1 e4g4 a diff]5t cry/all9e modification1 is =m$4 ,if ! sublimation pressure ( a sub/ance is great] ?an ! atmosph]ic pressure at any temp]ature bel[ ! po9t ( fusion1 !n ! sub/ance w sublime )\t melt+ :5 heat$ 9 an op5 vessel2 & fusion w be possible only at a pressure high] ?an ! atmosph]ic4 ,?is is f\nd1 = example1 9 ! case ( r$ phosphorus 7p4 #dg74 ,if1 h[ev]1 ! sublimation pressure ( a sub/ance at its triple po9t ,s-,l-,v is less ?an "o atmosph]e1 !n ! sub/ance w melt :5 heat$ 9 an op5 vessel4 ,9 ! case ( ! vaporization curve1 ! upp] limit lies at ! critical po9t :]e ! liquid ceases to exi/2#aad ! #ff l[] limit is det]m9$ by ! range ( ! meta/able /ate ( ! sup]cool$ liquid4 ,! int]polation & extrapolation ( vap\r-pressure curves is r5d]$ v easy by means ( a relation%ip :i* ,ramsay & ,"y#aae f\nd to exi/ betwe5 ! vap\r-pressure curves ( diff]5t sub/ances4 ,x 0 obs]v$ t 9 ! case ( closely relat$ sub/ances1 ! ratio ( ! absolute temp]atures correspond+ to equal vap\r pressures is con/ant1 i4e4 ,t#a_/,t'#a ,t#b_/,t'#b4 ,:5 ! two sub/ances are n closely relat$1 x 0 f\nd t ! relation%ip c\ld be express$ by ! equation ,t#a_/,t'#a ,t#b_/,t'#b c7t' - t7 :]e c is a con/ant hav+ a small positive or negative value1 & t' & t are ! temp]atures at :i* "o ( ! sub/ances has ! two values ( ! vap\r pressure 9 "q4 ,by means ( ?is equation1 if ! vap\r-pressure curve ( "o sub/ance is kn[n1 ! vap\r-pressure curve ( any o!r sub/ance c be calculat$ f ! values at any two temp]atures ( ! vap\r pressure ( t sub/ance4 ,fusion ,curve--,transition ,curve4--,! fusion curve repres5ts ! conditions ( equilibrium betwe5 ! solid & liquid phase2 x %[s ! *ange ( ! melt+ po9t ( a sub/ance ) *ange ( pressure4 ,z %[n 9 ,figs4 #ac & #ad1 ! fusion curve is incl9$ ei!r t[>ds ! pressure axis or away f x2 t is1 increase ( pressure c ei!r l[] or raise ! melt+ po9t4 ,x is easy to pr$ict 9 a qualitative mann] ! diff]5t effect ( pressure on ! melt+ po9t 9 ! two cases m5tion$1 if we consid] ! matt] 9 ! light ( ! !orem ( ,le ,*ateli] 7p4 #eh74 ,wat]1 on pass+ into ice1 exp&s2 !re=e1 if ! pressure on ! sy/em ice--wat] be increas$1 a reaction w take place :i* is accompani$ by a dim9ution 9 volume1 i4e4 ! ice w melt4 ,consequ5tly1 a l[] temp]ature w be requir$ 9 ord] to c\nt]act ! effect ( increase ( pressure2 or1 9 o!r words1 ! melt+ po9t w #fg be l[]$ by pressure4#aaf ,9 ! second case1 ! passage ( ! liquid to ! solid /ate is accompani$ by a dim9ution ( volume2 ! effect ( increase ( pressure w !re=e be ! rev]se ( t 9 ! previ\s case4 ,if ! value ( ! heat ( fusion & ! alt]ation ( volume accompany+ ! *ange ( /ate are kn[n1 x is possible to calculate quantitatively ! effect ( pressure4#aag ,we h already se5 7p4 #be7 t ! effect ( pressure on ! melt+ po9t ( a sub/ance 0 pr$ict$ z ! result ( !oretical consid]ations1 & 0 fir/ prov$ exp]im5tally 9 ! case ( ice4 ,soon aft]1 ,buns5#aah %[$ t ! melt+ po9t ( o!r sub/ances is also affect$ by pressure2 & 9 m rec5t ye>s1 ample exp]im5tal pro( ( ! *ange ( ! melt+ po9t ) ! pressure has be5 obta9$4 ,! *ange ( ! melt+ po9t is1 h[ev]1 small2 z a rule1 increase ( pressure by #a atm4 *anges ! melt+ po9t by ab\t #j4jc;deg1 b 9 ! case ( wat] ! *ange is mu* less 7#j4jjgf;deg71 & 9 ! case ( camphor mu* m 7#j4ac;deg74 ,9 o!r words1 if we take ! mean case1 an increase ( pressure ( m ?an #cj atm4 is requir$ to produce a *ange 9 ! melt+ po9t ( #a;deg4 ,inve/igations :i* 7 made ( ! influ5ce ( pressure on ! melt+-po9t1 %[$ t up to pressures ( sev]al hundr$ atmosph]es ! fusion curve is a /raight l9e4#aai ,tammann#abj has1 h[ev]1 f\nd t on increas+ ! pressure ! fusion curve no long] rema9s /raight1 b b5ds t[>ds ! pressure axis1 s t1 on suffici5tly increas+ ! pressure1 a maximum temp]ature might at l5g? be rea*$4 ,?is maximum has1 s f>1 h[ev]1 n be5 atta9$1 al?\gh ! melt+ po9t curves ( v>i\s sub/ances h be5 /udi$ up to pressures ( #dejj atm4 ,?is is to be acc\nt$ = p>tly #fh by ! fact t ! probable maximum temp]ature 9 ! case ( mo/ sub/ances lies at v great pressures1 & also by ! fact t o!r solid phases make _! appe>ance1 z1 = example1 9 ! case ( ice 7p4 #cb74 ,z to ! upp] limit ( ! fusion curve1 ! view has be5 express$#aba t j z 9 ! case ( liquid & vap\r1 s also 9 ! case ( solid & liquid1 !re exi/s a critical po9t at :i* ! solid & ! liquid phase become id5tical4 ,exp]im5tal evid5ce1 h[ev]1 does n appe> to fav\r ?is view4#abb ,! transition po9t1 l ! melt+ po9t1 is also influ5c$ by ! pressure1 & 9 ?is case also x is f\nd t pressure may ei!r raise or l[] ! transition po9t1 s t ! transition curve may be incl9$ ei!r away f or t[>ds ! pressure axis4 ,! direction ( ! transition curve c also be pr$ict$ if ! *ange ( volume accompany+ ! passage ( "o =m into ! o!r is kn[n4 ,9 ! case ( sulphur1 we saw t ! transition po9t is rais$ by increase ( pressure2 9 ! case ( ! transition ( rhomboh$ral into alpha-rhombic =m ( ammonium nitrate1 h[ev]1 ! transition po9t is l[]$ by pressure1 z %[n by ! foll[+ table4#abc ----------------------- ,temp]ature4 ,pressure4 ----------------------- #he4he;deg #a atm4 #hd4ch;deg #ajj #hc4jc;deg #bjj #hb4bi;deg #bej ----------------------- ,s f> z inve/igations h be5 c>ri$ out1 x appe>s t 9 mo/ cases ! transition curve is practically a /raight l9e4 ,x has1 h[ev]1 be5 f\nd 9 ! case ( ,glaub]'s salt1 t ) increase ( pressure ! transition curve passes ?r\gh a po9t ( maximum temp]ature1 & exhibits1 !re=e1 a =m simil> to t assum$ by ,tammann = ! fusion curve4#abd #fi ,susp5d$ ,trans=mation4 ,meta/able ,equilibria4--,hi!rto we h consid]$ only sy/ems 9 /able equilibrium4 ,we h1 h[ev]1 already se51 9 ! case ( wat]1 t on cool+ ! liquid d[n to ! triple po9t1 solidification did n necess>ily take place1 al?\gh ! conditions 7 su* z to all[ ( its =mation4 ,simil>ly1 we saw t rhombic sulphur c be heat$ above ! transition po9t1 & monocl9ic sulphur c be obta9$ at temp]atures bel[ ! transition po9t1 al?\gh 9 bo? cases trans=mation into a m /able =m is possible2 ! sy/em becomes meta/able4 ,! same reluctance to =m a new phase is obs]v$ also 9 ! ph5om5a ( sup]heat+ ( liquids1 & 9 ! hang+ ( m]cury 9 b>omet]s1 9 :i* case ! vap\r phase is n =m$4 ,9 g5]al1 !n1 we may say t a new phase w n necess>ily be =m$ imm$iately ! sy/em passes into su* a condition t ! exi/5ce ( t phase is possible2 b r1 in/ead ( ! sy/em und]go+ trans=mation s z to pass into ! mo/ /able condition "u ! exi/+ pressure & temp]ature1 ?is trans=mation w be susp5d$ or delay$1 & ! sy/em w become meta/able4 ,only 9 ! case ( ! =mation ( ! liquid f ! solid phase1 9 a "o-compon5t sy/em1 has ?is reluctance to =m a new phase n be5 obs]v$4 ,to ensure ! =mation ( ! new phase1 x is necess>y to h t phase pres5t4 ,! pres5ce ( ! solid phase w prev5t ! sup]cool+ ( ! liquid2 & ! pres5ce ( ! vap\r phase w prev5t ! sup]heat+ ( ! liquid4 ,h[ev]1 ev5 9 ! pres5ce ( ! m /able phase1 trans=mation ( ! meta/able phase occurs ) v v>y+ velocity2 9 "s cases s quickly z to appe> almo/ in/antane\s2 :ile 9 o!r cases1 ! *ange takes place s sl[ly z to require hundr$s ( ye>s = its a*ievem5t4 ,x is ?is sl[ rate ( trans=mation t r5d]s ! exi/5ce ( meta/able =ms possible1 :5 9 contact ) ! m /able phase4 ,?us1 = example1 al?\gh calcite is ! mo/ /able =m ( calcium c>bonate at ! ord9>y temp]ature1#abe ! less /able #gj modification1 aragonite1 nev]!less exi/s "u ! ord9>y conditions 9 an app>5tly v /able /ate4 ,z to ! am\nt ( ! new phase requir$ to br+ ab\t ! trans=mation ( ! meta/able phase1 quantitative measurem5ts h be5 c>ri$ out only 9 ! case ( ! initiation ( cry/allization 9 a sup]cool$ liquid4#abf ,z ! result ( ^! inve/igations1 x 0 f\nd t1 9 ! case ( sup]fus$ salol1 ! v small am\nt ( #a x #aj-g gm4 ( ! solid phase 0 suffici5t to induce cry/allization4 ,cry/allization ( a sup]cool$ liquid1 h[ev]1 c be initiat$ only by a nucleus ( ! same sub/ance 9 ! solid /ate1 or1 z has also be5 f\nd1 by a nucleus ( an isomorph\s solid phase2 x is n br\ght ab\t by ! pres5ce ( any *ance solid4 ,velocity ( ,trans=mation4--,att5tion has already be5 drawn to ! sluggi%ness ) :i* reciprocal trans=mation ( ! polymorphic =ms ( a sub/ance may occur4 ,9 ! case ( t91 = example1 x 0 f\nd t ! :ite modification1 al?\gh app>5tly possess+ p]man5ce1 is 9 reality 9 a meta/able /ate1 "u ! ord9>y conditions ( temp]ature & pressure4 ,?is great degree ( /ability is due to ! t>d9ess ) :i* trans=mation into ! grey =m occurs4 ,:at 0 f\nd 9 ! case ( t91 is met ) also 9 ! case ( all trans=mations 9 ! solid /ate1 b ! velocity ( ! *ange is less 9 "s cases ?an 9 o!rs1 & appe>s to decrease ) increase ( ! val5cy ( ! elem5t4#abg ,to ?is fact van't ,h(f attributes ! great p]man5ce ( _m really un/able 7or meta/able7 c>bon comp\nds4 ,ref]5ce has be5 made to ! fact t ! velocity ( trans=mation c be accel]at$ by v>i\s means4 ,"o ( ! mo/ important ( ^! is ! employm5t ( a liquid :i* has a solv5t action on ! solid phases4 ,j z we h se5 t at any giv5 temp]ature ! less /able =m has ! high] vap\r pressure1 b t at ! transition po9t ! vap\r pressure ( bo? =ms becomes id5tical1 s also x c be prov$ !oretically1 & be %[n exp]im5tally1 t #ga at a giv5 temp]ature ! solubility ( ! less /able =m is great] ?an t ( ! m /able1 b t at ! transition po9t ! solubility ( ! two =ms becomes id5tical4#abh ,if1 !n1 ! two solid phases are br\ght into contact ) a solv5t1 ! less /able phase w dissolve m abundantly ?an ! m /able2 ! solution w !re=e become sup]saturat$ ) respect to ! latt]1 :i* w be deposit$4 ,a gradual *ange ( ! less /able =m1 !re=e1 takes place ?r\gh ! m$ium ( ! solv5t4 ,9 ?is way ! m rapid conv]sion ( :ite t9 into grey 9 pres5ce ( a solution ( t9 ammonium *loride 7p4 #db7 is to be expla9$4 ,al?\gh1 z a rule1 solv5ts accel]ate ! trans=mation ( "o solid phase into ! o!r1 !y may also h a ret>d+ influ5ce on ! velocity ( trans=mation1 z 0 f\nd by ,re9d]s 9 ! case ( m]curic iodide4#abi ,! velocity ( inv]sion1 also1 is v>i\sly affect$ by diff]5t solv5ts1 & 9 "s cases1 at lea/1 x appe>s to be sl[] ! m visc\s ! solv5t2#acj inde$1 ,ka/le & ,re$ /ate t yell[ cry/als ( m]curic iodide1 :i*1 ord9>ily1 *ange ) consid]able velocity into ! r$ modification1 h be5 pres]v$ = m ?an a ye> "u vasel9e4 ,temp]ature1 also1 has a v consid]able influ5ce on ! velocity ( trans=mation4 ,! high] ! temp]ature1 & ! f>!r x is remov$ f ! equilibrium po9t 7transition po9t71 ! great] is ! velocity ( *ange4 ,above ! transition po9t1 ^! two factors act 9 ! same direction1 & ! velocity ( trans=mation w !re=e g on increas+ indef9itely ! high] ! temp]ature is rais$4 ,bel[ ! transition po9t1 h[ev]1 ! two factors act 9 opposite directions1 & ! m ! temp]ature is l[]$1 ! m is ! effect ( removal f ! equilibrium po9t c\nt]act$4 ,a po9t w !re=e be rea*$ at :i* ! velocity is a maximum4 ,r$uction ( ! temp]ature #gb bel[ ?is po9t causes a rapid fall+ (f 9 ! velocity ( *ange4 ,! po9t ( maximum velocity1 h[ev]1 is n def9ite1 b may be alt]$ by v>i\s causes4 ,?us1 ,coh5 f\nd t 9 ! case ( t91 ! po9t ( maximum velocity 0 alt]$ if ! metal _h already und]gone trans=mation2 & also by ! pres5ce ( diff]5t liquids4#aca ,la/ly1 ! pres5ce ( small quantities ( diff]5t sub/ances--catalytic ag5ts or catalyz]s--has a great influ5ce on ! velocity ( trans=mation4 ,?us1 e4g41 ! conv]sion ( :ite to r$ phosphorus is accel]at$ by ! pres5ce ( iod9e 7p4 #dg74 ,great] att5tion1 h[ev]1 has be5 paid to ! /udy ( ! velocity ( cry/allization ( a sup]cool$ liquid1 ! fir/ exp]im5ts 9 ?is direction hav+ be5 made by ,g]nez#acb on ! velocity ( cry/allization ( phosphorus & sulphur4 ,s9ce t "t1 ! velocity ( cry/allization ( o!r sup]cool$ liquids has be5 inve/igat$2 su* z acetic acid & ph5ol by ,moore2#acc sup]cool$ wat] by ,tumlirz2#acd & a numb] ( organic sub/ances by ,tammann1#ace ,fri$la5d] & ,tammann1#acf & by ,bogojawl5ski4#acg ,9 measur+ ! velocity ( cry/allization1 ! sup]cool$ liquids 7 conta9$ 9 n>r[ glass tubes1 & ! "t requir$ = ! cry/allization to advance along a c]ta9 l5g? ( ! tube 0 det]m9$1 ! velocity be+ express$ 9 millimetres p] m9ute4 ,! results :i* h s f> be5 obta9$ may be summ>iz$ z foll[s4 ,= any giv5 degree ( sup]cool+ ( a sub/ance1 ! velocity ( cry/allization is con/ant4 ,z ! degree ( sup]cool+ increases1 ! velocity ( cry/allization also increases1 until a c]ta9 po9t is rea*$ at :i* ! velocity is a maximum1 :i* has a def9ite *>act]i/ic value = ea* sub/ance4 ,?is maximum velocity rema9s con/ant ov] a c]ta9 range ( #gc temp]ature2 !reaft]1 ! velocity dim9i%es fairly rapidly1 &1 ) suffici5t sup]cool+1 may become z]o4 ,! liquid !n passes into a glassy mass1 :i* w rema9 7practically7 p]man5t ev5 9 contact ) ! cry/all9e solid4 ,9 ord9>y glass we h a famili> example ( a liquid :i* has be5 cool$ to a temp]ature at :i* cry/allization takes place ) v great sl[ness4 ,if1 h[ev]1 glass is heat$1 a temp]ature is rea*$1 mu* bel[ ! melt+ po9t ( ! glass1 at :i* cry/allization occurs ) appreciable velocity1 & we obs]ve ! ph5om5on ( devitrification4#ach ,:5 ! velocity ( cry/allization is /udi$ at temp]atures above ! maximum po9t1 x is f\nd t ! velocity is dim9i%$ by ! addition ( =eign sub/ances2 & 9 _m cases1 inde$1 x has be5 f\nd t ! dim9ution is ! same = equimolecul> quantities ( diff]5t sub/ances4 ,x w\ld h5ce appe> possible to utilize ?is behavi\r z a me?od = det]m9+ molecul> weights4#aci ,! rule is1 h[ev]1 by no means a univ]sal "o4 ,?us x has be5 f\nd by ,f4 ,drey]1#adj 9 /udy+ ! velocity ( cry/allization ( =manilide1 t ! dim9ution 9 ! velocity produc$ by equival5t am\nts ( diff]5t sub/ances is n ! same1 b t ! =eign sub/ances ex]cise a specific influ5ce4 ,fur!r1 von ,pick>dt's rule does n hold :5 ! =eign sub/ance =ms mix$ cry/als 7,*ap4 ,x47 ) ! cry/alliz+ sub/ance4#ada ,law ( ,successive ,reactions4--,:5 sulphur vap\r is cool$ at ! ord9>y temp]ature1 x fir/ ( all cond5ses to drops ( liquid1 :i* solidify 9 an amorph\s =m1 & only aft] "s "t und]go cry/allization2 or1 :5 phosphorus vap\r is cond5s$1 :ite phosphorus is fir/ =m$1 & n ! m /able =m--r$ phosphorus4 ,x has also be5 obs]v$ t ev5 at ! ord9>y temp]ature 7!re=e mu* bel[ ! transition po9t7 sulphur may cry/allize out f solution 9 b5z5e1 alcohol1 c>bon disulphide1 & o!r #gd solv5ts1 9 ! prismatic =m1 ! less /able prismatic cry/als !n und]go+ trans=mation into ! rhombic =m2#adb a simil> behavi\r has also be5 obs]v$ 9 ! trans=mation ( ! monotropic cry/all9e =ms ( sulphur4#adc ,_m o!r examples might be giv54 ,9 organic *emi/ry1 = in/ance1 x is (t5 f\nd t :5 a sub/ance is ?r[n out ( solution1 x is fir/ deposit$ z a liquid1 :i* passes lat] into ! m /able cry/all9e =m4 ,9 analysis1 also1 rapid precipitation f conc5trat$ solution (t5 causes ! sep>ation ( a less /able & m soluble amorph\s =m4 ,on acc\nt ( ! great frequ5cy ) :i* ! prior =mation ( ! less /able =m occurs1 ,o/wald#add has put =w>d ! law ( successive reactions1 :i* /ates t :5 a sy/em passes f a less /able condition x does n pass directly into ! mo/ /able ( ! possible /ates2 b into ! next m /able1 & s /ep by /ep into ! mo/ /able4 ,?is law expla9s ! =mation ( ! meta/able =ms ( monotropic sub/ances1 :i* w\ld o!rwise n be obta9able4 ,al?\gh x is n always possible to obs]ve ! =mation ( ! lea/ /able =m1 x %\ld be rememb]$ t t may q conceivably be due to ! great velocity ( trans=mation ( ! less /able into ! m /able =m4 ,f :at we h le>n$ ab\t ! velocity ( trans=mation ( meta/able phases1 we c und]/& t rapid cool+ to a l[ temp]ature w t5d to pres]ve ! less /able =m2 &1 on acc\nt ( ! influ5ce ( temp]ature 9 increas+ ! velocity ( *ange1 x c be se5 t ! =mation ( ! less /able =m w be m difficult to obs]ve 9 sup]heat$ ?an 9 sup]cool$ sy/ems4 ,! factors1 h[ev]1 :i* affect ! read9ess ) :i* #ge ! less /able modification is produc$1 appe> to be r v>i\s4#ade ,al?\gh a numb] ( at lea/ app>5t exceptions to ,o/wald's law h be5 f\nd1 x may nev]!less be accept$ z a v useful g5]alization :i* sums up v frequ5tly obs]v$ ph5om5a4 99 99 99 99 99 #gf ,,*apt] ,v ,,sy/ems ,,( ,,two ,,compon5ts--,,ph5om5a ,,( ,,dissociation ,9 ! prec$+ pages we h /udi$ ! behavi\r ( sy/ems consi/+ ( only "o compon5t1 or sy/ems 9 :i* all ! phases1 :e!r solid1 liquid1 or vap\r1 _h ! same *emical composition 7p4 #ac74 ,9 "s cases1 z1 = example1 9 ! case ( phosphorus & sulphur1 ! compon5t 0 an elem5t>y sub/ance2 9 o!r cases1 h[ev]1 e4g4 wat]1 ! compon5t 0 a comp\nd4 ,! sy/ems :i* we n[ proce$ to /udy are *>act]iz$ by ! fact t ! diff]5t phases h no long] all ! same *emical composition1 & _c1 !re=e1 accord+ to def9ition1 be consid]$ z "o-compon5t sy/ems4 ,9 mo/ cases1 little or no difficulty w be exp]i5c$ 9 decid+ z to ! numb] ( ! compon5ts1 if ! rules giv5 on pp4 #ab & #ac are borne 9 m9d4 ,if ! composition ( all ! phases1 ea* reg>d$ z a :ole1 is ! same1 ! sy/em is to be reg>d$ z ( ! fir/ ord]1 or a "o-compon5t sy/em2 if ! composition ( ! diff]5t phases v>ies1 ! sy/em mu/ conta9 m ?an "o compon5t4 ,if1 9 ord] to express ! composition ( all ! phases pres5t :5 ! sy/em is 9 equilibrium1 two ( ! con/itu5ts p>ticipat+ 9 ! equilibrium are necess>y & suffici5t1 ! sy/em is "o ( two compon5ts4 ,:i* two ( ! possible sub/ances are to be reg>d$ z compon5ts w1 h[ev]1 be to a c]ta9 ext5t a matt] ( arbitr>y *oice4 ,! pr9ciples affect+ ! *oice ( compon5ts w be/ be le>n$ by a /udy ( ! examples to be discuss$ 9 ! sequel4 #gg ,diff]5t ,sy/ems ( ,two ,compon5ts4--,apply+ ! ,phase ,rule ,p ,f ,c #b to sy/ems ( two compon5ts1 we see t 9 ord] t ! sy/em may be inv>iant1 !re mu/ be f\r phases 9 equilibrium toge!r2 two compon5ts 9 ?ree phases con/itute a univ>iant1 two compon5ts 9 two phases a biv>iant sy/em4 ,9 ! case ( sy/ems ( "o compon5t1 ! highe/ degree ( v>iability f\nd 0 two 7"o compon5t 9 "o phase72 b1 z is evid5t f ! =mula1 !re is a high] degree ( fre$om possible 9 ! case ( two-compon5t sy/ems4 ,two compon5ts exi/+ 9 only "o phase con/itute a t]v>iant sy/em1 or a sy/em ) ?ree degrees ( fre$om4 ,9 addition to ! pressure & temp]ature1 !re=e1 a ?ird v>iable factor mu/ be *os51 & z su* !re is tak5 ! conc5tration ( ! compon5ts4 ,9 sy/ems ( two compon5ts1 !re=e1 n only may !re be *ange ( pressure & temp]ature1 z 9 ! case ( "o-compon5t sy/ems1 b ! conc5tration ( ! compon5ts 9 ! diff]5t phases may also alt]2 a v>iation :i* did n require to be consid]$ 9 ! case ( "o-compon5t sy/ems4 ,illu/ration3 ,,fig4 #ah4 ,s9ce a two-compon5t sy/em may und]go ?ree possible #gh indep5d5t v>iations1 we %\ld require = ! graphic repres5tation ( all ! possible conditions ( equilibrium a sy/em ( ?ree co-ord9ates 9 space1 ?ree axes be+ *os51 say1 at "r angles to "o ano!r1 & repres5t+ ! ?ree v>iables--pressure1 temp]ature1 & conc5tration ( compon5ts 7,fig4 #ah74 ,a curve 7e4g4 ,,ab7 9 ! plane conta9+ ! pressure & temp]ature axes w\ld !n repres5t ! *ange ( pressure ) ! temp]ature1 ! conc5tration rema9+ unalt]$ 7pt-diagram72 "o 9 ! plane conta9+ ! pressure & conc5tration axes 7e4g4 ,,af or ,,df71 ! *ange ( pressure ) ! conc5tration1 ! temp]ature rema9+ con/ant 7pc-diagram71 :ile 9 ! plane conta9+ ! conc5tration & ! temp]ature axes1 ! simultane\s *ange ( ^! two factors at con/ant pressure w\ld be repres5t$ 7tc-diagram74 ,if ! po9ts on ^! ?ree curves are jo9$ toge!r1 a surface1 ,,abde1 w be =m$1 & any l9e on t surface 7e4g4 ,,fg1 or ,,gh1 or ,,gi7 w\ld repres5t ! simultane\s v>iation ( ! ?ree factors--pressure1 temp]ature1 conc5tration4 ,al?\gh we %all at a lat] po9t make "s use ( ^! solid figures1 we %all = ! pres5t employ ! m readily intelligible plane diagram4 ,! numb] ( diff]5t sy/ems :i* c be =m$ f two compon5ts1 z well z ! numb] ( ! diff]5t ph5om5a :i* c !re be obs]v$1 is mu* great] ?an 9 ! case ( "o compon5t4 ,9 ! case ( no two sub/ances1 h[ev]1 h all ! possible relation%ips be5 /udi$2 s t = ! purpose ( ga9+ an insight into ! v v>i$ behavi\r ( two-compon5t sy/ems1 a numb] ( diff]5t examples w be discuss$1 ea* ( :i* w s]ve to give a picture ( "s ( ! relation%ips4 ,al?\gh ! /rict classification ( ! diff]5t sy/ems accord+ to ! ,phase ,rule w\ld be bas$ on ! v>iability ( ! sy/ems1 ! /udy ( ! _m diff]5t ph5om5a1 & ! correlation ( ! comp>atively l>ge numb] ( diff]5t sy/ems1 w probably be r5d]$ easie/ by gr\p+ ^! diff]5t ph5om5a into classes1 ea* ( ^! classes be+ /udi$ ) ! help ( "o or m typical examples4 ,! ord] ( treatm5t adopt$ "h is1 ( c\rse1 q arbitr>y2 #gi b has be5 select$ f consid]ations ( simplicity & cle>ness4 ,,ph5om5a ,,( ,,dissociation4 ,biv>iant ,sy/ems4--,z ! fir/ examples ( ! equilibria betwe5 a sub/ance & its products ( dissociation1 we %all consid] v briefly ^? cases 9 :i* !re is "o solid phase 9 equilibrium ) vap\r4 ,ref]5ce has already be5 made to su* sy/ems 9 ! case ( ammonium *loride4 ,on be+ heat$1 ammonium *loride dissociates into ammonia & hydrog5 *loride4 ,s9ce1 h[ev]1 9 t case ! vap\r phase has ! same total composition z ! solid phase1 viz4 ,,nh#c ,h,cl ,,nh#d;,cl1 ! sy/em consi/s ( only "o compon5t exi/+ 9 two phases2 x is !re=e univ>iant1 & to ea* temp]ature !re w correspond a def9ite vap\r pressure 7dissociation pressure74#adf ,if1 h[ev]1 excess ( "o ( ! products ( dissociation be add$1 ! sy/em becomes "o ( two compon5ts4 ,9 ! fir/ place1 analysis ( ea* ( ! two phases yields z ! composition ( ea*1 solid3 ,,nh#d;,cl 7 ,,nh#c ,h,cl72 vap\r3 m,,nh#c n,h,cl4 ,obvi\sly ! smalle/ numb] ( sub/ances by :i* ! composition ( ! two phases c be express$ is two2 t is1 ! numb] ( compon5ts is two4 ,:at1 !n1 are ! compon5ts8 ,! *oice lies betwe5 ,,nh#c ,h,cl1 ,,nh#d;,cl ,,nh#c1 & ,,nh#d;,cl ,h,cl2 = ! ?ree sub/ances1 ammonium *loride1 ammonia1 hydrog5 *loride1 are ! only ones tak+ "p 9 ! equilibrium ( ! sy/em4 ,( ^! ?ree pairs ( compon5ts1 we %\ld obvi\sly *oose z ! mo/ simple ,,nh#c & ,h,cl1 = we c !n repres5t ! composition ( ! two phases z ! sum ( ! two compon5ts4 ,if "o ( ! o!r two possible pairs ( compon5ts be *os51 we %\ld h to introduce negative quantities ( "o ( ! compon5ts1 9 ord] to repres5t ! composition ( ! vap\r phase4 ,al?\gh x mu/ be all[$ t ! introduction ( negative quantities ( a compon5t 9 su* cases is q p]missible1 /ill x w be #hj bett] to adopt ! simpl] & m direct *oice1 :]eby ! composition ( ea* ( ! phases is repres5t$ z a sum ( two compon5ts 9 v>y+ proportions 7p4 #ab74 ,if1 !re=e1 we h a solid sub/ance1 su* z ammonium *loride1 :i* dissociates on volatilization1 & if ! products ( dissociation are add$ 9 v>y+ am\nts to ! sy/em1 we %all h1 9 ! s5se ( ! ,phase ,rule1 a two-compon5t sy/em exi/+ 9 two phases4 ,su* a sy/em w possess two degrees ( fre$om4 ,at any giv5 temp]ature1 n only ! pressure1 b also ! composition1 ( ! vap\r-phase1 i4e4 ! conc5tration ( ! compon5ts1 c v>y4 ,only aft] "o ( ^! indep5d5t v>iables1 pressure or composition1 has be5 arbitr>ily fix$ does ! sy/em become univ>iant1 & exhibit a def9ite1 con/ant pressure at a giv5 temp]ature4 ,n[1 al?\gh ! ,phase ,rule in=ms u t at a giv5 temp]ature *ange ( composition ( ! vap\r phase w be accompani$ by *ange ( pressure1 x does n ca/ any light on ! relation betwe5 ^! two v>iables4 ,?is relation%ip1 h[ev]1 c be calculat$ !oretically by means ( ! ,law ( ,mass ,action4#adg ,f ?is we le>n t 9 ! case ( a sub/ance :i* dissociates into equival5t quantities ( two gases1 ! product ( ! p>tial pressures ( ! gases is con/ant at a giv5 temp]ature4 ,?is has be5 prov$ exp]im5tally 9 ! case ( ammonium hydrosulphide1 ammonium cyanide1 phosphonium bromide1 & o!r sub/ances4#adh ,univ>iant ,sy/ems4--,9 ord] t a sy/em ( two compon5ts %all possess only "o degree ( fre$om1 ?ree phases mu/ be pres5t4 ,( su* sy/ems1 !re are sev5 possible1 viz4 ,s-,s-,s1 ,s-,s-,l1 ,s-,s-,v1 ,l-,l-,l1 ,s-,l-,l1 ,l-,l-,v1 ,s-,l-,v2 ,s d5ot+ solid1 ,l liquid1 & ,v vap\r4 ,9 ! pres5t *apt] we %all consid] only ! sy/ems ,s-,s-,v1 i4e4 ^? sy/ems 9 :i* !re are two solid phases & a vap\r phase pres5t4 #ha ,z an example ( ?is1 we may fir/ consid] ! well-kn[n case ( ! dissociation ( calcium c>bonate4 ,?is sub/ance on be+ heat$ dissociates into calcium oxide1 or quick-lime1 & c>bon dioxide1 z %[n by ! equation ,ca,c,o#c -- ,ca,o ,,co#b4 ,9 accordance ) our def9ition 7p4 #i71 we h "h two solid phases1 ! c>bonate & ! quick-lime1 & "o vap\r phase2 ! sy/em is !re=e univ>iant4 ,to ea* temp]ature1 !re=e1 !re w correspond a c]ta91 def9ite maximum pressure ( c>bon dioxide 7dissociation pressure71 & ?is w foll[ ! same law z ! vap\r pressure ( a pure liquid 7p4 #ba74 ,m p>ticul>ly1 x w be indep5d5t ( ! relative or absolute am\nts ( ! two solid phases1 & ( ! volume ( ! vap\r phase4 ,if ! temp]ature is ma9ta9$ con/ant1 increase ( volume w cause ! dissociation ( a fur!r am\nt ( ! c>bonate until ! pressure aga9 rea*es its maximum value correspond+ to ! giv5 temp]ature4 ,dim9ution ( volume1 on ! o!r h&1 w br+ ab\t ! comb9ation ( a c]ta9 quantity ( ! c>bon dioxide ) ! calcium oxide until ! pressure aga9 rea*es its orig9al value4 ,! dissociation pressure ( calcium c>bonate 0 fir/ /udi$ by ,debray1#adi b m exact measurem5ts h be5 made by ,le ,*ateli]1#aej :o f\nd ! foll[+ correspond+ values ( temp]ature & pressure3-- -------------------------------------- ,temp]ature4 ,pressure 9 cm4 m]cury4 -------------------------------------- #edg;deg #b4g #faj;deg #d4f #fbe;deg #e4f #gdj;deg #be4e #gde;deg #bh4i #haj;deg #fg4h #hab;deg #gf4c #hfe;deg #acc4c -------------------------------------- ,f ?is table we see t x is only at a temp]ature ( ab\t #hab;deg t ! pressure ( ! c>bon dioxide becomes equal to atmosph]ic pressure4 ,9 a vessel op5 to #hb ! air1 !re=e1 ! complete decomposition ( ! calcium c>bonate w\ld n take place bel[ ?is temp]ature by ! m]e heat+ ( ! c>bonate4 ,if1 h[ev]1 ! c>bon dioxide is remov$ z quickly z x is =m$1 say by a curr5t ( air1 !n ! entire decomposition c be made to take place at a mu* l[] temp]ature4 ,= ! dissociation equilibrium ( ! c>bonate dep5ds only on ! p>tial pressure ( ! c>bon dioxide1 & if ?is is kept small1 !n ! decomposition c proce$1 ev5 at a temp]ature bel[ t at :i* ! pressure ( ! c>bon dioxide is less ?an atmosph]ic pressure4 ,ammonia ,comp\nds ( ,metal ,*lorides4--,ammonia possesses ! prop]ty ( comb9+ ) v>i\s sub/ances1 *iefly ! halides ( metals1 to =m comp\nds :i* aga9 yield up ! ammonia on be+ heat$4 ,?us1 = example1 on pass+ ammonia ov] silv] *loride1 absorption ( ! gas takes place ) =mation ( ! sub/ances ,ag,cl1#c,,nh#c & #b;,ag,cl1#c,,nh#c1 accord+ to ! conditions ( ! exp]im5t4 ,^! 7 ! fir/ kn[n sub/ances belong+ to ?is class1 & 7 employ$ by ,f>aday 9 8 exp]im5ts on ! liquefaction ( ammonia4 ,simil> comp\nds h also be5 obta9$ by ! action ( ammonia on silv] bromide1 iodide1 cyanide1 & nitrate2 & ) ! halog5 comp\nds ( calcium1 z9c1 & magnesium1 z well z ) o!r salts4 ,! behavi\r ( ! ammonia comp\nds ( silv] *loride is typical = ! comp\nds ( ?is class1 & may be briefly consid]$ "h4 ,x 0 f\nd by ,isamb]t#aea t at temp]atures bel[ #ae;deg1 silv] *loride comb9$ ) ammonia to =m ! comp\nd ,ag,cl1#c,,nh#c1 :ile at temp]atures above #bj;deg ! comp\nd #b;,ag,cl1#c,,nh#c 0 produc$4 ,on heat+ ^! sub/ances1 ammonia 0 evolv$1 & ! pressure ( ?is gas 0 f\nd 9 ! case ( bo? comp\nds to be con/ant at a giv5 temp]ature1 b 0 great] 9 ! case ( ! =m] ?an 9 ! case ( ! latt] sub/ance2 ! pressure1 fur!r1 0 indep5d5t ( ! am\nt decompos$4 ,! behavi\r ( ^! two sub/ances is1 !re=e1 exactly analog\s to t %[n by calcium c>bonate1 & ! explanation is also simil>4 #hc ,reg>d$ f ! po9t ( view ( ! ,phase ,rule1 we see t we are "h deal+ ) two compon5ts1 ,ag,cl & ,,nh#c4 ,on be+ heat$1 ! comp\nds decompose accord+ to ! equations3-- #b7;,ag,cl1#c,,nh#c7 -- #b;,ag,cl1#c,,nh#c #c,,nh#c4 #b;,ag,cl1#c,,nh#c -- #b;,ag,cl #c,,nh#c4 ,!re are1 !re=e1 ?ree phases1 viz4 ,ag,cl1#c,,nh#c2 #b;,ag,cl1#c,,nh#c1 & ,,nh#c1 9 ! "o case2 & #b;,ag,cl1#c,,nh#c2 ,ag,cl1 & ,,nh#c 9 ! o!r4 ,^! two sy/ems are !re=e univ>iant1 & to ea* temp]ature !re mu/ correspond a def9ite pressure ( dissociation1 q irrespective ( ! am\nts ( ! phases pres5t4 ,simil>ly1 if1 at con/ant temp]ature1 ! volume is increas$ 7or if ! ammonia :i* is evolv$ is pump$ (f71 ! pressure w rema9 con/ant s long z two solid phases1 ,ag,cl1#c,,nh#c & #b;,ag,cl1#c,,nh#c1 are pres5t1 i4e4 until ! comp\nd ri*] 9 ammonia is completely decompos$1 :5 !re w be a sudd5 fall 9 ! pressure to ! value correspond+ to ! sy/em #b;,ag,cl1#c,,nh#c--;,ag,cl--,,nh#c4 ,! pressure w aga9 rema9 con/ant at con/ant temp]ature1 until all ! ammonia has be5 pump$ (f1 :5 !re w aga9 be a sudd5 fall 9 ! pressure to t ( ! sy/em =m$ by solid silv] *loride 9 contact ) its vap\r4 ,! rev]se *anges take place :5 ! pressure ( ! ammonia is gradually increas$4 ,if ! volume is cont9u\sly dim9i%$1 ! pressure w fir/ increase until x has rea*$ a c]ta9 value2 ! comp\nd #b;,ag,cl1#c,,nh#c c !n be =m$1 & ! pressure w n[ rema9 con/ant until all ! silv] *loride has disappe>$4 ,! pressure w aga9 rise1 until x has rea*$ ! value at :i* ! comp\nd ,ag,cl1#c,,nh#c c be =m$1 :5 x w aga9 rema9 con/ant until ! complete disappe>ance ( ! l[] comp\nd4 ,!re is no gradual *ange ( pressure on pass+ f "o sy/em to ano!r2 b ! *anges are abrupt1 z is dem&$ by ! ,phase ,rule1 & z exp]im5t has conclusively prov$4#aeb ,! dissociation pressures ( ! two comp\nds ( silv] #hd *loride & ammonia1 z det]m9$ by ,isamb]t1#aec are giv5 9 ! foll[+ table3-- ---------------------------------------- ---------- ,ag,cl1#c,,nh#c4 #b;,ag,cl1#c,,nh#c4 ---------------------------------------- -------- ,temp]ature4 ,pressure4 ,temp]ature4 ,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 ---------------------------------------- -------- ,! conditions = ! =mation ( ^! two comp\nds1 by pass+ ammonia ov] silv] *loride1 to :i* ref]5ce has already be5 made1 w be readily und]/ood f ! above tables4 ,9 ! case ( ! triammonia mono-*loride1 ! dissociation pressure becomes equal to atmosph]ic pressure at a temp]ature ( ab\t #bj;deg2 above ?is temp]ature1 !re=e1 x _c be =m$ by ! action ( ammonia at atmosph]ic pressure on silv] *loride4 ,! triammonia di*loride c1 h[ev]1 be =m$1 = its dissociation pressure at ?is temp]ature am\nts to only #i cm41 & becomes equal to ! atmosph]ic pressure only at a temp]ature ( ab\t #fh;deg2 & ?is temp]ature1 !re=e1 con/itutes ! limit above :i* no comb9ation c take place betwe5 silv] *loride & ammonia "u atmosph]ic pressure4 ,att5tion may be "h drawn to ! fact1 to :i* ref]5ce w also be made lat]1 t two solid phases are necess>y 9 ord] t ! dissociation pressure at a giv5 temp]ature %all be def9ite2 & = ! exact def9ition ( ?is pressure x is necess>y to "k1 n m]ely :at is ! sub/ance und]go+ dissociation1 b also :at is ! solid product ( dissociation =m$4 ,= ! def9ition ( ! equilibrium1 ! latt] is z important z ! =m]4 ,we %all pres5tly f9d pro( ( ?is 9 ! case #he ( an analog\s class ( ph5om5a1 viz4 ! dissociation ( salt hydrates4 ,salts ) ,wat] ( ,cry/allization4--,9 ! case ( ! dehydration ( cry/all9e salts conta9+ wat] ( cry/allization1 we meet ) ph5om5a :i* are 9 all respects simil> to ^? j /udi$4 ,a salt hydrate on be+ heat$ dissociates into a l[] hydrate 7or anhydr\s salt7 & wat] vap\r4 ,s9ce we are deal+ ) two compon5ts--salt & wat]#aed--;9 ?ree phases1 viz4 hydrate a1 hydrate b 7or anhydr\s salt71 & vap\r1 ! sy/em is univ>iant1 & to ea* temp]ature !re w correspond a c]ta91 def9ite vap\r pressure 7! dissociation pressure71 :i* w be indep5d5t ( ! relative or absolute am\nts ( ! phases1 i4e4 ( ! am\nt ( hydrate :i* has already und]gone dissociation or dehydration4 ,illu/ration3 ,,fig4 #ai4 ,! con/ancy ( ! dissociation pressure _h be5 prov$ exp]im5tally by sev]al inve/igators#aee a numb] ( ye>s be=e ! !oretical basis = its necessity _h be5 giv54 ,9 ! case ( salts capable ( =m+ m ?an "o hydrate1 we %\ld obta9 a s]ies ( dissociation curves 7pt-curves71 z 9 ! case ( ! diff]5t hydrates ( copp] sulphate4 ,9 ,fig4 #ai !re are repres5t$ diagrammatically ! vap\r-pressure curves ( ! foll[+ univ>iant sy/ems ( copp] sulphate & wat]3-- ,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 u n[ foll[ ! *anges :i* take place on #hf increas+ ! pressure ( ! aque\s vap\r 9 contact ) anhydr\s copp] sulphate1 ! temp]ature be+ mean:ile ma9ta9$ con/ant4 ,if1 />t+ f ! po9t ,d1 we sl[ly add wat] vap\r to ! sy/em1 ! pressure w gradually rise1 )\t =mation ( hydrate tak+ place2 = at pressures bel[ ! curve ,,oc only ! anhydr\s salt c exi/4 ,at ,e1 h[ev]1 ! hydrate ,cu,s,o#d1;,h#b,o w be =m$1 & z !re are n[ ?ree phases pres5t1 viz4 ,cu,s,o#d1 ,cu,s,o#d1;,h#b,o1 & vap\r1 ! sy/em becomes univ>iant2 & s9ce ! temp]ature is con/ant1 ! pressure mu/ also be con/ant4 ,cont9u$ addition ( vap\r w result m]ely 9 an increase 9 ! am\nt ( ! hydrate1 & a decrease 9 ! am\nt ( ! anhydr\s salt4 ,:5 ! latt] has entirely disappe>$1 i4e4 has pass$ into hydrat$ salt1 ! sy/em aga9 becomes biv>iant1 & passes along ! l9e ,,ef2 ! pressure gradually increases1 !re=e1 until at ,f ! hydrate #c;,h#b,o is =m$1 & ! sy/em aga9 becomes univ>iant2 ! ?ree phases pres5t are ,cu,s,o#d1;,h#b,o1 ,cu,s,o#d1c;,h#b,o1 vap\r4 ,! pressure w rema9 con/ant1 !re=e1 until ! hydrate #a;,h#b,o has disappe>$1 :5 x w aga9 increase till ,g is rea*$2 "h ! hydrate #e;,h#b,o is =m$1 & ! pressure once m rema9s con/ant until ! complete disappe>ance ( ! hydrate #c;,h#b,o has tak5 place4 ,conv]sely1 on dehydrat+ ,cu,s,o#d1e;,h#b,o at con/ant temp]ature1 we %\ld f9d t ! pressure w\ld ma9ta9 ! value correspond+ to ! dissociation pressure ( ! sy/em ,cu,s,o#d1e;,h#b,o--,cu,s,o#d1c;,h#b,o-- vap\r1 until all ! hydrate #e;,h#b,o _h disappe>$2 fur!r removal ( wat] w\ld !n cause ! pressure to fall abruptly to ! pressure ( ! sy/em ,cu,s,o#d1c;,h#b,o--,cu,s,o#d1;,h#b,o--v ap\r1 at :i* value x w\ld aga9 rema9 con/ant until ! tri-hydrate _h pass$ into ! monohydrate1 :5 a fur!r sudd5 dim9ution ( ! pressure w\ld occur4 ,?is behavi\r is repres5t$ diagrammatically 9 ,fig4 #bj1 ! values ( ! pressure be+ ^? at #ej;deg4 ,effloresc5ce4--,f ,fig4 #ai we are enabl$ to pr$ict ! conditions "u :i* a giv5 hydrat$ salt w effloresce :5 expos$ to ! air4 ,we h j le>n$ t copp] #hg sulphate p5tahydrate1 = example1 w n be =m$ unless ! pressure ( ! aque\s vap\r rea*es a c]ta9 value2 & t conv]sely1 if ! vap\r pressure falls bel[ ! dissociation pressure ( ! p5tahydrate1 ?is salt w und]go dehydration4 ,f ?is1 !n1 x is evid5t t a cry/all9e salt hydrate w effloresce :5 expos$ to ! air1 if ! p>tial pressure ( ! wat] vap\r 9 ! air is l[] ?an ! dissociation pressure ( ! hydrate4 ,at ! ord9>y temp]ature ! dissociation pressure ( copp] sulphate is less ?an ! pressure ( wat] vap\r 9 ! air1 & !re=e copp] sulphate does n effloresce4 ,9 ! case ( sodium sulphate decahydrate1 h[ev]1 ! dissociation pressure is great] ?an ! normal vap\r pressure 9 a room1 & ?is salt !re=e effloresces4 ,illu/ration3 ,,fig4 #bj4 ,indef9it5ess ( ! ,vap\r ,pressure ( a ,hydrate4--,ref]5ce has already be5 made 7p4 #hd71 9 ! case ( ! ammonia comp\nds ( ! metal *lorides1 to ! importance ( ! solid product ( dissociation = ! def9ition ( ! dissociation pressure4 ,simil>ly also 9 ! case ( a hydrat$ salt4 ,a salt hydrate 9 contact ) vap\r con/itutes only a biv>iant sy/em1 & c exi/ !re=e at diff]5t values ( temp]ature & pressure ( vap\r1 z is se5 f ! diagram1 ,fig4 #ai4 ,anhydr\s copp] sulphate c exi/ 9 contact ) wat] vap\r at all values ( temp]ature & pressure ly+ 9 ! field bel[ ! curve ,,oc2 & ! hydrate ,cu,s,o#d1;,h#b,o c exi/ 9 contact ) vap\r at all values ( temp]ature & pressure 9 ! field ,,boc4 ,simil>ly1 ea* ( ! o!r hydrates c exi/ 9 contact ) vap\r at diff]5t values ( temp]ature & pressure4 ,f ! ,phase ,rule1 h[ev]1 we le>n t1 9 ord] t at a giv5 temp]ature ! pressure ( a two-compon5t sy/em #hh may be con/ant1 !re mu/ be ?ree phases pres5t4 ,/rictly1 !re=e1 we c speak only ( ! vap\r pressure ( a sy/em2 & s9ce1 9 ! cases "u discussion1 ! hydrates dissociate into a solid & a vap\r1 any /atem5t z to ! vap\r pressure ( a hydrate has a def9ite mean+ only :5 ! second solid phase produc$ by ! dissociation is giv54 ,! ev]yday cu/om ( speak+ ( ! vap\r pressure ( a hydrat$ salt acquires a mean+ only ?r\gh ! assumption1 tacitly made1 t ! second solid phase1 or ! solid produc$ by ! dehydration ( ! hydrate1 is ! next l[] hydrate1 :]e m hydrates ?an "o exi/4 ,t a hydrate always dissociates 9 su* a way t ! next l[] hydrate is =m$ is1 h[ev]1 by no means c]ta92 inde$1 cases h be5 met ) :]e app>5tly ! anhydr\s salt1 & n ! l[] hydrate 7! exi/5ce ( :i* 0 possible71 0 produc$ by ! dissociation ( ! high] hydrate4#aef ,t a salt hydrate c exhibit diff]5t vap\r pressures accord+ to ! solid product ( dissociation1 c n only be prov$ !oretically1 b x has also be5 %[n exp]im5tally to be a fact4 ,?us ,ca,cl#b1f;,h#b,o c dissociate into wat] vap\r & ei!r ( two l[] hydrates1 ea* conta9+ f\r molecules ( wat] ( cry/allization1 & designat$ respectively z ,ca,cl#b1d;,h#b,oalpha1 & ,ca,cl#b1d;,h#b,obeta4 ,roozeboom#aeg has %[n t ! vap\r pressure :i* is obta9$ diff]s accord+ to :i* ( ^! two hydrates is =m$1 z c be se5 f ! foll[+ figures3-- ---------------------------------------- ------------------------------- ,pressure ( ,sy/em4 ,temp]ature4 ---------------------------------------- ----------------- ,ca,cl#b1f;,h#b,o2 ,ca,cl#b1 ,ca,cl#b1f;,h#b,o2 ,ca,cl#b1 #d;,h#b,oalpha2 vap\r4 #d;,h#b,obeta2 vap\r4 ---------------------------------------- ------------------------------ -#ae;deg #j4jbg cm4 #j4jbb cm4 #j #j4jib #j4jgf #aj #j4aib #j4afb #bj #j4cgh #j4cae #be #j4ejh #j4dcb #bi4b -- #j4efg #bi4h #j4fhj -- ---------------------------------------- ----------------------------- #hi ,by reason ( ! non-recognition ( ! importance ( ! solid dissociation product = ! def9ition ( ! dissociation pressure ( a salt hydrate1 _m ( ! old] det]m9ations lose mu* ( _! value4 ,susp5d$ ,trans=mation4--,j z 9 sy/ems ( "o compon5t we f\nd t a new phase 0 n necess>ily =m$ :5 ! conditions = its exi/5ce 7 e/abli%$1 s also we f9d t ev5 :5 ! vap\r pressure is l[]$ bel[ ! dissociation pressure ( a sy/em1 dissociation does n necess>ily occur4 ,?is is well kn[n 9 ! case ( ,glaub]'s salt1 fir/ obs]v$ by ,f>aday4 ,undamag$ cry/als ( ,na#b,,s#d1aj;,h#b,o c\ld be kept un*ang$ 9 ! op5 air1 al?\gh ! vap\r pressure ( ! sy/em ,na#b,,s#d1aj;,h#b,o--,na#b,,s#d--vap\r is great] ?an ! ord9>y pressure ( aque\s vap\r 9 ! air4 ,t is to say1 ! possibility ( ! =mation ( ! new phase ,na#b,,s#d 0 giv52 nev]!less ?is new phase did n appe>1 & ! sy/em !re=e became meta/able1 or un/able ) respect to ! anhydr\s salt4 ,:51 h[ev]1 a trace ( ! new phase--! anhydr\s salt--0 br\ght 9 contact ) ! hydrate1 trans=mation occurr$2 ! hydrate effloresc$4 ,! possibility ( susp5d$ trans=mation or ! non-=mation ( ! new phases mu/ also be grant$ 9 ! case :]e ! vap\r pressure is rais$ above t correspond+ to ! sy/em hydrate--anhydr\s salt 7or l[] hydrate7--vap\r2 9 ?is case ! =mation ( ! high] hydrate becomes a possibility1 b n a c]ta9ty4 ,al?\gh !re is no example ( ?is kn[n 9 ! case ( hydrat$ salts1 ! susp5sion ( ! trans=mation has be5 obs]v$ 9 ! case ( ! comp\nds ( ammonia ) ! metal *lorides 7p4 #hb74 ,hor/mann1#aeh = example1 f\nd t ! pressure ( ammonia 9 contact ) #b;,ag,cl1#c,,nh#c c\ld be rais$ to a value high] ?an ! dissociation pressure ( ,ag,cl1#c,,nh#c )\t ?is comp\nd be+ =m$4 ,we see1 !re=e1 t ev5 :5 ! exi/5ce ( ! high] comp\nd 9 contact ) ! l[] became possible1 ! high] comp\nd 0 n imm$iately =m$4 ,range ( ,exi/5ce ( ,hydrates4--,9 ,fig4 #ai ! vap\r #ij pressure curves ( ! diff]5t hydrates ( copp] sulphate are repres5t$ z ma9ta9+ _! relative positions ?r\gh\t ! :ole range ( temp]atures4 ,b ?is is n necess>ily ! case4 ,x is possible t at "s temp]ature ! vap\r pressure curve ( a l[] hydrate may cut t ( a high] hydrate4 ,at temp]atures above ! po9t ( int]section1 ! l[] hydrate w\ld h a high] vap\r pressure ?an ! high] hydrate1 & w\ld !re=e be meta/able ) respect to ! latt]4 ,! range ( /able exi/5ce ( ! l[] hydrate w\ld !re=e end at ! po9t ( int]section4 ,?is appe>s to be ! case ) ! two hydrates ( sodium sulphate1 to :i* ref]5ce w be made lat]4#aei ,con/ancy ( ,vap\r ,pressure & ! ,=mation ( ,comp\nds4--,we h se5 9 ! case ( ! salt hydrates t ! cont9u$ addition ( ! vap\r phase to ! sy/em caus$ an increase 9 ! pressure until at a def9ite value ( ! pressure a hydrate is =m$2 ! pressure !n becomes con/ant1 & rema9s s1 until "o ( ! solid phases has disappe>$4 ,conv]sely1 on )draw+ ! vap\r phase1 ! pressure rema9$ con/ant s long z any ( ! dissociat+ comp\nd 0 pres5t1 indep5d5tly ( ! degree ( ! decomposition 7p4 #hf74 ,?is behavi\r1 n[1 has be5 employ$ = ! purpose ( det]m9+ :e!r or n def9ite *emical comp\nds are =m$4 ,%\ld comp\nds be =m$ betwe5 ! vap\r phase & ! solid1 !n1 on cont9u$ addition or )drawal ( ! vap\r phase1 x w be f\nd t ! vap\r pressure rema9s con/ant = a c]ta9 "t1 & w !n sudd5ly assume a new value1 at :i* x w aga9 rema9 con/ant4 ,by ?is me?od1 ,ramsay#afj f\nd t no def9ite hydrates 7 =m$ 9 ! case ( f]ric & alum9ium oxides1 b t two are =m$ 9 ! case ( lead oxide1 viz4 #b,pb,o1,h#b,o & #c,pb,o1,h#b,o4 ,! me?od has also be5 appli$ to ! inve/igation ( ! s-call$ palladium hydride1#afa & ! results obta9$ appe> to %[ t no comp\nd is =m$4 ,ref]5ce w1 h[ev]1 be made to ?is case lat] 7,*ap4 ,x474 #ia ,measurem5t ( ! ,vap\r ,pressure ( ,hydrates4--,= ! purpose ( measur+ ! small pressures ex]t$ by ! vap\r ( salt hydrates1 use is v g5]ally made ( a diff]5tial manomet] call$ ! ,brem]-,fr[e9 t5simet]4#afb ,?is app>atus has ! =m %[n 9 ,fig4 #ba4 ,x consi/s ( a ,u-tube1 ! limbs ( :i* are b5t close toge!r1 & plac$ 9 front ( a millimetre scale4 ,! b5d ( ! tube is fill$ ) oil or o!r suitable liquid1 e4g4 bromonaph?al5e4 ,if x is desir$ to measure ! dissociation pressure (1 say1 a salt hydrate1 conc5trat$ sulphuric acid is plac$ 9 ! flask e1 & a quantity ( ! hydrate1 well dri$ & p[d]$1#afc 9 ! bulb d4 ,! necks ( ! bulbs d & e are !n seal$ (f4 ,s9ce1 z we h le>n$1 susp5d$ trans=mation may occur1 x is advisable to fir/ p>tially dehydrate ! salt1 9 ord] to ensure ! pres5ce ( ! second solid product ( dissociation2 ! value ( ! dissociation pressure be+ indep5d5t ( ! degree ( dissociation ( ! hydrate 7p4 #hf74 ,! small bulbs d & e hav+ be5 fill$1 ! app>atus is plac$ on its side1 s z to all[ ! liquid to run f ! b5d ( ! tube into ! bulbs a & b2 x is !n exhau/$ ?r\gh f by means ( a m]cury pump1 & seal$ (f4 ,! app>atus is n[ plac$ 9 a p]p5dicul> position 9 a !rmo/at1 & kept at con/ant temp]ature until equilibrium is e/abli%$4 ,s9ce ! vap\r pressure on ! side conta9+ ! sulphuric acid may be reg>d$ z z]o1 ! diff]5ce 9 level ( ! two surfaces ( liquid 9 ! ,u-tube gives directly ! dissociation pressure ( ! hydrate 9 t]ms ( ! p>ticul> liquid employ$2 if ! d5sity ( ! latt] is kn[n1 ! pressure c !n be calculat$ to cm4 ( m]cury4 ,illu/ration3 ,,fig4 #ba4 99 99 99 99 99 #ib ,,*apt] ,,vi ,,solutions ,def9ition4--,9 all ! cases :i* h be5 consid]$ 9 ! prec$+ pages1 ! diff]5t phases--) ! exception ( ! vap\r phase--consi/$ ( a s+le sub/ance ( def9ite composition1 or 7 def9ite *emical individuals4#afd ,b ?is inv>iability ( ! composition is by no means impos$ by ! ,phase ,rule2 on ! contr>y1 we %all f9d 9 ! examples :i* we n[ proce$ to /udy1 t ! p>ticipation ( phases ( v>iable composition 9 ! equilibrium ( a sy/em is 9 no way exclud$4 ,to su* phases ( v>iable composition !re is appli$ ! t]m solution4 ,a solution1 !re=e1 is to be def9$ z a homog5e\s mixture1 ! composition ( :i* c und]go cont9u\s v>iation )9 c]ta9 limits2 ! limits1 namely1 ( its exi/5ce4#afe ,f ?is def9ition we see t ! t]m solution is n re/rict$ to any p>ticul> physical /ate ( sub/ances1 b includes )9 its range n only ! liquid1 b also ! gase\s & solid /ates4 ,we may !re=e h solutions ( gases 9 liquids1 & ( gases 9 solids2 ( liquids 9 liquids or 9 solids2 ( solids 9 liquids1 or ( solids 9 solids4 ,solutions ( gases 9 gases are1 ( c\rse1 also possible2 s9ce1 h[ev]1 gas solutions nev] give rise to m ?an "o phase1 _! #ic treatm5t does n come )9 ! scope ( ! ,phase ,rule1 :i* deals ) het]og5e\s equilibria4 ,x %\ld also be emphasiz$ t ! def9ition ( solution giv5 above1 nei!r creates nor recognizes any di/9ction betwe5 solv5t & dissolv$ sub/ance 7solute72 &1 inde$1 a too p]si/5t use ( ^! t]ms & ! attempt to p]man5tly label ! "o or o!r ( two compon5ts z ! solv5t or ! solute1 c only obscure ! true relation%ips & aggravate ! difficulty ( _! int]pretation4 ,9 all cases x %\ld be rememb]$ t we are deal+ ) equilibria betwe5 two compon5ts 7we conf9e our att5tion 9 ! fir/ in/ance to su*71 ! solution be+ con/itut$ ( ^! compon5ts 9 v>iable & v>y+ am\nts4 ,! *ange f ! case :]e ! "o compon5t is 9 great excess 7ord9>ily call$ ! solv5t7 to t 9 :i* ! o!r compon5t pr$om9ates1 may be q gradual1 s t x is difficult or impossible to say at :at po9t ! "o compon5t ceases to be ! solv5t & becomes ! solute4 ,! adoption ( ?is /&po9t ne$ n1 h[ev]1 preclude "o f employ+ ! conv5tional t]ms solv5t & solute 9 ord9>y language1 especially :5 ref]5ce is made only to "s p>ticul> condition ( equilibrium ( ! sy/em1 :5 ! conc5tration ( ! two compon5ts 9 ! solution is widely diff]5t4 ,,solutions ,,( ,,gases ,,9 ,,liquids4 ,z ! fir/ class ( solutions to :i* we %all turn our att5tion1 !re may be *os5 ! solutions ( gases 9 liquids1 or ! equilibria betwe5 a liquid & a gas4 ,^! equilibria really con/itute a "p ( ! equilibria to be /udi$ m fully 9 ,*apt] ,,viii42 b s9ce ! two-phase sy/ems =m$ by ! solutions ( gases 9 liquids are among ! be/-kn[n ( ! two-compon5t sy/ems1 a %ort section may be "h allott$ to _! treatm5t4 ,:5 a gas is pass$ into a liquid1 absorption takes place to a great] or less ext5t1 & a po9t is at l5g? rea*$ :5 ! liquid absorbs no m ( ! gas2 a condition ( equilibrium is atta9$1 & ! liquid is said to be saturat$ #id ) ! gas4 ,9 ! light ( ! ,phase ,rule1 n[1 su* a sy/em is biv>iant 7two compon5ts 9 two phases72 & two ( ! v>iable factors1 pressure1 temp]ature1 & conc5tration ( ! compon5ts1 mu/ !re=e be *os5 9 ord] t ! condition ( ! sy/em may be def9$4 ,if ! conc5tration & ! temp]ature are fix$1 !n ! pressure is also def9$2 or "u giv5 conditions ( temp]ature & pressure1 ! conc5tration ( ! gas 9 ! solution mu/ h a def9ite value4 ,if1 h[ev]1 ! temp]ature alone is fix$1 ! conc5tration & ! pressure c alt]2 a fact s well kn[n t x does n require to be fur!r insi/$ on4 ,z to ! way 9 :i* ! solubility ( a gas 9 a liquid v>ies ) ! pressure1 ! ,phase ,rule ( c\rse does n /ate2 b guidance on ?is po9t is aga9 yield$ by ! !orem ( van't ,h(f & ,le ,*ateli]4 ,s9ce ! absorption ( a gas is 9 all cases accompani$ by a dim9ution ( ! total volume1 ?is process mu/ take place ) increase ( pressure4 ,?is1 inde$1 is /at$ 9 a quantitative mann] 9 ! law ( ,h5ry1 accord+ to :i* ! am\nt ( a gas absorb$ is proportional to ! pressure4 ,b ?is law mu/ be modifi$ 9 ! case ( gases :i* are v readily absorb$2 ! direction ( *ange ( conc5tration ) ! pressure w1 h[ev]1 /ill be 9 accordance ) ! !orem ( ,le ,*ateli]4 ,if1 on ! o!r h&1 ! pressure is fix$1 !n ! conc5tration w v>y ) ! temp]ature2 & s9ce ! absorption ( gases is 9 all cases accompani$ by ! evolution ( heat1 ! solubility is f\nd1 9 accordance ) ! !orem ( ,le ,*ateli]1 to dim9i% ) rise ( temp]ature4 ,9 consid]+ ! *anges ( pressure accompany+ *anges ( conc5tration & temp]ature1 a di/9ction mu/ be drawn betwe5 ! total pressure & ! p>tial pressure ( ! dissolv$ gas1 9 cases :]e ! solv5t is volatile4 ,9 ^! cases1 ! law ( ,h5ry applies n to ! total pressure ( ! vap\r1 b only to ! p>tial pressure ( ! dissolv$ gas4 #ie ,,solutions ,,( ,,liquids ,,9 ,,liquids4 ,:5 m]cury & wat] are br\ght toge!r1 ! two liquids rema9 side by side )\t mix+4 ,/rictly speak+1 m]cury und\bt$ly dissolves to a c]ta9 ext5t 9 ! wat]1 & wat] no d\bt dissolves1 al?\gh to a less ext5t1 9 ! m]cury2 ! am\nt ( sub/ance pass+ into solution is1 h[ev]1 s m9ute1 t x may1 = all practical purposes1 be left out ( acc\nt1 s long z ! temp]ature does n rise mu* above ! ord9>y4#aff ,on ! o!r h&1 if alcohol & wat] be br\ght toge!r1 complete miscibility takes place1 & "o homog5e\s solution is obta9$4 ,:e!r wat] be add$ 9 increas+ quantities to pure alcohol1 or pure alcohol be add$ 9 increas+ am\nt to wat]1 at no po9t1 at no degree ( conc5tration1 is a sy/em obta9$ conta9+ m ?an "o liquid phase4 ,at ! ord9>y temp]ature1 wat] & alcohol c =m only two phases1 liquid & vap\r4 ,if1 h[ev]1 wat] be add$ to e!r1 or if e!r be add$ to wat]1 solution w n occur to an indef9ite ext5t2 b a po9t w be rea*$ :5 ! wat] or ! e!r w no long] dissolve m ( ! o!r compon5t1 & a fur!r addition ( wat] on ! "o h&1 or e!r on ! o!r1 w cause ! =mation ( two liquid lay]s1 "o conta9+ excess ( wat]1 ! o!r excess ( e!r4 ,we %all1 !re=e1 expect to f9d all grades ( miscibility1 f almo/ p]fect immiscibility to p]fect miscibility1 or miscibility 9 all proportions4 ,9 cases ( p]fect immiscibility1 ! compon5ts d n affect "o ano!r1 & ! sy/em !re=e rema9s un*ang$4 ,su* cases d n call = treatm5t "h4 ,we h to conc]n ourselves "h only ) ! second & ?ird cases1 viz4 ) cases ( complete & ( p>tial miscibility4 ,!re is no ess5tial diff]5ce betwe5 ! two classes1 =1 z we %all see1 #if ! "o passes into ! o!r ) *ange ( temp]ature4 ,! =mal sep>ation into two gr\ps is bas$ on ! miscibility relations at ord9>y temp]atures4 ,p>tial or ,limit$ ,miscibility4--,9 accordance ) ! ,phase ,rule1 a pure liquid 9 contact ) its vap\r con/itutes a univ>iant sy/em4 ,if1 h[ev]1 a small quantity ( a second sub/ance is add$1 :i* is capable ( dissolv+ 9 ! fir/1 a biv>iant sy/em w be obta9$2 = !re are n[ two compon5ts &1 z be=e1 only two phases--! homog5e\s liquid solution & ! vap\r4 ,at con/ant temp]ature1 !re=e1 bo? ! composition ( ! solution & ! pressure ( ! vap\r c und]go *ange2 or1 if ! composition ( ! solution rema9s un*ang$1 ! pressure & ! temp]ature c alt]4 ,if ! second 7liquid7 compon5t is add$ 9 increas+ am\nt1 ! liquid w at fir/ rema9 homog5e\s1 & its composition & pressure w und]go a cont9u\s *ange2 :51 h[ev]1 ! conc5tration has rea*$ a def9ite value1 solution no long] takes place2 two liquid phases are produc$4 ,s9ce !re are n[ ?ree phases pres5t1 two liquids & vap\r1 ! sy/em is univ>iant2 at a giv5 temp]ature1 !re=e1 ! conc5tration ( ! compon5ts 9 ! two liquid phases1 z well z ! vap\r pressure1 mu/ h def9ite values4 ,addition ( "o ( ! compon5ts1 !re=e1 _c alt] ! conc5trations or ! pressure1 b c only cause a *ange 9 ! relative am\nts ( ! phases4 ,! two liquid phases c be reg>d$1 ! "o z a solution ( ! compon5t ,i4 9 compon5t ,,ii41 ! o!r z a solution ( compon5t ,,ii4 9 compon5t ,i4 ,if ! pressure is ma9ta9$ con/ant1 !n to ea* temp]ature !re w correspond a def9ite conc5tration ( ! compon5ts 9 ! two liquid phases2 & addition ( excess ( "o w m]ely alt] ! relative am\nts ( ! two solutions4 ,z ! temp]ature *anges1 ! composition ( ! two solutions w *ange1 & !re w !re=e be obta9$ two solubility curves1 "o %[+ ! solubility ( compon5t ,i4 9 compon5t ,,ii41 ! o!r %[+ ! solubility ( compon5t ,,ii4 9 compon5t ,i4 ,s9ce heat may be ei!r evolv$ or absorb$ :5 "o liquid dissolves 9 ano!r1 ! solubility may dim9i% or increase #ig ) rise ( temp]ature4 ,! two solutions :i* at a giv5 temp]ature correspond to "o ano!r are kn[n z conjugate solutions4 ,! solubility relations ( p>tially miscible liquids h be5 /udi$ by ,gu?rie1#afg & m especially by ,alexejeff#afh & by ,ro?mund4#afi ,a consid]able v>iety ( curves h be5 obta9$1 & we %all !re=e discuss only a few ( ! diff]5t cases :i* may be tak5 z typical ( ! re/4 ,ph5ol & ,wat]4--,:5 ph5ol is add$ to wat] at ! ord9>y temp]ature1 solution takes place1 & a homog5e\s liquid is produc$4 ,:51 h[ev]1 ! conc5tration ( ! ph5ol 9 ! solution has ris5 to ab\t #h p] c5t41 ph5ol ceases to be dissolv$2 & a fur!r addition ( x causes ! =mation ( a second liquid phase1 :i* consi/s ( excess ( ph5ol & a small quantity ( wat]4 ,9 ord9>y language x may be call$ a solution ( wat] 9 ph5ol4 ,if n[ ! temp]ature is rais$1 ?is second liquid phase w disappe>1 & a fur!r am\nt ( ph5ol mu/ be add$ 9 ord] to produce a sep>ation ( ! liquid into two lay]s4 ,9 ?is way1 by increas+ ! am\nt ( ph5ol & not+ ! temp]ature at :i* ! two lay]s disappe>1 ! s-call$ solubility curve ( ph5ol 9 wat] c be obta9$4 ,by not+ ! *ange ( ! solubility ) ! temp]ature 9 ?is mann]1 x is f\nd t at all temp]atures bel[ #fh4d;deg1 ! addition ( m ?an a c]ta9 am\nt ( ph5ol causes ! =mation ( two lay]s2 at temp]atures above ?is1 h[ev]1 two lay]s _c be =m$1 no matt] h[ mu* ph5ol is add$4 ,at temp]atures above #fh4d;deg1 !re=e1 wat] & ph5ol are miscible 9 all proportions4 ,on ! o!r h&1 if wat] is add$ to ph5ol at ! ord9>y temp]ature1 a liquid is produc$ :i* consi/s *iefly ( ph5ol1 & on increas+ ! am\nt ( wat] beyond a c]ta9 po9t1 two lay]s are =m$4 ,on rais+ ! temp]ature ^! two lay]s disappe>1 & a homog5e\s solution is aga9 obta9$4 ,! ph5om5a are exactly analog\s to ^? already describ$4 ,s9ce1 n[1 9 ! second #ih case ! conc5tration ( ! ph5ol 9 ! solution gradually decreases1 :ile 9 ! =m] case x gradually increases1 a po9t mu/ at l5g? be rea*$ at :i* ! composition ( ! two solutions becomes ! same4 ,on mix+ ! two solutions1 !re=e1 "o homog5e\s liquid w be obta9$4 ,b ! po9t at :i* two phases become id5tical is call$ a critical po9t1 s t1 9 accordance ) ?is def9ition1 ! temp]ature at :i* ! two solutions ( ph5ol & wat] become id5tical may be call$ ! critical solution temp]ature1 & ! conc5tration at ?is po9t may be call$ ! critical conc5tration4 ,illu/ration3 ,,fig4 #bb4 ,f :at has be5 said above1 x w be se5 t at any temp]ature bel[ ! critical solution temp]ature1 two conjugate solutions conta9+ wat] & ph5ol 9 diff]5t conc5tration c exi/ toge!r1 "o conta9+ excess ( wat]1 ! o!r excess ( ph5ol4 ,! foll[+ table gives ! composition ( ! two lay]s1 & ! values are repres5t$ graphically 9 ,fig4 #bb4agj ,,ph5ol ,,& ,,wat]4 ,c#a is ! p]c5tage am\nt ( ph5ol 9 ! fir/ lay]4 ,c#b second lay]4 ----------------------------- ,temp]ature4 ,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 ,! critical solution temp]ature = ph5ol & wat] is #fh4d;deg1 ! critical conc5tration #cf4a p] c5t4 ( ph5ol4 ,at all temp]atures above #fh4d;deg1 only homog5e\s solutions ( ph5ol & wat] c be obta9$2 wat] & ph5ol are !n miscible 9 all proportions4 ,at ! critical solution po9t ! sy/em exi/s 9 only two phases--liquid & vap\r4 ,x ought1 !re=e1 to possess two degrees ( fre$om4 ,! re/riction is1 h[ev]1 impos$ t ! composition ( ! two liquid phases1 coexi/+ at a po9t inf9itely ne> to ! critical po9t1 becomes ! same1 & ?is disposes ( "o ( ! degrees ( fre$om4 ,! sy/em is !re=e univ>iant2 & at a giv5 temp]ature ! pressure w h a def9ite value4 ,conv]sely1 if ! pressure is fix$ 7z is ! case :5 ! sy/em is "u ! pressure ( its own vap\r71 !n ! temp]ature w also be fix$2 t is1 ! critical solution temp]ature has a def9ite value dep5d+ only on ! sub/ances4 ,if ! vap\r phase is omitt$1 ! temp]ature w alt] ) ! pressure2 9 ?is case1 h[ev]1 z 9 ! case ( o!r cond5s$ sy/ems1 ! effect ( pressure is slight4 ,f ,fig4 #bb x is easy to pr$ict ! effect ( br++ toge!r wat] & ph5ol 9 any giv5 quantities at any temp]ature4 ,/>t ) a solution ( ph5ol & wat] hav+ ! composition repres5t$ by ! po9t x4 ,if to ?is solution ph5ol is add$ at con/ant temp]ature1 x w dissolve1 & ! composition ( ! solution w gradually *ange1 z %[n by ! dott$ l9e xy4 ,:51 h[ev]1 ! conc5tration has rea*$ ! value repres5t$ by ! po9t y1 two liquid lay]s w be =m$1 ! "o solution hav+ ! composition repres5t$ by y1 ! o!r t repres5t$ by y'4 ,! sy/em is n[ univ>iant1 & on fur!r addition ( ph5ol1 ! composition ( ! two liquid phases w rema9 un*ang$1 b _! relative am\nts w alt]4 ,! phase ri*] 9 ph5ol w increase 9 am\nt2 t ri*] 9 wat] w decrease1 & ultimately disappe>1 & !re w rema9 ! solution y'4 ,cont9u$ addition ( ph5ol w !n lead to ! po9t x'1 !re be+ n[ only "o liquid phase pres5t4 ,s9ce ! critical solution po9t repres5ts ! highe/ temp]ature at :i* two liquid phases consi/+ ( ph5ol & #ajj wat] c exi/ toge!r1 ^! two sub/ances c be br\ght toge!r 9 any am\nt :atev] at temp]atures high] ?an #fh4d;deg1 )\t ! =mation ( two lay]s4 ,x w !re=e be possible to pass f a sy/em repres5t$ by x to "o repres5t$ by x'1 )\t at any "t two liquid phases appe>+4 ,/>t+ ) x1 ! temp]ature is fir/ rais$ above ! critical solution temp]ature2 ph5ol is !n add$ until ! conc5tration rea*es ! po9t x#b4 ,on all[+ ! temp]ature to fall1 ! sy/em w !n pass into ! condition repres5t$ by x'4 ,illu/ration3 ,,fig4 #bc4 ,me?yle?ylketone & ,wat]4--,9 ! case j describ$1 ! solubility ( ea* compon5t 9 ! o!r increas$ cont9u\sly ) ! temp]ature4 ,!re are1 h[ev]1 cases :]e a maximum or m9imum ( solubility is f\nd1 e4g4 me?yle?ylketone & wat]4 ,! curve :i* repres5ts ! equilibria betwe5 ^! two sub/ances is giv5 9 ,fig4 #bc1 ! conc5tration values be+ conta9$ 9 ! foll[+ table3#aga-- ,,me?yle?ylketone ,,& ,,wat]4 ---------------------------------------- -------- ,temp]ature4 ,c#a p] c5t4 ,c#b p] c5t4 ---------------------------------------- -------- -#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 ,^! numb]s & ,fig4 #bc %[ cle>ly ! occurr5ce ( a m9imum 9 ! solubility ( ! ketone 9 wat]1 & also a m9imum 7at ab\t #aj;deg7 9 ! solubility ( wat] 9 me?yle?ylketone4 ,m9ima ( solubility h also be5 f\nd 9 o!r cases4 ,illu/ration3 ,,fig4 #bd4 ,trie?ylam9e & ,wat]4--,al?\gh 9 mo/ ( ! cases /udi$ ! solubility ( "o liquid 9 ano!r increases ) rise ( temp]ature1 ?is is n s 9 all cases4 ,?us1 at temp]atures bel[ #ah;deg1 trie?ylam9e & wat] mix toge!r 9 all proportions2 b1 on rais+ ! temp]ature1 ! homog5e\s solution becomes turbid & sep>ates into two lay]s4 ,9 ?is case1 !re=e1 ! critical solution temp]ature is f\nd 9 ! direction ( l[] temp]ature1 n 9 ! direction ( high]4#agb ,?is behavi\r is cle>ly %[n by ! graphic repres5tation 9 ,fig4 #bd1 & also by ! numb]s 9 ! foll[+ table3-- ,,trie?ylam9e ,,& ,,wat]4 ---------------------------------------- ------ ,temp]ature4 ,c#a p] c5t4 ,c#b p] c5t4 ---------------------------------------- ------ #gj;deg #a4f -- #ej;deg #b4i -- #cj;deg #e4f #if #be;deg #g4c #ie4e #bj;deg #ae4e #gc _/-#ah4e;deg _/-#cj _/-#cj ---------------------------------------- ------ ,g5]al ,=m ( ,conc5tration-,temp]ature ,curve4--,f ! prec$+ figures x w be se5 t ! g5]al #ajb =m ( ! solubility curve is some:at p>abolic 9 %ape2 9 ! case ( trie?ylam9e & wat]1 ! clos$ end ( ! curve is v flat4 ,s9ce = all liquids !re is a po9t 7critical po9t7 at :i* ! liquid & gase\s /ates become id5tical1 & s9ce all gases are miscible 9 all proportions1 x foll[s t !re mu/ be "s temp]ature at :i* ! liquids become p]fectly miscible4 ,9 ! case ( trie?ylam9e & wat]1 :i* has j be5 consid]$1 !re mu/ !re=e be an upp] critical solution temp]ature1 s t ! complete solubility relations w\ld be repres5t$ by a clos$ curve ( an ellipsoidal aspect4 ,an example ( su* a curve is furni%$ by nicot9e & wat]4 ,at temp]atures bel[ #fj;deg & above #baj;deg1 nicot9e & wat] mix 9 all proportions4#agc ,al?\gh x is possible t ?is is ! g5]al =m ( ! curve = all pairs ( liquids1 !re are z yet insuffici5t data to prove x4 ,) reg>d to ! clos$ end ( ! curve x may be said t x is cont9u\s2 ! critical solution po9t is n ! int]section ( two curves1 = su* a break 9 ! cont9uity ( ! curve c\ld occur only if !re 7 "s discont9uity 9 "o ( ! phases4 ,no su* discont9uity exi/s4 ,! curve is1 !re=e1 n to be consid]$ z two solubility curves cutt+ at a po9t2 x is a curve ( equilibrium betwe5 two compon5ts1 & s long z ! phases und]go cont9u\s *ange1 ! curve repres5t+ ! equilibrium mu/ also be cont9u\s4 ,z has already be5 emphasiz$1 a di/9ction betwe5 solv5t & solute is m]ely conv5tional 7p4 #ic74 ,pressure-,conc5tration ,diagram4--,9 consid]+ ! pressure-conc5tration diagram ( a sy/em ( two liquid compon5ts1 a di/9ction mu/ be drawn betwe5 ! total pressure ( ! sy/em & ! p>tial pressures ( ! compon5ts4 ,on /udy+ ! total pressure ( a sy/em1 x is f\nd t two cases c be obta9$4#agd ,s long z !re is only "o liquid phase1 ! sy/em is biv>iant4 ,! pressure !re=e c *ange ) ! conc5tration & ! temp]ature4 ,if ! temp]ature is ma9ta9$ #ajc con/ant1 ! pressure w v>y only ) ! conc5tration1 & ?is v>iation c !re=e be repres5t$ by a curve4 ,if1 h[ev]1 two liquid phases are =m$1 ! sy/em becomes univ>iant3 & if "o ( ! v>iables1 say ! temp]ature1 is arbitr>ily fix$1 ! sy/em no long] possesses any degree ( fre$om4 ,:5 two liquid phases are =m$1 !re=e1 ! conc5trations & ! vap\r pressure h def9ite values1 :i* are ma9ta9$ s long z ! two liquid phases are pres5t2 ! temp]ature be+ suppos$ con/ant4 ,9 ,fig4 #be is giv5 a diagrammatic repres5tation ( ! two k9ds ( pressure-conc5tration curves :i* h s f> be5 obta9$4 ,9 ! "o case1 ! vap\r pressure ( ! inv>iant sy/em 7at con/ant temp]ature7 lies high] ?an ! vap\r pressure ( ei!r ( ! pure compon5ts2 a ph5om5on :i* is v g5]ally f\nd 9 ! case ( p>tially miscible liquids1 e4g4 e!r & wat]4#age ,accord+ly1 by ! addition ( wat] to e!r1 or ( e!r to wat]1 !re is an increase 9 ! total vap\r pressure ( ! sy/em4 ,illu/ration3 ,,fig4 #be4 ,) reg>d to ! second type1 ! vap\r pressure ( ! sy/ems ) two liquid phases lies betwe5 t ( ! two s+le compon5ts4 ,an example ( ?is is f\nd 9 sulphur dioxide & wat]4#agf ,on add+ sulphur dioxide to wat] !re is an increase ( ! total vap\r pressure2 b on add+ wat] to liquid sulphur dioxide1 ! total vap\r pressure is dim9i%$4 ,! case t ! vap\r pressure ( ! sy/em ) two #ajd liquid phases is less ?an t ( ea* ( ! compon5ts is n possible4 ,) reg>d to ! p>tial pressure ( ! compon5ts1 ! behavi\r is m uni=m4 ,! p>tial pressure ( "o compon5t is 9 all cases l[]$ by ! addition ( ! o!r compon5t1 ! dim9ution be+ approximately proportional to ! am\nt add$4 ,if two liquid phases are pres5t1 ! p>tial pressure ( ! compon5ts1 z well z ! total pressure1 is con/ant1 & is ! same = bo? phases4 ,t is to say1 9 ! case ( ! two liquids1 saturat$ solution ( wat] 9 e!r1 & ( e!r 9 wat]1 ! p>tial pressure ( ! e!r 9 ! vap\r 9 contact ) ! "o solution is ! same z t 9 ! vap\r ov] ! o!r solution4#agg ,complete ,miscibility4--,al?\gh ! ph5om5a ( complete miscibility are "h treat$ "u a sep>ate head+1 x mu/ n be ?\ght t !re is any ess5tial diff]5ce betwe5 ^? cases :]e ! liquids exhibit limit$ miscibility & ^? 9 :i* only "o homog5e\s solution is =m$4 ,z has be5 already po9t$ out1 ! solubility relations alt] ) ! temp]ature2 & liquids :i* at "o temp]ature c dissolve 9 "o ano!r only to a limit$ ext5t1 are f\nd at "s o!r temp]ature to possess ! prop]ty ( complete miscibility4 ,conv]sely1 we may expect t liquids :i* at "o temp]ature1 say at ! ord9>y temp]ature1 are miscible 9 all proportions1 w be f\nd at "s o!r temp]ature to be only p>tially miscible4 ,?us1 = example1 x 0 f\nd by ,gu?rie t e?yl alcohol & c>bon disulphide1 :i* are miscible 9 all proportions at ! ord9>y temp]ature1 possess only limit$ miscibility at temp]atures bel[ -#ad4d;deg4#agh ,nev]!less1 x is d\btful if ! critical solution temp]ature is 9 all cases exp]im5tally realizable4 ,pressure-,conc5tration ,diagram4--,s9ce1 9 ! cases ( complete miscibility ( two liquid compon5ts1 !re are nev] m ?an two phases pres5t1 ! sy/em mu/ always be biv>iant2 & two ( ! v>iables pressure1 temp]ature or conc5tration ( ! compon5ts1 mu/ be arbitr>ily *os5 #aje be=e ! sy/em becomes def9$4 ,= ?is reason ! ,phase ,rule af=ds only a slight guidance 9 ! /udy ( su* equilibria2 & we %all !re=e n ent] 9 detail into ! behavi\r ( ^! homog5e\s mixtures4 ,all t ! ,phase ,rule c tell u 9 connection ) ^! solutions1 is t at con/ant temp]ature ! vap\r pressure ( ! solution v>ies ) ! composition ( ! liquid phase2 & if ! composition ( ! liquid phase rema9s un*ang$1 ! pressure also mu/ rema9 un*ang$4 ,?is con/ancy ( composition is exhibit$ n only by pure liquids1 b also by liquid solutions 9 all cases :]e ! vap\r pressure ( ! solution rea*es a maximum or m9imum value4 ,?is is ! case1 = example1 ) mixtures ( con/ant boil+ po9t4#agi 99 99 99 99 99 #ajf ,,*apt] ,,vii ,,solutions ,,( ,,solids ,,9 ,,liquids1 ,,only ,,"o ,,( ,,! ,,compon5ts ,,be+ ,,volatile ,g5]al4--,:5 a solid is br\ght into contact ) a liquid 9 :i* x c dissolve1 a c]ta9 am\nt ( x passes into solution2 & ! process cont9ues until ! conc5tration rea*es a def9ite value indep5d5t ( ! am\nt ( solid pres5t4 ,a condition ( equilibrium is e/abli%$ betwe5 ! solid & ! solution2 ! solution becomes saturat$4 ,s9ce ! numb] ( compon5ts is two1 & ! numb] ( phases ?ree1 viz4 solid1 liquid solution1 vap\r1 ! sy/em is univ>iant4 ,if1 !re=e1 "o ( ! factors1 pressure1 temp]ature1 or conc5tration ( ! compon5ts 79 ! solution#ahj71 is arbitr>ily fix$1 ! /ate ( ! sy/em becomes p]fectly def9$4 ,?us1 at any giv5 temp]ature1 ! vap\r pressure ( ! sy/em & ! conc5tration ( ! compon5ts h a def9ite value4 ,if ! temp]ature is alt]$1 ! vap\r pressure & also1 9 g5]al1 ! conc5tration w und]go *ange4 ,likewise1 if ! pressure v>ies1 :ile ! sy/em is isolat$ s t no heat c pass betwe5 x & its surr\nd+s1 ! conc5tration & ! temp]ature mu/ also und]go v>iation until !y atta9 values correspond+ to ! p>ticul> pressure4 ,t ! temp]ature has an influ5ce1 sometimes a v consid]able influ5ce1 on ! am\nt ( sub/ance pass+ into solution1 is suffici5tly well kn[n2 ! effect ( pressure1 al?\gh less app>5t1 is no less c]ta94 ,if at any giv5 temp]ature ! volume ( ! vap\r phase is dim9i%$1 #ajg vap\r w cond5se to liquid1 9 ord] t ! pressure may rema9 con/ant1 & s mu* ( ! solid w pass into solution t ! conc5tration may rema9 un*ang$2 =1 s long z ! ?ree phases are pres5t1 ! /ate ( ! sy/em _c alt]4 ,if1 h[ev]1 "o ( ! phases1 e4g4 ! vap\r phase1 disappe>s1 ! sy/em becomes biv>iant2 at any giv5 temp]ature1 !re=e1 !re may be diff]5t values ( conc5tration & pressure4 ,! direction 9 :i* *ange ( conc5tration w occur ) *ange ( pressure c be pr$ict$ by means ( ! !orem ( ,le ,*ateli]1 if x is kn[n :e!r solution is accompani$ by increase or dim9ution ( ! total volume4 ,if dim9ution ( ! total volume ( ! sy/em occurs on solution1 increase ( pressure w increase ! solubility2 9 ! rev]se case1 increase ( pressure w dim9i% ! solubility4 ,?is conclusion has also be5 v]ifi$ by exp]im5t1 z is %[n by ! foll[+ figures4#aha ---------------------------------------- ----------------------- ,*ange ( ,solubility 7at #ah;deg7 7grams salt volume by 9 #a gram ( solution74 dissolv+ #a gm4--------------------------- ,salt4 ( salt 9 ! saturat$ ,pressure ,pressure solution4 #a atm4 #ejj atm4 ---------------------------------------- -------------------- ,sodium *loride -#j4jg #j4bfd #j4bgj ,ammonium *loride #j4aj #j4bgb #j4beh ,alum -#j4jfg #j4aae #j4adb 7p #djj atm47 ---------------------------------------- --------------------- ,z c be se51 a l>ge increase ( ! pressure br+s ab\t a no m ?an appreciable alt]ation ( ! solubility2 a result :i* is due1 z 9 ! case ( ! alt]ation ( ! fusion po9t ) ! pressure1 to ! small *ange 9 volume accompany+ solution or increase ( pressure4 ,= all practical purposes1 !re=e1 ! solubility z det]m9$ "u atmosph]ic pressure may be tak5 z equal to ! true #ajh solubility1 t is1 ! solubility :5 ! sy/em is "u ! pressure ( its own vap\r4 ,! ,saturat$ ,solution4--,f :at has be5 said above1 x w be se5 t ! condition ( saturation ( a solution c be def9$ only ) respect to a c]ta9 solid phase2 if no solid is pres5t1 ! sy/em is undef9$1 = x !n consi/s ( only two phases1 & is !re=e biv>iant4 ,"u su* circum/ances n only c !re be at "o giv5 temp]ature solutions ( diff]5t conc5tration1 all conta9+ less ( "o ( ! compon5ts ?an :5 t compon5t is pres5t 9 ! solid =m1 b !re c also exi/ solutions conta9+ m ( t compon5t ?an corresponds to ! equilibrium :5 ! solid is pres5t4 ,9 ! =m] case ! solutions are unsaturat$1 9 ! latt] case !y are sup]saturat$ ) respect to a c]ta9 solid phase2 9 !mselves1 ! solutions are /able1 & are nei!r unsaturat$ nor sup]saturat$4 ,fur!r1 if ! solid sub/ance c exi/ 9 diff]5t allotropic modifications1 ! p>ticul> =m ( ! sub/ance :i* is 9 equilibrium ) ! solution mu/ be kn[n1 9 ord] t ! /atem5t ( ! solubility may be def9ite2 = ea* =m has its own solubility1 &1 z we %all see pres5tly1 ! less /able =m has ! great] solubility 7cf4 p4 #dg74 ,9 all det]m9ations ( ! solubility1 !re=e1 n only mu/ ! conc5tration ( ! compon5ts 9 ! solution be det]m9$1 b equal importance %\ld be atta*$ to ! *>act]isation ( ! solid phase pres5t4 ,9 ?is connection1 also1 "o o!r po9t may be emphasis$4 ,= ! production ( ! equilibrium betwe5 a solid & a liquid1 "t is necess>y1 & ?is "t n only v>ies ) ! /ate ( division ( ! solid & ! effici5cy ( ! /irr+1 b is also dep5d5t on ! nature ( ! sub/ance4#ahb ,consid]able c>e mu/ !re=e be tak5 t suffici5t "t is all[$ = equilibrium to be e/abli%$4 ,su* c>e is m especially ne$ful :5 *anges may occur 9 ! solid phase1 & neglect ( x has greatly dim9i%$ ! value ( _m ( ! old] det]m9ations ( solubility4 ,=m ( ! ,solubility ,curve4--,! solubility curve--t #aji is1 ! curve repres5t+ ! *ange ( conc5tration ( ! compon5ts 9 ! solution ) ! temp]ature--diff]s m>k$ly f ! curve ( vap\r pressure 7p4 #fc71 9 t x possesses no g5]al =m1 b may v>y 9 ! mo/ div]se mann]4 ,n only may ! curve h an almo/ /raight & horizontal c\rse1 or slope or curve upw>ds at v>y+ angles2 b x may ev5 slope d[nw>ds1 correspond+ to a decrease 9 ! solubility ) rise ( temp]ature2 may exhibit maxima or m9ima ( solubility1 or may1 z 9 ! case ( "s hydrat$ salts1 pass ?r\gh a po9t ( maximum temp]ature4 ,9 ! latt] case ! salt may possess two values ( solubility at ! same temp]ature4 ,we %all consid] ^! cases 9 ! foll[+ *apt]4 ,illu/ration3 ,,fig4 #bf4 ,! great v>iety ( =m %[n by solubility curves is at once app>5t f ,fig4 #bf1 9 :i* ! solubility curves ( v>i\s sub/ances 7n1 h[ev]1 drawn to scale7 are reproduc$4#ahc ,v>i$ z is ! =m ( ! solubility curve1 its direction1 nev]!less1 c be pr$ict$ by means ( ! !orem ( van't ,h(f & ,le ,*ateli]2 = 9 accordance ) t !orem 7p4 #eg7 increase ( solubility ) ! temp]ature mu/ occur 9 ^? cases :]e ! process ( solution is accompani$ by an absorption ( heat2 & a decrease 9 ! solubility ) rise ( temp]ature w be f\nd 9 cases :]e solution occurs ) evolution ( heat4 ,:]e !re is no heat effect accompany+ solution1 #aaj *ange ( temp]ature w be )\t influ5ce on ! solubility2 & if ! sign ( ! heat ( solution *anges1 ! direction ( ! solubility curve mu/ also *ange1 i4e4 mu/ %[ a maximum or m9imum po9t4 ,?is has 9 all cases be5 v]ifi$ by exp]im5t4#ahd ,9 apply+ ! !orem ( ,le ,*ateli] to ! c\rse ( ! solubility curve1 x %\ld be not$ t by heat ( solution !re is meant1 n ! heat effect produc$ on dissolv+ ! salt 9 a l>ge am\nt ( solv5t 7:i* is ! usual signification ( ! expression71 b ! heat :i* is absorb$ or evolv$ :5 ! salt is dissolv$ 9 ! almo/ saturat$ solution 7! s-call$ la/ heat ( solution74 ,n only does ! heat effect 9 ! two cases h a diff]5t value1 b x may ev5 h a diff]5t sign4 ,a /rik+ example ( ?is is af=d$ by cupric *loride1 z ! foll[+ figures %[3#ahe-- ---------------------------------------- ------------------- ,numb] ( gram-molecules ( ,cu,cl#b1 #b;,h#b,o dissolv$ 9 #aih ,heat effect4 gram-molecules ( wat]4 ---------------------------------------- ------------------ #a #cg ,k #b4jb #ff #d4ae #aje #g4jg #aag #i4ie #aag #aa #ia #ah4h -#aj #ai4f -#ca #bd4ge -#aih ---------------------------------------- -------------------- ,9 ! above table ! positive sign indicates evolution ( heat1 ! negative sign1 absorption ( heat2 & ! values ( ! heat effect are express$ 9 c5tuple calories4 ,judg+ f ! heat effect produc$ on dissolv+ cupric *loride 9 a l>ge bulk ( wat]1 we %\ld pr$ict t ! solubility ( t salt w\ld dim9i% ) rise ( temp]ature2 z a matt] ( fact1 x increases4 ,?is is 9 accordance ) ! fact t #aaa ! la/ heat ( solution is negative 7z express$ above71 i4e4 solution ( ! salt 9 ! almo/ saturat$ solution is accompani$ by absorption ( heat4 ,we are l$ to expect ?is f ! fact t ! heat ( solution *anges sign f positive to negative z ! conc5tration increases2 exp]im5t also %[$ x to be ! case4 ,despite its _m =ms1 x %\ld be p>ticul>ly not$ t ! solubility curve ( any sub/ance is cont9u\s1 s long z ! solid phase1 or solid sub/ance 9 contact ) ! solution1 rema9s un*ang$4 ,if any break or discont9u\s *ange 9 ! direction ( ! curve occurs1 x is a sign t ! solid phase has und]gone alt]ation4 ,conv]sely1 if x is kn[n t a *ange takes place 9 ! solid phase1 a break 9 ! solubility curve c be pr$ict$4 ,we %all pres5tly meet ) examples ( ?is4#ahf ,a4--,,anhydr\s ,,salt ,,& ,,wat]4 ,! ,solubility ,curve4--,9 /udy+ ! equilibria 9 ^? sy/ems ( two compon5ts 9 :i* ! liquid phase is a solution or phase ( v>y+ composition1 we %all 9 ! pres5t *apt] limit ! discussion to ^? cases :]e no comp\nds are =m$1 b :]e ! compon5ts cry/allise out 9 ! pure /ate4 ,s9ce "s ( ! be/-kn[n examples ( su* sy/ems are yield$ by ! solutions ( anhydr\s salts 9 wat]1 we %all fir/ ( all briefly consid] "s ( ! results :i* h be5 obta9$ ) !m4 ,= ! mo/ "p ! solubility curves h be5 /udi$ only at temp]atures ly+ betwe5 #j;deg & #ajj;deg1 ! solid phase 9 contact ) ! solution be+ ! anhydr\s salt4 ,= ! repres5tation ( ^! equilibria1 ! conc5tration-temp]ature #aab diagram is employ$1 ! conc5tration be+ express$ z ! numb] ( grams ( ! salt dissolv$ 9 #ajj grams ( wat]1 or z ! numb] ( gram-molecules ( salt 9 #ajj gram-molecules ( wat]4 ,! curves ?us obta9$ exhibit ! diff]5t =ms to :i* ref]5ce has already be5 made4 ,s long z ! salt rema9s un*ang$ ! curve w be cont9u\s1 b if ! salt alt]s its =m1 !n ! solubility curve w %[ a break4 ,illu/ration3 ,,fig4 #bg4 ,n[1 we h already se5 9 ,*apt] ,,iii4 t c]ta9 sub/ances are capable ( exi/+ 9 v>i\s cry/all9e =ms1 & ^! =ms are s relat$ to "o ano!r t at a giv5 temp]ature ! relative /ability ( ea* pair ( polymorphic =ms und]goes *ange4 ,s9ce ea* cry/all9e v>iety ( a sub/ance mu/ h its own solubility1 !re mu/ be a break 9 ! solubility curve at ! temp]ature ( transition ( ! two enantiotropic =ms4 ,at ?is po9t ! two solubility curves mu/ cut1 = s9ce ! two =ms are 9 equilibrium ) respect to _! vap\r1 !y mu/ also be 9 equilibrium ) respect to _! solutions4 ,f ! table on p4 #fc x is se5 t potassium nitrate1 ammonium nitrate1 silv] nitrate1 ?allium nitrate1 ?allium picrate1 are capable ( exi/+ 9 two or m diff]5t enantiotropic cry/all9e =ms1 ! range ( /ability ( ^! =ms be+ limit$ by def9ite temp]atures 7transition temp]ature74 ,s9ce ! transition po9t is n alt]$ by a solv5t 7provid$ ! latt] is n absorb$ by ! solid phase71 we %\ld f9d on /udy+ ! solubility ( ^! sub/ances 9 wat] t ! solubility curve w\ld exhibit a *ange 9 direction at ! temp]ature ( transition4 ,z a matt] ( fact ?is has be5 v]ifi$1 m especially 9 ! case ( ammonium nitrate#ahg #aac & ?allium picrate4#ahh ,! foll[+ table conta9s ! values ( ! solubility ( ammonium nitrate obta9$ by ,muell] & ,kaufmann1 ! solubility be+ express$ 9 gram-molecules ,,nh#d,,no#c 9 #ajj gram-molecules ( wat]4 ,9 ,fig4 #bg ^! results are repres5t$ graphically4 ,! equilibrium po9t 0 approa*$ bo? f ! side ( unsaturation & ( sup]saturation1 & ! condition ( equilibrium 0 controll$ by det]m9ations ( ! d5sity ( ! solution4 ,,solubility ,,( ,,ammonium ,,nitrate4 ---------------------------------------- -------------------- ,temp]ature4 ,solubility4 ,temp]ature4 ,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 ---------------------------------------- -------------------- ,f ! graphic repres5tation ( ! solubility giv5 9 ,fig4 #bg1 !re is se5 to be a di/9ct *ange 9 ! direction ( ! curve at a temp]ature ( #cb;deg2 & ?is break 9 ! curve corresponds to ! transition ( ! beta-rhombic into ! alpha-rhombic =m ( ammonium nitrate 7p4 #fc74 ,susp5d$ ,trans=mation & ,sup]saturation4--,z has already be5 le>n$1 ! trans=mation ( ! "o cry/all9e =m into ! o!r does n necess>ily take place imm$iately ! transition po9t has be5 pass$2 & x has !re=e be5 f\nd possible 9 a numb] ( cases to foll[ ! solubility curve ( a giv5 cry/all9e =m beyond ! po9t at :i* x ceases to be ! mo/ /able modification4 ,n[1 x w be readily se5 f ,fig4 #bg t if ! two solubility curves be prolong$ beyond ! po9t ( int]section1 ! solubility ( ! less /able =m is great] ?an t ( ! m /able4 ,a solution1 !re=e1 :i* is saturat$ ) respect to ! less /able =m1 i4e4 :i* is 9 equilibrium ) t =m1 is sup]saturat$ ) respect to ! m /able modification4 ,if1 #aad !re=e1 a small quantity ( ! m /able =m is introduc$ into ! solution1 ! latt] mu/ deposit su* an am\nt ( ! m /able =m t ! conc5tration ( ! solution corresponds to ! solubility ( ! /able =m at ! p>ticul> temp]ature4 ,s9ce1 h[ev]1 ! solution is n[ unsaturat$ ) respect to ! less /able v>iety1 ! latt]1 if pres5t1 mu/ pass into solution2 & ! two processes1 deposition ( ! /able & solution ( ! meta/able =m1 mu/ g on until ! latt] =m has entirely disappe>$ & a saturat$ solution ( ! /able =m is obta9$4 ,!re w ?us be a conv]sion1 ?r\gh ! m$ium ( ! solv5t1 ( ! less /able into ! m /able modification4 ,?is behavi\r is ( practical importance 9 ! det]m9ation ( transition po9ts 7v4 ,app5dix74 ,f ! above discussion x w be se5 h[ important is ! /atem5t ( ! solid phase = ! def9ition ( saturation & sup]saturation4#ahi ,solubility ,curve at ,high] ,temp]atures4--,on pass+ to ! consid]ation ( ! solubility curves at high] temp]atures1 two *ief cases mu/ be di/+ui%$4 7#a7 ,! two compon5ts 9 ! fus$ /ate c mix 9 all proportions4 7#b7 ,! two compon5ts 9 ! fus$ /ate _c mix 9 all proportions4 #a4 ,complete ,miscibility ( ! ,fus$ ,compon5ts4 ,illu/ration3 ,,fig4 #bh4 ,! be/ example ( ?is :i* has be5 /udi$1 s f> z anhydr\s salts & wat] are conc]n$1 is t ( silv] nitrate & wat]4 ,! solubility ( ?is salt at temp]atures #aae above #ajj;deg has be5 /udi$ *iefly by ,et>d#aij & by ,tild5 & ,%5/one4#aia ,! values obta9$ by ,et>d are giv5 9 ! foll[+ table1 & repres5t$ graphically 9 ,fig4 #bh4 ,,solubility ,,( ,,silv] ,,nitrate4 ---------------------------------------- ----------- ,temp]ature4 ,p>ts ( dry salt 9 #ajj p>ts ( 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 ---------------------------------------- ----------- ,9 ?is figure ! composition ( ! solution is express$ 9 p>ts ( silv] nitrate 9 #ajj p>ts by weight ( ! solution1 s t #ajj p] c5t4 repres5ts pure silv] nitrate4 ,z c be se51 ! solubility increases ) ! temp]ature4 ,at a temp]ature ( ab\t #afj;deg !re %\ld be a break 9 ! curve due to *ange ( cry/all9e =m 7p4 #fc74 ,su* a *ange 9 ! direction ( ! solubility curve1 h[ev]1 does n 9 any way alt] ! ess5tial nature ( ! relation%ips discuss$ "h1 & may = ! pres5t be left out ( acc\nt4 ,on foll[+ ! solubility curve ( silv] nitrate to high] temp]atures1 !re=e1 ! conc5tration ( silv] nitrate 9 ! solution gradually increases1 until at la/1 at a temp]ature ( #bjh;deg1#aib ! melt+ po9t ( pure silv] nitrate is rea*$1 & ! conc5tration ( ! wat] has become z]o4 ,! curve ?r\gh\t its :ole ext5t repres5ts ! equilibrium betwe5 silv] nitrate1 solution1 & vap\r4 ,conv]sely1 />t+ ) pure silv] nitrate 9 contact ) ! fus$ salt1 addition ( wat] w l[] ! melt+ po9t1 i4e4 w l[] ! temp]ature at :i* ! solid salt c exi/ 9 contact ) ! liquid2 #aaf & ! depression w be all ! great] ! l>g] ! am\nt ( wat] add$4 ,z ! conc5tration ( ! wat] 9 ! liquid phase is increas$1 !re=e1 ! sy/em w pass back along ! curve f high] to l[] temp]atures1 & f great] to small] conc5trations ( silv] nitrate 9 ! liquid phase4 ,! curve 9 ,fig4 #bh may1 !re=e1 be reg>d$ ei!r z ! solubility curve ( silv] nitrate 9 wat]1 or z ! freez+ po9t curve = silv] nitrate 9 contact ) a solution consi/+ ( t salt & wat]4 ,z ! temp]ature ( ! saturat$ solution falls1 silv] nitrate is deposit$1 & on l[]+ ! temp]ature suffici5tly a po9t w at la/ be rea*$ at :i* ice also beg9s to sep>ate out4 ,s9ce !re are n[ f\r phases co-exi/+1 viz4 silv] nitrate1 ice1 solution1 vap\r1 ! sy/em is inv>iant1 & ! po9t is a quadruple po9t4 ,?is quadruple po9t1 !re=e1 =ms ! l[] limit ( ! solubility curve ( silv] nitrate4 ,bel[ ?is po9t ! solution becomes meta/able4 ,ice z ,solid ,phase4--,ice melts or is 9 equilibrium ) wat] at a temp]ature ( #j;deg4 ,! melt+ po9t1 w1 h[ev]1 be l[]$ by ! solution ( silv] nitrate 9 ! wat]2 & ! great] ! conc5tration ( ! salt 9 ! solution ! great] w be ! depression ( ! temp]ature ( equilibrium4 ,on cont9u+ ! addition ( silv] nitrate1 a po9t w at l5g? be rea*$ at :i* ! salt is no long] dissolv$1 b rema9s 9 ! solid =m along ) ! ice4 ,we aga9 obta91 !re=e1 ! inv>iant sy/em ice--salt--solution--vap\r4 ,! temp]ature at :i* ?is inv>iant sy/em c exi/ has be5 f\nd by ,middelb]g#aic to be -#g4c;deg1 ! solution at ?is po9t conta9+ #dg4a p] c5t4 ( silv] nitrate4 ,! same g5]al behavi\r w be f\nd 9 ! case ( all o!r sy/ems ( two compon5ts belong+ to ?is class2 t is1 9 ! case ( sy/ems f :i* ! compon5ts cry/allise out 9 ! pure /ate1 & 9 :i* ! fus$ compon5ts are miscible 9 all proportions4 ,9 all su* cases1 !re=e1 ! solubility curves 7curves ( equilibrium7 c be repres5t$ diagrammatically z 9 ,fig4 #bi4 ,9 ?is figure ,,oa repres5ts ! solubility curve ( ! salt1 & ,,ob ! freez+ #aag po9t curve ( ice4 ,o is ! quadruple po9t at :i* ! inv>iant sy/em exi/s1 & may be reg>d$ z ! po9t ( int]section ( ! solubility curve ) ! freez+-po9t curve4 ,s9ce ?is po9t is fix$1 ! condition ( ! sy/em z reg>ds temp]ature1 vap\r pressure1 & conc5tration ( ! compon5ts 7or composition ( ! solution71 is p]fectly def9ite4 ,f ! way1 also1 9 :i* ! condition is atta9$1 x is evid5t t ! quadruple po9t is ! l[e/ temp]ature t c be obta9$ ) mixtures ( ! two compon5ts 9 pres5ce ( vap\r4 ,x is kn[n z ! cryohydric po9t1 or1 g5]ally1 ! eutectic po9t4#aid ,illu/ration3 ,,fig4 #bi4 ,cryohydrates4#aie--,on cool+ a solution ( common salt 9 wat] to a temp]ature ( -#c;deg1 ,gu?rie obs]v$ t ! hydrate ,na,cl1#b;,h#b,o sep>at$ out4 ,?is salt cont9u$ to be deposit$ until at a temp]ature ( -#bb;deg opaque cry/als made _! appe>ance1 & ! liquid pass$ into ! solid /ate )\t *ange ( temp]ature4 ,a simil> behavi\r 0 f\nd by ,gu?rie 9 ! case ( a l>ge numb] ( o!r salts1 a temp]ature bel[ t ( ! melt+ po9t ( ice be+ rea*$ at :i* on cont9u$ )drawal ( heat1 ! solution solidifi$ at a con/ant temp]ature4 ,:5 ! sy/em _h atta9$ ?is m9imum temp]ature1 x 0 f\nd t ! composition ( ! solid & ! liquid phases 0 ! same1 & rema9$ un*ang$ ?r\gh\t ! p]iod ( solidification4 ,?is is %[n by ! foll[+ figures1 :i* give ! composition ( diff]5t samples ( ! solid phase deposit$ f ! solution at con/ant temp]ature4#aif #aah --------------------------------- ,no4 ,temp]ature ( ,na,cl4 solidification4 ,p] c5t4 ------------------------------- #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 --------------------------------- ,conv]sely1 a mixture ( ice & salt conta9+ #bc4f p] c5t4 ( sodium *loride w melt at a def9ite & con/ant temp]ature1 & exhibit1 !re=e1 a behavi\r suppos$ to be *>act]i/ic ( a pure *emical comp\nd4 ,?is1 !n1 comb9$ ) ! fact t ! solid :i* 0 deposit$ 0 cry/all9e1 & t ! same con/ant temp]ature 0 atta9$1 no matt] ) :at proportions ( wat] & salt "o />t$1 l$ ,gu?rie to ! belief t ! solids :i* ?us sep>at$ at con/ant temp]ature 7 def9ite *emical comp\nds1 to :i* he gave ! g5]al "n cryohydrate4 ,a l>ge numb] ( su* cryohydrates 7 prep>$ & analys$ by ,gu?rie1 & a few ( ^! are giv5 9 ! foll[+ table1 toge!r ) ! temp]ature ( ! cryohydric po9t3#aig-- ,,cryohydrates4 ---------------------------------------- -------------------------- ,salt4 ,cryohydric po9t4 ,p]c5tage ( anhydr\s salt 9 ! cryohydrate4 ---------------------------------------- -------------------------- ,sodium bromide -#bd;deg #da4cc ,sodium *loride -#bb;deg #bc4fj ,potassium iodide -#bb;deg #eb4jg ,sodium nitrate -#ag4e;deg #dj4hj ,ammonium sulphate -#ag;deg #da4gj ,ammonium *loride -#ae;deg #ai4bg ,sodium iodide -#ae;deg #ei4de ,potassium bromide -#ac;deg #cb4ae ,potassium *loride -#aa4d;deg #bj4jc ,magnesium sulphate -#e;deg #ba4hf ,potassium nitrate -#b4f;deg #aa4bj ,sodium sulphate -#j4g;deg #d4ee ---------------------------------------- -------------------------- #aai ,! *emical individuality ( ^! cryohydrates 01 h[ev]1 call$ 9 "q by ,pfaundl]1#aih & disprov$ by ,(f]1#aii :o %[$ t 9 spite ( ! con/ancy ( ! melt+ po9t1 ! cryohydrates _h ! prop]ties1 n ( def9ite *emical comp\nds1 b ( mixtures2 ! argum5ts giv5 be+ t ! heat ( solution & ! specific volume are ! same = ! cryohydrate z = a mixture ( ice & salt ( ! same composition2 & x 0 fur!r %[n t ! cryohydrate _h n a def9ite cry/all9e =m1 b sep>at$ out z an opaque mass conta9+ ! two compon5ts 9 close juxtaposition4 ,! het]og5e\s nature ( cryohydrates c also be %[n by a microscopical exam9ation4 ,at ! cryohydric po9t1 !re=e1 we are n deal+ ) a s+le solid phase1 b ) two solid phases1 ice & salt2 ! cryohydric po9t1 !re=e1 z already /at$1 is a quadruple po9t & repres5ts an inv>iant sy/em4 ,al?\gh on cool+ a solution to ! cryohydric po9t1 sep>ation ( ice may occur1 x w n necess>ily take place2 ! sy/em may become meta/able4 ,simil>ly1 sep>ation ( salt may n take place imm$iately ! cryohydric po9t is rea*$4 ,x w1 !re=e1 be possible to foll[ ! curves ,,bo & ,,ao beyond ! quadruple po9t1#bjj :i* is !reby cle>ly se5 to be ! po9t ( int]section ( ! solubility curve ( ! salt & ! freez+-po9t curve ( ice4 ,at ?is po9t1 also1 ! curves ( ! univ>iant sy/ems ice--salt--vap\r & ice--salt--solution int]sect4 ,*anges at ! ,quadruple ,po9t4--,s9ce ! inv>iant sy/em ice--salt--solution--vap\r c exi/ only at a def9ite temp]ature1 addition or )drawal ( heat mu/ cause ! disappe>ance ( "o ( ! phases1 :]eby ! sy/em w become univ>iant4 ,s long z all f\r phases are pres5t ! temp]ature1 pressure1 & conc5tration ( ! compon5ts 9 ! solution mu/ rema9 con/ant4 ,:51 !re=e1 heat is add$ to or )drawn f ! sy/em1 mutually comp5satory *anges w take place )9 ! sy/em :]eby ! #abj condition ( ! latt] is pres]v$4 ,^! *anges c 9 all cases be =ese5 ) ! help ( ! !orem ( van't ,h(f & ,le ,*ateli]2 &1 aft] :at 0 said 9 ,*ap4 ,,iv41 ne$ only be briefly ref]r$ to "h4 ,9 ! fir/ place1 addition ( heat w cause ice to melt1 & ! conc5tration ( ! solution w be !reby alt]$2 salt mu/ !re=e dissolve until ! orig9al conc5tration is rea*$1 & ! heat ( fusion ( ice w be c\nt]act$ by ! heat ( solution ( ! salt4 ,*anges ( volume ( ! solid & liquid phases mu/ also be tak5 into acc\nt2 an alt]ation 9 ! volume ( ^! phases be+ comp5sat$ by cond5sation or evaporation4 ,all f\r phases w !re=e be involv$ 9 ! *ange1 & ! f9al /ate ( ! sy/em w be dep5d5t on ! am\nts ( ! diff]5t phases pres5t2 ! ultimate result ( addition or )drawal ( heat or ( *ange ( pressure at ! quadruple po9t w be "o ( ! f\r univ>iant sy/ems3 ice--solution--vap\r2 salt--solution--vap\r2 ice--salt--vap\r2 ice--salt--solution4 ,if ! vap\r phase disappe>1 !re w be left ! univ>iant sy/em ice--salt--solution1 & ! temp]ature at :i* ?is sy/em c exi/ w alt] ) ! pressure4 ,s9ce 9 ?is case ! influ5ce ( pressure is comp>atively slight1 ! temp]ature ( ! quadruple po9t w diff] only slightly f t ( ! cryohydric po9t z det]m9$ "u atmosph]ic pressure4 ,freez+ ,mixtures4--,n only w ! composition ( a univ>iant sy/em und]go *ange :5 ! temp]ature is v>i$1 b1 conv]sely1 if ! composition ( ! sy/em is caus$ to *ange1 correspond+ *anges ( temp]ature mu/ ensue4 ,?us1 if ice is add$ to ! univ>iant sy/em salt--solution--vap\r1 ! ice mu/ melt & ! temp]ature fall2 & if suffici5t ice is add$1 ! temp]ature ( ! cryohydric po9t mu/ be at l5g? rea*$1 = x is only at ?is temp]ature t ! f\r phases ice--salt--solution--vap\r c coexi/4 ,or1 on ! o!r h&1 if salt is add$ to ! sy/em ice--solution--vap\r1 ! conc5tration ( ! solution w increase1 ice mu/ melt1 & ! temp]ature mu/ !reby fall2 & ?is process also w g on until ! cryohydric po9t is rea*$4 ,9 bo? cases ice melts & !re is a *ange 9 ! #aba composition ( ! solution2 9 ! =m] case1 salt w be deposit$#bja because ! solubility dim9i%es z ! temp]ature falls2 9 ! latt]1 salt w pass into solution4 ,?is process may be accompani$ ei!r by an evolution or1 m g5]ally1 by absorption ( heat2 9 ! =m] case ! effect ( ! addition ( ice w be p>tially c\nt]act$2 9 ! latt] case x w be augm5t$4 ,^! pr9ciples are made use ( 9 ! prep>ation ( freez+ mixtures4 ,! l[e/ temp]ature :i* c be rea*$ by means ( ^! 7"u atmosph]ic pressure7 is ! cryohydric po9t4 ,?is temp]ature-m9imum is1 h[ev]1 n always atta9$ 9 ! prep>ation ( a freez+ mixture1 & t = v>i\s reasons4 ,! *ief ( ^! are radiation & ! heat absorb$ 9 cool+ ! solution produc$4 ,! l[] ! temp]ature falls1 ! m rapid does ! radiation become2 & ! rate at :i* ! temp]ature s9ks decreases z ! am\nt ( solution increases4 ,bo? ^! factors c\nt]act ! effect ( ! lat5t heat ( fusion & ! heat ( solution1 s t a po9t is rea*$ 7:i* may lie consid]ably above ! cryohydric po9t7 at :i* ! two oppos+ influ5ces balance4 ,! absorption ( heat by ! solution c be dim9i%$ by all[+ ! solution to dra9 (f z fa/ z x is produc$2 & ! effect ( radiation c be p>tially annull$ by increas+ ! rate ( cool+4 ,?is c be done by ! m intimate mix+ ( ! compon5ts4 ,s9ce1 "u atmosph]ic pressure1 ! temp]ature ( ! cryohydric po9t is con/ant1 ! cryohydrates are v valuable = ! production ( ba?s ( con/ant l[ temp]ature4 #b4 ,p>tial ,miscibility ( ! ,fus$ ,compon5ts4 ,on pass+ to ! /udy ( ! second class ( sy/ems ( two compon5ts belong+ to ?is gr\p1 namely1 ^? 9 :i* ! fus$ compon5ts are n miscible 9 all proportions1 we f9d t ! relation%ips are n q s simple z #abb 9 ! case ( silv] nitrate & wat]4 ,9 ! latt] case1 only "o liquid phase 0 possible2 9 ! cases n[ to be /udi$1 two liquid phases c be =m$1 & !re is a m>k$ discont9uity 9 ! solubility curve on pass+ f ! cryohydric po9t to ! melt+ po9t ( ! second 7non-volatile7 compon5t4 ,p>atoluid9e dissolves 9 wat]1 & ! solubility increases z ! temp]ature rises4#bjb ,at #dd4b;deg1 h[ev]1 p>atoluid9e 9 contact ) wat] melts1 & two liquid phases are =m$1 viz4 a solution ( wat] 9 fus$ p>atoluid9e & a solution ( fus$ p>atoluid9e 9 wat]4 ,we h1 !re=e1 ! ph5om5on ( melt+ "u ! solv5t4 ,?is melt+ po9t w1 ( c\rse1 be l[] ?an ! melt+ po9t ( ! pure sub/ance1 because ! solid is n[ 9 contact ) a solution1 &1 z we h already se51 addition ( a =eign sub/ance l[]s ! melt+ po9t4 ,su* cases ( melt+ "u ! solv5t are by no means r>e1 & a review ( ! relation%ips met ) may1 !re=e1 be und]tak5 "h4 ,z an example1 !re may be *os5 ! equilibrium betwe5 succ9ic nitrile1 ,c#b;,h#d7;,,cn7#b & wat]1 :i* has be5 fully /udi$ by ,s*re9emak]s4#bjc ,illu/ration3 ,,fig4 #cj4 ,if to ! sy/em ice--wat] at #j;deg succ9ic nitrile is add$1 ! temp]ature w fall2 & cont9u$ addition ( ! nitrile w lead at la/ to ! cryohydric po9t b 7,fig4 #cj71 at :i* solid nitrile1 ice1 solution1 & vap\r c coexi/4 ,! temp]ature ( ! cryohydric po9t is -#a4b;deg1 & ! composition ( ! solution is #a4bi mol4 ( nitrile 9 #ajj mol4 ( solution4 ,f a to b ! solid phase 9 contact ) ! solution is ice4 #abc ,if ! temp]ature be n[ rais$ s z to cause ! disappe>ance ( ! ice1 & ! addition ( nitrile be cont9u$1 ! conc5tration ( ! nitrile 9 ! solution w increase z repres5t$ by ! curve bc4 ,at ! po9t c 7#ah4e;deg71 :5 ! conc5tration ( ! nitrile 9 ! solution has increas$ to #b4e molecules p] c5t41 ! nitrile melts & two liquid phases are =m$2 ! conc5tration ( ! nitrile 9 ^! two phases is giv5 by ! po9ts c & c'4 ,z !re are n[ f\r phases pres5t1 viz4 solid nitrile1 solution ( fus$ nitrile 9 wat]1 solution ( wat] 9 fus$ nitrile1 & vap\r1 ! sy/em is inv>iant4 ,s9ce at ?is po9t ! conc5tration1 temp]ature1 & pressure are completely def9$1 addition or )drawal ( heat c only cause a *ange 9 ! relative am\nts ( ! phases1 b no v>iation ( ! conc5trations ( ! respective phases4 ,z a matt] ( fact1 cont9u$ addition ( nitrile & addition ( heat w cause an increase 9 ! am\nt ( ! liquid phase conta9+ excess ( nitrile 7i4e4 ! solution ( wat] 9 fus$ nitrile71 :]eas ! o!r liquid phase1 ! solution ( fus$ nitrile 9 wat]1 w gradually disappe>4 ,:5 x has completely disappe>$1 ! sy/em w be repres5t$ by ! po9t c'1 :]e ! molecul> conc5tration ( nitrile is n[ #ge p] c5t41 & aga9 becomes univ>iant1 ! ?ree phases be+ solid nitrile1 liquid phase conta9+ excess ( nitrile1 & vap\r2 & z ! am\nt ( ! wat] is dim9i%$ ! temp]ature ( equilibrium rises1 until at #ed;deg ! melt+ po9t ( ! pure nitrile is rea*$4 ,return n[ to ! po9t c4 ,at ?is po9t !re exi/s ! inv>iant sy/em solid nitrile1 two liquid phases1 vap\r4 ,if heat be add$1 ! solid nitrile w disappe>1 & !re w be left ! univ>iant sy/em1 consi/+ ( two liquid phases & vap\r4#bjd ,su* a sy/em w exhibit relation%ips simil> to ^? already /udi$ 9 ! previ\s *apt]4 ,z ! temp]ature rises1 ! mutual solubility ( ! two fus$ compon5ts becomes great]1 until at d 7#ee4e;deg7 ! critical solution temp]ature is rea*$1 & ! fus$ compon5ts become miscible 9 all proportions4 ,at all temp]atures & conc5trations ly+ to ! "r #abd ( ! curve abcdc'e !re c be only "o liquid phase2 9 ! field cdc' !re are two liquid phases4 ,f ! figure x w be easy to see :at w be ! result ( br++ toge!r succ9ic nitrile & wat] at diff]5t temp]atures & 9 diff]5t am\nts4 ,s9ce b is ! l[e/ temp]ature at :i* liquid c exi/ 9 /able equilibrium ) solid1 ice & succ9ic nitrile c be mix$ 9 any proportions at temp]atures bel[ b )\t und]go+ *ange4 ,betwe5 b & c succ9ic nitrile w be dissolv$ until ! conc5tration rea*es ! value on ! curve bc1 correspond+ to ! giv5 temp]ature4 ,on add+ ! nitrile to wat] at temp]atures betwe5 c & d1 x w dissolve until a conc5tration ly+ on ! curve cd is atta9$2 at ?is po9t two liquid phases w be =m$1 & fur!r addition ( nitrile w cause ! "o liquid phase 7t conta9+ excess ( nitrile7 to increase1 :ile ! o!r liquid phase w decrease1 until x f9ally disappe>s & !re is only "o liquid phase left1 t conta9+ excess ( nitrile4 ,?is c dissolve fur!r quantities ( ! nitrile1 & ! conc5tration w increase until ! curve c'e is rea*$1 :5 ! conc5tration w rema9 un*ang$1 & addition ( solid w m]ely increase ! am\nt ( ! solid phase4 ,if a solution repres5t$ by any po9t 9 ! field ly+ bel[ ! curve bcd is heat$ to a temp]ature above d1 ! critical solution temp]ature1 !n ! conc5tration ( ! nitrile c be increas$ to any desir$ am\nt )\t at any "t two liquid phases mak+ _! appe>ance2 ! sy/em c !n be cool$ d[n to a temp]ature repres5t$ by any po9t betwe5 ! curves dc'e4 ,9 ?is way x is possible to pass cont9u\sly f a solution conta9+ excess ( "o compon5t to solutions conta9+ excess ( ! o!r1 z repres5t$ by ! dott$ l9e xxxx 7v4 p4 #ajj74 ,at no po9t is !re =mation ( two liquid phases4 ,sup]saturation4--,j z susp5d$ trans=mation is r>ely met ) 9 ! passage f ! solid to ! liquid /ate1 s also x is f\nd 9 ! case ( ! melt+ ( sub/ances "u ! solv5t t susp5d$ fusion does n occur2 b t :5 ! temp]ature ( ! inv>iant po9t is rea*$ at :i*1 !re=e1 ! =mation ( two liquid lay]s is possible1 #abe ^! two liquid lay]s1 z a matt] ( fact1 make _! appe>ance4 ,susp5d$ trans=mation c1 h[ev]1 take place f ! side ( ! liquid phase1 j z wat] or o!r liquid c be cool$ bel[ ! normal freez+ po9t )\t solidification occurr+4 ,! "q1 !re=e1 arises z to ! relative solubilities ( ! solid & ! sup]cool$ liquid at ! same temp]ature4 ,illu/ration3 ,,fig4 #ca4 ,! answ] to ?is "q c at once be giv5 f :at we h already le>n$ 7p4 #aac71 if we recollect t at temp]atures bel[ ! po9t ( fusion "u ! solv5t1 ! solid =m1 at temp]atures above t po9t1 ! liquid =m1 is ! m /able2 at ?is temp]ature1 !re=e1 ! relative /ability ( ! solid & liquid =ms *anges4 ,s9ce1 z we h already se51 ! less /able =m has ! great] solubility1 x foll[s t ! sup]cool$ liquid1 be+ ! less /able =m1 mu/ h ! great] solubility4 ,?is 0 fir/ prov$ exp]im5tally by ,alexejeff#bje 9 ! case ( b5zoic acid & wat]1 ! solubility curves = :i* are giv5 9 ,fig4 #ca4 ,z c be se5 f ! figure1 ! prolongation ( ! curve = liquid--liquid1 :i* repres5ts ! solubility ( ! sup]cool$ liquid b5zoic acid1 lies above t = ! solubility ( ! #abf solid b5zoic acid 9 wat]2 ! solution saturat$ ) respect to ! sup]cool$ liquid is !re=e sup]saturat$ ) respect to ! solid =m4 ,a simil> behavi\r has be5 f\nd 9 ! case ( o!r sub/ances4#bjf ,pressure-,temp]ature ,diagram4--,hav+ consid]$ ! *anges :i* occur 9 ! conc5tration ( ! compon5ts 9 a solution ) ! temp]ature1 we may conclude ! discussion ( ! equilibrium betwe5 a salt & wat] by /udy+ ! v>iation ( ! vap\r pressure4 ,s9ce 9 sy/ems ( two compon5ts ! two phases1 solution & vap\r1 con/itute a biv>iant sy/em1 ! vap\r pressure is undef9$1 & may h diff]5t values at ! same temp]ature1 dep5d+ on ! conc5tration4 ,9 ord] t !re may be = ea* temp]ature a def9ite correspond+ pressure ( ! vap\r1 a ?ird phase mu/ be pres5t4 ,?is condition is satisfi$ by ! sy/em solid--liquid 7solution7--vap\r2 t is1 by ! saturat$ solution 7p4 #ajh74 ,9 ! case ( a saturat$ solution1 !re=e1 ! pressure ( ! vap\r at any giv5 temp]ature is con/ant4 ,vap\r ,pressure ( ,solid--,solution--,vap\r4--,x has long be5 kn[n t ! addition ( a non-volatile solid to a liquid 9 :i* x is soluble l[]s ! vap\r pressure ( ! solv5t2 & ! dim9ution ( ! pressure is approximately proportional to ! am\nt ( sub/ance dissolv$ 7,law ( ,babo74 ,! vap\r-pressure curve1 !re=e1 ( a solution ( a salt 9 wat] mu/ lie bel[ t = pure wat]4 ,fur!r1 9 ! case ( a pure liquid1 ! vaporization curve is a function only ( ! temp]ature 7p4 #fc71 :]eas1 9 ! case ( a solution1 ! pressure v>ies bo? ) ! temp]ature & ! conc5tration4 ,^! two factors1 h[ev]1 act 9 opposite directions2 = al?\gh ! vap\r pressure 9 all cases increases z ! temp]ature rises1 increase ( conc5tration1 z we h se51 l[]s ! vap\r pressure4 ,aga91 s9ce ! conc5tration itself v>ies ) ! temp]ature1 two cases h to be consid]$1 viz4 :]e ! conc5tration increases ) rise ( #abg temp]ature1 & :]e ! conc5tration dim9i%es ) rise ( temp]ature4 ,! relations :i* are f\nd "h w be be/ und]/ood ) ! help ( ,fig4 #cb4bjg ,9 ?is figure1 ,,ob repres5ts ! sublimation curve ( ice1 & ,,bc ! vaporization curve ( wat]2 ! curve = ! solution mu/ lie bel[ ?is1 & mu/ cut ! sublimation curve ( ice at "s temp]ature bel[ ! melt+ po9t4 ,! po9t ( int]section ,a is ! cryohydric po9t4 ,if ! solubility increases ) rise ( temp]ature1 ! increase ( ! vap\r pressure due to ! latt] w be p>tially annull$4 ,s9ce at fir/ ! effect ( increase ( temp]ature m ?an c\nt]acts ! depress+ action ( increase ( conc5tration1 ! vap\r pressure w increase on rais+ ! temp]ature above ! cryohydric po9t4 ,if ! elevation ( temp]ature is cont9u$1 h[ev]1 to ! melt+ po9t ( ! salt1 ! effect ( increas+ conc5tration makes itself m & m felt1 s t ! vap\r-pressure curve ( ! solution falls m & m bel[ t ( ! pure liquid1 & ! pressure w ultimately become equal to t ( ! pure salt2 t is to say1 practically equal to z]o4 ,! curve w !re=e be ( ! g5]al =m ,,amf %[n 9 ,fig4 #cb4 ,if ! solubility %\ld dim9i% ) rise ( temp]ature1 ! two factors1 temp]ature & conc5tration1 w act 9 ! same direction1 & ! vap\r-pressure curve w rise relatively m rapid ?an t ( ! pure liquid2 s9ce1 h[ev]1 ! pure salt is ultimately obta9$1 ! vap\r-pressure curve mu/ 9 ?is case also f9ally approa* ! value z]o4 ,illu/ration3 ,,fig4 #cb4 ,o!r ,univ>iant ,sy/ems4--,besides ! univ>iant sy/em #abh salt--solution--vap\r already consid]$1 ?ree o!rs are possible1 viz4 ice--solution--vap\r1 ice--salt--solution1 & ice--salt--vap\r4 ,! fusion po9t ( a sub/ance is l[]$1 z we h se51 by ! addition ( a =eign sub/ance1 & ! depression is all ! great] ! l>g] ! quantity ( sub/ance add$4 ,! vap\r pressure ( ! wat]1 also1 is l[]$ by ! solution 9 x ( o!r sub/ances1 s t ! vap\r pressure ( ! sy/em ice--solution--vap\r mu/ decrease z ! temp]ature falls f ! fusion po9t ( ice to ! cryohydric po9t4 ,?is curve is repres5t$ by ,,ba 7,fig4 #cb71 & is co9cid5t ) ! sublimation curve ( ice4 ,?is1 at fir/ sight1 /range fact w be readily und]/ood :5 we consid] t s9ce ice & solution are toge!r 9 equilibrium ) ! same vap\r1 !y mu/ h ! same vap\r pressure4 ,= suppose at any giv5 temp]ature equilibrium to h be5 e/abli%$ 9 ! sy/em ice--solution--vap\r1 removal ( ! ice w n alt] ?is equilibrium4 ,suppose1 n[1 ! ice & ! solution plac$ "u a bell-j> s t !y h a common vap\r1 b are n !mselves 9 contact2 !n1 if !y d n h ! same vap\r pressure1 di/illation mu/ take place & ! solution w become m dilute or m conc5trat$4 ,s9ce1 at ! completion ( ?is process1 ! ice & solution are n[ 9 equilibrium :5 !y are n 9 contact1 !y mu/ also be 9 equilibrium :5 !y are 9 contact 7p4 #cb74 ,b if di/illation has tak5 place ! conc5tration ( ! solution mu/ h alt]$1 s t ! ice w n[ be 9 equilibrium ) a solution ( a diff]5t conc5tration f be=e4 ,b accord+ to ! ,phase ,rule ice _c at "o & ! same temp]ature be 9 equilibrium ) two solutions ( diff]5t conc5tration1 = ! sy/em ice--solution--vap\r is univ>iant1 & at any giv5 temp]ature1 !re=e1 n only ! pressure b also ! conc5tration ( ! compon5ts 9 ! solution mu/ be con/ant4 ,di/illation c\ld n1 !re=e1 take place f ! ice to ! solution or vice v]sa2 t is to say1 ! solution & ! ice mu/ h ! same vap\r pressure--! sublimation pressure ( ice4 ,! reason ( ! co9cid5ce is ! non-volatility ( ! salt3 _h #abi ! salt a measurable vap\r pressure itself1 ! sublimation curve ( ice & ! curve = ice--solution--vap\r w\ld no long] fall toge!r4 ,! curve ,,ao repres5ts ! pressures ( ! sy/em ice--salt--vap\r4 ,?is curve w also be co9cid5t ) ! sublimation curve ( ice1 on acc\nt ( ! non-volatility ( ! salt4 ,! equilibria ( ! f\r? univ>iant sy/em ice--salt--solution are repres5t$ by ,,ae4 ,s9ce ?is is a cond5s$ sy/em1 ! effect ( a small *ange ( temp]ature w be to cause a l>ge *ange ( pressure1 z 9 ! case ( ! fusion po9t ( a pure sub/ance4 ,! direction ( ?is curve w dep5d on :e!r !re is an increase or dim9ution ( volume on solidification2 b ! effect 9 any giv5 case c be pr$ict$ ) ! help ( ! !orem ( ,le ,*ateli]4 ,s9ce ! cryohydric po9t is a quadruple po9t 9 a two-compon5t sy/em1 x repres5ts an inv>iant sy/em4 ,! condition ( ! sy/em is1 !re=e1 completely def9$2 ! f\r phases1 ice1 salt1 solution1 vap\r1 c co-exi/ only :5 ! temp]ature1 pressure1 & conc5tration ( ! solution h con/ant & def9ite values4 ,addition or )drawal ( heat1 !re=e1 c cause no alt]ation ( ! condition ( ! sy/em except a v>iation ( ! relative am\nts ( ! phases4 ,addition ( heat at con/ant volume w ultimately lead to ! sy/em salt--solution--vap\r or ! sy/em ice--solution--vap\r1 accord+ z ice or salt disappe>s fir/4 ,?is is readily app>5t f ! diagram 7,fig4 #cb71 = ! sy/ems ice--salt--solution & ice--salt--vap\r c exi/ only at temp]atures bel[ ! cryohydric po9t 7provid$ ! curve = ice--salt--solution slopes t[>ds ! pressure axis74 ,biv>iant ,sy/ems4--,besides ! univ>iant sy/ems already discuss$1 v>i\s biv>iant sy/ems are possible1 ! conditions = ! exi/5ce ( :i* are repres5t$ by ! diff]5t areas ( ,fig4 #cb4 ,!y are z foll[s3-- ,area4 ,sy/em4 ,,oamf ,salt--vap\r4 ,,cbamf ,solution--vap\r2 salt--solution4 ,,eabd ,salt--solution2 ice--solution4 ,,eao ,ice--salt4 #acj ,deliquesc5ce4--,z is evid5t f ,fig4 #cb1 salt c exi/ 9 contact ) wat] vap\r at pressures "u ^? repres5t$ by ,,oamf4 ,if1 h[ev]1 ! pressure ( ! vap\r is increas$ until x rea*es a value ly+ on ?is curve at temp]atures above ! cryohydric po9t1 solution w be =m$2 = ! curve ,,amf repres5ts ! equilibria betwe5 salt--solution--vap\r4 ,f ?is1 !re=e1 x is cle> t if ! pressure ( ! aque\s vap\r 9 ! atmosph]e is great] ?an t ( ! saturat$ solution ( a salt1 t salt w1 on be+ plac$ 9 ! air1 =m a solution2 x w deliquesce4 ,sep>ation ( ,salt on ,evaporation4--,) ! help ( ,fig4 #cb x is possible to /ate 9 a g5]al mann] :e!r or n salt w be deposit$ :5 a solution is evaporat$ "u a con/ant pressure4#bjh ,! curve ,,amf 7,fig4 #cb7 is ! vap\r-pressure curve ( ! saturat$ solutions ( ! salt1 i4e4 x repres5ts1 z we h se51 ! maximum vap\r pressure at :i* salt c exi/ 9 contact ) solution & vap\r4 ,! dott$ l9e aa repres5ts atmosph]ic pressure4 ,if1 n[1 an unsaturat$ solution1 ! composition ( :i* is repres5t$ by ! po9t x1 is heat$ 9 an op5 vessel1 ! temp]ature w rise1 & ! vap\r pressure ( ! solution w increase4 ,! sy/em w1 !re=e1 pass along a l9e repres5t$ diagrammatically by xx'4 ,at ! po9t x' ! vap\r pressure ( ! sy/em becomes equal to #a atm42 & z ! vessel is op5 to ! air1 ! pressure _c fur!r rise2 ! solution boils4 ,if ! heat+ is cont9u$1 wat] passes (f1 ! conc5tration increases1 & ! boil+ po9t rises4 ,! sy/em w !re=e pass along ! l9e x'm1 until at ! po9t m solid salt sep>ates out 7provid$ sup]saturation is exclud$74 ,! sy/em is n[ univ>iant1 & cont9u$ heat+ w no long] cause an alt]ation ( ! conc5tration2 z wat] passes (f1 solid salt w be deposit$1 & ! solution w evaporate to dryness4 ,if1 h[ev]1 ! atmosph]ic pressure is repres5t$ n by aa b by bb1 !n1 z ,fig4 #cb %[s1 ! maximum vap\r #aca pressure ( ! sy/em salt--solution--vap\r nev] rea*es ! pressure ( #a atm4 ,fur!r1 s9ce ! curve bb lies 9 ! area ( ! biv>iant sy/em solution--vap\r !re c at no po9t be a sep>ation ( ! solid =m2 = ! sy/em solid--solution--vap\r c exi/ only along ! curve ,,amf4 ,on evaporat+ ! solution ( a salt 9 an op5 vessel1 !re=e1 salt c be deposit$ only if at "s temp]ature ! pressure ( ! saturat$ solution is equal to ! atmosph]ic pressure4 ,?is is f\nd to be ! case ) mo/ salts4 ,9 ! case ( aque\s solutions ( sodium & potassium hydroxide1 h[ev]1 ! vap\r pressure ( ! saturat$ solution nev] rea*es ! value ( #a atm41 & on evaporat+ ^! solutions1 !re=e1 9 an op5 vessel1 !re is no sep>ation ( ! solid4 ,only a homog5e\s fus$ mass is obta9$4 ,if1 h[ev]1 ! evaporation be c>ri$ out "u a pressure :i* is l[] ?an ! maximum pressure ( ! saturat$ solution1 sep>ation ( ! solid sub/ance w be possible4 ,g5]al ,summ>y4--,! sy/ems :i* h be5 discuss$ 9 ! pres5t *apt] conta9$ wat] z "o ( _! compon5ts1 & an anhydr\s salt z ! o!r4 ,x w1 h[ev]1 be cle> t ! relation%ips :i* 7 f\nd 9 ! case ( ^! w be f\nd also 9 o!r cases :]e x is a "q ( ! equilibria betwe5 two compon5ts1 :i* cry/allize out 9 ! pure /ate1 & only "o ( :i* possesses a measurable vap\r pressure4 ,a simil> behavi\r w1 = example1 be f\nd 9 ! case ( _m pairs ( organic sub/ances2 & 9 all cases ! equilibria w be repres5t$ by a diagram ( ! g5]al appe>ance ( ,fig4 #bi or ,fig4 #cj4 ,t is to say3 ,/>t+ f ! fusion po9t ( compon5t ,i41 ! sy/em w pass1 by progressive addition ( compon5t ,,ii41 to regions ( l[] temp]ature1 until at la/ ! cryohydric or eutectic po9t is rea*$4 ,on fur!r addition ( compon5t ,,ii41 ! sy/em w pass to regions ( high] temp]ature1 ! solid phase n[ be+ compon5t ,,ii4 ,if ! fus$ compon5ts are miscible ) "o ano!r 9 all proportions a cont9u\s curve w be obta9$ lead+ up to ! po9t ( fusion ( compon5t ,,ii4 ,slight *anges ( direction1 x is true1 due to *anges 9 ! cry/all9e =m1 may be f\nd along ?is curve1 #acb b ?r\gh\t its :ole c\rse !re w be b "o liquid phase4 ,if1 on ! o!r h&1 ! fus$ compon5ts are n miscible 9 all proportions1 !n ! second curve w exhibit a m>k$ discont9uity1 & two liquid phases w make _! appe>ance4 99 99 99 99 99 #acc ,,*apt] ,,viii ,,solutions ,,( ,,solids ,,9 ,,liquids1 ,,only ,,"o ,,( ,,! ,,compon5ts ,,be+ ,,volatile ,b4--,,hydrat$ ,,salt ,,& ,,wat]4 ,9 ! prec$+ *apt] we discuss$ ! behavi\r ( sy/ems =m$ ( two compon5ts1 only "o ( :i* 0 volatile1 9 ^? cases :]e ! two compon5ts sep>at$ f solution 9 ! pure /ate4 ,9 ! pres5t *apt] we %all consid] ^? sy/ems 9 :i* comb9ation betwe5 ! compon5ts c occur ) ! =mation ( def9ite comp\nds2 su* z are f\nd 9 ! case ( cry/all9e salt hydrates4 ,s9ce a n inconsid]able am\nt ( /udy has be5 devot$ to ! sy/ems =m$ by hydrat$ salts & wat]1 sy/ems :i* are ( great *emical int]e/ & importance1 ! behavi\r ( ^! w fir/ call = discussion 9 "s detail1 & x w be f\nd lat] t ! relation%ips :i* exi/ 9 su* sy/ems appe> also 9 a l>ge numb] ( o!r two-compon5t sy/ems4 ,! sy/ems belong+ to ?is gr\p may be divid$ into two classes accord+ z ! comp\nds =m$ possess a def9ite melt+ po9t1 i4e4 =m a liquid phase ( ! same composition1 or d n d s4 ,we %all consid] ! latt] fir/4 #a4 ,! ,comp\nds =m$ d n h a ,def9ite ,melt+ ,po9t4 ,conc5tration-,temp]ature ,diagram4--,9 ! case ( salts :i* c =m cry/all9e hydrates1 ! temp]ature-conc5tration diagram1 repres5t+ ! equilibria ( ! #acd diff]5t possible sy/ems1 mu/ necess>ily be some:at m complicat$ ?an :]e no su* comb9ation ( ! compon5ts occurs4 ,=1 z has already be5 po9t$ out1 ea* sub/ance has its own solubility curve2 & !re w !re=e be z _m solubility curves z !re are solid phases possible1 ! curve = ea* p>ticul> solid phase be+ cont9u\s s long z x rema9s un*ang$ 9 contact ) ! solution4 ,z an example ( ! relation%ips met ) 9 su* cases1 we %all fir/ ( all consid] ! sy/ems =m$ ( sodium sulphate & wat]4 ,illu/ration3 ,,fig4 #cc4 ,sodium ,sulphate & ,wat]4--,at ! ord9>y temp]atures1 sodium sulphate cry/allises f wat] ) t5 molecules ( wat] ( cry/allisation1 =m+ ,glaub]'s salt4 ,on det]m9+ ! solubility ( ?is salt 9 wat]1 x is f\nd t ! solubility increases z ! temp]ature rises1 ! values ( ! solubility1 repres5t$ graphically by ! curve ,,ac 7,fig4 #cc71 be+ giv5 9 ! foll[+ table4#bji ,! numb]s d5ote grams ( sodium sulphate1 calculat$ z anhydr\s salt1 dissolv$ by #ajj grams ( wat]4 ,,solubility ,,( ,na#b,,s#d1aj;,h#b,o4 -------------------------- ,temp]ature4 ,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 cont9u+ ! inve/igation at high] temp]atures1 x 0 f\nd t ! solubility no long] increas$1 b decreas$ ) rise ( temp]ature4 ,at ! same "t1 x 0 obs]v$ t ! solid phase 0 n[ diff]5t f t 9 contact ) ! solution at temp]atures bel[ #cc;deg2 = :]eas 9 ! latt] case ! solid phase 0 sodium sulphate decahydrate1 at temp]atures above #cc;deg ! solid phase 0 ! anhydr\s salt4 ,! c\rse ( ! solubility curve ( anhydr\s sodium sulphate is %[n by ,,bd1 & ! values ( ! solubility are giv5 9 ! foll[+ table3--#baj ,,solubility ,,( ,,anhydr\s ,,sodium ,,sulphate4 -------------------------- ,temp]ature4 ,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 -------------------------- ,z is evid5t f ! figure1 ! solubility curve :i* is obta9$ :5 anhydr\s sodium sulphate is pres5t z ! solid phase1 cuts ! curve repres5t+ ! solubility ( ! decahydrate1 at a temp]ature ( ab\t #cc;deg4 ,if a solution ( sodium sulphate :i* has be5 saturat$ at a temp]ature ( ab\t #cd;deg be cool$ d[n to a temp]ature bel[ #ag;deg1 :ile c>e is tak5 t ! solution is protect$ aga9/ access ( p>ticles ( ,glaub]'s salt1 cry/als ( a second hydrate ( sodium sulphate1 hav+ ! composition ,na#b,,s#d1g;,h#b,o1 sep>ate out4 ,on det]m9+ ! composition ( ! solutions 9 equilibrium ) ?is hydrate at diff]5t temp]atures1 ! foll[+ values 7 obta9$1 ^! values be+ repres5t$ by ! curve ,,fe 7,fig4 #cc73-- #acf ,,solubility ,,( ,na#b,,s#d1g;,h#b,o4 -------------------------- ,temp]ature4 ,solubility4 -------------------------- #j;deg #ai4fb #aj;deg #cj4di #ae;deg #cg4dc #ah;deg #da4fc #bj;deg #dd4gc #be;deg #eb4id #bf;deg #ed4ig -------------------------- ,s9ce1 z has already be5 /at$1 ea* solid sub/ance has its own solubility curve1 !re are ?ree sep>ate curves to be consid]$ 9 ! case ( sodium sulphate & wat]4 ,:]e two curves cut1 ! solution mu/ be saturat$ ) respect to two solid phases2 at ! po9t ,b1 !re=e1 ! po9t ( int]section ( ! solubility curve ( anhydr\s sodium sulphate ) t ( ! decahydrate1 ! solution mu/ be saturat$ ) respect to ^! two solid sub/ances4 ,b a sy/em ( two compon5ts exi/+ 9 f\r phases1 anhydr\s salt--hydrat$ salt--solution--vap\r1 is inv>iant2 & ?is inv>iability w rema9 ev5 if only ?ree phases are pres5t1 provid$ t "o ( ! factors1 pressure1 temp]ature1 or conc5tration ( compon5ts reta9s a con/ant value4 ,?is is ! case :5 solubilities are det]m9$ 9 op5 vessels2 ! pressure is !n equal to atmosph]ic pressure4 ,"u ^! circum/ances1 !n1 ! sy/em1 anhydr\s sodium sulphate--decahydrate--solution1 w possess no degree ( fre$om1 & c exi/1 !re=e1 only at "o def9ite temp]ature & :5 ! solution has a c]ta9 def9ite composition4 ,! temp]ature ( ?is po9t is #cb4dhb;deg on a m]cury !rmomet]1 or #cb4cgi;deg on ! hydrog5 !rmomet]4#baa #acg ,susp5d$ ,trans=mation4--,al?\gh x is possible = ! anhydr\s salt to make its appe>ance at ! temp]ature ( ! quadruple po9t1 x w n necess>ily d s2 & x is !re=e possible to foll[ ! solubility curve ( sodium sulphate decahydrate to a high] temp]ature4 ,s9ce1 h[ev]1 ! solubility ( ! decahydrate at temp]atures above ! quadruple po9t is great] ?an t ( ! anhydr\s salt1 ! solution :i* is saturat$ ) respect to ! =m] w be sup]saturat$ ) respect to ! latt]4 ,on br++ a small quantity ( ! anhydr\s salt 9 contact ) ! solution1 !re=e1 anhydr\s salt w be deposit$2 & all ! hydrat$ salt pres5t w ultimately und]go conv]sion into ! anhydr\s salt1 ?r\gh ! m$ium ( ! solution4 ,9 ?is case1 z 9 all cases1 ! solid phase1 :i* is ! mo/ /able at ! temp]ature ( ! exp]im5t1 has at t temp]ature ! lea/ solubility4 ,simil>ly1 ! solubility curve ( anhydr\s sodium sulphate has be5 foll[$ to temp]atures bel[ #cb4e;deg4 ,bel[ ?is temp]ature1 h[ev]1 ! solubility ( ?is salt is great] ?an t ( ! decahydrate1 & ! saturat$ solution ( ! anhydr\s salt w !re=e be sup]saturat$ = ! decahydrate1 & w deposit ?is salt if a nucleus is add$ to ! solution4 ,f ?is we see t at temp]atures above #cb4e;deg ! anhydr\s salt is ! /able =m1 :ile ! decahydrate is un/able 7or meta/able72 at temp]atures bel[ #cb4e;deg ! decahydrate is /able4 ,?is temp]ature1 !re=e1 is ! transition temp]ature = decahydrate & anhydr\s salt4 ,f ,fig4 #cc we see fur!r t ! solubility curve ( ! anhydr\s salt 7:i* at all temp]atures bel[ #cb4e;deg is meta/able7 is cut by ! solubility curve ( ! heptahydrate2 & ?is po9t ( int]section 7at a temp]ature ( #bd4b;deg7 mu/ be ! transition po9t = heptahydrate & anhydr\s salt4 ,s9ce at all temp]atures ! solubility ( ! heptahydrate is great] ?an t ( ! decahydrate1 ! =m] hydrate mu/ be meta/able ) respect to ! latt]2 s t ?r\gh\t its :ole c\rse ! solubility curve ( ! heptahydrate #ach repres5ts only meta/able equilibria4 ,sodium sulphate1 !re=e1 =ms only "o /able hydrate1 ! decahydrate4 ,! solubility relations ( sodium sulphate illu/rate v cle>ly ! importance ( ! solid phase = ! def9ition ( saturation & sup]saturation4 ,s9ce ! solubility curve ( ! anhydr\s salt has be5 foll[$ backw>ds to a temp]ature ( ab\t #ah;deg1 x is readily se51 f ,fig4 #cc1 t at a temp]ature (1 say1 #bj;deg ?ree diff]5t saturat$ solutions ( sodium sulphate are possible1 accord+ z ! anhydr\s salt1 ! heptahydrate or ! decahydrate1 is pres5t z ! solid phase4 ,two ( ^! solutions1 h[ev]1 w\ld be meta/able & sup]saturat$ ) respect to ! decahydrate4 ,fur!r1 ! behavi\r ( sodium sulphate & wat] furni%es a v good example ( ! fact t a break 9 ! solubility curve occurs :51 & only :51 ! solid phase und]goes *ange4 ,s long z ! decahydrate1 = example1 rema9$ unalt]$ 9 contact ) ! solution1 ! solubility curve 0 cont9u\s2 b :5 ! anhydr\s salt appe>$ 9 ! solid phase1 a di/9ct *ange 9 ! direction ( ! solubility curve 0 obs]v$4 ,dehydration by ,means ( ,anhydr\s ,sodium ,sulphate4--,! *ange 9 ! relative /ability ( sodium sulphate decahydrate & anhydr\s salt 9 pres5ce ( wat] at a temp]ature ( #cb4e;deg expla9s :y ! latt] salt _c be employ$ = dehydration purposes at temp]atures above ! transition po9t4 ,! dehydrat+ action ( ! anhydr\s salt dep5ds on ! =mation ( ! decahydrate2 b s9ce at temp]atures above #cc;deg ! latt] is un/able1 & _c be =m$ 9 pres5ce ( ! anhydr\s salt1 ?is salt _c1 ( c\rse1 effect a dehydration above t temp]ature4 ,pressure-,temp]ature ,diagram4--,! consid]ation ( ! pressure-temp]ature relations ( ! two compon5ts1 sodium sulphate & wat]1 mu/ include n only ! vap\r pressure ( ! saturat$ solutions1 b also t ( ! cry/all9e hydrates4 ,! vap\r pressures ( salt hydrates h already be5 treat$ 9 a g5]al mann] 7,*ap4 ,v471 s t x is only necess>y "h to po9t out ! connection betwe5 ! two classes ( sy/ems4 #aci ,9 mo/ cases ! vap\r pressure ( a salt hydrate1 i4e4 ! vap\r pressure ( ! sy/em hydrate--anhydr\s salt 7or l[] hydrate7--vap\r1 is at all temp]atures l[] ?an t ( ! sy/em anhydr\s salt 7or l[] hydrate7--solution--vap\r4 ,?is1 h[ev]1 is n a necessity2 & cases are kn[n :]e ! vap\r pressure ( ! =m] sy/em is1 "u c]ta9 circum/ances1 equal to or high] ?an t ( ! latt]4 ,an example ( ?is is f\nd 9 sodium sulphate decahydrate4 ,on heat+ ,na#b,,s#d1aj;,h#b,o1 a po9t is rea*$ at :i* ! dissociation pressure into anhydr\s salt & wat] vap\r becomes equal to ! vap\r pressure ( ! saturat$ solution ( ! anhydr\s salt1 z is app>5t f ! foll[+ measurem5ts2#bab ! diff]5ces 9 pressure be+ express$ 9 millimetres ( a p>ticul> oil4 ,temp]ature3 #bi4j;deg #cj4hc;deg #ca4gi;deg #cb4ji;deg #cb4ce;deg #cb4f;deg ,diff]5ce ( pressure3 #bc4h #aj4h #e4f #c4f #a4f #j ,at #cb4f;deg1 !re=e1 ! vap\r pressures ( ! two sy/ems ,na#b,,s#d1aj;,h#b,o--,na#b,,s#d--vap\r ,na#b,,s#d--solution--vap\r are equal2 at ?is temp]ature ! f\r phases1 ,na#b,,s#d1aj;,h#b,o2 ,na#b,,s#d2 solution2 vap\r1 c coexi/4 ,f ?is x is evid5t t :5 sodium sulphate decahydrate is heat$ to #cb4f;deg1 ! two new phases anhydr\s salt & solution w be =m$ 7susp5d$ trans=mation be+ suppos$ exclud$71 & ! hydrate w appe> to und]go p>tial fusion2 & dur+ ! process ( melt+ ! vap\r pressure & temp]ature w rema9 con/ant4#bac ,?is is1 h[ev]1 n a true b a s-call$ incongru5t melt+ po9t2 = ! composition ( ! liquid phase is n ! same z t ( ! solid4 ,z has already be5 po9t$ out 7p4 #acg71 we are deal+ "h ) ! transition po9t ( ! decahydrate & anhydr\s salt1 i4e4 ) ! reaction ,na#b,,s#d1aj;,h#b,o -- ,na#b,,s#d #aj;,h#b,o4 ,s9ce at ! po9t ( p>tial fusion ( ! decahydrate f\r #adj phases c coexi/1 ! po9t is a quadruple po9t 9 a two-compon5t sy/em1 & ! sy/em at ?is po9t is !re=e inv>iant4 ,! temp]ature ( ?is po9t is !re=e p]fectly def9ite1 & on ?is acc\nt ! proposal has be5 made to adopt ?is z a fix$ po9t 9 !rmometry4#bad ,! temp]ature is1 ( c\rse1 practically ! same z t at :i* ! two solubility curves int]sect 7p4 #aab74 ,if1 h[ev]1 ! vap\r phase disappe>s1 ! sy/em becomes univ>iant1 & ! equilibrium temp]ature und]goes *ange ) *ange ( pressure4 ,! transition curve has be5 det]m9$ by ,tammann1#bae & %[n to pass ?r\gh a po9t ( maximum temp]ature4 ,illu/ration3 ,,fig4 #cd4 ,! vap\r pressure ( ! diff]5t sy/ems ( sodium sulphate & wat] c be/ be /udi$ ) ! help ( ! diagram 9 ,fig4 #cd4baf ,! curve ,,abcd repres5ts ! vap\r-pressure curve ( ! saturat$ solution ( anhydr\s sodium sulphate4 ,,gc is ! pressure curve ( decahydrate anhydr\s salt1 :i*1 z we h se51 cuts ! curve ,,abcd at ! transition temp]ature1 #cb4f;deg4 ,s9ce at ?is po9t ! solution is saturat$ ) respect to bo? ! anhydr\s salt & ! decahydrate1 ! vap\r-pressure curve ( ! saturat$ solution ( ! latt] mu/ also pass ?r\gh ! po9t ,c4#bag ,z at temp]atures bel[ ?is po9t ! solubility ( ! decahydrate is less ?an t ( ! anhydr\s salt1 ! vap\r pressure ( ! solution w1 9 accordance ) ,babo's law 7p4 #abf71 be high] ?an t ( ! solution ( ! anhydr\s salt2 :i* 0 also f\nd exp]im5tally to be ! case 7curve ,,hc74 #ada ,9 connection ) ! vap\r pressure ( ! saturat$ solutions ( ! anhydr\s salt & ! decahydrate1 att5tion mu/ be drawn to a conspicu\s deviation f :at 0 f\nd to hold 9 ! case ( "o-compon5t sy/ems 9 :i* a vap\r phase 0 pres5t 7p4 #ca74 ,!re1 x 0 se5 t ! vap\r pressure ( ! m /able sy/em 0 always l[] ?an t ( ! less /able2 9 ! pres5t case1 h[ev]1 we f9d t ?is is no long] s4 ,we h already le>n$ t at temp]atures bel[ #cb4e;deg ! sy/em decahydrate--solution--vap\r is m /able ?an ! sy/em anhydr\s salt--solution--vap\r2 b ! vap\r pressure ( ! latt] sy/em is1 z has j be5 /at$1 l[] ?an t ( ! =m]4 ,at temp]atures above ! transition po9t ! vap\r pressure ( ! saturat$ solution ( ! decahydrate w be l[] ?an t ( ! saturat$ solution ( ! anhydr\s salt4 ,?is behavi\r dep5ds on ! fact t ! less /able =m is ! m soluble1 & t ! dim9ution ( ! vap\r pressure increases ) ! am\nt ( salt dissolv$4 ,) reg>d to sodium sulphate heptahydrate ! same consid]ations w hold z 9 ! case ( ! decahydrate4 ,s9ce at #bd;deg ! f\r phases heptahydrate1 anhydr\s salt1 solution1 vap\r c coexi/1 ! vap\r-pressure curves ( ! sy/ems hydrate--anhydr\s salt--vap\r 7curve ,,eb7 & hydrate--solution--vap\r 7curve ,,fb7 mu/ cut ! pressure curve ( ! saturat$ solution ( ! anhydr\s salt at ! above temp]ature1 z repres5t$ 9 ,fig4 #cd by ! po9t ,b4 ,?is con/itutes1 !re=e1 a second quadruple po9t1 :i* is1 h[ev]1 meta/able4 ,f ! diagram x is also evid5t t ! dissociation pressure ( ! heptahydrate is high] ?an t ( ! decahydrate1 al?\gh x conta9s less wat] ( cry/allization4 ,! sy/em heptahydrate--anhydr\s salt--vap\r mu/ be meta/able ) respect to ! sy/em decahydrate--anhydr\s salt--vap\r1 & w pass into ! latt]4#bah ,:e!r or n !re is a temp]ature at :i* ! vap\r-pressure curves ( ! two sy/ems int]sect1 & bel[ :i* ! heptahydrate becomes ! m /able =m1 is n kn[n4 #adb ,9 ! case ( sodium sulphate !re is only "o /able hydrate4 ,o!r salts are kn[n :i* exhibit a simil> behavi\r2 & we %all !re=e expect t ! solubility relation%ips w be repres5t$ by a diagram simil> to t = sodium sulphate4 ,a consid]able numb] ( su* cases h1 inde$1 be5 f\nd1#bai & 9 "s cases !re is m ?an "o meta/able hydrate4 ,?is is f\nd1 = example1 9 ! case ( nickel iodate1#bbj ! solubility curves = :i* are giv5 9 ,fig4 #ce4 ,z c be se5 f ! figure1 susp5d$ trans=mation occurs1 ! solubility curves hav+ 9 "s cases be5 foll[$ to a consid]able di/ance beyond ! transition po9t4 ,"o ( ! mo/ brilliant examples1 h[ev]1 ( susp5d$ trans=mation 9 ! case ( salt hydrates1 & ! sluggi% transition f ! less /able to ! m /able =m1 is f\nd 9 ! case ( ! hydrates ( calcium *romate4#bba ,illu/ration3 ,,fig4 #ce4 ,9 ! prec$+ cases1 ! dissociation-pressure curve ( ! hydrat$ salt cuts ! vap\r-pressure curve ( ! saturat$ #adc solution ( ! anhydr\s salt4 ,x c1 h[ev]1 happ5 t ! dissociation-pressure curve ( "o hydrate cuts ! solubility curve1 n ( ! anhydr\s salt1 b ( a l[] hydrate2 9 ?is case !re w be m ?an "o /able hydrate1 ea* hav+ a /able solubility curve2 & ^! curves w int]sect at ! temp]ature ( ! transition po9t4 ,v>i\s examples ( ?is behavi\r are kn[n1 & we *oose = illu/ration ! solubility relation%ips ( b>ium acetate & its hydrates#bbb 7,fig4 #cf74 ,illu/ration3 ,,fig4 #cf4 ,at temp]atures above #j;deg1 b>ium acetate c =m two /able hydrates1 a trihydrate & a monohydrate4 ,! solubility ( ! trihydrate increases v rapidly ) rise ( temp]ature1 & has be5 det]m9$ up to #bf4a;deg4 ,at temp]atures above #bd4g;deg1 h[ev]1 ! trihydrate is meta/able ) respect to ! monohydrate2 = at ?is temp]ature ! solubility curve ( ! latt] hydrate cuts t ( ! =m]4 ,?is is1 !re=e1 ! transition temp]ature = ! trihydrate & monohydrate4 ,! solubility curve ( ! monohydrate succe$s t ( ! trihydrate1 & exhibits a conspicu\s po9t ( m9imum solubility at ab\t #cj;deg4 ,bel[ #bd4g;deg ! #add monohydrate is ! less /able hydrate1 b its solubility has be5 det]m9$ to a temp]ature ( #bb;deg4 ,at #da;deg ! solubility curve ( ! monohydrate int]sects t ( ! anhydr\s salt1 & ?is is !re=e ! transition temp]ature = ! monohydrate & anhydr\s salt4 ,above ?is temp]ature ! anhydr\s salt is ! /able solid phase4 ,its solubility curve also passes ?r\gh a m9imum4 ,! diagram ( solubilities ( b>ium acetate n only illu/rates ! way 9 :i* ! solubility curves ( ! diff]5t /able hydrates ( a salt succe$ "o ano!r1 b x has also an int]e/ & importance f ano!r po9t ( view4 ,9 ,fig4 #cf !re is also %[n a fa9tly drawn curve :i* is cont9u\s ?r\gh\t its :ole c\rse4 ,?is curve repres5ts ! solubility ( b>ium acetate z det]m9$ by ,krasnicki4#bbc ,s9ce1 h[ev]1 ?ree diff]5t solid phases c exi/ "u ! conditions ( exp]im5t1 x is evid5t1 f :at has already be5 /at$ 7p4 #aaa71 t ! diff]5t equilibria betwe5 b>ium acetate & wat] c\ld n be repres5t$ by "o cont9u\s curve4 ,ano!r po9t :i* ^! exp]im5ts illu/rate & :i* x is ( ! highe/ importance to be> 9 m9d is1 t 9 mak+ det]m9ations ( ! solubility ( salts :i* are capable ( =m+ hydrates1 x is n only necess>y to det]m9e ! composition ( ! solution1 b x is ( equal importance to det]m9e ! composition ( ! solid phase 9 contact ) x4 ,9 view ( ! fact1 also1 t ! solution equilibrium is 9 _m cases e/abli%$ ) comp>ative sl[ness1 x is necess>y to confirm ! po9t ( equilibrium1 ei!r by approa*+ x f high] z well z f l[] temp]atures1 or by actually det]m9+ ! rate ) :i* ! condition ( equilibrium is atta9$4 ,?is c be accompli%$ by actual weigh+ ( ! dissolv$ salt or by det]m9ations ( ! d5sity ( ! solution1 z well z by o!r me?ods4 #ade #b4 ,! ,comp\nds =m$ h a ,def9ite ,melt+ ,po9t4 ,9 ! cases :i* h j be5 consid]$ we saw t ! salt hydrates on be+ heat$ did n und]go complete fusion1 b t a solid 0 deposit$ consi/+ ( a l[] hydrate or ( ! anhydr\s salt4 ,x has1 h[ev]1 be5 long kn[n t c]ta9 cry/all9e salt hydrates 7e4g4 sodium ?iosulphate1 ,na#b,s#b,o#c1e;,h#b,o1 sodium acetate1 ,na,c#b;,h#c,o#b1c;,h#b,o7 melt completely 9 _! wat] ( cry/allization1 & yield a liquid ( ! same composition z ! cry/all9e salt4 ,9 ! case ( sodium ?iosulphate p5tahydrate ! temp]ature ( liquefaction is #ef;deg2 9 ! case ( sodium acetate trihydrate1 #eh;deg4 ,^! two salts1 !re=e1 h a def9ite melt+ po9t4 ,= ! purpose ( /udy+ ! behavi\r ( su* salt hydrates1 we %all *oose n ! cases :i* h j be5 m5tion$1 b two o!rs :i* h be5 m fully /udi$1 viz4 ! hydrates ( calcium *loride & ( f]ric *loride4 ,solubility ,curve ( ,calcium ,*loride ,hexahydrate4#bbd--;,al?\gh calcium *loride =ms sev]al hydrates1 ea* ( :i* possesses its own solubility1 x is nev]!less ! solubility curve ( ! hexahydrate :i* w *iefly int]e/ u at pres5t1 & we %all !re=e fir/ discuss t curve by itself4 ,illu/ration3 ,,fig4 #cg4 ,! solubility ( ?is salt has be5 det]m9$ f ! cryohydric po9t1 :i* lies at ab\t -#ee;deg1 up to ! melt+ po9t ( ! salt4#bbe ,! solubility increases ) rise ( temp]ature1 z is %[n by ! figures 9 ! foll[+ table1 & by ! 7diagrammatic7 curve ,,ab 9 ,fig4 #cg4 ,9 ! table1 ! numb]s "u ! head+ solubility d5ote ! numb] ( grams ( ,ca,cl#b dissolv$ 9 #ajj grams #adf ( wat]2 ^? "u ! head+ composition1 ! numb] ( gram-molecules ( wat] 9 ! solution to "o gram-molecule ( ,ca,cl#b4 ,,solubility ,,( ,,calcium ,,*loride ,,hexahydrate4 ---------------------------------------- - ,temp]ature4 ,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 ---------------------------------------- - ,s f> z ! fir/ portion ( ! curve is conc]n$1 x resembles ! mo/ g5]al type ( solubility curve4 ,9 ! pres5t case ! solubility is s great & increases s rapidly ) rise ( temp]ature1 t a po9t is rea*$ at :i* ! wat] ( cry/allization ( ! salt is suffici5t = its complete solution4 ,?is temp]ature is #cj4b;deg2 & s9ce ! composition ( ! solution is ! same z t ( ! solid salt1 viz4 #a mol4 ( ,ca,cl#b to #f mols4 ( wat]1 ?is temp]ature mu/ be ! melt+ po9t ( ! hexahydrate4 ,at ?is po9t ! hydrate w fuse or ! solution w solidify )\t *ange ( temp]ature & )\t *ange ( composition4 ,su* a melt+ po9t is call$ a congru5t melt+ po9t4 ,b ! solubility curve ( calcium *loride hexahydrate diff]s m>k$ly f ! o!r solubility curves hi!rto consid]$ 9 t x possesses a retr(lex portion1 repres5t$ 9 ! figure by ,,bc4 ,z is evid5t f ! figure1 !re=e1 calcium *loride hexahydrate exhibits ! peculi> &1 z x 0 at fir/ ?\ght1 impossible behavi\r t x c be 9 equilibrium at "o & ! same temp]ature ) two diff]5t solutions1 "o ( :i* conta9s m1 ! o!r less1 wat] ?an ! solid hydrate2 = x mu/ be rememb]$ t #adg ?r\gh\t ! :ole c\rse ( ! curve ,,abc ! solid phase pres5t 9 equilibrium ) ! solution is ! hexahydrate4 ,su* a behavi\r1 h[ev]1 on ! "p ( calcium *loride hexahydrate w appe> less /range if "o reflects t ! melt+ po9t ( ! hydrate w1 l ! melt+ po9t ( o!r sub/ances1 be l[]$ by ! addition ( a second sub/ance4 ,if1 !re=e1 wat] is add$ to ! hydrate at its melt+ po9t1 ! temp]ature at :i* ! solid hydrate w be 9 equilibrium ) ! liquid phase 7solution7 w be l[]$2 or if1 on ! o!r h&1 anhydr\s calcium *loride is add$ to ! hydrate at its melt+ po9t 7or :at is ! same ?+1 if wat] is remov$ f ! solution71 ! temp]ature at :i* ! hydrate w be 9 equilibrium ) ! liquid w also be l[]$2 i4e4 ! hydrate w melt at a l[] temp]ature4 ,9 ! =m] case we h ! hydrate 9 equilibrium ) a solution conta9+ m wat]1 9 ! latt] case ) a solution conta9+ less wat] ?an is conta9$ 9 ! hydrate itself4 ,x has already be5 /at$ 7p4 #aji7 t ! solubility curve 79 g5]al1 ! equilibrium curve7 is cont9u\s s long z ! solid phase rema9s un*ang$2 & we %all !re=e expect t ! curve ,,abc w be cont9u\s4 ,=m]ly1 h[ev]1 x 0 consid]$ by "s t ! curve 0 n cont9u\s1 b t ! melt+ po9t is ! po9t ( int]section ( two curves1 a solubility curve & a fusion curve4 ,al?\gh ! e>li] solubility det]m9ations 7 insuffici5t to decide ?is po9t conclusively1 m rec5t inve/igation has prov$ beyond d\bt t ! curve is cont9u\s & exhibits no break4#bbf #adh ,al?\gh 9 tak+ up ! discussion ( ! equilibria betwe5 calcium *loride & wat]1 x 0 desir$ especially to call att5tion to ! =m ( ! solubility curve 9 ! case ( salt hydrates possess+ a def9ite melt+ po9t1 nev]!less1 = ! sake ( complet5ess1 brief m5tion may be made ( ! o!r sy/ems :i* ^! two compon5ts c =m4 ,illu/ration3 ,,fig4 #ch4 ,besides ! hexahydrate1 ! solubility curve ( :i* has already be5 describ$1 calcium *loride c also cry/allize 9 two diff]5t =ms1 ea* ( :i* conta9s f\r molecules #adi ( wat] ( cry/allization2 ^! are di/+ui%$ z alpha-tetrahydrate1 & beta-tetrahydrate4 ,two o!r hydrates are also kn[n1 viz4 a dihydrate & a monohydrate4 ,! solubility curves ( ^! diff]5t hydrates are giv5 9 ,fig4 #ch4 ,on foll[+ ! solubility curve ( ! hexahydrate f ! ord9>y temp]ature upw>ds1 x is se5 t at a temp]ature ( #bi4h;deg repres5t$ by ! po9t ,h1 x cuts ! solubility curve ( ! alpha-tetrahydrate4 ,?is po9t is !re=e a quadruple po9t at :i* ! f\r phases hexahydrate1 alpha-tetrahydrate1 solution1 & vap\r c coexi/4 ,x is also ! transition po9t = ^! two hydrates4 ,s9ce1 at temp]atures above #bi4h;deg1 ! alpha-tetrahydrate is ! /able =m1 x is evid5t f ! data giv5 be=e 7p4 #adf71 z also f ,fig4 #ch1 t ! portion ( ! solubility curve ( ! hexahydrate ly+ above ?is temp]ature repres5ts meta/able equilibria4 ,! realization ( ! meta/able melt+ po9t ( ! hexahydrate is1 !re=e1 due to susp5d$ trans=mation4 ,at ! transition po9t1 #bi4h;deg1 ! solubility ( ! hexahydrate & alpha-tetrahydrate is #ajj4f p>ts ( ,ca,cl#b 9 #ajj p>ts ( wat]4 ,! retr(lex portion ( ! solubility curve ( ! hexahydrate ext5ds to only #a;deg bel[ ! melt+ po9t ( ! hydrate4 ,at #bi4b;deg cry/als ( a new hydrate1 beta-tetrahydrate1 sep>ate out1 & ! solution1 :i* n[ conta9s #aab4h p>ts ( ,ca,cl#b to #ajj p>ts ( wat]1 is saturat$ ) respect to ! two hydrates4 ,?r\gh\t its :ole ext5t ! solubility curve ,,edf ( ! beta-tetrahydrate repres5ts meta/able equilibria4 ,! upp] limit ( ! solubility curve ( beta-tetrahydrate is rea*$ at #ch4d;deg 7,f71 ! po9t ( int]section ) ! curve = ! dihydrate4 ,above #bi4h;deg ! /able hydrate is ! alpha-tetrahydrate2 & its solubility curve ext5ds to #de4c;deg 7,k71 at :i* temp]ature x cuts ! solubility curve ( ! dihydrate4 ,! curve ( ! latt] hydrate ext5ds to #age4e;deg 7,l71 & is !n succe$$ by ! curve = ! monohydrate4 ,! solubility curve ( ! anhydr\s salt does n beg9 until a temp]ature ( ab\t #bfj;deg4 ,! :ole diagram1 !re=e1 %[s a succession ( /able hydrates1 a meta/able hydrate1 a meta/able melt+ po9t & retr(lex solubility curve4 #aej ,pressure-,temp]ature ,diagram4--,! complete /udy ( ! equilibria betwe5 ! two compon5ts calcium *loride & wat] w\ld require ! discussion ( ! vap\r pressure ( ! diff]5t sy/ems1 & its v>iation ) ! temp]ature4 ,= our pres5t purpose1 h[ev]1 su* a discussion w\ld n be ( great value1 & w !re=e be omitt$ "h2 9 g5]al1 ! same relation%ips w\ld be f\nd z 9 ! case ( sodium sulphate 7p4 #ach71 except t ! r\nd$ portion ( ! solubility curve ( ! hexahydrate w\ld be repres5t$ by a simil> r\nd$ portion 9 ! pressure curve4#bbg ,z 9 ! case ( sodium sulphate1 ! transition po9ts ( ! diff]5t hydrates w\ld be indicat$ by breaks 9 ! curve ( pressures4 ,f9ally1 m5tion may aga9 be made ( ! diff]5ce ( ! pressure ( dissociation ( ! hexahydrate accord+ z x becomes dehydrat$ to ! alpha- or ! beta-tetrahydrate 7p4 #hh74 ,! ,indiff]5t ,po9t4--,we h already se5 t at #cj4b;deg calcium *loride hexahydrate melts congru5tly1 & t1 provid$ ! pressure is ma9ta9$ con/ant1 addition or )drawal ( heat w cause ! complete liquefaction or solidification1 )\t ! temp]ature ( ! sy/em und]go+ *ange4 ,?is behavi\r1 !re=e1 is simil> to1 b is n q ! same z ! fusion ( a simple sub/ance su* z ice2 & ! diff]5ce is due to ! fact t 9 ! case ( ! hexahydrate ! emission ( vap\r by ! liquid phase causes an alt]ation 9 ! composition ( ! latt]1 ow+ to ! non-volatility ( ! calcium *loride2 :]eas 9 ! case ( ice ?is is1 ( c\rse1 n s4 ,consid]1 h[ev]1 = ! pres5t t ! vap\r phase is abs5t1 & t we are deal+ ) ! two-phase sy/em solid--solution4 ,!n1 s9ce !re are two compon5ts1 ! sy/em is biv>iant4 ,= any giv5 value ( ! pressure1 !re=e1 we %\ld expect t ! sy/em c\ld exi/ at diff]5t temp]atures2 :i*1 inde$1 is ! case4 ,x has1 h[ev]1 already be5 not$ t :5 ! composition ( ! liquid phase becomes ! same z t ( ! solid1 ! sy/em !n behaves z a univ>iant sy/em2 =1 at a giv5 pressure1 ! sy/em solid--solution c exi/ only at "o temp]ature1 *ange ( temp]ature produc+ complete trans=mation 9 #aea "o or o!r direction4 ,! v>iability ( ! sy/em has !re=e be5 dim9i%$4 ,?is behavi\r w p]haps be m cle>ly und]/ood :5 "o reflects t s9ce ! composition ( ! two phases is ! same1 ! sy/em may be reg>d$ z be+ =m$ ( "o compon5t1 j z ! sy/em ,,nh#d;,cl -- ,,nh#c ,h,cl 0 reg>d$ z be+ compos$ ( "o compon5t :5 ! vap\r _h ! same total composition z ! solid 7p4 #ac74 ,"o compon5t 9 two phases1 h[ev]1 con/itutes a univ>iant sy/em1 & we c !re=e see t calcium *loride hexahydrate 9 contact ) solution ( ! same composition w con/itute a univ>iant sy/em4 ,! temp]ature ( equilibrium w1 h[ev]1 v>y ) ! pressure2#bbh if ! latt] is con/ant1 ! temp]ature w also be con/ant4 ,a po9t su* z has j be5 ref]r$ to1 :i* repres5ts ! special behavi\r ( a sy/em ( two 7or m7 compon5ts1 9 :i* ! composition ( two phases becomes id5tical1 is kn[n z an indiff]5t po9t1#bbi & x has be5 %[n#bcj t at a giv5 pressure ! temp]ature 9 ! indiff]5t po9t is ! maximum or m9imum temp]ature possible at ! p>ticul> pressure#bca 7cf4 critical solution temp]ature74 ,at su* a po9t a sy/em loses "o degree ( fre$om1 or behaves l a sy/em ( ! next l[] ord]4 ,! ,hydrates ( ,f]ric ,*loride4--,a bett] illu/ration ( ! =mation ( comp\nds possess+ a def9ite melt+ po9t1 & ( ! exi/5ce ( retr(lex solubility curves1 is af=d$ by ! hydrates ( f]ric *loride1 :i* n only possess def9ite po9ts ( fusion1 b ^! melt+ po9ts are /able4 ,a v brief description ( ! relations met ) w suffice4#bcb #aeb ,f]ric *loride c =m no less ?an f\r /able hydrates1 viz4 ,fe#b;,cl#f1ab;,h#b,o1 ,fe#b;,cl#f1g;,h#b,o1 ,fe#b;,cl#f1e;,h#b,o1 & ,fe#b;,cl#f1d;,h#b,o1 & ea* ( ^! hydrates possesses a def9ite1 /able melt+ po9t4 ,on analogy ) ! behavi\r ( calcium *loride1 !re=e1 we %all expect t ! solubility curves ( ^! diff]5t hydrates w exhibit a s]ies ( temp]ature maxima2 ! po9ts ( maximum temp]ature repres5t+ sy/ems 9 :i* ! composition ( ! solid & liquid phases is ! same4 ,a graphical repres5tation ( ! solubility relations is giv5 9 ,fig4 #ci1 & ! composition ( ! diff]5t saturat$ solutions :i* c be =m$ is giv5 9 ! foll[+ tables1 ! composition be+ express$ 9 molecules ( ,fe#b;,cl#f to #ajj molecules ( wat]4 ,! figures pr9t$ 9 ?ick type ref] to transition & melt+ po9ts4 ,illu/ration3 ,,fig4 #ci4 #aec ,,composition ,,( ,,! ,,saturat$ ,,solutions ,,( ,,f]ric ,,*loride ,,& ,,its ,,hydrates4 7,! "n plac$ at ! head ( ea* table is ! solid phase47 ,,ice4 --------------------------- ,temp]ature4 ,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 --------------------------- ,temp]ature4 ,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 --------------------------- ,temp]ature4 ,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 --------------------------- ,temp]ature4 ,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 --------------------------- ,temp]ature4 ,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,,anhydr\s74 --------------------------- ,temp]ature4 ,composition4 --------------------------- #bj;deg #aa4ce #ff;deg #bi4bj #gj;deg #bi4db #ge;deg #bh4ib #hj;deg #bi4bj #ajj;deg #bi4ge --------------------------- ,! l[e/ portion ( ! curve1 ,,ab1 repres5ts ! equilibria betwe5 ice & solutions conta9+ f]ric *loride4 ,x repres5ts1 9 o!r words1 ! l[]+ ( ! fusion po9t ( ice by addition ( f]ric *loride4 ,at ! po9t ,b 7-#ee;deg71 ! cryohydric po9t 7p4 #aag7 is rea*$1 at :i* ! solution is 9 equilibrium ) ice & f]ric *loride dodecahydrate4 ,z #aed has already be5 %[n1 su* a po9t repres5ts an inv>iant sy/em2 & ! liquid phase w1 !re=e1 solidify to a mixture ( ice & hydrate )\t *ange ( temp]ature4 ,if heat is add$1 ice w melt & ! sy/em w pass to ! curve ,,bcdn1 :i* is ! solubility curve ( ! dodecahydrate4 ,at ,c 7#cg;deg71 ! po9t ( maximum temp]ature1 ! hydrate melts completely4 ,! retr(lex portion ( ?is curve c be foll[$ backw>ds to a temp]ature ( #h;deg1 b bel[ #bg4d;deg 7,d71 ! solutions are sup]saturat$ ) respect to ! heptahydrate2 po9t ,d is ! eutectic po9t = dodecahydrate & heptahydrate4 ,! curve ,,def is ! solubility curve ( ! heptahydrate1 ,e be+ ! melt+ po9t1 #cb4e;deg4 ,on fur!r increas+ ! quantity ( f]ric *loride1 ! temp]ature ( equilibrium is l[]$ until at ,f 7#cj;deg7 ano!r eutectic po9t is rea*$1 at :i* ! heptahydrate & p5tahydrate c co-exi/ ) solution4 ,!n foll[ ! solubility curves = ! p5tahydrate1 ! tetrahydrate1 & ! anhydr\s salt2 ,g 7#ef;deg7 is ! melt+ po9t ( ! =m] hydrate1 ,j 7#gc4e;deg7 ! melt+ po9t ( ! latt]4 ,h & ,k1 ! po9ts at :i* ! curves int]sect1 repres5t eutectic po9ts2 ! temp]ature ( ! =m] is #ee;deg1 t ( ! latt] #ff;deg4 ,! dott$ portions ( ! curves repres5t meta/able equilibria4 ,z is se5 f ! diagram1 a rem>kable s]ies ( solubility curves is obta9$1 ea* pass+ ?r\gh a po9t ( maximum temp]ature1 ! :ole s]ies ( curves =m+ an undulat+ fe/oon4 ,to ! "r ( ! s]ies ( curves ! diagram repres5ts unsaturat$ solutions2 to ! left1 sup]saturat$4 ,if an unsaturat$ solution1 ! composition ( :i* is repres5t$ by a po9t 9 ! field to ! "r ( ! solubility curves1 is cool$ d[n1 ! result obta9$ w diff] accord+ z ! composition ( ! solution is ! same z t ( a cryohydric po9t1 or ( a melt+ po9t1 or has an int]m$iate value4 ,?us1 if a solution repres5t$ by x#a is cool$ d[n1 ! composition w rema9 un*ang$ z indicat$ by ! horizontal dott$ l9e1 until ! po9t ,d is rea*$4 ,at ?is po9t1 dodecahydrate & heptahydrate w sep>ate out1 & ! liquid w ultimately solidify completely to a mixture or conglom]ate ( ^! two hydrates2 ! temp]ature ( #aee ! sy/em rema9+ con/ant until complete solidification has tak5 place4 ,if1 on ! o!r h&1 a solution ( ! composition x#c is cool$ d[n1 f]ric *loride dodecahydrate w be =m$ :5 ! temp]ature has fall5 to t repres5t$ by ,c1 & ! solution w completely solidify1 )\t alt]ation ( temp]ature1 ) =mation ( ?is hydrate4 ,9 bo? ^! cases1 !re=e1 a po9t is rea*$ at :i* complete solidification occurs )\t *ange ( temp]ature4 ,some:at diff]5t1 h[ev]1 is ! result :5 ! solution has an int]m$iate composition1 z repres5t$ by x#b or x#d4 ,9 ! =m] case ! dodecahydrate w fir/ ( all sep>ate out1 b on fur!r )drawal ( heat ! temp]ature w fall1 ! solution w become relatively ri*] 9 f]ric *loride1 ow+ to sep>ation ( ! hydrate1 & ultimately ! eutectic po9t ,d w be rea*$1 at :i* complete solidification w occur4 ,simil>ly ) ! second solution4 ,f]ric *loride dodecahydrate w fir/ be =m$1 & ! temp]ature w gradually fall1 ! composition ( ! solution foll[+ ! curve ,,cb until ! cryohydric po9t ,b is rea*$1 :5 ! :ole w solidify to a conglom]ate ( ice & dodecahydrate4 ,susp5d$ ,trans=mation4--,n only c ! upp] bran* ( ! solubility curve ( ! dodecahydrate be foll[$ backw>ds to a temp]ature ( #h;deg1 or ab\t #ai;deg bel[ ! temp]ature ( transition to ! heptahydrate2 b susp5d$ trans=mation has also be5 obs]v$ 9 ! case ( ! heptahydrate & ! p5tahydrate4 ,to su* an ext5t is ?is ! case t ! solubility curve ( ! latt] hydrate has be5 foll[$ d[nw>ds to its po9t ( int]section ) ! curve = ! dodecahydrate4 ,?is po9t ( int]section1 repres5t$ 9 ,fig4 #ci by ,m1 lies at a temp]ature ( ab\t #ae;deg2 & at ?is temp]ature1 !re=e1 x is possible = ! two solid phases dodecahydrate & p5tahydrate to coexi/1 s t ,m is a eutectic po9t = ! dodecahydrate & ! p5tahydrate4 ,x is1 h[ev]1 a meta/able eutectic po9t1 = x lies 9 ! region ( sup]saturation ) respect to ! heptahydrate2 & x c be realiz$ only because ( ! fact t ! latt] hydrate is n readily =m$4 ,evaporation ( ,solutions at ,con/ant ,temp]ature4--,on #aef evaporat+ dilute solutions ( f]ric *loride at con/ant temp]ature1 a rem>kable s]ies ( *anges is obs]v$1 :i*1 h[ev]1 w be und]/ood ) ! help ( ,fig4 #dj4 ,suppose an unsaturat$ solution1 ! composition ( :i* is repres5t$ by ! po9t x#a1 is evaporat$ at a temp]ature ( ab\t #ag;deg - #ah;deg4 ,z wat] passes (f1 ! composition ( ! solution w foll[ ! dott$ l9e ( con/ant temp]ature1 until at ! po9t :]e x cuts ! curve ,,bc ! solid hydrate ,fe#b;,cl#f1ab;,h#b,o sep>ates out4 ,z wat] cont9ues to be remov$1 ! hydrate mu/ be deposit$ 79 ord] t ! solution %all rema9 saturat$71 until f9ally ! solution dries up to ! hydrate4 ,z dehydration proce$s1 ! heptahydrate c be =m$1 & ! dodecahydrate w f9ally pass into ! heptahydrate2 & ?is1 9 turn1 into ! p5tahydrate4 ,illu/ration3 ,,fig4 #dj4 ,b ! heptahydrate is n always =m$ by ! dehydration ( ! dodecahydrate1 & ! behavi\r on evaporation is !re=e some:at p]plex+ at fir/ sight4 ,aft] ! solution has dri$ to ! dodecahydrate1 z expla9$ above1 fur!r removal ( wat] causes liquefaction1 & ! sy/em is n[ repres5t$ by ! po9t ( int]section at a2 at ?is po9t ! solid hydrate is 9 equilibrium ) a solution conta9+ relatively m f]ric *loride4 ,if1 !re=e1 evaporation is cont9u$1 ! solid hydrate mu/ pass into solution 9 ord] t ! composition ( ! latt] may rema9 un*ang$1 s t ultimately a liquid w aga9 be obta9$4 ,a v slight fur!r dehydration w br+ ! solution into ! /ate repres5t$ by b1 at :i* ! p5tahydrate is =m$1 & ! solution w at la/ disappe> & leave ?is hydrate alone4 ,)\t ! in=mation to be obta9$ f ! curves 9 ,figs4 #ci & #dj1 ! ph5om5a :i* w\ld be obs]v$ on c>ry+ out ! evaporation at a temp]ature ( ab\t #ca - #cb;deg #aeg w\ld be /ill m bewild]+4 ,! composition ( ! diff]5t solutions =m$ w be repres5t$ by ! p]p5dicul> l9e x#babcde4 ,evaporation w fir/ cause ! sep>ation ( ! dodecahydrate1 & !n total disappe>ance ( ! liquid phase4 ,!n liquefaction w occur1 & ! sy/em w n[ be repres5t$ by ! po9t #b1 9 :i* condition x w rema9 until ! solid hydrate has disappe>$4 ,foll[+ ?is !re w be deposition ( ! heptahydrate 7po9t #c71 ) subsequ5t disappe>ance ( ! liquid phase4 ,fur!r dehydration w aga9 cause liquefaction1 :5 ! conc5tration ( ! solution w be repres5t$ by ! po9t #d2 ! heptahydrate w ultimately disappe>1 & !n w ensue ! deposition ( ! p5tahydrate1 & complete solidification w result4 ,on evaporat+ a solution1 !re=e1 ( ! composition x#b1 ! foll[+ s]ies ( ph5om5a w be obs]v$3 solidification to dodecahydrate2 liquefaction2 solidification to heptahydrate2 liquefaction2 solidification to p5tahydrate4#bcc ,al?\gh f]ric *loride & wat] =m ! l>ge/ & be/-/udi$ s]ies ( hydrates possess+ def9ite melt+ po9ts1 examples ( simil> hydrates are n few 9 numb]2 & m c>eful inve/igation is con/antly add+ to ! li/4#bcd ,9 all ^! cases ! solubility curve w %[ a po9t ( maximum temp]ature1 at :i* ! hydrate melts1 & w end1 above & bel[1 9 a cryohydric po9t4 ,conv]sely1 if su* a curve is f\nd 9 a sy/em ( two compon5ts1 we c argue t a def9ite comp\nd ( ! compon5ts possess+ a def9ite melt+ po9t is =m$4 ,inevaporable ,solutions4--,if a saturat$ solution 9 contact ) two hydrates1 or ) a hydrate & anhydr\s salt is heat$1 ! temp]ature & composition ( ! solution w1 ( c\rse1 rema9 un*ang$ s long z ! two solid phases are pres5t1 = su* a sy/em is inv>iant4 ,9 addition to ?is1 h[ev]1 ! quantity ( ! solution w also rema9 un*ang$1 ! wat] :i* evaporates be+ suppli$ by ! high] hydrate4 ,! same ph5om5on is also obs]v$ 9 ! case ( cryohydric po9ts :5 ice is a solid phase2 s long z ! latt] is pres5t1 evaporation w be accompani$ #aeh by fusion ( ! ice1 & ! quantity ( solution w rema9 con/ant4 ,su* solutions are call$ inevaporable4#bce ,illu/ration3 ,,fig4 #da4 ,illu/ration4--,9 ord] to illu/rate ! application ( ! pr9ciples ( ! ,phase ,rule to ! /udy ( sy/ems =m$ by a volatile & a non-volatile compon5t1 a brief description may be giv5 ( ! behavi\r ( sulphur dioxide & potassium iodide1 :i* has =m$ ! subject ( a rec5t inve/igation4 ,aft] x _h be5 f\nd#bcf t liquid sulphur dioxide has ! prop]ty ( dissolv+ potassium iodide1 & t ! solutions ?us obta9$ pres5t c]ta9 peculi>ities ( behavi\r1 ! "q arose z to :e!r or n comp\nds are =m$ betwe5 ! sulphur dioxide & ! potassium iodide1 & if s1 :at ^! comp\nds are4 ,to f9d an answ] to ?is "q1 ,wald5 & ,c5tn]szw]#bcg made a complete inve/igation ( ! solubility curves 7equilibrium curves7 ( ^! two compon5ts1 ! inve/igation ext5d+ f ! freez+ po9t to ! critical po9t ( sulphur dioxide4 ,= conv5i5ce ( ref]5ce1 ! results :i* !y obta9$ are repres5t$ diagrammatically 9 ,fig4 #da4 ,! freez+ po9t 7,a7 ( pure sulphur dioxide 0 f\nd to be -#gb4g;deg4 ,addition ( potassium iodide l[]$ ! freez+ po9t1 b ! maximum depression obta9$ 0 v small1 & 0 rea*$ :5 ! conc5tration ( ! potassium iodide 9 ! solution 0 only #j4ccf mols4 p] c5t4 ,beyond ?is po9t1 an increase 9 ! conc5tration ( ! iodide 0 accompani$ by an elevation ( ! freez+ po9t1 ! *ange ( ! freez+ po9t ) ! conc5tration be+ repres5t$ by ! curve ,,bc4 ,! solid #aei :i* sep>at$ f ! solutions repres5t$ by ,,bc 0 a bright yell[ cry/all9e sub/ance4 ,at ! po9t ,c 7-#bc4d;deg7 a temp]ature-maximum 0 rea*$2 & z ! conc5tration ( ! potassium iodide 0 cont9u\sly increas$1 ! temp]ature ( equilibrium fir/ fell & !n sl[ly rose1 until at #j4bf;deg 7,e7 a second temp]ature-maximum 0 regi/]$4 ,on pass+ ! po9t ,d1 ! solid :i* 0 deposit$ f ! solution 0 a r$ cry/all9e sub/ance4 ,on )draw+ sulphur dioxide f ! sy/em1 ! solution became turbid1 & ! temp]ature rema9$ con/ant4 ,! inve/igation 0 n pursu$ f>!r at ?is po9t1 ! att5tion be+ !n direct$ to ! equilibria at high] temp]atures4 ,:5 a solution ( potassium iodide 9 liquid sulphur dioxide conta9+ #a4di p] c5t4 ( potassium iodide 0 heat$1 solid 7potassium iodide7 0 deposit$ at a temp]ature ( #if4d;deg4 ,solutions conta9+ m ?an ab\t #c p] c5t4 ( ! iodide sep>at$1 on be+ heat$1 into two lay]s1 & ! temp]ature at :i* ! liquid became het]og5e\s fell z ! conc5tration 0 increas$2 a temp]ature-m9imum be+ obta9$ ) solutions conta9+ #ab p] c5t4 ( potassium iodide4 ,on ! o!r h&1 solutions conta9+ #cj4i p] c5t4 ( ! iodide1 on be+ heat$1 deposit$ potassium iodide2 :ile a solution conta9+ #bd4e p] c5t4 ( ! salt fir/ sep>at$ into two lay]s at #hi4c;deg1 & !n1 on cool+1 solid 0 deposit$ & "o ( ! liquid lay]s disappe>$4 ,su* are1 9 brief1 ! results ( exp]im5t2 _! int]pretation 9 ! light ( ! ,phase ,rule is ! foll[+3-- ,! curve ,,ab is ! freez+-po9t curve ( solid sulphur dioxide 9 contact ) solutions ( potassium iodide4 ,,bcd is ! solubility curve ( ! yell[ cry/all9e solid :i* is deposit$ f ! solutions4 ,c1 ! temp]ature-maximum1 is ! melt+ po9t ( ?is yell[ solid1 & ! composition ( ! latt] mu/ be ! same z t ( ! solution at ?is po9t 7p4 #ade71 :i* 0 f\nd to be t repres5t$ by ! =mula ,,ki1#ad,,s#b4 ,b is !re=e ! eutectic po9t1 at :i* solid sulphur dioxide & ! comp\nd ,,ki1#ad,,s#b c exi/ toge!r 9 equilibrium ) solution & vap\r4 ,! curve ,,de is ! solubility curve ( ! r$ cry/all9e solid1 & ! #afj po9t ,e1 at :i* ! composition ( solution & solid is ! same1 is ! melt+ po9t ( ! solid4 ,! composition ( ?is sub/ance 0 f\nd to be ,,ki1#d,,s#b4bch ,d is1 !re=e1 ! eutectic po9t at :i* ! comp\nds ,,ki1#ad,,s#b & ,,ki1#d,,s#b c coexi/ 9 equilibrium ) solution & vap\r4 ,! curve ,,de does n exhibit a retr(lex portion2 on ! contr>y1 on attempt+ to obta9 m conc5trat$ solutions 9 equilibrium ) ! comp\nd ,,ki1#d,,s#b1 a new solid phase 7probably potassium iodide7 0 =m$4 ,s9ce at ?is po9t !re are f\r phases 9 equilibrium1 viz4 ! comp\nd ,,ki1#d,,s#b1 potassium iodide1 solution1 & vap\r1 ! sy/em is inv>iant4 ,e is1 !re=e1 ! transition po9t = ,,ki1#d,,s#b & ,,ki4 ,pass+ to high] temp]atures1 ,,fg is ! solubility curve ( potassium iodide 9 sulphur dioxide2 at ,g two liquid phases are =m$1 & ! sy/em !re=e becomes inv>iant 7cf4 p4 #aba74 ,! curve ,,ghk is ! solubility curve = two p>tially miscible liquids2 & s9ce complete miscibility occurs on l[]+ ! temp]ature1 ! curve is simil> to t obta9$ ) trie?ylam9e & wat] 7p4 #aja74 ,k is also an inv>iant po9t at :i* potassium iodide is 9 equilibrium ) two liquid phases & vap\r4 ,! complete inve/igation ( ! equilibria betwe5 sulphur dioxide & potassium iodide1 !re=e1 %[s t ^! two compon5ts =m ! comp\nds ,,ki1#ad,,s#b & ,,ki1#d,,s#b2 & t :5 solutions hav+ a conc5tration betwe5 ^? repres5t$ by ! po9ts ,g & ,k are heat$1 sep>ation into two lay]s occurs4 ,! temp]atures & conc5trations ( ! diff]5t *>act]i/ic po9ts are z foll[s3-- ---------------------------------------- --------------------- ,composition ( ,po9t4 ,temp]ature4 ! solution p] c5t4 ,,ki4 ---------------------------------------- --------------------- ,a 7m4p4 ( ,,s#b7 -#gb4g;deg -- ,b 7eutectic po9t7 -- #j4hf ,c 7m4p4 ( ,,ki1#ad,,s#b7 -#bc4d;deg #ag4fc ,e 7m4p4 ( ,,ki1#d,,s#b7 #j4bf;deg #ci4cc ,g 7,,ki two liquid phases7 7ab\t7 #hh;deg #bd4j ,h 7critical solution po9t7 #gg4c;deg #ab ,k 7,,ki two liquid phases7 7ab\t7 #hh;deg #b4g ---------------------------------------- --------------------- 99 99 99 99 99 #afa ,,*apt] ,,ix ,,equilibria ,,betwe5 ,,two ,,volatile ,,compon5ts ,g5]al4--,9 ! two prec$+ *apt]s c]ta9 re/rictions 7 impos$ on ! discussion ( ! equilibria betwe5 two compon5ts2 b 9 ! pres5t *apt] ! re/riction t only "o ( ! compon5ts is volatile w be all[$ to fall1 & ! g5]al behavi\r ( two volatile#bci compon5ts1 ea* ( :i* is capable ( =m+ a liquid solution ) ! o!r1 w be /udi$4 ,z we %all see1 h[ev]1 ! removal ( ! previ\s re/riction produces no alt]ation 9 ! g5]al aspect ( ! equilibrium curves = conc5tration & temp]ature1 b *anges to "s ext5t ! appe>ance ( ! pressure-temp]ature diagram4 ,! latt] w\ld become /ill m complicat$ if acc\nt 7 tak5 n only ( ! total pressure b also ( ! p>tial pressures ( ! two compon5ts 9 ! vap\r phase2 ?is complication1 h[ev]1 w n be introduc$ 9 ! pres5t discussion4#bdj ,9 ?is *apt] we %all consid] ! sy/ems =m$ by ! two compon5ts iod9e & *lor9e1 & sulphur dioxide & wat]4 ,iod9e & ,*lor9e4--,! diff]5t sy/ems furni%$ by iod9e & *lor9e1 r5d]$ classical by ! /udies ( ,/ort5bek]1#bda =m a v complete example ( equilibria 9 a two-compon5t sy/em4 ,we %all fir/ ( all consid] ! #afb relations betwe5 conc5tration & temp]ature1 ) ! help ( ! accompany+ diagram1 ,fig4 #db4 ,illu/ration3 ,,fig4 #db4 ,conc5tration-,temp]ature ,diagram4--,9 ?is diagram ! temp]atures are tak5 z ! abscissae1 & ! composition ( ! solution1 express$ 9 atoms ( *lor9e to "o atom ( iod9e1#bdb is repres5t$ by ! ord9ates4 ,9 ! diagram1 ,a repres5ts ! melt+ po9t ( pure iod9e1 #aad;deg4 ,if *lor9e is add$ to ! sy/em1 a solution ( *lor9e 9 liquid iod9e is obta9$1 & ! temp]ature at :i* solid iod9e is 9 equilibrium ) ! liquid solution w be all ! l[] ! great] ! conc5tration ( ! *lor9e4 ,we !re=e obta9 ! curve ,,abf1 :i* repres5ts ! composition ( ! solution #afc ) :i* solid iod9e is 9 equilibrium at diff]5t temp]atures4 ,?is curve c be foll[$ d[n to #j;deg1 b at temp]atures bel[ #g4i;deg 7,b7 x repres5ts meta/able equilibria4 ,at ,b iod9e mono*loride c be =m$1 & if pres5t ! sy/em becomes inv>iant2 ,b is !re=e a quadruple po9t at :i* ! f\r phases1 iod9e1 iod9e mono*loride1 solution1 & vap\r1 c coexi/4 ,cont9u$ )drawal ( heat at ?is po9t w !re=e lead to ! complete solidification ( ! solution to a mixture or conglom]ate ( iod9e & iod9e mono*loride1 :ile ! temp]ature rema9s con/ant dur+ ! process4 ,b is ! eutectic po9t = iod9e & iod9e mono*loride4 ,j z we f\nd 9 ! case ( aque\s salt solutions t at temp]atures above ! cryohydric or eutectic po9t1 two diff]5t solutions c\ld exi/1 "o 9 equilibrium ) ice1 ! o!r 9 equilibrium ) ! salt 7or salt hydrate71 s 9 ! case ( iod9e & *lor9e !re c be two solutions above ! eutectic po9t ,b1 "o conta9+ a l[] proportion ( *lor9e 9 equilibrium ) iod9e1 ! o!r conta9+ a high] proportion ( *lor9e 9 equilibrium ) iod9e mono*loride4 ,! composition ( ! latt] solution is repres5t$ by ! curve ,,bcd4 ,z ! conc5tration ( *lor9e is increas$1 ! temp]ature at :i* !re is equilibrium betwe5 iod9e mono*loride & solution rises until a po9t is rea*$ at :i* ! composition ( ! solution is ! same z t ( ! solid4 ,at ?is po9t 7,c71 iod9e mono*loride melts4 ,addition ( "o ( ! compon5ts w l[] ! temp]ature ( fusion1 & a cont9u\s curve1#bdc exhibit+ a retr(lex portion z 9 ! case ( ,ca,cl#b1f;,h#b,o1 w be obta9$4 ,at temp]atures bel[ its melt+ po9t1 !re=e1 iod9e mono*loride c be 9 equilibrium ) two diff]5t solutions4 ,! upp] portion ( ?is curve1 ,,cd1 c be foll[$ d[nw>ds to a temp]ature ( #bb4g;deg4 ,at ?is temp]ature iod9e tri*loride c sep>ate out1 & a second quadruple #afd po9t 7,d7 is obta9$4 ,?is is ! eutectic po9t = iod9e mono*loride & iod9e tri*loride4 ,by addition ( heat & increase 9 ! am\nt ( *lor9e1 ! iod9e mono*loride disappe>s1 & ! sy/em passes along ! curve ,,de1 :i* repres5ts ! composition ( ! solutions 9 equilibrium ) solid iod9e tri*loride4 ,! conc5tration ( *lor9e 9 ! solution increases z ! temp]ature is rais$1 until at ! po9t ,e1 :]e ! solution has ! same composition z ! solid1 ! maximum temp]ature is rea*$2 ! iod9e tri*loride melts4 ,on increas+ /ill fur!r ! conc5tration ( *lor9e 9 ! solution1 ! temp]ature ( equilibrium falls1 & a cont9u\s curve1 simil> to t = ! mono*loride1 is obta9$4 ,! upp] bran* ( ?is curve has be5 foll[$ d[n to a temp]ature ( #cj;deg1 ! solution at ?is po9t conta9+ #ii4f p] c5t4 ( *lor9e4#bdd ,! v r\nd$ =m ( ! curve is due to ! tri*loride be+ l>gely dissociat$ 9 ! liquid /ate4 ,"o curve /ill rema9s to be consid]$4 ,z has already be5 m5tion$1 iod9e mono*loride c exi/ 9 two cry/all9e =ms1 only "o ( :i*1 h[ev]1 is /able at temp]atures bel[ ! melt+ po9t2 ! two =ms are monotropic 7p4 #dd74 ,! /able =m :i* melts at #bg4b;deg1 is call$ ! alpha-=m1 :ile ! less /able v>iety1 melt+ at #ac4i;deg1 is kn[n z ! beta-=m4 ,if1 n[1 ! pres5ce ( alpha-,i,cl is exclud$1 x is possible to obta9 ! beta-=m1 & to /udy ! conditions ( equilibrium betwe5 x & solutions ( iod9e & *lor9e1 f ! eutectic po9t ,f to ! melt+ po9t ,g4 ,z ! beta-,i,cl becomes less /able 9 pres5ce ( excess ( *lor9e1 x has n be5 possible to /udy ! retr(lex portion ( ! curve repres5t$ by ! dott$ cont9uation ( ,,fg4 ,! foll[+ table gives "s ( ! num]ical data f :i* ,fig4 #db 0 con/ruct$4#bde #afe ,,iod9e ,,& ,,*lor9e4 ,i4 ,inv>iant sy/ems4 ---------------------------------------- --------------------------------- ,phases pres5t4 ,temp]- ,pressure4------------------------------ --------------------- ature4 ,solid4 ,liquid4 ,vap\r4 ---------------------------------------- ----------------------------- #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 ,melt+ po9ts4 ,a4 ,iod9e1#bdf #aad4ae;deg 7pressure #hi4h mm474 ,c4 alpha-,iod9e mono*loride1 #bg4b;deg 7pressure #cg mm474 ,e4 ,iod9e tri*loride1 #aja;deg 7pressure #af atm474 ,g4 beta-,iod9e mono*loride1 #ac4i;deg4 ,s9ce ! vap\r pressure at ! melt+ po9t ( iod9e tri*loride am\nts to #af atm41 ! exp]im5ts mu/ ( c\rse be c>ri$ out 9 clos$ vessels4 ,at #fc4g;deg ! vap\r pressure ( ! sy/em tri*loride--solution--vap\r is equal to #a atm4 ,pressure-,temp]ature ,diagram4--,9 ?is diagram !re are repres5t$ ! values ( ! vap\r pressure ( ! saturat$ solutions ( *lor9e & iod9e4 ,to give a complete picture ( ! relations betwe5 pressure1 temp]ature1 & conc5tration1 a solid model w\ld be requir$1 ) ?ree axes at "r angles to "o ano!r along :i* c\ld be measur$ ! values ( pressure1 temp]ature1 & conc5tration ( ! compon5ts 9 ! solution4 ,in/ead ( ?is1 h[ev]1 !re may be employ$ ! accompany+ projection figure#bdg 7,fig4 #dc71 ! l[] portion ( :i* %[s ! projection ( ! equilibrium curve on ! surface conta9+ ! conc5tration & temp]ature axes1 :ile ! upp] portion is ! projection on ! plane conta9+ ! pressure & temp]ature axes4 ,! l[] portion is !re=e a conc5tration-temp]ature diagram2 #aff ! upp] portion1 a pressure-temp]ature diagram4 ,! correspond+ po9ts ( ! two diagrams are jo9$ by dott$ l9es4 ,illu/ration3 ,,fig4 #dc4 ,correspond+ to ! po9t ,c1 ! melt+ po9t ( pure iod9e1 !re is ! po9t ,c#a1 :i* repres5ts ! vap\r pressure ( iod9e at its melt+ po9t4 ,at ?is po9t ?ree curves cut3 #a1 ! sublimation curve ( iod9e2 #b1 ! vaporization curve ( fus$ iod9e2 #c1 ,c#a;,b#a1 ! vap\r-pressure curve ( ! saturat$ solutions 9 equilibrium ) solid iod9e4 ,/>t+1 !re=e1 ) ! sy/em solid iod9e--liquid iod9e1 addition ( *lor9e w cause ! temp]ature ( equilibrium to fall cont9u\sly1 :ile ! vap\r pressure w fir/ increase1 pass ?r\gh a maximum & !n fall cont9u\sly #afg until ! eutectic po9t1 ,b 7,b#a71 is rea*$4#bdh ,at ?is po9t ! sy/em is inv>iant1 & ! pressure w !re=e rema9 con/ant until all ! iod9e has disappe>$4 ,z ! conc5tration ( ! *lor9e increases 9 ! mann] repres5t$ by ! curve ,bf,h1 ! pressure ( ! vap\r also increases z repres5t$ by ! curve ,b#a;f#a;,h#a4 ,at ,h#a1 ! eutectic po9t = iod9e mono*loride & iod9e tri*loride1 ! pressure aga9 rema9s con/ant until all ! mono*loride has disappe>$4 ,z ! conc5tration ( ! solution passes along ! curve ,,hf1 ! pressure ( ! vap\r increases z repres5t$ by ! curve ,h#a;,f#a2 ,f#a repres5ts ! pressure ( ! vap\r at ! melt+ po9t ( iod9e tri*loride4 ,if ! conc5tration ( ! *lor9e 9 ! solution is cont9u\sly increas$ f ?is po9t1 ! vap\r pressure fir/ increases & !n decreases1 until ! eutectic po9t = iod9e tri*loride & solid *lor9e is rea*$ 7,d#a74 ,curves ,cl#b solid & ,cl#b liquid repres5t ! sublimation & vaporization curves ( *lor9e1 ! melt+ po9t ( *lor9e be+ -#ajb;deg4 ,al?\gh complete measurem5ts ( ! vap\r pressure ( ! diff]5t sy/ems ( pure iod9e to pure *lor9e h n be5 made1 ! exp]im5tal data are nev]!less suffici5t to all[ ( ! g5]al =m ( ! curves be+ indicat$ ) c]ta9ty4 ,biv>iant ,sy/ems4--,to ^!1 only a brief ref]5ce ne$ be made4 ,s9ce !re are two compon5ts1 two phases w =m a biv>iant sy/em4 ,! fields 9 :i* ^! sy/ems c exi/ are %[n 9 ,fig4 #dc & ,fig4 #dd1 :i* is a m diagrammatic repres5tation ( a portion ( ,fig4 #dc4 ,i4 ,iod9e--vap\r4 ,,ii4 ,solution--vap\r4 ,,iii4 ,iod9e tri*loride--vap\r4 ,,iv4 ,iod9e mono*loride--vap\r4 ,illu/ration3 ,,fig4 #dd4 ,! conditions = ! exi/5ce ( ^! sy/ems w probably be be/ und]/ood f ,fig4 #dd4 ,s9ce ! curve ,b',a' #afh repres5ts ! pressures "u :i* ! sy/em iod9e--solution--vap\r c exi/1 increase ( volume 7dim9ution ( pressure7 w cause ! volatilization ( ! solution1 & ! sy/em iod9e--vap\r w rema94 ,if1 !re=e1 we />t ) a sy/em repres5t$ by a1 dim9ution ( pressure at con/ant temp]ature w lead to ! condition repres5t$ by x4 ,on ! o!r h&1 increase ( pressure at a w lead to ! cond5sation ( a portion ( ! vap\r phase4 ,s9ce1 n[1 ! conc5tration ( *lor9e 9 ! vap\r is great] ?an 9 ! solution1 cond5sation ( vap\r w\ld increase ! conc5tration ( *lor9e 9 ! solution2 a c]ta9 am\nt ( iod9e mu/ !re=e pass into solution 9 ord] t ! composition ( ! latt] %all rema9 un*ang$4#bdi ,if1 !re=e1 ! volume ( vap\r be suffici5tly great1 cont9u$ dim9ution ( volume w ultimately lead to ! disappe>ance ( all ! iod9e1 & !re w rema9 only solution & vap\r 7field ,,ii474 ,z ! dim9ution ( volume is cont9u$1 ! vap\r pressure & ! conc5tration ( ! *lor9e 9 ! solution w increase1 until :5 ! pressure has rea*$ ! value b1 iod9e mono*loride c sep>ate out4 ,! sy/em1 !re=e1 aga9 becomes univ>iant1 & at con/ant temp]ature ! pressure & composition ( ! phases mu/ rema9 un*ang$4 ,dim9ution ( volume w !re=e n effect an increase ( pressure1 b a cond5sation ( ! vap\r2 & s9ce ?is is ri*] 9 *lor9e ?an ! #afi solution1 solid iod9e mono*loride mu/ sep>ate out 9 ord] t ! conc5tration ( ! solution rema9 un*ang$4#bej ,z ! result1 !re=e1 we obta9 ! biv>iant sy/em iod9e mono*loride--vap\r4 ,a detail$ discussion ( ! effect ( a cont9u$ increase ( pressure w n be necess>y4 ,f :at has already be5 said & ) ! help ( ,fig4 #dd1 x w readily be und]/ood t ?is w lead successively to ! univ>iant sy/em 7c71 iod9e mono*loride--solution--vap\r2 ! biv>iant sy/em solution--vap\r 7field ,,ii472 ! univ>iant sy/em 7d71 iod9e tri*loride--solution--vap\r2 & ! biv>iant sy/em x'1 iod9e tri*loride--vap\r4 ,if ! temp]ature ( ! exp]im5t is above ! melt+ po9t ( ! mono*loride1 !n ! sy/ems 9 :i* ?is comp\nd occurs w n be =m$4 ,sulphur ,dioxide & ,wat]4--,9 ! case j /udi$ we h se5 t ! compon5ts c comb9e to =m def9ite comp\nds possess+ /able melt+ po9ts4 ,! curves ( equilibrium1 !re=e1 resemble 9 _! g5]al aspect ^? ( calcium *loride & wat]1 or ( f]ric *loride & wat]4 ,9 ! case ( sulphur dioxide & wat]1 h[ev]1 ! melt+ po9t ( ! comp\nd =m$ _c be realiz$1 because transition to ano!r sy/em occurs2 retr(lex conc5tration-temp]ature curves are !re=e n f\nd "h1 b ! curves exhibit breaks or sudd5 *anges 9 direction at ! transition po9ts1 z 9 ! case ( ! sy/ems =m$ by sodium sulphate & wat]4 ,! case ( sulphur dioxide & wat] is also ( int]e/ f ! fact t two liquid phases c be =m$4 ,! phases :i* occur are--,solid3 ice1 sulphur dioxide hydrate1 ,,s#b1g;,h#b,o4 ,liquid3 two solutions1 ! "o conta9+ excess ( sulphur dioxide1 ! o!r excess ( wat]1 & repres5t$ by ! symbols ,,s#b wavy x,h#b,o 7solution ,i471 & ,h#b,o wavy y,,s#b 7solution ,,ii474 ,vap\r3 a mixture ( sulphur dioxide & wat] vap\r 9 v>y+ proportions4 ,s9ce !re are two compon5ts1 sulphur dioxide & wat]1 ! numb] ( #agj possible sy/ems is consid]able4 ,only ! foll[+1 h[ev]1 h be5 /udi$3-- ,i4 ,inv>iant ,sy/ems3 ,f\r co-exi/+ phases4 7a7 ,ice1 hydrate1 solution1 vap\r4 7b7 ,hydrate1 solution ,i41 solution ,,ii41 vap\r4 ,,ii4 ,univ>iant ,sy/ems3 ,?ree co-exi/+ phases4 7a7 ,hydrate1 solution ,i41 vap\r4 7b7 ,hydrate1 solution ,,ii41 vap\r4 7c7 ,solution ,i41 solution ,,ii41 vap\r4 7d7 ,hydrate1 solution ,i41 solution ,,ii4 7e7 ,hydrate1 ice1 vap\r4 7f7 ,ice1 solution ,,ii41 vap\r4 7g7 ,ice1 hydrate1 solution ,,ii4 ,,iii4 ,biv>iant ,sy/ems3 ,two co-exi/+ phases4 7a7 ,hydrate1 solution ,i4 7b7 ,hydrate1 solution ,,ii4 7c7 ,hydrate1 vap\r4 7d7 ,hydrate1 ice4 7e7 ,solution ,i41 solution ,,ii4 7f7 ,solution ,i41 vap\r4 7g7 ,solution ,i41 ice4 7h7 ,solution ,,ii41 vap\r4 7i7 ,solution ,,ii41 ice4 7j7 ,ice1 vap\r4 ,illu/ration3 ,,fig4 #de4 ,pressure-,temp]ature ,diagram4#bea--;,if sulphur dioxide is pass$ into wat] at #j;deg1 a solution w be =m$ & ! temp]ature at :i* ice c exi/ 9 equilibrium ) ?is solution w fall m & m z ! conc5tration ( ! sulphur dioxide increases4 ,at -#b4f;deg1 h[ev]1 a cryohydric po9t is rea*$ at :i* solid hydrate sep>ates out1 & ! sy/em becomes inv>iant4 ,! curve ,,ab 7,fig4 #de7 !re=e repres5ts ! pressure ( ! sy/em ice--solution ,,ii4--vap\r1 & ,b repres5ts ! temp]ature & pressure at :i* ! inv>iant sy/em ice--hydrate--solution ,,ii4--vap\r c exi/4 ,at ?is po9t ! temp]ature is -#b4f;deg1 & ! pressure #ba4a cm4 ,if heat is )drawn f ?is sy/em1 ! solution w ultimately #aga solidify to a mixture ( ice & hydrate1 & !re w be obta9$ ! univ>iant sy/em ice--hydrate--vap\r4 ,! vap\r pressure ( ?is sy/em has be5 det]m9$ d[n to a temp]ature ( -#i4e;deg1 at :i* temp]ature ! pressure am\nts to #ae cm4 ,! pressures = ?is sy/em are repres5t$ by ! curve ,,bc4 ,if at ! po9t ,b ! volume is dim9i%$1 ! pressure mu/ rema9 con/ant1 b ! relative am\nts ( ! diff]5t phases w und]go *ange4 ,if suitable quantities ( ^! are pres5t1 dim9ution ( volume w ultimately lead to ! total cond5sation ( ! vap\r phase1 & !re w rema9 ! univ>iant sy/em ice--hydrate--solution4 ,! temp]ature ( equilibrium ( ?is sy/em w alt] ) ! pressure1 b1 z 9 ! case ( ! melt+ po9t ( a simple sub/ance1 great diff]5ces ( pressure w cause only comp>atively small *anges 9 ! temp]ature ( equilibrium4 ,! *ange ( ! cryohydric po9t ) ! pressure is repres5t$ by ! l9e ,,be2 ! actual values h n be5 det]m9$1 b ! curve mu/ slope t[>ds ! pressure axis because fusion is accompani$ by dim9ution ( volume1 z 9 ! case ( pure ice4 #agb ,a f\r? univ>iant sy/em c be =m$ at ,b4 ,?is is ! sy/em hydrate--solution ,,ii4--vap\r4 ,! conditions = ! exi/5ce ( ?is sy/em are repres5t$ by ! curve ,,bf1 :i* may !re=e be reg>d$ z ! vap\r-pressure curve ( ! saturat$ solution ( sulphur dioxide heptahydrate 9 wat]4 ,unlike ! curve = iod9e tri*loride--solution--vap\r1 ?is curve _c be foll[$ to ! melt+ po9t ( ! hydrate4 ,be=e ?is po9t is rea*$1 a second liquid phase appe>s1 & an inv>iant sy/em consi/+ ( hydrate--solution ,i4--solution ,,ii4--vap\r is =m$4 ,we h "h1 !re=e1 ! ph5om5on ( melt+ "u ! solution z 9 ! case ( succ9ic nitrile & wat] 7p4 #abb74 ,?is po9t is repres5t$ 9 ! diagram by ,f2 ! temp]ature at ?is po9t is #ab4a;deg1 & ! pressure #agg4c cm4 ,! range ( /able exi/5ce ( ! hydrate is !re=e f -#b4f;deg to #ab4a;deg2 nev]!less1 ! curve ,,fb has be5 foll[$ d[n to a temp]ature ( -#f;deg1 at :i* po9t ice =m$ spontane\sly4 ,s long z ! f\r phases hydrate1 two liquid phases1 & vap\r are pres5t1 ! condition ( ! sy/em is p]fectly def9$4 ,by alt]+ ! conditions1 h[ev]1 "o ( ! phases c be made to disappe>1 & a univ>iant sy/em w !n be obta9$4 ,?us1 if ! vap\r phase is made to disappe>1 ! univ>iant sy/em solution ,i4--solution ,,ii4--hydrate1 w be left1 & ! temp]ature at :i* ?is sy/em is 9 equilibrium w v>y ) ! pressure4 ,?is is repres5t$ by ! curve ,,fi2 "u a pressure ( #bbe atm4 ! temp]ature ( equilibrium is #ag4a;deg4 ,increase ( pressure1 !re=e1 raises ! temp]ature at :i* ! ?ree phases c coexi/4 ,aga91 addition ( heat to ! inv>iant sy/em at ,f w cause ! disappe>ance ( ! solid phase1 & !re w be =m$ ! univ>iant sy/em solution ,i4--solution ,,ii4--vap\r4 ,9 ! case ( ?is sy/em ! vap\r pressure increases z ! temp]ature rises1 z repres5t$ by ! curve ,,fg4 ,su* a sy/em is analog\s to ! case ( e!r & wat]1 or o!r two p>tially miscible liquids 7p4 #ajc74 ,z ! temp]ature *anges1 ! composition ( ! two liquid phases w und]go *ange2 b ?is sy/em has n be5 /udi$ fully4 ,! f\r? curve1 :i* ends at ! quadruple po9t ,f1 is #agc t repres5t+ ! vap\r pressure ( ! sy/em hydrate--solution ,i4--vap\r 7,,fh74 ,?is curve has be5 foll[$ to a temp]ature ( #j;deg1 ! pressure at ?is po9t be+ #aac cm4 ,! meta/able prolongation ( ,,gf has also be5 det]m9$4 ,al?\gh1 !oretically1 ?is curve mu/ lie bel[ ,,fh1 x 0 f\nd t ! diff]5ce 9 ! pressure = ! two curves 0 )9 ! error ( exp]im5t4 ,biv>iant ,sy/ems4--,! diff]5t biv>iant sy/ems1 consi/+ ( two phases1 :i* c exi/ )9 ! range ( temp]ature & pressure includ$ 9 ,fig4 #de1 7 giv5 on p4 #agj4 ,! conditions "u :i* ^! sy/ems c exi/ are repres5t$ by ! areas 9 ! diagram1 & ! fields ( ! diff]5t biv>iant sy/ems are indicat$ by lett]s1 correspond+ to ! lett]s on p4 #agj4 ,j z 9 ! case ( "o-compon5t sy/ems 7p4 #bi71 we f\nd t ! field ly+ betwe5 any two curves gave ! conditions ( exi/5ce ( t phase :i* 0 common to ! two curves1 s also 9 ! case ( two-compon5t sy/ems1 a biv>iant two-phase sy/em occurs 9 ! field enclos$#beb by ! two curves to :i* ! two phases are common4 ,z c be se51 ! same biv>iant sy/em c occur 9 m ?an "o field4 ,z is evid5t f ,fig4 #de1 ?ree diff]5t biv>iant sy/ems are capable ( exi/+ 9 ! area ,,hfi2 :i* ( ^! w be obta9$ w dep5d on ! relative masses ( ! diff]5t phases 9 ! univ>iant or inv>iant sy/em4 ,?us1 />t+ ) a sy/em repres5t$ by a po9t on ! curve ,,hf1 dim9ution ( volume at con/ant temp]ature w cause ! cond5sation ( a portion ( ! vap\r1 :i* is ri* 9 sulphur dioxide2 s9ce ?is w\ld increase ! conc5tration ( sulphur dioxide 9 ! solution1 x mu/ be c\nt]act$ by ! passage ( a portion ( ! hydrate 7:i* is relatively poor 9 sulphur dioxide7 into ! solution4 ,if1 !re=e1 ! am\nt ( hydrate pres5t is relatively v small1 ! f9al result ( ! compression w be ! production ( ! sy/em f1 solution ,i4--vap\r4 ,on ! o!r h&1 if ! vap\r is pres5t 9 relatively small am\nt1 x w be ! fir/ phase to disappe>1 #agd & ! biv>iant sy/em a1 hydrate--solution ,i41 w be obta9$4 ,f9ally1 if we />t ) ! inv>iant sy/em at ,f1 compression w cause ! cond5sation ( vap\r1 :ile ! composition ( ! two solutions w rema9 un*ang$4 ,:5 all ! vap\r has disappe>$1 ! univ>iant sy/em hydrate--solution ,i4--solution ,,ii4 w be left4 ,if1 n[1 ! pressure is /ill fur!r increas$1 :ile ! temp]ature is kept bel[ #ab;deg1 m & m hydrate mu/ be =m$ at ! exp5se ( ! two liquid phases 7because #ab;deg is ! l[] limit = ! coexi/5ce ( ! two liquid phases71 & if ! am\nt ( ! solution ,i4 7conta9+ excess ( sulphur dioxide7 is relatively small1 x w disappe> be=e solution ,,ii41 & !re w be obta9$ ! biv>iant sy/em hydrate--solution ,,ii4 7biv>iant sy/em b74 ,9 a simil> mann]1 acc\nt c be tak5 ( ! =mation ( ! o!r biv>iant sy/ems4 ,a behavi\r simil> to t ( sulphur dioxide & wat] is %[n by *lor9e & wat] & by brom9e & wat]1 al?\gh ^! h n be5 s fully /udi$4#bec ,9 ! case ( hydrog5 bromide & wat]1 & ( hydrog5 *loride & wat]1 a hydrate1 viz4 ,h,br1#b;,h#b,o & ,h,cl1#b;,h#b,o1 is =m$ :i* possesses a def9ite melt+ po9t1 z 9 ! case ( iod9e tri*loride4 ,9 ^! cases1 !re=e1 a retr(lex curve is obta9$4 ,fur!r1 j z 9 ! case ( ! *lorides ( iod9e ! upp] bran* ( ! retr(lex curve end$ 9 a eutectic po9t1 s also 9 ! case ( ! hydrate ,h,br1#b;,h#b,o ! upp] bran* ( ! curve ends 9 a eutectic po9t at :i* ! sy/em dihydrate--monohydrate--solution--vap\r c exi/4 ,be=e ! melt+ po9t ( ! monohydrate is rea*$1 two liquid phases are =m$1 z 9 ! case ( sulphur dioxide & wat]4 99 99 99 99 99 #age ,,*apt] ,x ,,solid ,,solutions4 ,,mix$ ,,cry/als ,g5]al4--,) ! conception ( gase\s & liquid solutions1 e "o is famili>4 ,gases c mix 9 all proportions to =m homog5e\s solutions4 ,gases c dissolve 9 or be absorb$ by liquids2 & solids1 also1 :5 br\ght 9 contact ) liquids1 pass into solution & yield a homog5e\s liquid phase4 ,on ! o!r h&1 ! conception ( a solid solution is "o :i* 9 _m cases is f\nd m difficult to appreciate2 & ! exi/5ce & behavi\r ( solid solutions1 9 spite ( _! n uncommon occurr5ce & importance1 are 9 g5]al comp>atively little kn[n4 ,! reason ( ?is is to be f\nd1 to "s ext5t1 no d\bt1 9 ! fact t ! t]m solid solution 0 introduc$ at a comp>atively rec5t date1#bed b x is probably also due 9 "s measure to a some:at hazy compreh5sion ( ! def9ition ( ! t]m solution itself4 ,z has already be5 said 7p4 #ib71 a solution is a homog5e\s phase1 ! composition ( :i* c v>y cont9u\sly )9 c]ta9 limits2 ! def9ition involves1 !re=e1 no condition z to ! physical /ate ( ! sub/ances4 ,accord+ly1 solid solutions are homog5e\s solid phases1 ! composition ( :i* c und]go cont9u\s v>iation )9 c]ta9 limits4 ,j z we saw t ! range ( v>iation ( composition is m limit$ 9 ! case ( liquids ?an 9 ! case ( gases1 s also we f9d t ! limits ( miscibility are 9 g5]al /ill m re/rict$ 9 ! case ( solids4 ,examples ( complete miscibility are1 h[ev]1 n unkn[n ev5 9 ! case ( solid sub/ances4 ,solid solutions h long be5 kn[n1 al?\gh1 ( c\rse1 #agf !y 7 n def9$ z su*4 ,?us1 ! ph5om5a ( occlusion ( gases by metals & o!r sub/ances 7occlusion ( hydrog5 by palladium2 occlusion ( hydrog5 by iron7 are due to ! =mation ( solid solutions4 ,! same is probably also true ( ! ph5om5a ( adsorption1 z 9 ! removal ( organic col\r+ matt] by *>coal1 al?\gh1 9 ?is case1 surface t5sion no d\bt plays a consid]able "p4#bee ,z examples ( ! solution ( gases 9 solids !re may be cit$ 79 addition to ! ph5om5a ( occlusion already m5tion$71 ! hydrat$ silicates & ! zeolites4 ,dur+ dehydration ^! cry/all9e sub/ances rema9 cle> & transp>5t1 & ! pressure ( ! wat] vap\r :i* !y emit v>ies ) ! degree ( hydration or ! conc5tration ( wat] 9 ! m9]al4#bef ,z examples ( ! solution ( solids 9 solids we h ! cem5tation ( iron by *>coal1 ! =mation ( glass1 & ! cry/allization toge!r ( isomorph\s sub/ances4 ,al?\gh we h "h spok5 ( ! glasses z solid solutions1 x %\ld be m5tion$ t ! t]m solid is us$ 9 its popul> s5se4 ,/rictly speak+1 ! glasses are to be reg>d$ z sup]cool$ liquids 7see also p4 #ec1 footnote74 ,9 discuss+ ! equilibria 9 sy/ems conta9+ a solid solution1 x is ( ess5tial importance to rememb] t a solid solution con/itutes only "o phase1 a phase ( v>y+ composition1 z 9 ! case ( liquid solutions4 ,solution ( ,gases 9 ,solids4--,comp>atively little "w has be5 done 9 ?is connection1 ! inve/igations be+ limit$ *iefly to ! ph5om5a ( occlusion or adsorption ( gases by *>coal4#beg ,we %all1 !re=e1 indicate only briefly #agg & 9 a g5]al mann]1 ! behavi\r :i* ! ,phase ,rule enables u to =esee4#beh ,9 deal+ ) ! sy/ems =m$ by ! two phases gas--solid1 ?ree *ief cases call = m5tion3-- ,i4 ,! gas is n absorb$ by ! solid1 b :5 ! pressure rea*es a c]ta9 value1 comb9ation ( ! two compon5ts c result4 ,illu/ration3 ,fig4 #df4 ,! graphic repres5tation ( su* a sy/em is %[n 9 ,fig4 #df1 ! ord9ates be+ ! pressures ( ! gas1 & ! abscissae ! conc5trations ( ! gase\s compon5t 9 ! solid phase4 ,s9ce !re is no =mation ( a solid solution1 ! conc5tration ( gas 9 ! solid phase rema9s z]o until ! pressure has increas$ to ! po9t ,a4 ,at ?is po9t comb9ation c take place4 ,!re w n[ be ?ree phases pres5t1 viz4 solid compon5t1 comp\nd1 & vap\r4 ,! sy/em is !re=e univ>iant1 & if ! temp]ature is ma9ta9$ con/ant1 ! vap\r pressure w be con/ant1 irrespective ( ! am\nt ( comp\nd =m$1 i4e4 irrespective ( ! relative am\nts ( gas & solid4 ,?is is indicat$ by ! l9e ,,ab4 ,:5 ! solid compon5t has entirely disappe>$1 ! sy/em ceases to be univ>iant1 & if no absorption occurs1 ! pressure w increase aga91 z %[n by ,,bc4 ,if a second comp\nd c be =m$1 !n a second pc-l9e w be obta9$1 simil> to ! prec$+4 ,to ?is gr\p belong ! salt hydrates 7,*ap4 ,,vii474 ,,ii4 ,! gas may be absorb$ & may also =m a comp\nd4 ,if absorption ( gas occurs ) =mation ( a solid solution1 !n1 z ! sy/em consi/s ( two phases1 solution--vap\r1 x is biv>iant4 ,at con/ant temp]ature1 !re=e1 ! pressure w /ill v>y ) ! conc5tration ( ! gase\s compon5t 9 ! solid phase4 ,?is is repres5t$ by ! curve ,,ab 9 ,fig4 #dg4 ,:51 h[ev]1 ! pressure has rea*$ a c]ta9 value1 comb9ation c take place2 & s9ce !re are n[ ?ree phases pres5t1 ! sy/em is #agh univ>iant1 & at con/ant temp]ature ! pressure is con/ant1 z %[n by ! l9e ,,bc4 ,,iii4 ,absorption ( gas occurs1 b at a c]ta9 conc5tration ! solid solution c sep>ate into two immiscible solid solutions4 ,we h se51 9 ,*apt] ,,vi41 t two liquids c =m two immiscible solutions1 & ! same has also be5 f\nd true ( solid solutions1 z we %all pres5tly le>n m fully4 ,if1 n[1 two immiscible solutions are =m$1 !n ! sy/em w become univ>iant1 & at con/ant temp]ature ! pc-curve w be a /raight l9e1 z 9 ! case ( ! =mation ( a comp\nd 7cf4 p4 #hf74 ,! behavi\r ( ?is sy/em w1 !re=e1 also be repres5t$ diagrammatically by ,fig4 #dg4 ,illu/ration3 ,,fig4 #dg4 ,palladium & ,hydrog54--,! ph5om5on ( ! absorption ( hydrog5 by palladium1 to :i* ,graham gave ! "n occlusion1 is "o t has claim$ ! att5tion ( sev]al inve/igators4 ,al?\gh ,graham 0 n ( op9ion t a comp\nd is =m$1 b r t ! gas und]goes v great cond5sation1 acts z a quasi-metal 7to :i* he gave ! "n hydrog5ium71 & =ms a homog5e\s alloy ) ! palladium1 lat] inve/igations1 especially ^? ( ,troo/ & ,hautefeuille1#bei po9t$ to ! =mation ( a def9ite *emical comp\nd1 hav+ ! =mula ,pd#b;,h4 ,?is conclusion has1 h[ev]1 n be5 confirm$ by subsequ5t inve/igation4#bfj ,roozeboom & ,hoitsema#bfa s\ght to arrive at a f9al decision z to ! nature ( ! ph5om5on by an inve/igation ( ! equilibrium betwe5 hydrog5 & palladium on ! basis ( ! ,phase ,rule classification giv5 above4 ,if a comp\nd is =m$1 dim9ution ( volume w\ld cause no increase ( pressure1 b only an increase 9 ! am\nt ( ! comp\nd4 ,z ?is is ! only case ( gas absorption :i* has be5 #agi accurately /udi$ f ?is po9t ( view1 a brief acc\nt ( ! results obta9$ w be giv5 "h1 al?\gh ^! are n s cle> & free f ambiguity z "o w\ld desire4 ,! sci5ti/s j m5tion$ inve/igat$ ! v>iation ( ! pressure ( hydrog5 ) ! am\nt absorb$ by ! metal at diff]5t temp]atures1 & a few ( _! results1 typical ( all1 are repres5t$ graphically 9 ,fig4 #dh2 ! curves indicat+ ! v>iation ( ! gas pressure ) ! conc5tration ( ! hydrog5 9 ! palladium at ! temp]atures #abj;deg1 #agj;deg1 & #bjj;deg4 ,z c be se51 ! curve consi/s ( ?ree p>ts1 an asc5d+ portion :i* passes gradually & cont9u\sly into an almo/ horizontal b slightly asc5d+ middle "p1 :i* 9 turn passes )\t break into a second rapidly asc5d+ curve4 ,?is1 z ,fig4 #dh indicates1 is ! g5]al =m ( ! curve2 b ! l5g? ( ! middle portion v>ies ) ! temp]ature1 be+ %ort] at high] ?an at l[] temp]atures4 ,illu/ration3 ,,fig4 #dh4 ,:at is ! int]pretation to be put on ^! curves8 ,) reg>d to ! two end portions1 ^! repres5t biv>iant1 two-phase sy/ems1 consi/+ ( a solid solution & gas4 ,!y correspond1 !re=e1 to curve ,,ab 9 ,fig4 #dg4 ,if ! middle portion 7 horizontal1 x w\ld indicate ei!r ! =mation ( a comp\nd or ( two immiscible solid solutions4 ,if a comp\nd ,pd#b;,h 7 =m$1 !n ! middle portion w\ld at all temp]atures end at ! same value ( ! conc5tration1 viz4 t correspond+ to #j4e atoms ( hydrog5 to #a atom ( palladium4 ,z ! figure %[s1 h[ev]1 ?is is n ! case2 ! high] ! temp]ature1 ! l[] is ! conc5tration at :i* ! middle passes into ! t]m9al portion ( ! curve4 #ahj ,su* a behavi\r w\ld1 h[ev]1 agree ) ! assumption ( ! =mation ( two solid solutions1 ! miscibility ( :i* increases ) ! temp]ature1 z 9 ! case ( ! liquid solutions ( ph5ol & wat] 7p4 #ig74 ,nev]!less1 al?\gh ! assumption ( ! =mation ( two solid solutions is m satisfactory ?an t ( ! =mation ( a comp\nd1 x does n entirely expla9 ! facts4 ,if two solid solutions are =m$1 ! pressure curve %\ld be horizontal1 b ?is is n ! case2 & ! deviation f ! horizontal does n appe> to be due to impurities ei!r 9 ! gas or 9 ! metal1 b is app>5tly a peculi>ity ( ! sy/em4 ,fur!r1 ! gradual in/ead ( abrupt passage ( ! ?ree portions ( ! curve into "o ano!r rema9s unexpla9$4 ,hoitsema has express$ ! op9ion t ! occlusion ( hydrog5 by palladium is a process ( cont9u\s absorption1 ! peculi> =m ( ! curve--! flat middle portion--be+ possibly due to a cond5sation ( ! gas1 ev5 at temp]atures f> above ! critical temp]ature ( liquid hydrog54 ,:ile1 !re=e1 ! occlusion ( hydrog5 by palladium /ill pres5ts "s unexpla9$ ph5om5a1 ! behavi\r f\nd by ,hoitsema w\ld appe> to disprove conclusively ! =mation ( a def9ite *emical comp\nd4#bfb ,,solution ,,( ,,solids ,,9 ,,solids4 ,,mix$ ,,cry/als4 ,! introduction by van't ,h(f ( ! t]m solid solution result$ f ! discov]y ( a numb] ( deviations f ! ,ra\lt-van't ,h(f law = ! depression ( ! freez+ po9t by dissolv$ sub/ances4 ,9 all cases1 ! depression 0 too small2 9 "s in/ances1 inde$1 ! freez+ po9t may be rais$4 ,to expla9 ^! irregul>ities1 van't ,h(f assum$ t ! dissolv$ sub/ance cry/alliz$ out along ) ! solid solv5t2 & he %[$ h[ ?is w\ld acc\nt = ! #aha deviations f ! law ( ! depression ( ! freez+ po9t1 :i* _h be5 develop$ on ! assumption t only ! pure solv5t cry/alliz$ out f ! solution4#bfc ,! mix$ cry/als :i* 7 ?us obta9$1 & :i* van't ,h(f call$ dilute solid solutions1 %[$ great resemblance 9 _! behavi\r to ord9>y liquid solutions1 & obey$ ! laws applicable to ^!4 ,^! laws1 h[ev]1 c no long] be appli$ 9 ! case ( ! conc5trat$ solid solutions =m$ by ! cry/allization toge!r ( isomorph\s sub/ances1 & kn[n z isomorph\s mixtures4 ,inde$1 x has be5 cont5d$#bfd t ^! isomorph\s mixtures %\ld n be consid]$ z solid solutions at all1 al?\gh no %>p l9e ( dem>cation c be drawn betwe5 ! two classes4 ,! diff]5ces1 h[ev]1 9 ! behavi\r ( ! two gr\ps are ( a quantitative r ?an a qualitative nature2 & s9ce we are conc]n$ at pres5t only ) ! qualitative behavi\r1 we %all make no di/9ction betwe5 ! cry/all9e solid solutions & ! isomorph\s mixtures1 b %all /udy ! behavi\r ( ! two classes "u ! head ( mix$ cry/als4 ,mix$ cry/als c be =m$ ei!r by sublimation#bfe or f a liquid phase2 & 9 ! latt] case ! mix$ cry/als c be deposit$ ei!r f solution 9 a common solv5t or f a mixture ( ! fus$ compon5ts4 ,9 ?is me?od ( =mation1 :i* alone w be discuss$ 9 ! pres5t *apt]1 we are deal+ ) ! fusion curves ( two sub/ances1 :]e1 h[ev]1 ! liquid solution is 9 equilibrium n ) "o ( ! pure compon5ts1 b ) a solid solution or mix$ cry/al4 ,! simple s*eme 7,fig4 #bi1 p4 #aag7 :i* 0 obta9$ 9 ! case ( two compon5ts :i* cry/allize out 9 ! pure /ate1 is no long] suffici5t 9 ! case ( ! =mation ( mix$ cry/als4 ,) ! help ( ! ,phase ,rule1 h[ev]1 ! diff]5t possible sy/ems c be classifi$2 & examples ( ! diff]5t cases pr$ict$ by ! ,phase ,rule h also be5 obta9$ by exp]im5t4 #ahb ,we %all n[ consid] briefly ! =mation ( mix$ cry/als by isomorph\s sub/ances2 ! consid]ation ( ! =mation ( mix$ cry/als ( isodimorph\s sub/ances w1 on acc\nt ( ! complexity ( ! relation%ips1 n be und]tak5 "h4#bff ,=mation ( ,mix$ ,cry/als ( ,isomorph\s ,sub/ances4 ,= ! purpose ( repres5t+ ! relation%ips f\nd "h we %all employ a temp]ature-conc5tration diagram1#bfg 9 :i* ! ord9ates repres5t ! temp]ature & ! abscissae ! conc5tration ( ! compon5ts4 ,s9ce !re are two solutions1 ! liquid & ! solid1 & s9ce ! conc5tration ( ! compon5ts 9 ^! two phases is n1 9 g5]al1 ! same1 two curves w be requir$ = ea* sy/em1 "o relat+ to ! liquid phase1 ! o!r relat+ to ! solid4 ,! temp]ature at :i* solid beg9s to be deposit$ f ! liquid solution w be call$ ! freez+ po9t ( ! mixture1 & ! temp]ature at :i* ! solid solution j beg9s to liquefy w be call$ ! melt+ po9t ( ! solid solution4 ,! temp]ature-conc5tration curve = ! liquid phase w !re=e be ! freez+-po9t curve2 t = ! solid solution1 ! melt+-po9t curve4 ,! latt] w be repres5t$ by a dott$ l9e4#bfh #ahc ,i4--,,! ,,two ,,compon5ts ,,c ,,=m ,,an ,,unbrok5 ,,s]ies ,,( ,,mix$ ,,cry/als4 ,s9ce1 z has already be5 po9t$ out 7p4 #agf71 a mix$ cry/al 7solid solution7 con/itutes only "o phase1 x is evid5t t if ! two compon5ts are miscible ) "o ano!r 9 all proportions 9 ! solid /ate1 !re c nev] be m ?an "o solid phase pres5t1 viz4 ! solid solution or mix$ cry/al4 ,if ! compon5ts are completely miscible 9 ! solid /ate1 !y w also be completely miscible 9 ! liquid /ate1 & !re c !re=e be only "o liquid phase4 ,! sy/em c at no po9t become inv>iant1 because !re c nev] be m ?an ?ree phases pres5t4 ,:51 !re=e1 ! two compon5ts =m a cont9u\s s]ies ( mix$ cry/als1 ! equilibrium curve mu/ also be cont9u\s4 ,( ^! sy/ems ?ree types are f\nd4 ,illu/ration3 ,,fig4 #di4 7a7 ,! freez+ po9ts ( all mixtures lie betwe5 ! freez+ po9ts ( ! pure compon5ts 7,curve ,i41 ,fig4 #di74 ,examples4--,?is type ( curve is repres5t$ by ! mix$ cry/als ( naph?al5e & beta-naph?ol4#bfi ,! addition ( beta-naph?ol to naph?al5e raises ! freez+ po9t ( ! latt]1 & ! rise is directly proportional to ! am\nt ( naph?ol add$4 ,! freez+ po9t curve is !re=e a /raight l9e jo9+ ! melt+ po9ts ( ! two compon5ts4 ,?is behavi\r1 h[ev]1 is r exceptional1 ! freez+-po9t curve ly+ g5]ally above1 sometimes also bel[1 ! /raight l9e jo9+ ! melt+ po9ts ( ! pure compon5ts4 ,?us ! freez+-po9t curve ( mixtures ( alpha-mono*loroc9namic aldehyde & alpha-monobromoc9namic aldehyde#bgj lies above ! #ahd /raight l9e jo9+ ! melt+ po9ts ( ! pure compon5ts 7#ca4bb;deg & #fi4ef;deg71 z is evid5t f ! foll[+ table3-- ---------------------------------------- ------------------------------ ,molecules ( bromo- c9namic aldehyde 9 ,freez+ po9t4 ,deviation f /raight #ajj mols4 ( mixture4 l9e4 ---------------------------------------- ------------------------------ #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 -- ---------------------------------------- ------------------------------ ,melt+-po9t ,curve4--,?is curve1 l ! freez+-po9t curve1 mu/ also be cont9u\s1 & ! melt+ po9ts ( ! diff]5t solid solutions w lie betwe5 ! melt+ po9ts ( ! pure compon5ts4 ,?is is repres5t$ by ! dott$ l9e 9 ,fig4 #di1 ,i4 ,! relative position ( ! two curves1 :i* c be d$uc$ ) ! help ( !rmodynamics & also by exp]im5tal det]m9ation1 is f\nd 9 all cases to be 9 accordance ) ! foll[+ rule3 ,at any giv5 temp]ature1 ! conc5tration ( t compon5t by ! addition ( :i* ! freez+ po9t is depress$1 is great] 9 ! liquid ?an 9 ! solid phase2 or1 conv]sely1 ! conc5tration ( t compon5t by ! addition ( :i* ! freez+ po9t is rais$1 is great] 9 ! solid ?an 9 ! liquid phase4 ,an illu/ration ( ?is rule is af=d$ by ! two sub/ances *loro- & bromo-c9namic aldehyde already m5tion$4 ,z c be se5 f ! above table1 ! addition ( *loroc9namic aldehyde l[]s ! melt+ po9t ( ! bromo-comp\nd4 ,9 accordance ) ! rule1 !re=e1 ! conc5tration ( ! *loro-comp\nd 9 ! liquid phase mu/ be great] ?an 9 ! solid phase2 & ?is 0 f\nd exp]im5tally4 ,at a temp]ature ( #di4dd;deg1 ! liquid conta9$ #eh4eb p] c5t41 ! solid only #eb4eg p] c5t4 ( ! *loroc9namic aldehyde4 ,f ?is x w also be cle> t on cool+ a fus$ mixture ( two sub/ances capable ( =m+ mix$ cry/als1 #ahe ! temp]ature ( solidification w n rema9 con/ant dur+ ! sep>ation ( ! solid2 nor1 on ! o!r h&1 w ! temp]ature ( liquefaction ( ! solid solution be con/ant4 ,?us1 = example1 if a liquid solution ( two compon5ts1 ,a & ,b1 hav+ ! composition repres5t$ by ! po9t x 7,fig4 #ej71 is all[$ to cool1 ! sy/em w pass along ! l9e xx'4 ,at ! temp]ature ( ! po9t a1 mix$ cry/als w be deposit$1 ! composition ( :i* w be t repres5t$ by b4 ,z ! temp]ature cont9ues to fall1 m & m solid w be deposit$2 & s9ce ! solid phase is relatively ri* 9 ! compon5t ,b1 ! liquid w become relatively poor] 9 ?is4 ,! composition ( ! liquid solution w !re=e pass along ! curve ad1 ! composition ( ! solid solution at ! same "t pass+ along ! curve bc2 at ! po9t c ! liquid w solidify completely4#bga ,illu/ration3 ,,fig4 #ej4 ,conv]sely1 if mix$ cry/als ( ! composition & at ! temp]ature x' are heat$1 liquefaction w beg9 at ! temp]ature c1 yield+ a liquid ( ! composition d4 ,on cont9u+ to add heat1 ! temp]ature ( ! mass w rise1 m ( ! solid w melt1 & ! composition ( ! two phases w *ange z repres5t$ by ! curves da & cb4 ,:5 ! temp]ature has ris5 to a1 complete liquefaction w h occurr$4 ,! process ( solidification or ( liquefaction is !re=e ext5d$ ov] a temp]ature int]val ac4 ,ev5 :5 ! freez+-po9t curve is a /raight l9e jo9+ #ahf ! melt+ po9ts ( ! pure compon5ts1 ! melt+-po9t curve w n necess>ily co9cide ) ! freez+-po9t curve1 al?\gh x may approa* v ne> to x2 complete co9cid5ce c take place only :5 ! melt+ po9ts ( ! two compon5ts are id5tical4 ,an example ( ?is w be giv5 lat] 7,*ap4 ,,xii474 7b7 ,! freez+-po9t curve passes ?r\gh a maximum 7,curve ,,ii41 ,fig4 #di74 ,illu/ration3 ,,fig4 #ea4 ,?is curve exhibits ! greate/ degree ( contra/ to ! freez+-po9t curve :i* is obta9$ :5 ! pure compon5ts cry/allize out4 ,=1 s9ce ! curve passes ?r\gh a maximum1 x is evid5t t ! freez+ po9t ( ea* ( ! compon5ts mu/ be rais$ by ! addition ( ! o!r compon5t4 ,example4--,v few cases belong+ to ?is type are kn[n4 ,! be/ example is f\nd 9 ! freez+-po9t curve ( mixtures ( d- & l-c>voxime#bgb 7,c#aj;,h#ad,n4,,oh74 ,! freez+ po9ts & melt+ po9ts ( ! diff]5t mixtures ( d- & l-c>voxime are giv5 9 ! foll[+ table1 & repres5t$ graphically 9 ,fig4 #ea3-- ---------------------------------------- ------------------------- ,p] c5t4 ( ,p] c5t4 ( ,freez+ po9t4 ,melt+ po9t4 d-c>voxime4 l-c>voxime4 ---------------------------------------- ------------------------- #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 ,9 ?is figure1 ! melt+-po9t curve1 i4e4 ! temp]ature-conc5tration curve = ! mix$ cry/als1 is repres5t$ by ! l[] curve4 ,s9ce ! addition ( ! laevo-=m to ! dextro-=m raises ! melt+ po9t ( ! latt]1 ! conc5tration ( ! laevo-=m 7on ! "r-h& bran* ( ! curve7 mu/1 9 accordance ) ! rule giv51 be great] 9 ! solid phase ?an 9 ! liquid4 ,simil>ly1 s9ce addition ( ! dextro-=m raises ! melt+ po9t ( ! laevo-=m1 ! solid phase 7on ! left-h& bran* ( ! curve7 mu/ be ri*] 9 dextro- ?an 9 laevo-c>voxime4 ,at ! maximum po9t1 ! melt+-po9t & freez+-po9t curves t\*2 at ?is po9t1 !re=e1 ! composition ( ! solid & liquid phases mu/ be id5tical4 ,x is evid5t1 !re=e1 t at ! maximum po9t ! liquid w solidify1 or ! solid w liquefy completely )\t *ange ( temp]ature2 &1 accord+ly1 mix$ cry/als ( ! composition repres5t$ by ! maximum po9t w exhibit a def9ite melt+ po9t1 & w 9 ?is respect behave l a simple sub/ance4 7c7 ,! freez+-po9t curve passes ?r\gh a m9imum 7,curve ,,iii41 ,fig4 #di74 ,9 ?is case1 z 9 ! case ( ^? sy/ems :]e ! pure compon5ts are deposit$1 a m9imum freez+ po9t is obta9$4 ,9 ! latt] case1 h[ev]1 !re are two freez+-po9t curves :i* int]sect at a eutectic po9t2 9 ! case :]e mix$ cry/als are =m$ !re is only "o cont9u\s curve4 ,on "o side ( ! m9imum po9t ! liquid phase conta9s relatively m1 on ! o!r side relatively less1 ( ! "o compon5t ?an does ! solid phase2 :ile at ! m9imum po9t ! composition ( ! two phases is ! same4 ,at ?is po9t1 !re=e1 complete solidification or complete liquefaction w occur )\t *ange ( temp]ature1 & ! mix$ cry/als w accord+ly exhibit a def9ite melt+ po9t4 ,illu/ration3 ,,fig4 #eb4 #ahh ,example4--,z an example ( ?is !re may be tak5 ! mix$ cry/als ( m]curic bromide & iodide4#bgc ,m]curic bromide melts at #bcf4e;deg1 & m]curic iodide at #bee4d;deg4 ,! mix$ cry/al ( def9ite con/ant melt+ po9t 7m9imum po9t7 conta9s #ei mols4 p] c5t4 ( m]curic bromide1 ! melt+ po9t be+ #baf4a;deg4 ,! num]ical data are conta9$ 9 ! foll[+ table1 & repres5t$ graphically 9 ,fig4 #eb3-- ---------------------------------------- ------------- ,mols4 p] c5t4 ( ,hg,br#b4 ,freez+ po9t4 ,melt+ po9t4 ---------------------------------------- ------------- #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 ---------------------------------------- ------------- ,illu/ration3 ,,fig4 #ec4 ,fractional ,cry/allization ( ,mix$ ,cry/als4--,) ! help ( ! diagrams already giv5 x w be possible to pr$ict :at w be ! result ( ! fractional cry/allization ( a fus$ mixture ( two sub/ances :i* c =m mix$ cry/als4 ,suppose1 = example1 a fus$ mixture ( ! composition x 7,fig4 #ec7 is cool$ d[n2 !n1 z we h already se51 :5 ! temp]ature has fall5 to a1 mix$ cry/als ( composition1 b1 are deposit$4 ,if ! temp]ature is all[$ to fall #ahi to x'1 & ! solid !n sep>at$ f ! liquid1 ! mix$ cry/als s obta9$ w h ! composition repres5t$ by e4 ,if1 n[1 ! mix$ cry/als e are completely fus$ & ! fus$ mass all[$ to cool1 sep>ation ( solid w occur :5 ! temp]ature has fall5 to ! po9t f4 ,! mix$ cry/als :i* are deposit$ h n[ ! composition repres5t$ by g1 i4e4 !y are ri*] 9 ,b ?an ! orig9al mix$ cry/als4 ,by repeat+ ?is process1 ! composition ( ! successive crops ( mix$ cry/als :i* are obta9$ approximates m & m to t ( ! pure compon5t ,b1 :ile1 on ! o!r h&1 ! composition ( ! liquid phase produc$ t5ds to t ( pure ,a4 ,by a sy/ematic & me?odical repetition ( ! process ( fractional cry/allization1 !re=e1 a practically complete sep>ation ( ! compon5ts c be effect$2 a p]fect sep>ation is !oretically impossible4 ,f ?is x w be readily und]/ood t 9 ! case ( sub/ances ! freez+ po9t ( :i* passes ?r\gh a maximum1 fractional cry/allization w ultimately lead to mix$ cry/als hav+ ! composition ( ! maximum po9t1 :ile ! liquid phase w m & m assume ! composition ( ei!r pure ,a or pure ,b1 accord+ z ! initial composition 0 on ! ,a side or ! ,b side ( ! maximum po9t4 ,9 ^? cases1 h[ev]1 :]e ! curves exhibit a m9imum1 ! solid phase :i* sep>ates out w ultimately be "o ( ! pure compon5ts1 :ile a liquid phase w f9ally be obta9$ :i* has ! composition ( ! m9imum po9t4 ,,ii4--,,! ,,two ,,compon5ts ,,d ,,n ,,=m ,a ,,cont9u\s ,,s]ies ,,( ,,mix$ ,,cry/als4 ,?is case corresponds to t ( ! p>tial miscibility ( liquids4 ,! solid compon5t ,a c dissolve ! compon5t ,b until ! conc5tration ( ! latt] 9 ! mix$ cry/al has rea*$ a c]ta9 value4 ,addition ( a fur!r am\nt ( ,b w n alt] ! composition ( ! mix$ cry/al1 b !re w be =m$ a second solid phase consi/+ #aij ( a solution ( ,a 9 ,b4 ,at ?is po9t ! f\r phases1 mix$ cry/als conta9+ excess ( ,a1 mix$ cry/als conta9+ excess ( ,b1 liquid solution1 vap\r1 c coexi/2 ?is w !re=e be an inv>iant po9t4 ,! temp]ature-conc5tration curves w !re=e no long] be cont9u\s1 b w exhibit a break or discont9uity at ! po9t at :i* ! inv>iant sy/em is =m$4 7a7 ,! freez+-po9t curve exhibits a transition po9t 7,curve ,i41 ,fig4 #ed74 ,z is evid5t f ! figure1 addition ( ,b raises ! melt+ po9t ( ,a1 &1 9 accordance ) ! rule previ\sly giv51 ! conc5tration ( ,b 9 ! mix$ cry/als w be great] ?an 9 ! solution4 ,?is is repres5t$ 9 ! figure by ! dott$ curve ,,ad4 ,on ! o!r h&1 addition ( ,a l[]s ! melt+ po9t ( ,b1 & ! two curves ,,bc & ,,be are obta9$ = ! liquid & solid phases respectively4 ,at ! temp]ature ( ! l9e ,,cde ! liquid solution ( ! composition repres5t$ by ,c is 9 equilibrium ) ! two diff]5t mix$ cry/als repres5t$ by ,d & ,e4 ,at ?is temp]ature1 !re=e1 ! tc-curve = ! solid phase exhibits a discont9uity2 &1 s9ce ! solid phase und]goes *ange at ?is po9t1 ! freez+-po9t curve mu/ %[ a break 7p4 #aaa74 ,illu/ration3 ,,fig4 #ed4 ,example4--,curves ( ! =m giv5 9 ,fig4 #ed ,i4 h be5 f\nd exp]im5tally 9 ! case ( silv] nitrate & sodium nitrate4#bgd ,! foll[+ table conta9s ! num]ical data1 :i* are also repres5t$ graphically 9 ,fig4 #ee3-- #aia ---------------------------------------- ------------- ,molecules ,na,n,o#c ,freez+ po9t4 ,melt+ po9t4 p] c5t4 ---------------------------------------- ------------- #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 ---------------------------------------- ------------- ,! temp]ature ( ! transition po9t is #bag4e;deg2 at ?is po9t ! liquid conta9s #ai4e1 & ! two conjugate solid solutions #bf & #ch molecules ( sodium nitrate p] c5t4 respectively4 ,illu/ration3 ,,fig4 #ee4 ,illu/ration3 ,,fig4 #ef4 7b7 ,! freez+-po9t curve exhibits a eutectic po9t 7,curve ,,ii41 ,fig4 #ed74 #aib ,9 ?is case ! freez+ po9t ( ea* ( ! compon5ts is l[]$ by ! addition ( ! o!r1 until at la/ a po9t is rea*$ at :i* ! liquid solution solidifies to a mixture or conglom]ate ( two mix$ cry/als4 ,examples4--,curves belong+ to ?is class h be5 obta9$ 9 ! case ( potassium & ?allium nitrates#bge & ( naph?al5e & mono*loracetic acid4#bgf ,! data = ! latt] are giv5 9 ! foll[+ table & repres5t$ 9 ,fig4 #ef3-- ---------------------------------------- --------------------------------- ,liquid solution4 ,solid solution4 ---------------------------------------- -------------------- ,temp]ature4 ,p] c5t4 ,p] c5t4 ,p] c5t4 ,p] c5t4 naph?al5e4 acid4 naph?al5e4 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 ! eutectic po9t ! liquid solution is 9 equilibrium ) two diff]5t mix$ cry/als ! composition ( :i* is repres5t$ by ,d & ,e respectively4 ,if1 !re=e1 a fus$ mixture conta9+ ! two compon5ts ,a & ,b 9 ! proportions repres5t$ by ,c is cool$ d[n1 x w1 :5 ! temp]ature has rea*$ ! po9t ,c1 solidify completely to a conglom]ate ( mix$ cry/als1 ,d & ,e4 ,illu/ration3 ,,fig4 #eg4 ,illu/ration3 ,,fig4 #eh4 ,*anges 9 ,mix$ ,cry/als ) ! ,temp]ature4--,9 ! case ( ! diff]5t types ( sy/ems repres5t$ 9 ,fig4 #di1 a homog5e\s liquid solution ( ! two compon5ts w exi/ at temp]atures above ! freez+-po9t curve1 a homog5e\s mix$ cry/al at temp]atures bel[ ! melt+-po9t curve1 :ile at any po9t betwe5 ! freez+-po9t & melt+-po9t #aic curves ! mixture w sep>ate into a solid phase & a liquid phase4 ,9 ! case1 h[ev]1 ( ! two types %[n 9 ,fig4 #ed ! relation%ips are some:at m complicat$4 ,z be=e1 ! area above ! freez+-po9t curve gives ! conditions "u :i* homog5e\s liquid solutions c exi/2 b bel[ ! melt+-po9t curve two diff]5t mix$ cry/als c coexi/4 ,?is w be be/ und]/ood f ,figs4 #eg & #eh4 ,d & ,e repres5t1 z we h se51 ! composition ( two mix$ cry/als :i* are 9 equilibrium ) ! liquid solution at ! temp]ature ( ! po9t ,c4 ,^! two mix$ cry/als repres5t1 9 ! "o case1 a saturat$ solution ( ,b 9 ,a 7po9t ,d71 & ! o!r a saturat$ solution ( ,a 9 ,b 7po9t ,e74 ,j z we saw t ! mutual solubility ( two liquids v>i$ ) ! temp]ature1 s also 9 ! case ( two solids2 z ! temp]ature alt]s1 ! solubility ( ! two solid compon5ts 9 "o ano!r w *ange4 ,?is alt]ation is indicat$ diagrammatically 9 ,figs4 #eg & #eh by ! dott$ curve simil> to ! solubility curves = two mutually soluble liquids 7p4 #aja74 ,suppose1 n[1 t a mix$ cry/al ( ! composition x is cool$ d[n1 x w rema9 un*ang$ until1 :5 ! temp]ature has fall5 to t'1 ! homog5e\s mix$ cry/al breaks up into a conglom]ate ( two mix$ cry/als ! composition ( #aid :i* is repres5t$ by x' & x respectively4 ,f ?is1 !n1 x c be se5 t 9 ! case ( sub/ances :i* =m two solid solutions1 ! mix$ cry/als :i* are desposit$ f ! liquid fus$ mass ne$ n rema9 un*ang$ 9 ! solid /ate1 b may at "s l[] temp]ature lose _! homog5eity4 ,?is fact is ( consid]able importance = ! =mation ( alloys4#bgg ,a good example ( ?is w soon be met ) 9 ! case ( ! iron & c>bon alloys4 ,! alloys ( copp] & t9 also furni% examples ( ! great *anges :i* may take place 9 ! alloy betwe5 ! temp]ature at :i* x sep>ates out f ! fus$ mass & ! ord9>y temp]ature4 ,?us1 = example1 "o ( ! alloys ( copp] & t9 :i* sep>ates out f ! liquid z a solid solution breaks up1 on cool+1 into ! comp\nd ,cu#c,sn & liquid3#bgh a /rik+ example ( a solid sub/ance p>tially liquefy+ on be+ cool$4 99 99 99 99 99 #aie ,,*apt] ,,xi ,,equilibrium ,,betwe5 ,,dynamic ,,isom]ides ,x has long be5 kn[n t c]ta9 sub/ances1 e4g4 acetoacetic e/]1 are capable :5 9 solution or 9 ! fus$ /ate1 ( react+ z if !y possess$ two diff]5t con/itutions2 & 9 ord] to expla9 ?is behavi\r ! view 0 advanc$ 7by ,la>7 t 9 su* cases a hydrog5 atom oscillat$ betwe5 two positions 9 ! molecule1 be+ at "o "t atta*$ to oxyg51 at ano!r "t to c>bon1 z repres5t$ by ! =mula-- ,,*#c4;,c--,,*4,,co#b;,c#b;,h#e 4 4 ,o-,h ,:5 ! hydrog5 is 9 "o position1 ! sub/ance w act z an hydroxy-comp\nd2 ) hydrog5 9 ! o!r position1 z a ketone4 ,sub/ances possess+ ?is d\ble function are call$ tautom]ic4 ,d\bt1 h[ev]1 arose z to ! validity ( ! above explanation1 & ?is d\bt 0 confirm$ by ! isolation ( ! two isom]ides 9 ! solid /ate1 & also by ! fact t ! velocity ( *ange ( ! "o isom]ide into ! o!r c\ld 9 "s cases be quantitatively measur$4 ,^! & o!r obs]vations !n l$ to ! view1 9 h>mony ) ! laws ( *emical dynamics1 t tautom]ic sub/ances 9 ! dissolv$ or fus$ /ate repres5t a mixture ( two isom]ic =ms1 & t equilibrium is e/abli%$ n by intra- b by int]-molecul> *ange1 z express$ by ! equation-- ,,*#c4;,,co4,,*#b4;,,co#b;,c#b;,h#e -- ,,*#c4;,c7,,oh73,,*4,,co#b;,c#b;,h#e #aif ,9 ! solid /ate1 ! "o or o!r ( ! isom]ides repres5ts ! /able =m2 b 9 ! liquid /ate 7solution or fusion7 ! /able condition is an equilibrium betwe5 ! two =ms4 ,a simil> behavi\r is also f\nd 9 ! case ( o!r isom]ic sub/ances :]e ! isom]ism is due to diff]5ce ( /ructure1 i4e4 /ructure isom]ism 7e4g4 9 ! case ( ! oximes ,c#f;,h#e4;,c4,h ,c#f;,h#e4;,c4,h & 71 ,n4,,oh ,,ho4,n or to diff]5ce 9 configuration1 i4e4 /]eoisom]ism 7e4g4 optically active sub/ances71 or to polym]ism 7e4g4 acetaldehyde & p>aldehyde74 ,9 all su* cases1 al?\gh ! diff]5t solid =ms correspond to a s+le def9ite con/itution1 9 ! liquid /ate a condition ( equilibrium betwe5 ! two modifications is e/abli%$4 ,z a g5]al "n = ^! diff]5t classes ( sub/ances1 ! t]m dynamic isom]ides has be5 introduc$2 & ! diff]5t k9ds ( isom]ism are class$ toge!r "u ! title dynamic isom]ism4#bgi ,by reason ( ! importance ( ^! ph5om5a 9 ! /udy m especially ( ,organic ,*emi/ry1 a brief acc\nt ( ! equilibrium relations exhibit$ by sy/ems compos$ ( dynamic isom]ides may be giv5 "h4#bhj ,9 /udy+ ! fusion & solidification ( ^? sub/ances :i* exhibit ! relation%ips ( dynamic isom]ism1 ! ph5om5a obs]v$ w v>y some:at accord+ z ! rev]sible trans=mation ( ! "o =m into ! o!r takes place ) measurable velocity at temp]atures 9 ! neighb\rhood ( ! melt+ po9ts1 or only at "s high] temp]ature4 ,if ! trans=mation is v rapid1 ! sy/em w behave l a "o-compon5t sy/em1 b if ! isom]ic *ange is comp>atively sl[1 ! behavi\r w be t ( a two-compon5t sy/em4 ,temp]ature-,conc5tration ,diagram4--,! relation%ips :i* are met ) "h w be mo/ readily und]/ood ) #aig ! help ( ,fig4 #ei4 ,suppose1 9 ! fir/ in/ance1 t isom]ic trans=mation does n take place at ! temp]ature ( ! melt+ po9t1 !n ! freez+ po9t curve w h ! simple =m ,,acb2 ! =mation ( comp\nds be+ = ! pres5t exclud$4 ,?is is ! simple/ type ( curve1 & gives ! composition ( ! solutions 9 equilibrium ) ! "o modification 7alpha modification7 at diff]5t temp]atures 7curve ,,ac72 & ( ! solutions 9 equilibrium ) ! o!r modification 7beta modification7 at diff]5t temp]atures 7curve ,,bc74 ,c is ! eutectic po9t at :i* ! two solid isom]ides c exi/ side by side 9 contact ) ! solution4 ,illu/ration3 ,,fig4 #ei4 ,n[1 suppose t isom]ic trans=mation takes place ) measurable velocity4 ,if ! pure alpha-modification is heat$ to a temp]ature t' above its melt+ po9t1 & ! liquid ma9ta9$ at t temp]ature until equilibrium has be5 e/abli%$1 a c]ta9 am\nt ( ! beta-=m w be pres5t 9 ! liquid1 ! composition ( :i* w be repres5t$ by ! po9t x'4 ,! same condition ( equilibrium w also be rea*$ by />t+ ) pure beta4 ,simil>ly1 if ! temp]ature ( ! liquid is ma9ta9$ at ! temp]ature t1 equilibrium w be rea*$1 we %all suppose1 :5 ! solution has ! composition x4 ,! curve ,,de1 !re=e1 :i* passes ?r\gh all ! diff]5t values ( x correspond+ to diff]5t values ( t1 w repres5t ! *ange ( equilibrium ) ! temp]ature4 ,x w slope to ! "r 7z 9 ! figure7 if ! trans=mation ( alpha into beta is accompani$ by absorption ( heat2 to ! left if ! trans=mation is accompani$ by evolution ( heat1 9 accordance ) van't ,h(f's ,law ( movable equilibrium4 ,if trans=mation occurs )\t heat effect1 ! equilibrium w be indep5d5t ( ! #aih temp]ature1 & ! equilibrium curve ,,de w !re=e be p]p5dicul> & p>allel to ! temp]ature axis4 ,we mu/ n[ f9d ! mean+ ( ! po9t ,d4 ,suppose ! pure alpha- or pure beta-=m heat$ to ! temp]ature t'1 & ! temp]ature ma9ta9$ con/ant until ! liquid has ! composition x' correspond+ to ! equilibrium at t temp]ature4 ,if ! temp]ature is n[ all[$ to fall suffici5tly sl[ly s t ! condition ( equilibrium is cont9ually readju/$ z ! temp]ature *anges1 ! composition ( ! solution w gradually alt] z repres5t$ by ! curve x',d4 ,s9ce ,d is on ! freez+ po9t curve ( pure alpha1 ?is =m w be deposit$ on cool+2 & s9ce ,d is also on ! equilibrium curve ( ! liquid1 ,d is ! only po9t at :i* solid c exi/ 9 /able equilibrium ) ! liquid phase4 7,! vap\r phase may be omitt$ f consid]ation1 z we %all suppose ! exp]im5ts c>ri$ out 9 op5 vessels47 ,all sy/ems consi/+ ( ! two hylotropic#bha isom]ic sub/ances alpha & beta w1 !re=e1 ultimately freeze at ! po9t ,d1 :i* is call$ ! natural freez+ po9t#bhb ( ! sy/em2 provid$1 ( c\rse1 t suffici5t "t is all[$ = equilibrium to be e/abli%$4 ,f ?is x is app>5t t ! /able modification at temp]atures 9 ! neighb\rhood ( ! melt+ po9t is t :i* is 9 equilibrium ) ! liquid phase at ! natural freez+ po9t4 ,f :at has be5 said1 x w be easy to pr$ict :at w be ! behavi\r ( ! sy/em "u diff]5t conditions4 ,if pure alpha is heat$1 a temp]ature w be rea*$ at :i* x w melt1 b ?is melt+ po9t w be %>p only if ! velocity ( isom]ic trans=mation is comp>atively sl[2 i4e4 sl[ 9 comp>ison ) ! det]m9ation ( ! melt+ po9t4 ,if ! sub/ance be ma9ta9$ 9 ! fus$ condition = "s "t1 a c]ta9 am\nt ( ! beta modification w be =m$1 & on l[]+ ! temp]ature ! pure alpha =m w be deposit$1 n at ! temp]ature ( ! melt+ po9t1 b at "s l[] temp]ature dep5d+ on ! conc5tration ( ! beta modification 9 ! liquid phase4 ,if isom]ic trans=mation #aii takes place sl[ly 9 comp>ison ) ! rate at :i* deposition ( ! solid occurs1 ! liquid w become increas+ly ri* 9 ! beta modification1 & ! freez+ po9t w1 !re=e1 s9k cont9u\sly4 ,at ! eutectic po9t1 h[ev]1 ! beta modification w also be deposit$1 & ! temp]ature w rema9 con/ant until all has become solid4 ,if1 on ! o!r h&1 ! velocity ( trans=mation is suffici5tly rapid1 !n z quickly z ! alpha modification is deposit$1 ! equilibrium betwe5 ! two isom]ic =ms 9 ! liquid phase w cont9u\sly readju/ itself1 & ! end-po9t ( solidification w be ! natural freez+ po9t4 ,simil>ly1 />t+ ) ! pure beta modification1 ! freez+ po9t aft] fusion w gradually fall ow+ to ! =mation ( ! alpha modification2 & ! composition ( ! liquid phase w pass along ! curve ,,bc4 ,if1 n[1 ! rate ( cool+ is n too great1 or if ! velocity ( isom]ic trans=mation is suffici5tly rapid1 complete solidification w n occur at ! eutectic po9t2 = at ?is temp]ature solid & liquid are n 9 /able equilibrium ) "o ano!r4 ,on ! contr>y1 a fur!r quantity ( ! beta modification w und]go isom]ic *ange1 ! liquid phase w become ri*] 9 ! alpha =m1 & ! freez+ po9t w rise2 ! solid phase 9 contact ) ! liquid be+ n[ ! alpha modification4 ,! freez+ po9t w cont9ue to rise until ! po9t ,d is rea*$1 at :i* complete solidification w take place )\t fur!r *ange ( temp]ature4 ,! diagram also all[s u to pr$ict :at w be ! result ( rapidly cool+ a fus$ mixture ( ! two isom]ides4 ,suppose t ei!r ! alpha or ! beta modification has be5 ma9ta9$ 9 ! fus$ /ate at ! temp]ature t' suffici5tly long = equilibrium to be e/abli%$4 ,! composition ( ! liquid phase w be repres5t$ by x'4 ,if ! liquid is n[ rapidly cool$1 ! composition w rema9 un*ang$ z repres5t$ by ! dott$ l9e x',g4 ,at ! temp]ature ( ! po9t ,g solid alpha modification w be deposit$4 ,if ! cool+ is n c>ri$ bel[ ! po9t ,g1 s z to cause complete solidification1 ! freez+ po9t w be f\nd to rise ) "t1 ow+ to ! conv]sion ( "s ( ! beta =m into ! alpha =m #bjj 9 ! liquid phase2 & ?is w cont9ue until ! composition ( ! liquid has rea*$ ! po9t ,d4 ,f :at has j be5 said1 x c also be se5 t if ! freez+ po9t curves c be obta9$ by actual det]m9ation ( ! freez+ po9ts ( diff]5t syn!tic mixtures ( ! two isom]ides1 x w be possible to det]m9e ! condition ( equilibrium 9 ! fus$ /ate at any giv5 temp]ature )\t hav+ rec\rse to analysis4 ,all t is necess>y is to rapidly cool ! fus$ mass1 aft] equilibrium has be5 e/abli%$1 & f9d ! freez+ po9t at :i* solid is deposit$2 t is1 f9d ! po9t at :i* ! l9e ( con/ant temp]ature cuts ! freez+ po9t curve4 ,! composition correspond+ to ?is temp]ature gives ! composition ( ! equilibrium mixture at ! giv5 temp]ature4 ,x w be evid5t1 f :at has gone be=e1 t ! degree ( complet5ess ) :i* ! diff]5t curves c be realis$ w dep5d on ! velocity ) :i* isom]ic *ange takes place1 & on ! rapidity ) :i* ! det]m9ations ( ! freez+ po9t c be c>ri$ out4 ,z ! two extremes we h1 on ! "o h&1 practically in/antane\s trans=mation1 & on ! o!r1 practically inf9ite sl[ness ( trans=mation4 ,9 ! =m] case1 only "o melt+ & freez+ po9t w be f\nd1 viz4 ! natural freez+ po9t2 9 ! latt] case1 ! two isom]ides w behave z two p]fectly indep5d5t compon5ts1 & ! equilibrium curve ,,de w n be realis$4 ,! diagram :i* is obta9$ :5 isom]ic trans=mation does n occur )9 measurable "t at ! temp]ature ( ! melt+ po9t is some:at diff]5t f t already giv5 9 ,fig4 #ei4 ,9 ?is case1 ! two freez+ po9t curves ,,ac & ,,bc 7,fig4 #fj7 c be readily realiz$1 z no isom]ic *ange occurs 9 ! liquid phase4 ,suppose1 h[ev]1 t at a high] temp]ature1 t'1 rev]sible isom]ic trans=mation c take place1 ! composition ( ! liquid phase w alt] until at ! po9t x' a condition ( equilibrium is rea*$2 & ! composition ( ! liquid at high] temp]atures w be repres5t$ by ! curve x',f4 ,bel[ ! temp]ature t' ! position ( ! equilibrium curve is hypo!tical2 b z ! temp]ature #bja falls ! velocity ( trans=mation dim9i%es1 & at la/ becomes practically z]o4 ,! equilibrium curve c !re=e be reg>d$ z divid+ into two bran*es x',g & x',h4 ,at temp]atures betwe5 ,g & t' ! alpha modification c und]go isom]ic *ange lead+ to a po9t on ! curve ,gx'2 & ! beta modification c und]go *ange lead+ to a po9t on ! curve ,hx'4 ,! same condition ( equilibrium is !re=e n rea*$ f ea* side1 & we are !re=e deal+ n ) true b ) false equilibrium 7p4 #e74 ,bel[ ! temp]atures ,g & ,h1 isom]ic trans=mation does n occur 9 measurable "t4 ,we %all n1 h[ev]1 ent] into a detail$ discussion ( ! equilibria 9 su* sy/ems1 m especially z !y are n sy/ems 9 true equilibrium1 & z ! temp]ature at :i* true equilibrium c be e/abli%$ ) appreciable velocity alt]s "u ! influ5ce ( catalytic ag5ts4#bhc ,examples ( su* sy/ems w no d\bt be f\nd 9 ! case ( optically active sub/ances1 :]e bo? isom]ides are app>5tly q /able at ! melt+ po9t4 ,9 ! case ( su* sub/ances1 also1 ! action ( catalytic ag5ts 9 produc+ isom]ic trans=mation 7racemisation7 is well kn[n4 ,illu/ration3 ,,fig4 #fj4 ,trans=mation ( ! ,un/able into ! ,/able ,=m4--,z has already be5 /at$1 ! /able modification 9 ! neighb\rhood ( ! melt+ po9t is t "o :i* is 9 equilibrium ) ! liquid phase at ! natural freez+ po9t4 ,9 ! case ( polymorphic sub/ances1 we h se5 7p4 #ci7 t t =m :i* is /able 9 ! neighb\rhood ( ! melt+ po9t melts at ! high] temp]ature4 ,t 0 a #bjb consequ5ce ( ! fact t ! two polymorphic =ms on melt+ gave id5tical liquid phases4 ,9 ! pres5t case1 h[ev]1 ! above rule does n apply1 = ! simple reason t ! liquid phase obta9$ by ! fusion ( ! "o modification is n id5tical ) t obta9$ by ! fusion ( ! o!r4 ,9 ! case ( isom]ic sub/ances1 !re=e1 ! =m ( l[] melt+ po9t may be ! m /able2 & :]e ?is behavi\r is f\nd x is a sign t ! two =ms are isom]ic 7or polym]ic7 & n polymorphic4#bhd ,an example ( ?is is f\nd 9 ! case ( ! isom]ic b5zaldoximes 7p4 #bjc74 ,s9ce 9 ,fig4 #ei ! alpha modification has be5 repres5t$ z ! /able =m1 ! trans=mation ( ! beta into ! alpha =m w be possible at all temp]atures d[n to ! transition po9t4 ,at temp]atures bel[ ! eutectic po9t1 trans=mation w occur )\t =mation ( a liquid phase2 b at temp]atures above ! eutectic po9t liquefaction c take place4 ,?is w be m readily und]/ood by draw+ a l9e ( con/ant temp]ature1 ,,hk1 at "s po9t betwe5 ,c & ,b4 ,!n if ! beta modification is ma9ta9$ = a suffici5tly long "t at t temp]ature1 a c]ta9 am\nt ( ! alpha modification w be =m$2 & :5 ! composition ( ! mixture has rea*$ ! po9t ,h1 fusion w occur4 ,if ! temp]ature is ma9ta9$ con/ant1 isom]ic trans=mation w cont9ue to take place 9 ! liquid phase until ! equilibrium po9t = t temp]ature is rea*$4 ,if ?is temp]ature is high] ?an ! natural melt+ po9t1 ! mixture w rema9 liquid all ! "t2 b if x is bel[ ! natural melt+ po9t1 !n ! alpha modification w be deposit$ :5 ! sy/em rea*es ! condition repres5t$ by ! po9t on ! curve ,,ac correspond+ to ! p>ticul> temp]ature4 ,z isom]ic trans=mation cont9ues1 ! freez+ po9t ( ! sy/em w rise until x rea*es ! natural freez+ po9t ,d4 ,simil>ly1 if ! alpha modification is ma9ta9$ at a temp]ature above t ( ! po9t ,d1 liquefaction w ultimately occur1 & ! sy/em w aga9 rea* ! f9al /ate repres5t$ by ,d4#bhe #bjc ,examples4--,b5zaldoximes4 ,! relation%ips :i* h j be5 discuss$ f ! !oretical po9t ( view w be r5d]$ cle>] by a brief description ( cases :i* h be5 exp]im5tally inve/igat$4 ,! fir/ we %all consid] is t ( ! two isom]ic b5zaldoximes3#bhf-- ,c#f;,h#e4;,c4,h ,c#f;,h#e4;,c4,h ,,ho4,n ,n4,,oh ,b5zantialdoxime ,b5zsynaldoxime 7alpha-modification74 7beta-modification74 ,fig4 #fa gives a graphic repres5tation ( ! results obta9$4 ,! melt+ po9t ( ! alpha modification is #cd-ce;deg2 ! melt+ po9t ( ! un/able beta-modification be+ #acj;deg4 ,! freez+ curves ,,ac & ,,bc 7 obta9$ by det]m9+ ! freez+ po9ts ( diff]5t mixtures ( kn[n composition1 & ! numb]s s obta9$ are giv5 9 ! foll[+ table4 #bjd ---------------------------------------- ------------ ,grams ( ! alpha modification 9 #ajj gm4 ( mixture4 ,freez+ po9t4 ---------------------------------------- ----------- #bf4b #aja;deg #di4b #gi;deg #gc4g #df;deg #ia4g #bf4b;deg #ie4j #bh4f;deg #if4j #cj4j;deg ---------------------------------------- ------------ ,illu/ration3 ,,fig4 #fa4 ,! eutectic po9t ,c 0 f\nd to lie at #be-bf;deg1 & ! natural freez+ po9t ,d 0 f\nd to be #bg4g;deg4 ,! equilibrium curve ,,de 0 det]m9$ by heat+ ! liquid mixtures at diff]5t temp]atures until equilibrium 0 atta9$1 & !n rapidly cool+ ! liquid4 ,9 all cases ! freez+ po9t 0 practically t ( ! po9t ,d4 ,f ?is x is se5 t ! equilibrium curve mu/ be a /raight l9e p>allel to ! temp]ature axis2 &1 !re=e1 isom]ic trans=mation 9 ! case ( ! two b5zaldoximes is n accompani$ by any heat effect 7p4 #aig74 ,?is behavi\r has also be5 f\nd 9 ! case ( acetaldoxime4#bhg ,! isom]ic b5zaldoximes are also ( int]e/ f ! fact t ! /able modification has ! l[] melt+ po9t 7v4 p4 #bjb74 ,acetaldehyde & ,p>aldehyde4--,z a second example ( ! equilibria betwe5 two isom]ides1 we %all take ! two isom]ic 7polym]ic7 =ms ( acetaldehyde1 :i* h rec5tly be5 exhau/ively /udi$4#bhh #bje ,9 ! case ( ^! two sub/ances ! reaction #c;,,*#c4;,,*o -- 7,,*#c4;,,*o7#c takes place at ! ord9>y temp]ature ) v great sl[ness4 ,= ?is reason x is possible to det]m9e ! freez+ po9t curves ( acetaldehyde & p>aldehyde4 ,! ?ree *ief po9ts on ^! curves1 repres5t$ graphically 9 ,fig4 #fb1 are3-- m4p4 ( acetaldehyde - #aah4de;deg m4p4 ( p>aldehyde #ab4ee;deg eutectic po9t - #aai4i;deg ,illu/ration3 ,,fig4 #fb4 ,9 ord] to det]m9e ! position ( ! natural melt+ po9t1 x 0 necess>y1 on acc\nt ( ! sl[ness ( trans=mation1 to employ a catalytic ag5t 9 ord] to increase ! velocity ) :i* ! equilibrium 0 e/abli%$4 ,a drop ( conc5trat$ sulphuric acid s]v$ ! purpose4 ,9 pres5ce ( a trace ( ?is sub/ance1 isom]ic trans=mation v spe$ily occurs1 & leads to ! condition ( equilibrium4 ,/>t+ 9 ! "o case ) fus$ p>aldehyde1 & 9 ! o!r case ) acetaldehyde1 ! same freez+ po9t1 viz4 #f4ge;deg1 0 obta9$1 ! solid phase be+ p>aldehyde4 ,?is temp]ature1 #f4ge;deg1 is !re=e ! natural freez+ po9t1 & p>aldehyde1 ! solid 9 equilibrium ) ! liquid phase at ?is po9t1 is ! /able =m4 ,) reg>d to ! *ange ( equilibrium ) ! temp]ature1 x 0 f\nd t :]eas ! liquid phase conta9$ #aa4g molecules p] c5t4 ( acetaldehyde at ! natural freez+ po9t1 ! liquid at ! temp]ature ( #da4f;deg conta9s #df4f molecules p] c5t4 ( acetaldehyde4 ,z ! temp]ature #bjf rises1 !re=e1 !re is increas$ =mation ( acetaldehyde1 or a decreas+ am\nt ( polym]isation4 ,?is is 9 h>mony ) ! fact t ! polym]isation ( acetaldehyde is accompani$ by evolution ( heat4 ,:ile speak+ ( ^! isom]ides1 x may be m5tion$ t at ! temp]ature #da4f;deg ! equilibrium mixture has a vap\r pressure equal to ! atmosph]ic pressure4 ,at ?is temp]ature1 !re=e1 ! equilibrium mixture 7obta9$ quickly ) ! help ( a trace ( sulphuric acid7 boils4#bhi 99 99 99 99 99 #bjg ,,*apt] ,,xii ,,summ>y4--,,application ,,( ,,! ,,phase ,,rule ,,to ,,! ,,/udy ,,( ,,sy/ems ,,( ,,two ,,compon5ts ,9 ?is conclud+ *apt] on two-compon5t sy/ems1 x is propos$ to indicate briefly h[ ! ,phase ,rule has be5 appli$ to ! elucidation ( a numb] ( problems connect$ ) ! equilibria betwe5 two compon5ts1 & h[ x has be5 employ$ = ! int]pretation ( ! data obta9$ by exp]im5t4 ,x is hop$ t ! practical value ( ! ,phase ,rule may !reby become m app>5t1 & its application to o!r cases be r5d]$ easi]4 ,! int]e/ & importance ( inve/igations into ! conditions ( equilibrium betwe5 two sub/ances1 lie 9 ! det]m9ation n only ( ! conditions = ! /able exi/5ce ( ! p>ticipat+ sub/ances1 b also ( :e!r or n *emical action takes place betwe5 ^! two compon5ts2 & if comb9ation occurs1 9 ! det]m9ation ( ! nature ( ! comp\nds =m$ & ! range ( _! exi/5ce4 ,9 all su* inve/igations1 ! ,phase ,rule becomes ( conspicu\s value on acc\nt ( ! fact t its pr9ciples af=d1 z x 71 a t\*/one by :i* ! "* ( ! sy/em c be det]m9$1 & t f ! =m ( ! equilibrium curves obta9$1 conclusions c be drawn z to ! nature ( ! int]action betwe5 ! two sub/ances4 ,9 ord] to exemplify ! application ( ! pr9ciples ( ! ,phase ,rule m fully ?an has already be5 done1 illu/rations w be drawn f inve/igations on ! int]action ( organic comp\nds2 on ! equilibria betwe5 optically active comp\nds2 & on alloys4 #bjh ,summ>y ( ! ,diff]5t ,sy/ems ( ,two ,compon5ts4--,be=e pass+ to ! consid]ation ( ! application ( ! ,phase ,rule to ! inve/igation ( p>ticul> problems1 x w be well to collect toge!r ! diff]5t types ( equilibrium curves ) :i* we are already acqua9t$2 to comp>e !m ) "o ano!r1 9 ord] t we may !n employ ^! *>act]i/ic curves = ! int]pretation ( ! curves obta9$ z ! result ( exp]im5t4 ,9 inve/igat+ ! equilibria betwe5 two compon5ts1 ?ree *ief classes ( curves w be obta9$ accord+ z-- ,i4 ,no comb9ation takes place betwe5 ! two compon5ts4 ,,ii4 ,! compon5ts c =m def9ite comp\nds4 ,,iii4 ,! compon5ts sep>ate out 9 ! =m ( mix$ cry/als4 ,! diff]5t types ( curves :i* are obta9$ 9 ^! ?ree cases are repres5t$ 9 ,figs4 #fc1 #fd1 #fe4 ,^! diff]5t diagrams repres5t ! :ole s]ies ( equilibria1 f ! melt+ po9t ( ! "o compon5t 7,a7 to t ( ! o!r compon5t 7,b74 ,! curves repres5t1 9 all cases1 ! composition ( ! solution1 or phase ( v>iable composition2 ! temp]ature be+ measur$ along "o axis1 & ! composition along ! o!r4 ,we %all n[ recapitulate v briefly ! *>act]i/ics ( ! diff]5t curves4 ,illu/ration3 ,,fig4 #fc4 ,if no comp\nd is =m$ betwe5 ! two compon5ts1 #bji ! g5]al =m ( ! equilibrium curve w be t ( curve ,i4 or ,,ii41 ,fig4 #fc4 ,type ,i4 is ! simple/ =m ( curve f\nd1 & consi/s1 z ! diagram %[s1 ( only two bran*es1 ,,ac & ,,bc1 meet+ at ! po9t ,c1 :i* lies bel[ ! melt+ po9t ( ei!r compon5t4 ,! solid phase :i* is 9 equilibrium ) ! solutions ,,ac is pure ,a2 t 9 equilibrium ) ,,bc1 pure ,b4 ,c is ! eutectic po9t4 ,al?\gh at ! eutectic po9t ! solution solidifies entirely )\t *ange ( temp]ature1 ! solid :i* is deposit$ is n a homog5e\s solid phase1 b a mixture1 or conglom]ate ( ! two compon5ts4 ,! eutectic po9t1 !re=e1 repres5ts ! melt+ or freez+ po9t1 n ( a comp\nd1 b ( a mixture 7p4 #aai74 ,curve ,,ii41 ,fig4 #fc1 is obta9$ :5 two liquid phases are =m$4 ,c is an eutectic po9t1 ,d & ,f are transition po9ts at :i* !re c co-exi/ ! f\r phases--solid1 two liquid phases1 vap\r4 ,,def repres5ts ! *ange 9 ! composition ( ! two liquid phases ) rise ( temp]ature2 ! curve might also h ! rev]s$ =m ) ! critical solution po9t bel[ ! transition po9ts ,d & ,f4 ,illu/ration3 ,,fig4 #fd4 ,9 ! second class ( sy/ems 7,fig4 #fd71 t 9 :i* comb9ation betwe5 ! compon5ts occurs1 !re are aga9 two types accord+ z ! comp\nd =m$ has a def9ite melt+ po9t 7i4e4 c exi/ 9 equilibrium ) a solution ( ! same composition71 or und]goes only p>tial fusion2 t is1 exhibits a transition po9t4 ,if a comp\nd possess+ a def9ite melt+ po9t is =m$1 ! equilibrium curve w h ! g5]al =m %[n by curve ,i41 ,fig4 #fd4 ,a1 ,b1 & ,d are ! melt+ po9ts ( pure ,a1 pure ,b1 & ( ! comp\nd ,ax,by respectively4 ,,ac #baj is ! freez+ po9t curve ( ,a 9 pres5ce ( ,b2 ,,be t ( ,b 9 pres5ce ( ,a2 & ,,dc & ,,de ! freez+ po9t curves ( ! comp\nd 9 pres5ce ( a solution conta9+ excess ( "o ( ! compon5ts4 ,c & ,e are eutectic po9ts at :i* mixtures ( ,a & ,ax,by1 or ,b & ,ax,by c co-exi/ 9 contact ) solution4 ,! curve ,,cde may be l>ge or small1 & ! melt+ po9t ( ! comp\nd1 ,d1 may lie above or bel[ t ( ea* ( ! compon5ts1 or may h an int]m$iate position4 ,if m ?an "o comp\nd c be =m$1 a s]ies ( curves simil> to ,,cde w be obta9$ 7cf4 p4 #aeb74 ,on ! o!r h&1 if ! comp\nd und]goes transition to ano!r solid phase at a temp]ature bel[ its melt+ po9t1 a curve ( ! =m ,,ii41 ,fig4 #fd1 w be f\nd4 ,?is corresponds to ! case :]e a comp\nd c exi/ only 9 contact ) solutions conta9+ excess ( "o ( ! compon5ts4 ,! meta/able cont9uation ( ! equilibrium curve = ! comp\nd is indicat$ by ! dott$ l9e1 ! summit ( :i* w\ld be ! melt+ po9t ( ! comp\nd4 ,be=e ?is temp]ature is rea*$1 h[ev]1 ! solid comp\nd ceases to be able to exi/ 9 contact ) solution1 & transition to a diff]5t solid phase occurs at ! po9t ,e 7cf4 p4 #acd74 ,?is po9t1 !re=e1 repres5ts ! limit ( ! exi/5ce ( ! comp\nd ,,ab4 ,if a s]ies ( comp\nds c be =m$ none ( :i* possess a def9ite melt+ po9t1 !n a s]ies ( curves w be obta9$ :i* d n exhibit a temp]ature-maximum1 & !re w be only "o eutectic po9t4 ,! limits ( exi/5ce ( ea* comp\nd w be m>k$ by a break 9 ! curve 7cf4 p4 #adc74 ,illu/ration3 ,,fig4 #fe4 ,turn+1 la/ly1 to ! ?ird class ( sy/ems1 9 :i* =mation ( mix$ cry/als c occur1 five diff]5t types ( curves c be obta9$1 z %[n 9 ,fig4 #fe4 ,) reg>d to ! fir/ ?ree types1 curves ,i41 ,,ii41 & ,,iii41 #baa ^! diff] entirely f ^? ( ! previ\s classes1 9 t !y are cont9u\s2 !y exhibit no eutectic po9t1 & no transition po9t4 ,curve ,,ii4 be>s "s resemblance to ! melt+-po9t curve ( a comp\nd 7e4g4 ,,cde1 ,fig4 #fd1 ,i471 b diff]s m>k$ly f x 9 n end+ 9 eutectic po9ts4 ,fur!r1 9 ! case ( ! =mation ( a comp\nd1 ! composition ( ! solid phase rema9s un*ang$ ?r\gh\t ! :ole curve betwe5 ! eutectic po9ts2 :]eas1 :5 mix$ cry/als are produc$1 ! composition ( ! solid phase v>ies ) ! composition ( ! liquid solution4 ,on pass+ ?r\gh ! maximum1 ! relative proportions ( ,a & ,b 9 ! solid & ! liquid phase und]go *ange2 on ! "o side ( ! maximum1 ! solid phase conta9s relatively m ,a1 & on ! o!r side ( ! maximum1 relatively m ,b ?an ! liquid phase4 ,la/ly1 :5 mix$ cry/als are =m$1 ! temp]ature at :i* complete solidification occurs *anges z ! composition ( ! solution *anges1 :]eas 9 ! case ( ! =mation ( comp\nds1 ! temp]ature ( complete solidification = all solutions is a eutectic po9t4 ,! ?ird type ( curve1 ,fig4 #fe1 c be di/+ui%$ 9 a simil> mann] f ! ord9>y eutectic curve1 ,fig4 #fc1 ,i41 to :i* x be>s a c]ta9 resemblance4 ,:]eas 9 ! case ( ! latt]1 ! eutectic po9t is ! temp]ature ( complete solidification ( all solutions1 ! po9t ( m9imum temp]ature 9 ! case ( ! =mation ( mix$ cry/als1 is ! solidification po9t only ( solutions hav+ "o p>ticul> composition2 t1 namely1 ( ! m9imum po9t4 ,= all o!r solutions1 ! temp]ature ( complete solidification is diff]5t4 ,:]eas1 also1 9 ! case ( ! simple eutectic curve1 ! solid :i* sep>ates out f ! solutions repres5t$ by ei!r curve rema9s ! same ?r\gh\t ! :ole ext5t ( t curve1 ! composition ( ! mix$ cry/al v>ies ) v>iation ( ! composition ( ! liquid phase1 & ! relative proportions ( ! two compon5ts 9 ! solid & ! liquid phase are rev]s$ on pass+ ?r\gh ! m9imum4#bij ,9 a simil> mann]1 type ,,iv41 ,fig4 #fe1 c be di/+ui%$ f type ,,ii41 ,fig4 #fd1 by ! fact t x does n exhibit a #bab eutectic po9t1 & t ! composition ( ! solid phase und]goes cont9u\s v>iation ) v>iation ( ! liquid phase on ei!r side ( ! transition po9t4 ,la/ly1 type ,v41 :i* does exhibit a eutectic po9t1 diff]s f ! eutectic curve ( ,fig4 #fc1 9 t ! eutectic po9t does n con/itute ! po9t ( complete solidification = all solutions1 & t ! composition ( ! solid phase v>ies ) ! composition ( ! liquid phase4 ,su*1 !n1 are ! *ief g5]al types ( equilibrium curves = two-compon5ts2 !y are ! patt]n curves ) :i* o!r curves1 exp]im5tally det]m9$1 c be comp>$2 & f ! comp>ison x w be possible to draw conclusions z to ! nature ( ! equilibria betwe5 ! two compon5ts "u inve/igation4 #a4 ,organic ,comp\nds4 ,illu/ration3 ,,fig4 #ff4 ,! pr9ciples ( ! ,phase ,rule h be5 appli$ to ! inve/igation ( ! equilibria betwe5 organic comp\nds1 & ,figs4 #ff-fi reproduce "s ( ! results :i* h be5 obta9$4#bia #bac ,fig4 #ff1 ! freez+ po9t curve 7curve ( equilibrium7 = o-nitroph5ol & p-toluid9e1 %[s a curve ( ! simple/ type#bib 7type ,i41 ,fig4 #fc71 9 :i* two bran*es meet at an eutectic po9t4 ,! solid phase 9 equilibrium ) solutions repres5t$ by ! left-h& bran* ( ! curve 0 o-nitroph5ol 7m4p4 #dd4a;deg72 t 9 equilibrium ) ! solutions repres5t$ by ! "r-h& bran*1 0 p-toluid9e 7m4p4 #dc4c;deg74 ,at ! eutectic po9t 7#ae4f;deg71 ^! two solid phases c\ld co-exi/ ) ! liquid phase4 ,?is equilibrium curve1 !re=e1 %[s t o-nitroph5ol & p-toluid9e d n comb9e ) "o ano!r4 ,9 connection ) ?is curve1 att5tion may be call$ to ! int]e/+ fact t al?\gh ! solid produc$ by cool+ ! liquid phase at ! eutectic po9t has a composition approximat+ to t ( a comp\nd ( equimolecul> proportions ( ! ph5ol & toluid9e1 & a con/ant melt+ po9t1 x is nev]!less a mixture4 ,al?\gh1 z a rule1 ! con/itu5ts ( ! eutectic mixture are n pres5t 9 simple molecul> proportions1 !re is no reason :y !y %\ld n be s2 & x is !re=e necess>y to bew>e ( assum+ ! =mation ( comp\nds 9 su* cases4#bic ,fig4 #fg1 on ! o!r h&1 indicates ) p]fect c]ta9ty ! =mation ( a comp\nd betwe5 ph5ol & alpha-naph?ylam9e4#bid 7,cf4 curve ,i41 ,fig4 #fd47 ,ph5ol freezes at #dj4d;deg1 b ! addition ( alpha-naph?ylam9e l[]s ! freez+ po9t z repres5t$ by ! curve ,,ac4 ,at ,c 7#af4j;deg7 ! comp\nd ,c#f;,h#e,,oh1,c#aj;,h#g,,nh#b is =m$1 & ! sy/em becomes inv>iant4 ,on increas+ ! am\nt ( ! am9e1 ! temp]ature ( equilibrium rises1 ! solid phase n[ be+ ! comp\nd4 ,at ,d1 ! curve passes ?r\gh a maximum 7#bh4h;deg71 at :i* ! solid & liquid phases h ! same composition4 ,?is is ! melt+ po9t ( ! comp\nd4 ,fur!r addition ( ! am9e l[]s ! temp]ature ( equilibrium1 until at ,e solid alpha-naph?ylam9e sep>ates out1 & a second eutectic po9t 7#bd4j;deg7 is obta9$4 ,,be is ! #bad freez+-po9t curve ( alpha-naph?ylam9e 9 pres5ce ( ph5ol1 ! freez+ po9t ( ! pure am9e be+ #dh4c;deg4 ,on acc\nt ( ! great sluggi%ness ) :i* ! comp\nd ( ph5ol & alpha-naph?ylam9e cry/allizes1 x 0 f\nd possible to foll[ ! freez+ po9t curves ( ph5ol & ! am9e to temp]atures consid]ably bel[ ! eutectic po9ts1 z %[n by ! curves ,,cf & ,,eg4 ,illu/ration3 ,,fig4 #fg4 ,ph5ol c also comb9e ) p-toluid9e 9 equimolecul> proportions2 & ?is comp\nd is ( int]e/1 f ! fact t x exi/s 9 two cry/all9e =ms melt+ at #bh4e;deg & #cj;deg4 ,ea* ( ^! =ms n[ mu/ h its own equilibrium curve1 & x 0 f\nd t ! int]m$iate portion ( ! freez+ po9t curve 0 duplicat$1 z %[n 9 ,fig4 #fh4bie #bae ,illu/ration3 ,,fig4 #fh4 ,illu/ration3 ,,fig4 #fi4 #baf ,la/ly1 a curve is giv51 ,fig4 #fi1bif :i* corresponds ) curve ,,ii41 ,fig4 #fd4 ,picric acid & b5z5e c =m a comp\nd1 :i*1 h[ev]1 c exi/ only 9 contact ) solutions conta9+ excess ( b5z5e4 ,:5 ! temp]ature is rais$1 a po9t 7,k7 is rea*$ at :i* ! comp\nd melts ) sep>ation ( solid picric acid4 ,! po9t1 ,k1 is1 !re=e1 a transition po9t2 analysis1 h[ev]1 %[$ t ! composition ( ! solution at ?is po9t is v ne>ly t ( ! comp\nd ,c#f;,h#b7,,no#b7c,,oh1,c#f;,h#f1 s t ! melt+ po9t ( ! comp\nd c almo/ be rea*$4 ,! fusion ( ! comp\nd ( b5z5e & picric acid ) sep>ation ( ! latt] is analog\s to ! 7p>tial7 fusion ( ,glaub]'s salt ) sep>ation ( anhydr\s sodium sulphate4 #b4 ,optically ,active ,sub/ances4 ,! "q z to :e!r a resolvable inactive body is a mixture ( ! two oppositely active con/itu5ts 7a dl-mixture71 or a racemic comp\nd1 is "o :i* has giv5 rise to consid]able discussion dur+ ! pa/ decade2 & sev]al inve/igators h endeav\r$ to e/abli% g5]al rules by :i* ! "q c\ld be decid$4 ,9 ! case ( inactive liquids x is a matt] ( great difficulty to arrive at a c]ta9 conclusion z to :e!r "o is deal+ ) a mixture or a comp\nd1 = 9 ?is case ! usual physical me?ods give b a dubi\s answ]2 & al?\gh ! exi/5ce ( a racemate 9 ! liquid /ate 79 ! case ( con9e7 has be5 ass]t$1#big mo/ *emi/s incl9e to ! belief t su* a ?+ is improbable4 ,ev5 9 ! case ( cry/all9e sub/ances1 :]e ! diff]5ces betwe5 ! v>i\s =ms is great]1 x 0 n always easy to discrim9ate betwe5 ! dl-mixture & ! racemic comp\nd4 ,! occurr5ce ( hemih$ral faces 0 consid]$ by ,pa/eur to be a suffici5t crit]ion = an optically active sub/ance4 ,x has1 h[ev]1 be5 f\nd t hemih$ry 9 cry/als1 al?\gh a frequ5t accompanim5t ( #bag optical activity1 is by no means a necess>y or con/ant expression ( ?is prop]ty4 ,o!r rules1 also1 :i* 7 giv51 al?\gh 9 "s cases reliable1 7 9 o!r cases insuffici5t2 & all 7 9 s f> unsatisfactory t !y lack$ a !oretical basis4 ,) ! help ( ! ,phase ,rule1 h[ev]1 x is possible f a /udy ( ! solubility or fusion curves ( ! optically active & inactive sub/ances1 to decide ! nature ( ! inactive sub/ance1 at lea/ "u c]ta9 conditions4 ,on acc\nt ( ! int]e/ & importance :i* ^! comp\nds possess1 a brief description ( ! application ( ! ,phase ,rule to ! /udy ( su* sub/ances w be giv5 "h2#bih ! two optical antipodes be+ reg>d$ z ! two compon5ts4 ,9 ! pres5t *apt] we %all consid] only ! fusion curves1 ! solubility curves be+ discuss$ 9 ! next section on ?ree-compon5t sy/ems4 ,! rules :i* are h]eby obta9$1 h ref]5ce only to ! nature ( ! inactive sub/ance 9 ! neighb\rhood ( ! melt+ po9ts4 ,i4 ,! inactive sub/ance is a dl-mixture4 ,9 ?is case ! fusion curves w h ! simple =m %[n 9 type ,i1 ,fig4 #fc4 ,a & ,b are ! melt+ po9ts ( ! two optical isom]ides1 & ,c ! eutectic po9t at :i* ! inactive mixture consi/+ ( equal am\nts ( d- & l-=m melts4 ,ow+ to ! simil> effect ( ! "o =m on ! freez+ po9t ( ! o!r1 ! figure is symmetrical4 ,no example ( ?is simple case has be5 inve/igat$4 ,,ii4 ,! two compon5ts =m a racemic comp\nd4 ,9 ?is case !re w be ?ree melt+ po9t curves z 9 ,fig4 #fd1 type ,i4 ,9 ?is case also ! figure mu/ be symmetrical4 ,examples4--,z examples ( ?is1 may be tak5 dime?yl t>trate & m&elic acid1 ! freez+ po9t curves ( :i* are giv5 9 ,figs4 #gj & #ga4bii ,z c be se51 ! curve = ! racemic t>trate occupies a l>ge "p ( ! diagram1 #bah :ile t = racemic m&elic acid is mu* small]4 ,9 ! case ( dime?yldiacetyl t>trate1 ?is middle portion is /ill less4 ,illu/ration3 ,,fig4 #gj4 ,illu/ration3 ,,fig4 #ga4 ,illu/ration3 ,,fig4 #gb4 ,active dime?yl t>trate melts at #dc4c;deg2 racemic dime?yl t>trate at #hi4d;deg4 ,active m&elic acid melts at #acb4h;deg2 ! racemic acid at #aah4j;deg4 ,9 ! "o case1 !re=e1 ! racemic comp\nd has a high]1 9 ! o!r a l[] melt+ po9t ?an ! active =ms4 #bai ,9 ! case ( p>tially racemic comp\nds 7i4e4 ! comp\nd ( a racemate ) an optically active sub/ance7 ! type ( curve w be ! same1 b ! figure w no long] be symmetrical4 ,su* a curve has be5 f\nd 9 ! case ( ! l-m5?yl e/]s ( d- & l-m&elic acid 7,fig4 #gb74cjj ,! freez+ po9t ( l-m5?yl d-m&elate is #ig4b;deg1 ( l-m5?yl l-m&elate #gg4f;deg1 & ( l-m5?yl r-m&elate #hc4g4;deg ,x w be obs]v$ t ! summit ( ! curve = ! p>tially racemic m&elate is v flat1 indicat+ t ! comp\nd is l>gely dissociat$ into its compon5ts at ! temp]ature ( fusion4 ,,iii4 ,! inactive sub/ance is a pseudo-racemic mix$ cry/al4 ,9 cases :]e ! active compon5ts c =m mix$ cry/als1 ! freez+-po9t curve w exhibit "o ( ! =ms giv5 9 ,fig4 #fe4 ,! inactive mix$ cry/al conta9+ #ej p] c5t4 ( ! dextro & laevo comp\nd1 is kn[n z a pseudo-racemic mix$ cry/al4#cja ,s f>1 only curves ( ! types ,i4 & ,,ii4 h be5 obta9$4 ,examples4--,! two active camphor oximes are ( int]e/ f ! fact t !y =m a cont9u\s s]ies ( mix$ cry/als1 all ( :i* h ! same melt+ po9t4 ,! curve :i* is obta9$ 9 ?is case is1 !re=e1 a /raight l9e jo9+ ! melt+ po9ts ( ! pure active compon5ts2 ! melt+ po9t ( ! active isom]ides & ( ! :ole s]ies ( mix$ cry/als be+ #aah4h;deg4 ,illu/ration3 ,,fig4 #gc4 ,9 ! case ( ! c>voximes mix$ cry/als are also =m$1 b ! equilibrium curve 9 ?is case exhibits a maximum 7,fig4 #gc74 ,at ?is maximum po9t ! composition ( ! solid & ( ! liquid solution is ! same4 ,s9ce ! curve mu/ be symmetrical1 ?is maximum po9t mu/ occur 9 ! case ( ! solution conta9+ #ej p] c5t4 #bbj ( ea* compon5t1 :i* w !re=e be inactive4 ,fur!r1 ?is inactive mix$ cry/al w melt & solidify at ! same temp]ature1 & behave1 !re=e1 l a *emical comp\nd 7p4 #ahg74 ,! melt+ po9t ( ! active comp\nds is #gb;deg2 t ( ! inactive pseudo-racemic mix$ cry/al is #ia4d;deg4 ,trans=mations4--,z has already be5 rem>k$1 ! conclusions :i* c be drawn f ! fusion curves reg>d+ ! nature ( ! inactive sub/ances =m$ hold only = temp]atures 9 ! neighb\rhood ( ! melt+ po9ts4 ,at temp]atures bel[ ! melt+ po9t trans=mation may occur2 e4g4 a racemate may break up into a dl-mixture1 or a pseudo-racemic mix$ cry/al may =m a racemic comp\nd4 ,we %all at a lat] po9t meet ) examples ( a racemic comp\nd *ang+ into a dl-mixture at a def9ite transition po9t2 & ! pseudo-racemic mix$ cry/al ( camphoroxime is an example ( ! second trans=mation4 ,al?\gh at temp]atures 9 ! neighb\rhood ( ! melt+ po9t ! two active camphoroximes =m only mix$ cry/als b no comp\nd1 a racemic comp\nd is =m$ at temp]atures bel[ #ajc;deg4 ,at ?is temp]ature ! inactive pseudo-racemic mix$ cry/al *anges into a racemic comp\nd2 & 9 ! case ( ! o!r mix$ cry/als trans=mation to racemate & 7excess (7 active compon5t also occurs1 al?\gh at a l[] temp]ature ?an 9 ! case ( ! inactive mix$ cry/al4 ,al?\gh ?is behavi\r is "o ( consid]able importance1 ?is brief ref]5ce to x mu/ suffice "h4#cjb #c4 ,alloys4 ,"o ( ! mo/ important classes ( sub/ances 9 ! /udy ( :i* ! ,phase ,rule has be5 ( v consid]able importance1 is t =m$ by ! mixtures or comp\nds ( metals ) "o ano!r kn[n z alloys4 ,al?\gh 9 ! inve/igation ( ! nature ( ^! bodies v>i\s me?ods are employ$1 "o ( ! mo/ important is ! det]m9ation ( ! "* ( ! freez+-po9t curve2 = f ! =m ( ?is1 valuable in=mation c1 z we h already le>n$1 be #bba obta9$ reg>d+ ! nature ( ! solid sub/ances :i* sep>ate out f ! molt5 mixture4 ,al?\gh x is impossible "h to discuss fully ! exp]im5tal results & ! (t5times v complicat$ relation%ips :i* ! /udy ( ! alloys has br\ght to light1 a brief ref]5ce to ^! bodies w be advisable on acc\nt bo? ( ! sci5tific int]e/ & ( ! indu/rial importance atta*+ to !m4#cjc ,we h already se5 t !re are ?ree *ief types ( freez+-po9t curves 9 sy/ems ( two compon5ts1 viz4 ^? obta9$ :5 7#a7 ! pure compon5ts cry/allize out f ! molt5 mass2 7#b7 ! compon5ts =m "o or m comp\nds2 7#c7 ! compon5ts =m mix$ cry/als4 ,9 ! case ( ! metals1 repres5tatives ( ^! ?ree classes are also f\nd4 #a4 ,! compon5ts sep>ate out 9 ! pure /ate4 ,9 ?is case ! freez+-po9t curve is ( ! simple type1 ,fig4 #fc1 ,i4 ,su* curves h be5 obta9$ 9 ! case ( a numb] ( pairs ( metals1 e4g4 z9c--cadmium1 z9c--alum9ium1 copp]--silv] 7,heycock & ,neville71 t9--z9c1 bismu?--lead 7,gauti]71 & 9 o!r cases4 ,f molt5 mixtures repres5t$ by "o bran* ( ! freez+-po9t curve "o ( ! metals w be deposit$2 :ile f mixtures repres5t$ by ! o!r bran*1 ! o!r metal w sep>ate out4 ,at ! eutectic po9t ! molt5 mass w solidify to a het]og5e\s mixture ( ! two metals1 =m+ :at is kn[n z ! eutectic alloy4 ,su* an alloy1 !re=e1 w melt at a def9ite temp]ature l[] ?an ! melt+ po9t ( ei!r ( ! pure metals4 #bbb ,9 ! foll[+ table are giv5 ! temp]ature & ! composition ( ! liquid at ! eutectic po9t1 = ?ree pairs ( metals3-- ---------------------------------------- --------------------------- ,temp]ature4 ,composition ( liquid4 ---------------------------------------- --------------------------- ,z9c--cadmium #bfd4e;deg #gc4e atoms p] c5t4 ( cadmium4 ,z9c--alum9ium #chj4e;deg #aa alum9ium4 ,copp]--silv] #ggh;deg #dj copp]4 ---------------------------------------- --------------------------- ,! melt+ po9ts ( ! pure metals are1 z9c1 #dai;deg2 cadmium1 #cbb;deg2 silv]1 #ifj;deg2 copp]1 #ajha;deg2 alum9ium1 #fej;deg4 #b4 ,! two metals c =m "o or m comp\nds4 ,9 ?is case !re w be obta9$ n only ! freez+-po9t curves ( ! pure metals1 b ea* comp\nd =m$ w h its own freez+-po9t curve1 exhibit+ a po9t ( maximum temp]ature1 & end+ on ei!r side 9 an eutectic po9t4 ,! simple/ curve ( ?is type w be obta9$ :5 only "o comp\nd is =m$1 z is ! case ) m]cury & ?allium4#cjd ,?is curve is repres5t$ 9 ,fig4 #gd1 :]e ! summit ( ! int]m$iate curve corresponds ) a composition ,tl,hg#b4 ,simil> curves are also giv5 by nickel & t91 by alum9ium & silv]1 & by o!r metals1 ! =mation ( def9ite comp\nds betwe5 ^! pairs ( metals be+ !reby indicat$4#cje ,illu/ration3 ,,fig4 #gd4 #bbc ,a curve belong+ to ! same type1 b m complicat$1 is obta9$ ) gold & alum9ium2#cjf 9 ?is case1 sev]al comp\nds are =m$1 "s ( :i* h a def9ite melt+ po9t1 :ile o!rs exhibit only a transition po9t4 ,! *ief comp\nd is ,au,al#b1 :i* has practically ! same melt+ po9t z pure gold4 #c4 ,! two metals =m mix$ cry/als 7solid solutions74 ,! simple/ case 9 :i* ! metals cry/allize out toge!r is f\nd 9 silv] & gold4#cjg ,! freez+-po9t curve 9 ?is case is an almo/ /raight l9e jo9+ ! freez+ po9ts ( ! pure metals 7cf4 curve ,i41 ,fig4 #fe1 p4 #baj74 ,^! two metals1 !re=e1 c =m an unbrok5 s]ies ( mix$ cry/als4 ,9 "s cases1 h[ev]1 ! two metals d n =m an unbrok5 s]ies ( mix$ cry/als4 ,9 ! case ( z9c & silv]1#cjh = example1 ! addition ( silv] raises ! freez+ po9t ( ! mixture1 until a transition po9t is rea*$4 ,?is corresponds ) curve ,,iv41 ,fig4 #fe4 ,silv] & copp]1 & gold & copp]1 on ! o!r h&1 d n =m unbrok5 s]ies ( mix$ cry/als1 b ! freez+-po9t curve exhibits an eutectic po9t1 z 9 curve ,v41 ,fig4 #fe4 ,n only may !re be ^! ?ree diff]5t types ( curves1 b !re may also be comb9ations ( ^!4 ,?us ! two metals may n only =m comp\nds1 b "o ( ! metals may n sep>ate out 9 ! pure /ate at all1 b =m mix$ cry/als4 ,9 ?is case ! freez+ po9t may rise 7z 9 ! case ( silv] & z9c71 & "o ( ! eutectic po9ts w be abs5t4 ,iron-,c>bon ,alloys4--,( all ! diff]5t b9>y alloys1 probably ! mo/ important are ^? =m$ by iron & c>bon3 alloys consi/+ n ( two metals1 b ( a metal & a non-metal4 ,on acc\nt ( ! importance ( ^! alloys1 an attempt w be made to describe 9 brief "s ( ! mo/ important relation%ips met )4 ,be=e proce$+ to discuss ! applications ( ! ,phase ,rule to ! /udy ( ! iron-c>bon alloys1 h[ev]1 ! ma9 #bbd facts ) :i* we h to deal may be /at$ v briefly4 ,) reg>d to ! metal itself1 x is kn[n to exi/ 9 ?ree diff]5t allotropic modifications1 call$ alpha-1 beta-1 & gamma-f]rite respectively4 ,l ! two modifications ( sulphur & ( t91 ^! diff]5t =ms exhibit transition po9ts at :i* ! relative /ability ( ! =ms *anges4 ,?us ! transition po9t = alpha- & beta-f]rite is ab\t #ghj;deg2 & bel[ ?is temp]ature ! alpha- =m1 above x ! beta- =m is /able4 ,= beta- & gamma-f]rite1 ! transition po9t is ab\t #hgj;deg1 ! gamma- =m be+ ! /able modification above ?is temp]ature4 ,! diff]5t modifications ( iron also possess diff]5t prop]ties4 ,?us1 alpha-f]rite is magnetic1 b does n possess ! p[] ( dissolv+ c>bon2 beta-f]rite is non-magnetic1 & likewise does n dissolve c>bon2 gamma-f]rite is also non-magnetic1 b possesses ! p[] ( dissolv+ c>bon1 & ( ?us giv+ rise to solid solutions ( c>bon 9 iron4 ,v>i\s alloys ( iron & c>bon1 also1 h to be di/+ui%$4 ,fir/ ( all1 !re is h>d /eel1 :i* conta9s v>y+ am\nts ( c>bon up to #b p] c5t4 ,microscopic exam9ation %[s t ^! mixtures are all homog5e\s2 & !y are !re=e to be reg>d$ z solid solutions ( c>bon 9 iron 7gamma-f]rite74 ,to ^! solutions ! "n m>t5site has be5 giv54 ,pe>lite conta9s ab\t #j4h p] c5t4 ( c>bon1 &1 on microscopic exam9ation1 is f\nd to be a het]og5e\s mixture4 ,if heat$ above #fgj;deg1 pe>lite becomes homog5e\s1 & =ms m>t5site4 ,la/ly1 !re is a def9ite comp\nd ( iron & c>bon1 iron c>bide or cem5tite1 hav+ ! =mula ,fe#c;,c4 ,a %ort description may n[ be giv5 ( ! application ( ! ,phase ,rule to ! two-compon5t sy/em iron--c>bon2 & ( ! diagram %[+ h[ ! diff]5t sy/ems are relat$1 & ) ! help ( :i* ! behavi\r ( ! diff]5t mixtures "u giv5 conditions c be pr$ict$4 ,al?\gh1 ) reg>d to ! ma9 features ( ?is diagram1 ! diff]5t areas to be mapp$ & ! position ( ! fronti] l9es1 !re is g5]al agreem5t2 a f9al decision has n yet be5 rea*$ ) reg>d to ! int]pretation to be put on all ! curves4 ,illu/ration3 ,,fig4 #ge4 ,! *ief relation%ips met ) 9 ! case ( ! #bbe iron-c>bon alloys are repres5t$ graphically 9 ,fig4 #ge4cji ,! curve ,,ac is ! freez+-po9t curve = iron1#caj ,,bc ! unkn[n freez+-po9t curve = graphite4 ,c is an eutectic po9t4 ,suppose1 n[1 t we />t ) a mixture ( iron & c>bon1 repres5t$ by ! po9t x4 ,on l[]+ ! temp]ature1 a po9t1 y1 w be rea*$ at :i* solid beg9s to sep>ate out4 ,?is solid phase1 h[ev]1 is n pure iron1 b a solid solution ( c>bon 9 iron1 hav+ ! composition repres5t$ by y' 7cf4 p4 #ahe74 ,z ! temp]ature cont9ues to fall1 ! #bbf composition ( ! liquid phase *anges 9 ! direction ( y,c1 :ile ! composition ( ! solid :i* sep>ates out *anges 9 ! direction y',d2 &1 f9ally1 :5 ! composition ( ! molt5 mass is t ( ! po9t ,c 7#d4c p] c5t4 ( c>bon71 ! :ole mass solidifies to a het]og5e\s mixture ( two solid solutions1 "o ( :i* is repres5t$ by ,d 7conta9+ #b p] c5t4 ( c>bon71 :ile ! o!r w consi/ practically ( pure graphite1 & is n %[n 9 ! figure4 ,! temp]ature ( ! eutectic po9t is #aacj;deg4 ,ev5 bel[ ! solidification po9t1 h[ev]1 *anges c take place4 ,z has be5 said1 ! solid phase :i* f9ally sep>ates out f ! molt5 mass is a solid solution repres5t$ by ! po9t ,d2 & ! curve ,,de repres5ts ! *ange 9 ! composition ( ?is solid solution ) ! temp]ature4 ,z indicat$ 9 ! figure1 ,,de =ms a "p ( a curve repres5t+ ! mutual solubility ( graphite 9 iron & iron 9 graphite2 ! latt] solutions1 h[ev]1 n be+ %[n1 z !y w\ld lie f> outside ! diagram4 ,z ! temp]ature falls bel[ #aacj;deg1 m & m graphite sep>ates out1 until at ,e1 :5 ! temp]ature is #ajjj;deg1 ! solid solution conta9s only #a4h p] c5t4 ( c>bon4 ,at ?is temp]ature cem5tite also beg9s to be =m$1 s t z ! temp]ature cont9ues to fall1 sep>ation ( cem5tite 7repres5t$ by ! l9e ,e',f'7 occurs1 & ! composition ( ! solid solution und]goes alt]ation1 z repres5t$ by ! curve ,,ef4 ,bel[ ! temp]ature ( ! po9t ,f 7#fgj;deg7 ! m>t5site becomes het]og5e\s1 & =ms pe>lite4 ,f ! above description1 !re=e1 x foll[s t if we />t ) a molt5 mixture ( iron & c>bon1 ! composition ( :i* is repres5t$ by any po9t betwe5 ,d & ,c 7f #b to #d4c p] c5t4 ( c>bon71 we %all obta91 on cool+ ! mass1 fir/ ( all solid solutions1 ! composition ( :i* w be repres5t$ by po9ts on ! l9e ,,ad2 t !n1 aft] ! mass has completely solidifi$ at #aacj;deg1 fur!r cool+ w lead to a sep>ation ( graphite & a *ange 9 ! composition ( ! m>t5site 7f #b to #a4h p] c5t4 ( c>bon74 ,on cool+ bel[ #ajjj;deg1 h[ev]1 ! m>t5site & graphite w give rise to cem5tite & solid solutions #bbg conta9+ less c>bon ?an be=e1 until1 at temp]atures bel[ #fgj;deg1 we are left ) a mixture ( pe>lite & cem5tite4 ,we h already said t iron consi/s 9 ?ree allotropic modifications1 ! regions ( /ability ( :i* are sep>at$ by def9ite transition po9ts4 ,! transition po9t = alpha- & beta-f]rite 7#ghj;deg7 is repres5t$ 9 ,fig4 #ge by ! po9t ,h2 & ! transition po9t = beta- & gamma-f]rite 7#hgj;deg7 by ! po9t ,i4 ,s9ce nei!r ! alpha- nor ! beta-f]rite dissolves c>bon1 ! transition po9t w be unaffect$ by addition ( c>bon1 & we !re=e obta9 ! horizontal transition curve ,,hg4 ,9 ! case ( ! beta- & gamma-f]rite1 h[ev]1 ! latt] dissolves c>bon1 & ! transition po9t is consequ5tly affect$ by ! am\nt ( c>bon pres5t4 ,?is is %[n by ! l9e ,,ig4 ,if a m>t5site conta9+ less c>bon ?an t repres5t$ by ! po9t ,g is cool$ d[n f a temp]ature (1 say1 #ijj;deg1 !n :5 ! temp]ature has fall5 to t1 repres5t$ by a po9t on ! curve ,,ig1 beta-f]rite w sep>ate out1 &1 z ! temp]ature falls1 ! composition ( ! solid solution w alt] z repres5t$ by ,,ig4 ,on pass+ bel[ ! temp]ature ( ,,hg1 ! beta-f]rite w be conv]t$ into alpha-f]rite1 &1 z ! temp]ature falls1 ! latt] w sep>ate out m & m1 :ile ! composition ( ! solid solution alt]s 9 ! direction ,,gf4 ,on pass+ to /ill l[] temp]atures1 ! solid solution at ,f 7#j4h p] c5t4 ( c>bon7 breaks up into pe>lite4 ,if ! p]c5tage ( c>bon 9 ! orig9al solid solution 0 betwe5 t repres5t$ by ! po9ts ,g & ,f1 !n1 on cool+ d[n1 no beta-f]rite1 b only alpha-f]rite w\ld sep>ate out4 ,we see1 !re=e1 t :5 m>t5site is all[$ to cool sl[ly1 x yields a het]og5e\s mixture ei!r ( f]rite & pe>lite 7:5 ! orig9al mixture conta9$ up to #j4h p] c5t4 ( c>bon71 or pe>lite & cem5tite 7:5 ! orig9al mixture conta9$ betwe5 #j4h & #b p] c5t4 ( c>bon74 ,^! het]og5e\s mixtures con/itute s(t /eels1 or1 :5 ! c>bon cont5t is l[1 wr\ght iron4 ,! case1 h[ev]1 is diff]5t if ! solid solution ( c>bon 9 iron is rapidly cool$ 7qu5*$7 f a temp]ature above ! curve ,,igfe to a temp]ature bel[ ?is #bbh curve4 ,9 ?is case1 ! rapid cool+ does n all[ "t = ! v>i\s *anges :i* h be5 describ$ to take place2 s t ! homog5e\s solid solution1 on be+ rapidly cool$1 rema9s homog5e\s4 ,9 ?is way h>d /eel is obta9$4 ,by v>y+ ! rapidity ( cool+1 z is done 9 ! temp]+ ( /eel1 v>y+ degrees ( h>dness c be obta9$4 ,! int]pretation ( ! curves giv5 above is t due ess5tially to ,roozeboom1 :o conclud$ f ! exp]im5tal data t at temp]atures bel[ #ajjj;deg ! /able sy/ems are m>t5site & cem5tite1 or f]rite & cem5tite1 graphite be+ labile4 ,x has1 h[ev]1 be5 po9t$ out1 m especially by ,e4 ,heyn1#caa t ?is is n 9 h>mony ) ! facts ( metallurgy1 :i* %[ t graphite is und\bt$ly =m$ on sl[ cool+1 & m especially :5 small quantities ( silicon are pres5t 9 ! iron4#cab ,:ile1 !re=e1 ! relation%ips repres5t$ by ,fig4 #ge are obta9$ "u c]ta9 conditions 7especially :5 manganese is pres5t71 ,heyn consid]s t all ! curves 9 t figure1 except ,,acb1 repres5t meta/able sy/ems--sy/ems1 !re=e1 ak9 to sup]cool$ liquids4 ,rapid cool+ w fav\r ! production ( ! meta/able sy/ems conta9+ cem5tite1 & !re=e give rise to relation%ips repres5t$ by ,fig4 #ge2 :]eas sl[ cool+ w lead to ! /able sy/em f]rite & graphite4 ,pres5ce ( silicon t5ds to prev5t1 pres5ce ( manganese t5ds to assi/1 ! production ( ! meta/able sy/ems4 ,al?\gh ?is view put =w>d by ,heyn has n be5 conclusively prov$1 x mu/ be said t !re is mu* evid5ce 9 its fav\r4 ,fur!r inve/igation is1 h[ev]1 requir$ be=e a f9al decision z to ! int]pretation ( ! curves c be rea*$4 ,det]m9ation ( ! ,composition ( ,comp\nds1 )\t ,analysis4--,s9ce ! equilibrium betwe5 a solid & a liquid phase dep5ds n only on ! composition ( ! liquid 7solution7 b also on t ( ! solid1 x is necess>y #bbi to det]m9e ! composition ( ! latt]4 ,9 "s cases ?is is easily effect$ by sep>at+ ! solid f ! liquid phase & analyz+ x4 ,9 o!r cases1 h[ev]1 ?is me?od is inapplicable1 or is accompani$ by difficulties1 due ei!r to ! fact t ! solid phase und]goes decomposition 7e4g4 :5 x conta9s a volatile con/itu5t71 or to ! difficulty ( completely sep>at+ ! "m liquor2 z1 = example1 9 ! case ( alloys4 ,9 all su* cases1 !re=e1 rec\rse mu/ be _h to o!r me?ods4 ,9 ! fir/ place1 syn!tic me?ods may be employ$4#cac ,9 ?is case we />t ) a solution ( ! two compon5ts1 to :i* a ?ird sub/ance is add$1 :i*1 h[ev]1 does n ent] into ! solid phase4#cad ,we w assume t ! initial solution conta9s x gm4 ( ,a & y gm4 ( ,b to #a gm4 ( ,c4 ,aft] ! solution has be5 cool$ d[n to su* a temp]ature t solid sub/ance sep>ates out1 a portion ( ! liquid phase is remov$ ) a pipette & analyz$4 ,if1 n[1 ! composition ( ! solution is su* t !re are x' gm4 ( ,a & y' gm4 ( ,b to #a gm4 ( ,c41 !n ! composition ( ! solid phase is x - x' gm4 ( ,a & y - y' gm4 ( ,b4 ,:5 x x'1 ! solid phase is pure ,b2 :5 y y'1 ! solid phase is pure ,a4 ,we h assum$ "h t !re is only "o solid phase pres5t1 conta9+ ,a & ,b4 ,to make sure t ! solid phase is n a solid solution 9 :i* ,a & ,b are pres5t 9 ! same ratio z 9 ! liquid solution1 a second det]m9ation ( ! composition mu/ be made1 ) diff]5t initial & end conc5trations4 ,if ! solid phase is a solid solution1 ! composition w n[ be f\nd diff]5t f t f\nd previ\sly4 ,! composition ( ! solid phase c1 h[ev]1 be det]m9$ 9 ano!r mann]1 viz4 by /udy+ ! fusion curve & ! curve ( cool+4 ,f ! =m ( ! fusion curve alone1 x is possible to decide :e!r ! two compon5ts #bcj =m a comp\nd or n2 & if ! comp\nds :i* may be =m$ h a def9ite melt+ po9t1 ! position ( ! latt] gives at once ! composition ( ! comp\nds 7cf4 p4 #bca74 ,?is me?od1 h[ev]1 _c be appli$ :5 ! comp\nds und]go decomposition be=e ! melt+ po9t is rea*$4 ,9 su* cases1 h[ev]1 ! =m ( ! cool+ curve enables "o to decide ! composition ( ! solid phase4#cae ,if a solution is all[$ to cool sl[ly1 & ! temp]ature not$ at def9ite times1 ! graphic repres5tation ( ! rate ( cool+ w give a cont9u\s curve2 e4g4 ab 9 ,fig4 #gf4 ,s soon1 h[ev]1 z a solid phase beg9s to be =m$1 ! rate ( cool+ alt]s abruptly1 & ! cool+ curve !n exhibits a break1 or *ange 9 direction 7po9t b74 ,:5 ! eutectic po9t is rea*$1 ! temp]ature rema9s con/ant1 until all ! liquid has solidifi$4 ,?is is repres5t$ by ! l9e cd4 ,:5 complete solidification has occurr$1 ! fall ( temp]ature aga9 becomes uni=m 7de74 ,illu/ration3 ,,fig4 #gf4 ,illu/ration3 ,,fig4 #gg4 ,illu/ration3 ,,fig4 #gh4 ,! l5g? ( "t dur+ :i* ! temp]ature rema9s con/ant at ! po9t c1 dep5ds1 ( c\rse1 on ! eutectic solution4 ,if1 !re=e1 we take equal am\nts ( solution hav+ a diff]5t initial composition1 ! p]iod ( con/ant temp]ature 9 ! cool+ curve w evid5tly be greate/ 9 ! case ( ! solution hav+ ! composition ( ! eutectic po9t2 & ! p]iod w become less & less z we increase ! am\nt ( "o ( ! compon5ts4 ,! relation%ip betwe5 initial composition ( solution & ! duration ( con/ant temp]ature at ! eutectic po9t is repres5t$ by ! curve a'c'b' 7,fig4 #gg74 ,:5 a comp\nd possess+ a def9ite melt+ po9t is =m$1 x behaves z a pure sub/ance4 ,if1 !re=e1 ! initial composition ( ! #bca solution is ! same z t ( ! comp\nd1 no eutectic solution w be obta9$2 & !re=e no l9e ( con/ant temp]ature1 su* z cd 7,fig4 #gf74 ,9 su* a case1 if we repres5t graphically ! relation betwe5 ! initial composition ( ! solution & ! duration ( con/ant temp]ature1 a diagram is obta9$ su* z %[n 9 ,fig4 #gh4 ,! two maxima on ! "t-composition curve repres5t eutectic po9ts1 & ! m9ima1 a'1 b'1 e'1 pure sub/ances4 ,! position ( e' gives ! composition ( ! comp\nd4 ,:5 a s]ies ( comp\nds is =m$1 !n = ea* comp\nd a m9imum is f\nd on ! "t-composition curve4 ,illu/ration3 ,,fig4 #gi4 ,if ! comp\nd =m$ has no def9ite melt+ po9t1 ! diagram obta9$ is l t %[n 9 ,fig4 #gi4 ,if we />t ) a solution1 ! composition ( :i* is repres5t$ by a po9t betwe5 d & b1 !n1 on cool+1 b w sep>ate out fir/1 & ! temp]ature w fall until ! po9t d is rea*$4 ,! temp]ature !n rema9s con/ant until ! compon5t b1 :i* has sep>at$ out1 is conv]t$ into ! comp\nd4 ,aft] ?is ! temp]ature aga9 falls1 until x aga9 rema9s con/ant at ! eutectic po9t c4 ,9 ! case ( ! fir/ halt1 ! p]iod ( con/ant temp]ature is greate/ :5 ! initial composition ( ! solution is ! same z t ( ! comp\nd2 & x becomes %ort] & %ort] ) #bcb increase 9 ! am\nt ( ei!r compon5t4 ,9 ?is way we obta9 ! "t-composition curve b'ed'1 ( :i* ! maximum po9t e gives ! composition ( ! comp\nd4 ,on ! o!r h&1 ! p]iod ( con/ant temp]ature = ! eutectic po9t c is greate/ 9 ! case ( solutions hav+ ! same initial composition z t correspond+ ) ! eutectic po9t2 & x decreases ! m ! initial composition approa*es t ( ! pure compon5t a or ! compon5t e4 ,9 ?is way we obta9 ! "t-composition curve a'c'e'4 ,"h also ! po9t e' repres5ts ! composition ( ! comp\nd4 ,we see1 !re=e1 t f ! graphic repres5tation ( ! freez+-po9t curve1 & f ! duration ( ! temp]ature-arre/s on ! cool+ curve1 = solutions ( diff]5t initial composition1 x is possible1 )\t hav+ rec\rse to analysis1 to decide :at solid phases are =m$1 & :at is _! composition4 ,=mation ( ,m9]als4--,important & int]e/+ z is ! application ( ! ,phase ,rule to ! /udy ( alloys1 its application to ! /udy ( ! conditions regulat+ ! =mation ( m9]als is no less s2 & al?\gh we d n propose to consid] diff]5t cases 9 detail "h1 /ill att5tion mu/ be drawn to c]ta9 po9ts connect$ ) ?is int]e/+ subject4 ,9 ! fir/ place1 x w be evid5t f :at has already be5 said1 t t m9]al :i* fir/ cry/allizes out f a molt5 magma is n necess>ily ! "o ) ! highe/ melt+ po9t4 ,! composition ( ! fus$ mass mu/ be tak5 into acc\nt4 ,:5 ! sy/em consi/s ( two compon5ts :i* d n =m a comp\nd1 "o or o!r ( ^! w sep>ate out 9 a pure /ate1 accord+ z ! composition ( ! molt5 mass lies on "o or o!r side ( ! eutectic composition2 & ! sep>ation ( ! "o compon5t w cont9ue until ! composition ( ! eutectic po9t is rea*$4 ,fur!r cool+ w !n lead to ! simultane\s sep>ation ( ! two compon5ts4 ,if1 h[ev]1 ! two compon5ts =m a /able comp\nd 7e4g4 or?oclase1 f a fus$ mixture ( silica & potassium alum9ate71 !n ! freez+-po9t curve w resemble t #bcc %[n 9 ,fig4 #fd2 i4e4 !re w be a middle curve possess+ a dy/ectic po9t1 & end+ on ei!r side at a eutectic po9t4 ,?is curve w\ld repres5t ! conditions "u :i* or?oclase is 9 equilibrium ) ! molt5 magma4 ,if ! initial composition ( ! magma is repres5t$ by a po9t betwe5 ! two eutectic po9ts1 or?oclase w sep>ate fir/4 ,! composition ( ! magma w !reby *ange1 & ! mass w f9ally solidify to a mixture ( or?oclase & silica1 or or?oclase & potassium alum9ate1 accord+ to ! initial composition4 ,:at has j be5 said holds1 h[ev]1 only = /able equilibria1 & x mu/ n be =gott5 t complications c arise ow+ to susp5d$ trans=mation 7:51 = example1 ! magma is rapidly cool$7 & ! production ( meta/able equilibria4 ,^! conditions occur v frequ5tly 9 nature4 ,! /udy ( ! =mation ( m9]als f ! po9t ( view ( ! ,phase ,rule is /ill 9 its initial /ages1 b ! results :i* h already be5 obta9$ give promise ( a ri* h>ve/ 9 ! future4#caf 99 99 99 99 99 #bcd ,,*apt] ,,xiii ,,sy/ems ,,( ,,?ree ,,compon5ts ,g5]al4--,x has already be5 made evid5t t an increase 9 ! numb] ( ! compon5ts f "o to two gives rise to a consid]able increase 9 ! possible numb] ( sy/ems1 & introduces n a few complications into ! equilibrium relations ( ^!4 ,no less is ?is ! case :5 ! numb] ( compon5ts increases f two to ?ree2 & al?\gh examples ( all ! possible types ( sy/ems ( ?ree compon5ts h n be5 inve/igat$1 nor1 inde$1 any "o type fully1 nev]!less1 among ! sy/ems :i* h be5 /udi$ exp]im5tally1 cases occur :i* n only possess a high sci5tific int]e/1 b are also ( great indu/rial importance4 ,on acc\nt n only ( ! numb]1 b m especially ( ! complexity ( ! sy/ems con/itut$ ( ?ree compon5ts1 no attempt w be made to give a full acc\nt1 or1 inde$1 ev5 a survey ( all ! cases :i* h be5 subject$ to a m or less complete exp]im5tal inve/igation2 on ! contr>y1 only a few ( ! m important classes w be select$1 & ! mo/ important po9ts 9 connection ) ! behavi\r ( ^! describ$4 ,on apply+ ! ,phase ,rule ,p ,f ,c #b to ! sy/ems ( ?ree compon5ts1 we see t 9 ord] t ! sy/em %all be inv>iant1 no few] ?an five phases mu/ be pres5t toge!r1 & an inv>iant sy/em w !re=e exi/ at a qu9tuple po9t4 ,s9ce ! numb] ( liquid phases c nev] exce$ ! numb] ( ! compon5ts1 & s9ce !re c be only "o vap\r phase1 x is evid5t t 9 ?is case1 #bce z 9 o!rs1 !re mu/ always be at lea/ "o solid phase pres5t at ! qu9tuple po9t4 ,z ! numb] ( phases dim9i%es1 ! v>iability ( ! sy/em c increase f "o to f\r1 s t 9 ! la/ case ! condition ( ! sy/em w n be completely def9$ until n only ! temp]ature & ! total pressure ( ! sy/em1 b also ! conc5trations ( two ( ! compon5ts h be5 fix$4 ,or1 in/ead ( ! conc5trations1 ! p>tial pressures ( ! compon5ts may also be tak5 z indep5d5t v>iables4 ,graphic ,repres5tation4--,hi!rto ! conc5trations ( ! compon5ts h be5 repres5t$ by means ( rectangul> co-ord9ates1 al?\gh ! num]ical relation%ips h be5 express$ 9 two diff]5t ways4 ,9 ! "o case1 ! conc5tration ( ! "o compon5t 0 express$ 9 t]ms ( a fix$ am\nt ( ! o!r compon5t4 ,?us1 ! solubility ( a salt 0 express$ by ! numb] ( grams ( salt dissolv$ by #ajj grams ( wat] or o!r solv5t2 & ! numb]s s obta9$ 7 measur$ along "o ( ! co-ord9ates4 ,! second co-ord9ate 0 !n employ$ to indicate ! *ange ( ano!r indep5d5t v>iable1 e4g4 temp]ature4 ,9 ! o!r case1 ! comb9$ weights ( ! two compon5ts ,a & ,b 7 put equal to unity1 & ! conc5tration ( ! "o express$ z a fraction ( ! :ole am\nt4 ,?is me?od all[s ( ! repres5tation ( ! complete s]ies ( conc5trations1 f pure ,a to pure ,b1 & 0 employ$1 = example1 9 ! graphic repres5tation ( ! freez+ po9t curves4 ,ev5 9 ! case ( ?ree compon5ts rectangul> co-ord9ates c also be employ$1 &1 inde$1 are ! mo/ conv5i5t 9 ^? cases :]e ! behavi\r ( two ( ! compon5ts to "o ano!r is v diff]5t f _! behavi\r to ! ?ird compon5t2 z1 = example1 9 ! case ( two salts & wat]4 ,9 ^! cases1 ! composition ( ! sy/em c be repres5t$ by measur+ ! am\nts ( ea* ( ! two compon5ts 9 a giv5 weight ( ! ?ird1 along two co-ord9ates at "r angles to "o ano!r2 & ! *ange ( ! sy/em ) ! temp]ature c !n be repres5t$ by a ?ird axis at "r angles to ! fir/ two4 ,9 ^? cases1 #bcf h[ev]1 :]e ! ?ree compon5ts behave 9 mu* ! same mann] t[>ds "o ano!r1 ! rectangul> co-ord9ates are n at all suitable1 & in/ead ( ^! a triangul> diagram is employ$4 ,v>i\s me?ods h be5 propos$ = ! graphic repres5tation ( sy/ems ( ?ree compon5ts by means ( a triangle1 b only two ( ^! h be5 employ$ to any consid]able ext5t2 & a %ort description ( ^! two me?ods w !re=e suffice4#cag ,illu/ration3 ,,fig4 #hj4 ,9 ! me?od propos$ by ,gibbs an equilat]al triangle ( unit height is us$ 7,fig #hj74cah ,! quantities ( ! diff]5t compon5ts are express$ z fractional p>ts ( ! :ole1 & ! sum ( _! conc5trations is !re=e equal to unity1 & c be repres5t$ by ! height ( ! triangle4 ,! corn]s #bcg ( ! triangle repres5t ! pure sub/ances ,a1 ,b1 & ,c respectively4 ,a po9t on "o ( ! sides ( ! triangle w give ! composition ( a mixture 9 :i* only two compon5ts are pres5t1 :ile a po9t )9 ! triangle w repres5t ! composition ( a t]n>y mixture4 ,s9ce e po9t )9 ! triangle has ! prop]ty t ! sum ( ! p]p5dicul>s f t po9t on ! sides ( ! triangle is equal to unity 7! height ( ! triangle71 x is evid5t t ! composition ( a t]n>y mixture c be repres5t$ by fix+ a po9t )9 ! triangle su* t ! l5g?s ( ! p]p5dicul>s f ! po9t to ! sides ( ! triangle are equal respectively to ! fractional am\nts ( ! ?ree compon5ts pres5t2 ! fractional am\nt ( ,a1 ,b1 or ,c be+ repres5t$ by ! p]p5dicul> di/ance f ! side ( ! triangle opposite ! corn]s ,a1 ,b1 & ,c respectively4 ,! location ( ?is po9t is simplifi$ by divid+ ! normals f ea* ( ! corn]s on ! opposite side into t5 or "o hundr$ p>ts1 & draw+ ?r\gh ^! divisions l9es at "r angles to ! normal & p>allel to ! side ( ! triangle4 ,a network ( rhomboh$ra is ?us obta9$1 & ! position ( any po9t c be read (f 9 practically ! same mann] z 9 ! case ( rectangul> co-ord9ates4 ,?us ! po9t ,p 9 ,fig4 #hj repres5ts a t]n>y mixture ( ! composition ,a #j4e1 ,b #j4c1 ,c #j4b2 ! p]p5dicul>s ,pa1 ,pb1 & ,pc be+ equal respectively to #j4e1 #j4b1 & #j4c ( ! height ( ! triangle4 ,ano!r me?od ( repres5tation1 due to ,roozeboom1 consi/s 9 employ+ an equilat]al triangle1 ! l5g? ( ^: side is made equal to unity1 or "o hundr$2 ! sum ( ! fractional or p]c5tage am\nts ( ! ?ree compon5ts be+ repres5t$ !re=e by a side ( ! triangle4 ,9 ?is case ! composition ( a t]n>y mixture is obta9$ by det]m9+1 n ! p]p5dicul> di/ance ( a po9t ,p f ! ?ree sides ( ! triangle1 b ! di/ance 9 a direction p>allel to ! sides ( ! triangle 7,fig4 #ha74 ,conv]sely1 9 ord] to repres5t a mixture consi/+ ( a1 b1 & c p>ts ( ! compon5ts ,a1 ,b1 & ,c respectively1 "o side ( ! triangle1 say ,,ab1 is fir/ ( all divid$ into t5 or "o #bch hundr$ p>ts2 a portion1 ,bx a1 is !n measur$ (f1 & repres5ts ! am\nt ( ,a pres5t4 ,simil>ly1 a portion1 ,ax' b1 is measur$ (f & repres5ts ! fractional am\nt ( ,b1 :ile ! rema9d]1 xx' c1 repres5ts ! am\nt ( ,c4 ,f x & x' l9es are drawn p>allel to ! sides ( ! triangle1 & ! po9t ( int]section1 ,p1 repres5ts ! composition ( ! t]n>y mixture ( giv5 composition2 =1 z is evid5t f ! figure1 ! di/ance ( ! po9t ,p f ! ?ree sides ( ! triangle1 :5 measur$ 9 directions p>allel to ! sides1 is equal to a1 b1 & c respectively4 ,f ! division m>ks on ! side ,,ab1 x is se5 t ! po9t ,p 9 ?is figure also repres5ts a mixture ( #j4e p>ts ( ,a1 #j4b p>ts ( ,b1 & #j4c p>ts ( ,c4 ,?is gives exactly ! same result z ! previ\s me?od4 ,! employm5t ( a "r-angl$ isosceles triangle has also be5 sugge/$1#cai b is n 9 g5]al use4 ,illu/ration3 ,,fig4 #ha4 ,9 employ+ ! triangul> diagram1 x w be ( use to note a prop]ty ( ! equilat]al triangle4 ,a l9e drawn f "o corn] ( ! triangle to ! opposite side1 repres5ts ! composition ( all mixtures 9 :i* ! relative am\nts ( two ( ! compon5ts rema9 un*ang$4 ,?us1 z ,fig4 #hb %[s1 if ! compon5t ,c is add$ to a mixture x1 9 :i* ,a & ,b are pres5t 9 ! proportions ( a 3 b1 a mixture x'1 :i* is !reby obta9$1 also conta9s ,a & ,b 9 ! ratio a 3 b4 ,= ! two triangles ,,acx & ,,bcx are simil> to ! two triangles ,,hcx' & ,,kcx'2 &1 #bci !re=e1 ,ax 3 ,bx ,hx' 3 ,kx'4 ,b ,ax ,dx & ,bx ,ex2 fur!r ,hx' ,fx' & ,kx' ,gx'4 ,!re=e1 ,dx 3 ,ex ,fx' 3 ,gx' b 3 a4 ,at all po9ts on ! l9e ,cx1 !re=e1 ! ratio ( ,a to ,b is ! same4 ,illu/ration3 ,,fig4 #hb4 ,illu/ration3 ,,fig4 #hc4 ,if x is desir$ to repres5t at ! same "t ! *ange ( ano!r indep5d5t v>iable1 e4g4 temp]ature1 ?is c be done by measur+ ! latt] along axes drawn p]p5dicul> to ! corn]s ( ! triangle4 ,9 ?is way a "r prism 7,fig4 #hc7 is obta9$1 & ea* section ( ?is cut p>allel to ! base repres5ts !re=e an iso!rmal surface4 99 99 99 99 99 #bdj ,,*apt] ,,xiv ,,solutions ,,( ,,liquids ,,9 ,,liquids ,we h already se5 7p4 #ie7 t :5 two liquids are br\ght toge!r1 !y may mix 9 all proportions & =m "o homog5e\s liquid phase2 or1 only p>tial miscibility may occur1 & two phases be =m$ consi/+ ( two mutually saturat$ solutions4 ,9 ! latt] case1 ! conc5tration ( ! compon5ts 9 ei!r phase & also ! vap\r pressure ( ! sy/em _h1 at a giv5 temp]ature1 p]fectly def9ite values4 ,9 ! case ( ?ree liquid compon5ts1 a simil> behavi\r may be f\nd1 al?\gh complete miscibility ( ?ree compon5ts ) ! =mation ( only "o liquid phase is ( mu* r>] occurr5ce ?an 9 ! case ( two compon5ts4 ,:5 only p>tial miscibility occurs1 v>i\s cases are met ) accord+ z ! ?ree compon5ts =m "o1 two1 or ?ree pairs ( p>tially miscible liquids4 ,fur!r1 :5 two ( ! compon5ts are only p>tially miscible1 ! addition ( ! ?ird may cause ei!r an increase or a dim9ution 9 ! mutual solubility ( ^!4 ,an increase 9 ! mutual solubility is g5]ally f\nd :5 ! ?ird compon5t dissolves readily 9 ea* ( ! o!r two2 b :5 ! ?ird compon5t dissolves only sp>+ly 9 ! o!r two1 its addition dim9i%es ! mutual solubility ( ! latt]4 ,we %all consid] "h only a few examples illu/rat+ ! ?ree *ief cases :i* c occur1 viz4 7#a7 ,a & ,b1 & also ,b & ,c are miscible 9 all proportions1 :ile ,a & ,c are only p>tially miscible4 7#b7 ,a & ,b are miscible 9 all proportions1 b ,a & ,c & ,b & ,c are only p>tially miscible4 7#c7 ,a & ,b1 ,b & ,c1 & ,a & ,c are only p>tially miscible4 ,a1 ,b1 & ,c "h repres5t ! ?ree compon5ts4 #a4--,! ?ree compon5ts =m only "o pair ( p>tially miscible liquids4 #bda ,an example ( ?is is f\nd 9 ! ?ree sub/ances3 *lor(orm1 wat]1 & acetic acid4#cbj ,*lor(orm & acetic acid1 & wat] & acetic acid1 are miscible ) "o ano!r 9 all proportions1 b *lor(orm & wat] are only p>tially miscible ) "o ano!r4 ,if1 !re=e1 *lor(orm is %ak5 ) a l>g] quantity ( wat] ?an x c dissolve1 two lay]s w be =m$ consi/+ "o ( a saturat$ solution ( wat] 9 *lor(orm1 ! o!r ( a saturat$ solution ( *lor(orm 9 wat]4 ,! composition ( ^! two solutions at a temp]ature ( ab\t #ah;deg1 w be repres5t$ by ! po9ts a & b 9 ,fig4 #hd2 a repres5t+ a solution ( ! composition3 *lor(orm1 #ii p] c5t42 wat]1 #a p] c5t42 & b a solution ( ! composition3 *lor(orm1 #j4h p] c5t42 wat]1 #ii4b p] c5t4 ,:5 acetic acid is add$1 x di/ributes itself betwe5 ! two liquid lay]s1 & two conjugate t]n>y solutions1 consi/+ ( *lor(orm1 wat]1 & acetic acid are !reby produc$ :i* are 9 equilibrium ) "o ano!r1 & ! composition ( :i* w be repres5t$ by two po9ts inside ! triangle4 ,9 ?is way a s]ies ( pairs ( t]n>y solutions w be obta9$ by ! addition ( acetic acid to ! mixture ( *lor(orm & wat]4 ,by ?is addition1 also1 n only d ! two liquid phases become increas+ly ri* 9 acetic acid1 b ! mutual solubility ( ! *lor(orm & wat] increases2 s t ! lay] a becomes relatively ri*] 9 wat]1 & lay] b relatively ri*] 9 *lor(orm4 ,?is is se5 f ! foll[+ table1 :i* gives ! p]c5tage composition ( diff]5t conjugate t]n>y solutions at #ah;deg4 ---------------------------------------- --------------------------------- ,heavi] lay]4 ,light] lay]4 ---------------------------------------- --------------------------------- ,*lor(orm4 ,wat]4 ,acetic acid4 ,*lor(orm4 ,wat]4 ,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 ! cont9u$ addition ( acetic acid1 ! composition ( ! successive conjugate solutions 9 equilibrium ) "o ano!r becomes1 z ! table %[s1 m ne>ly ! same1 & a po9t is at l5g? rea*$ at :i* ! two solutions become id5tical4 ,?is w !re=e be a critical po9t 7p4 #ih74 ,increas$ addition ( acetic acid beyond ?is po9t w lead to a s+le homog5e\s solution4 ,^! relation%ips are repres5t$ graphically by ! curve a,kb1 ,fig4 #hd4 ,! po9ts on ! bran* a,k repres5t ! composition ( ! solutions relatively ri* 9 *lor(orm 7heavi] lay]71 ^? on ! curve b,k ! composition ( solutions relatively ri* 9 wat] 7light] lay]72 & ! po9ts on ^! two bran*es repres5t+ conjugate solutions are jo9$ toge!r by tie-l9es4 ,?us1 ! po9ts a'b' repres5t conjugate solutions1 & ! l9e a'b' is a tie-l9e4 ,illu/ration3 ,,fig4 #hd4 ,s9ce1 n[1 acetic acid :5 add$ to a het]og5e\s mixture ( *lor(orm & wat] does n ent] 9 equal am\nts into ! two lay]s1 b 9 am\nts dep5d+ on its coeffici5t ( di/ribution betwe5 *lor(orm & wat]1#cba ! #bdc tie-l9es w n be p>allel to ,,ab1 b w be incl9$ at an angle4 ,z ! solutions become m ne>ly ! same1 ! tie-l9es dim9i% 9 l5g?1 & at la/1 :5 ! conjugate solutions become id5tical1 %r9k to a po9t4 ,= ! reason t ! tie-l9es are1 9 g5]al1 n p>allel to ! side ( ! triangle1 ! critical po9t at :i* ! tie-l9e vani%es w n be at ! summit ( ! curve1 b some:]e bel[ ?is1 z repres5t$ by ! po9t ,k4 ,! curve a,kb1 fur!r1 =ms ! b\nd>y betwe5 ! het]og5e\s & homog5e\s sy/ems4 ,a mixture ( *lor(orm1 wat]1 & acetic acid repres5t$ by any po9t outside ! curve a,kb1 w =m only "o homog5e\s phase2 :ile any mixture repres5t$ by a po9t )9 ! curve1 w sep>ate into two lay]s hav+ ! composition repres5t$ by ! ends ( ! tie-l9e pass+ ?r\gh t po9t4 ,?us1 a mixture ( ! total composition x1 w sep>ate into two lay]s hav+ ! composition a' & b' respectively4 ,s9ce ?ree compon5ts exi/+ 9 ?ree phases 7two liquid & a vap\r phase7 con/itute a biv>iant sy/em1 ! f9al result1 i4e4 ! composition ( ! two lay]s & ! total vap\r pressure1 w n dep5d m]ely on ! temp]ature1 z 9 ! case ( two-compon5t sy/ems 7p4 #ajb71 b also on ! composition ( ! mixture ) :i* we />t4 ,at con/ant temp]ature1 h[ev]1 all mixtures1 ! composition ( :i* is repres5t$ by a po9t on "o & ! same tie-l9e1 w sep>ate into ! same two liquid phases1 al?\gh ! relative am\nts ( ! two phases w v>y4 ,if we omit ! vap\r phase1 ! condition ( ! sy/em w dep5d on ! pressure z well z on ! temp]ature & composition ( ! initial mixture4 ,by keep+ ! pressure con/ant1 e4g4 at atmosph]ic pressure 7by work+ ) op5 vessels71 ! sy/em aga9 becomes biv>iant4 ,we see1 !re=e1 t ! position ( ! curve a,kb1 or1 9 o!r words1 ! composition ( ! diff]5t conjugate t]n>y solutions1 w v>y ) ! temp]ature1 & only ) ! temp]ature1 if we assume ei!r con/ancy ( pressure or ! pres5ce ( ! vap\r phase4 ,s9ce at ! critical po9t ! condition is impos$ t ! two liquid phases become id5tical1 "o degree ( fre$om is !reby #bdd lo/1 & !re=e only "o degree ( fre$om rema9s4 ,! critical po9t1 !re=e1 dep5ds on ! temp]ature1 & only on ! temp]ature2 always on ! assumption1 ( c\rse1 t ! pressure is con/ant1 or t a vap\r phase is pres5t4 ,fig4 #hd1 !re=e1 repres5ts an iso!rmal 7p4 #bci74 ,x is ( importance to note t ! composition ( ! diff]5t t]n>y solutions obta9$ by ! addition ( acetic acid to a het]og5e\s mixture ( *lor(orm & wat]1 w dep5d n only on ! am\nt ( acetic acid add$1 b also on ! relative am\nts ( *lor(orm & wat] at ! comm5cem5t4 ,suppose1 = example1 t we />t ) *lor(orm & wat] 9 ! proportions repres5t$ by ! po9t c' 7,fig4 #hd74 ,on mix+ ^!1 two liquid lay]s hav+ ! composition a & b respectively w be =m$4 ,s9ce by ! addition ( acetic acid ! relative am\nts ( ^! two sub/ances 9 ! sy/em z a :ole _c und]go alt]ation1 ! total composition ( ! diff]5t t]n>y sy/ems :i* w be obta9$ mu/ be repres5t$ by a po9t on ! l9e ,cc' 7p4 #bch74 ,?us1 = example1 by ! addition ( acetic acid a sy/em may be obta9$1 ! total composition ( :i* is repres5t$ by ! po9t c4 ,su* a sy/em1 h[ev]1 w sep>ate into two conjugate t]n>y solutions1 ! composition ( :i* w be repres5t$ by ! ends ( ! tie-l9e pass+ ?r\gh ! po9t c4 ,s long z ! total composition ( ! sy/em lies bel[ ! po9t ,s1 i4e4 ! po9t ( int]section ( ! l9e ,cc' ) ! b\nd>y curve1 two liquid lay]s w be =m$2 :ile all sy/ems hav+ a total composition repres5t$ by a po9t on ! l9e ,cc'1 above ,s1 w =m only "o homog5e\s solution4 ,f ! figure1 also1 x is evid5t t z ! am\nt ( acetic acid is increas$1 ! relative am\nts ( ! two liquid lay]s =m$ diff] m & m until at ,s a limit+ position is rea*$1 :5 ! am\nt ( ! "o liquid lay] dw9dles to n\ght1 & only "o solution rema9s4 ,! same reason+ c be c>ri$ ?r\gh = diff]5t initial am\nts ( *lor(orm & wat]1 b x w\ld be fruitless to discuss all ! diff]5t sy/ems :i* c be obta9$4 ,! reason = ! prec$+ discussion 0 to %[ t #bde al?\gh ! addition ( acetic acid to a mixture ( *lor(orm & wat] w1 9 all cases1 lead ultimately to a limit+ sy/em1 beyond :i* homog5eity occurs1 t po9t is n necess>ily ! critical po9t4 ,on ! contr>y1 9 ord] t addition ( acetic acid %all lead to ! critical mixture1 x is necess>y to />t ) a b9>y mixture ( *lor(orm & wat] 9 ! proportions repres5t$ by ! po9t c'4 ,9 ?is case1 addition ( acetic acid w give rise to a s]ies ( conjugate t]n>y solutions1 ! composition ( :i* w gradually approa* to "o ano!r1 & at la/ become id5tical4 ,f ! =ego+ x w be evid5t t ! am\nt ( acetic acid requir$ to produce a homog5\s solution1 w dep5d on ! relative am\nts ( *lor(orm & wat] f :i* we />t1 & c be asc]ta9$ by jo9+ ! corn] ,c ) ! po9t on ! l9e ,,ab repres5t+ ! total composition ( ! initial b9>y sy/em4 ,! po9t :]e ?is l9e int]sects ! b\nd>y curve a,kb w indicate ! m9imum am\nt ( acetic acid :i*1 "u ^! p>ticul> conditions1 is necess>y to give "o homog5e\s solution4 ,retrograde ,solubility4--,z a consequ5ce ( ! fact t acetic acid di/ributes itself unequally betwe5 *lor(orm & wat]1 & ! critical po9t ,k1 !re=e1 does n lie at ! summit ( ! curve1 x is possible to />t ) a homog5e\s solution 9 :i* ! p]c5tage am\nt ( acetic acid is great] ?an at ! critical po9t1 & to pass f ?is fir/ to a het]og5\s & !n aga9 to a homog5\s sy/em m]ely by alt]+ ! relative am\nts ( *lor(orm & wat]4 ,?is ph5om5on1 to :i* ! t]m retrograde solubility is appli$1 w be obs]v$ n only 9 ! case ( *lor(orm1 wat]1 & acetic acid1 b 9 all o!r sy/ems 9 :i* ! critical po9t lies bel[ ! highe/ po9t ( ! b\nd>y curve = het]og5e\s sy/ems4 ,?is w be se5 f ! diagram1 ,fig4 #he4 ,/>t+ ) ! homog5e\s sy/em repres5t$ by x1 9 :i*1 !re=e1 ! conc5tration ( ,c is great] ?an 9 ! critical mixture 7,k71 if ! relative am\nts ( ,a & ,b are alt]$ 9 ! direction xx'1 :ile ! am\nt ( ,c is ma9ta9$ con/ant1 ! sy/em w become het]og5e\s :5 ! composition rea*es ! po9t y1 & w rema9 #bdf het]og5e\s ) *ang+ composition until ! po9t y' is pass$1 :5 x w aga9 become homog5e\s4 ,if ! relative conc5tration ( ,c is increas$ above t repres5t$ by ! l9e ,,ss1 ?is ph5om5on w1 ( c\rse1 no long] be obs]v$4 ,illu/ration3 ,,fig4 #he4 ,relation%ips simil> to ^? describ$ = *lor(orm1 wat]1 & acetic acid are also f\nd 9 ! case ( a numb] ( o!r trios1 e4g4 e!r1 wat]1 & alcohol2 *lor(orm1 wat]1 & alcohol4#cbb ,!y h also be5 obs]v$ 9 ! case ( a consid]able numb] ( molt5 metals4#cbc ,?us1 molt5 lead & silv]1 z well z molt5 z9c & silv]1 mix 9 all proportions2 b molt5 lead & z9c are only p>tially miscible ) "o ano!r4 ,:5 melt$ toge!r1 !re=e1 ! la/ two metals w sep>ate into two liquid lay]s1 "o ri* 9 lead1 ! o!r ri* 9 z9c4 ,if silv] is n[ add$1 & ! temp]ature ma9ta9$ above ! freez+ po9t ( ! mixture1 ! silv] passes = ! mo/ "p1 9 accordance ) ! law ( di/ribution1 into ! upp] lay]1 :i* is ri* 9 z9c2 silv] be+ m soluble 9 molt5 z9c ?an 9 molt5 lead4 ,?is is cle>ly %[n by ! foll[+ figures3--#cbd #bdg ---------------------------------------- ---------- ,heavi] alloy4 ,light] alloy4 ---------------------------------------- ---------- ,p]c5tage am\nt ( ,p]c5tage am\nt ( ,silv]4 ,lead4 ,z9c4 ,silv]4 ,lead4 ,z9c4 ---------------------------------------- ---------- #a4be #if4fi #b4jf #ch4ia #c4ab #eg4ig #a4ga #if4dc #a4hf #de4ja #c4cg #ea4fb #e4ee #ic4af #a4bi #ed4ic #d4ba #dj4hf ---------------------------------------- ---------- ,! numb]s 9 ! same horizontal r[ give ! composition ( ! conjugate alloys1 & x is evid5t t ! upp] lay] consi/s almo/ entirely ( silv] & z9c4 ,on all[+ ! mixture to cool slightly1 ! upp] lay] solidifies fir/1 & c be sep>at$ f ! /ill molt5 lead lay]4 ,x is on ?is behavi\r ( silv] t[>ds a mixture ( molt5 lead & z9c t ! ,p>kes's me?od = ! desilv]ization ( lead dep5ds4#cbe ,if alum9ium is also add$1 a /ill l>g] proportion ( silv] passes into ! light] lay]1 & ! desilv]ization ( ! lead is m complete4#cbf ,illu/ration3 ,,fig4 #hf4 ,illu/ration3 ,,fig4 #hg4 ,! ,influ5ce ( ,temp]ature4--,z has already be5 said1 a t]n>y sy/em exi/+ 9 ?ree phases possesses two degrees ( fre$om2 & ! /ate ( ! sy/em is !re=e dep5d5t n only on ! relative conc5tration ( ! compon5ts1 b also on ! temp]ature4 ,z ! temp]ature *anges1 !re=e1 ! b\nd>y curve ( ! het]og5e\s sy/em w also alt]2 & 9 ord] to repres5t ?is alt]ation we %all make use ( ! "r prism1 9 :i* ! temp]ature is measur$ upw>ds4 ,9 ?is way ! b\nd>y curve passes into a b\nd>y surface 7call$ a d9]ic surface71 z %[n 9 ,fig4 #hf4 ,9 ?is figure ! curve akb is ! iso!rmal = ! t]n>y sy/em2 ! curve a,kb %[s ! *ange 9 ! b9>y sy/em ,,ab ) ! temp]ature1 ) #bdh a critical po9t at ,k4 ,?is curve has ! same mean+ z ^? giv5 9 ,*apt] ,,vi4 ,! curve k,k is a critical curve jo9+ toge!r ! critical po9ts ( ! diff]5t iso!rmals4 ,9 su* a case z is %[n 9 ,fig4 #hf1 !re does n exi/ any real critical temp]ature = ! t]n>y sy/em1 = z ! temp]ature is rais$1 ! am\nt ( ,c 9 ! critical solution becomes less & less1 & at ,k only two compon5ts1 ,a & ,b1 are pres5t4 ,9 ! case1 h[ev]1 repres5t$ 9 ,fig4 #hg1 a real t]n>y critical po9t is f\nd4 ,9 ?is figure ak'b is an iso!rmal1 ak is ! curve = ! b9>y sy/em1 & ,k is ! t]n>y critical po9t4 ,all po9ts outside ! helmet-%ap$ b\nd>y surface repres5t homog5e\s t]n>y solutions1 :ile all po9ts )9 ! surface belong to het]og5e\s sy/ems4 ,above ! temp]ature ( ! po9t ,k1 ! ?ree compon5ts are miscible 9 all proportions4 ,an example ( a t]n>y sy/em yield+ su* a b\nd>y surface is t consi/+ ( ph5ol1 wat]1 & acetone4#cbg ,9 ?is case ! critical temp]ature ,k is #ib;deg1 & ! composition at ?is t]n>y critical po9t is-- ,wat] #ei p] c5t4 ,acetone #ab ,ph5ol #bi ,illu/ration3 ,,fig4 #hh4 ,! diff]5ce betwe5 ! two classes ( sy/ems j m5tion$1 is se5 v cle>ly by a glance at ! ,figs4 #hh & #hi1 :i* %[ ! projection ( ! iso!rmals on ! base ( ! prism4 ,9 ,fig4 #hh1 ! projections yield p>aboloid curves1 ! two bran*es ( :i* are cut by "o side ( ! triangle2 & ! critical po9t is repres5t$ by a po9t on #bdi ?is side4 ,9 ! second case 7,fig4 #hi71 h[ev]1 ! projections ( ! iso!rmals =m ellipsoidal curves surr\nd+ ! supreme critical po9t1 :i* n[ lies inside ! triangle4 ,at l[] temp]atures1 ^! iso!rmal b\nd>y curves are cut by a side ( ! triangle2 at ! critical temp]ature1 k1 ( ! b9>y sy/em ,,ab1 ! b\nd>y curve t\*es ! side ,,ab1 :ile at /ill high] temp]atures ! b\nd>y curve comes to lie entirely )9 ! triangle4 ,at any giv5 temp]ature1 !re=e1 betwe5 ! critical po9t ( ! b9>y sy/em 7k71 & ! supreme critical po9t ( ! t]n>y sy/em 7,k71 ea* pair ( ! ?ree compon5ts are miscible ) "o ano!r 9 all proportions2 = ! region ( het]og5e\s sy/ems is n[ b\nd$ by a clos$ curve ly+ entirely )9 ! triangle4 ,outside ?is curve only homog5e\s sy/ems are f\nd4 ,b9>y mixtures1 !re=e1 repres5t$ by any po9t on "o ( ! sides ( ! triangle mu/ be homog5e\s1 = !y all lie outside ! b\nd>y curve = het]og5e\s /ates4 ,illu/ration3 ,,fig4 #hi4 #b4 ,! ?ree compon5ts c =m two pairs ( p>tially miscible liquids4 ,9 ! case ( ! ?ree compon5ts wat]1 alcohol1 & succ9ic nitrile1 wat] & alcohol are miscible 9 all proportions1 b n s wat] & succ9ic nitrile1 or alcohol & succ9ic nitrile4 ,illu/ration3 ,,fig4 #ij4 ,illu/ration3 ,,fig4 #ia4 ,z we h already se5 7p4 #abb71 wat] & succ9ic nitrile c =m two liquid lay]s betwe5 ! temp]atures #ah4e;deg & #ee4e;deg2 :ile alcohol & nitrile c =m two liquid lay]s betwe5 #ac;deg & #ca;deg4 ,if1 !n1 betwe5 ^! two temp]ature limits1 alcohol is add$ to a het]og5e\s mixture ( wat] & nitrile1 or wat] is add$ to a mixture ( alcohol & nitrile1 two het]og5e\s t]n>y sy/ems w be =m$1 #bej & two b\nd>y curves w be obta9$ 9 ! triangul> diagram1 z %[n 9 ,fig4 #ij4cbh ,on *ang+ ! temp]ature1 ! b\nd>y curves w also und]go alt]ation1 9 a mann] simil> to t j discuss$4 ,z ! temp]ature falls1 ! two curves w spread out m & m into ! c5tre ( ! triangle1 & might at la/ meet "o ano!r2 :ile at /ill l[] temp]atures we may imag9e ! curves /ill fur!r exp&+ s t ! two het]og5e\s regions fl[ into "o ano!r & =m a b& on ! triangul> diagram 7,fig4 #ia74 ,?is1 c]ta9ly1 has n be5 realiz$ 9 ! case ( ! ?ree compon5ts m5tion$1 because at a temp]ature high] ?an t at :i* ! two het]og5e\s regions c\ld fuse toge!r1 solid sep>ates out4 ,illu/ration3 ,,fig4 #ib4 ,! gradual expansion ( a p>aboloid into a b&-l area ( het]og5e\s t]n>y sy/ems1 has1 h[ev]1 be5 obs]v$ 9 ! case ( wat]1 ph5ol1 & anil9e4#cbi ,9 ,fig4 #ib are %[n ?ree iso!rmals1 viz4 ^? = #adh;deg1 #ie;deg1 & #ej;deg4 ,at #adh;deg1 wat] & anil9e =m two lay]s hav+ ! composition-- ,wat]1 #hc4e p] c5t4 wat]1 #bj p] c5t4 & ,anil9e1 #af4e anil9e1 #hj #bea & ! critical po9t k' has ! composition-- ,wat]1 #fe2 ph5ol1 #ac4b2 anil9e1 #ba4h p] c5t4 ,at #ie;deg1 ! composition ( ! two b9>y solutions is-- ,wat]1 #ic p] c5t4 wat] #h p] c5t4 & ,anil9e1 #g anil9e1 #ib :ile ! po9t k has ! composition ,wat]1 #fi4i2 ph5ol1 #bf4f2 anil9e1 #c4e p] c5t4 ,at #ej;deg1 ! region ( het]og5e\s /ates n[ =ms a b&1 & ! two lay]s =m$ by wat] & anil9e h ! composition-- ,wat]1 #if4e p] c5t4 wat]1 #e4e p] c5t4 & ,anil9e1 #c4e anil9e1 #id4e :ile ! two lay]s =m$ by wat] & ph5ol h ! composition-- ,wat]1 #hi p] c5t4 wat]1 #ch p] c5t4 & ,ph5ol1 #aa ph5ol1 #fb ,all mixtures ( wat]1 ph5ol1 & anil9e1 !re=e1 ! composition ( :i* is repres5t$ by any po9t )9 ! b& abcd1 w =m two t]n>y solutions2 :ile if ! composition is repres5t$ by a po9t outside ! b&1 only "o homog5e\s solution w be produc$4 #c4 ,! ?ree compon5ts =m ?ree pairs ( p>tially miscible liquids4 ,illu/ration3 ,,fig4 #ic4 ,! ?ird *ief case :i* c occur is t no two ( ! compon5ts are completely miscible ) "o ano!r4 ,9 ?is case1 !re=e1 we %all obta9 ?ree p>aboloid b\nd>y curves1 z %[n 9 ,fig4 #ic4 ,if1 n[1 we imag9e ^! ?ree curves to exp& 9 t[>ds ! c5tre ( ! triangle1 z might happ51 = example1 by l[]+ ! temp]ature1 a po9t w #beb be rea*$ at :i* ! curves p>tly ov]lap1 & we %all get ! appe>ance %[n 9 ,fig4 #id4 ,! po9ts a1 b1 & c repres5t ! po9ts :]e ! ?ree curves cut1 & ! triangle abc is a region :]e ! curves ov]lap4 ,f ?is diagram we c see t any mixture hav+ a composition repres5t$ by a po9t 9 "o ( ! cle> spaces at ! corn]s ( ! l>g] triangle1 w =m a homog5e\s solution2 if ! composition corresponds to any po9t ly+ 9 "o ( ! quadrilat]al regions x#a1 x#b or x#c1 two t]n>y solutions w be =m$2 :ile1 if ! composition is repres5t$ by any po9t 9 ! inn] triangle1 sep>ation into ?ree lay]s w occur4 ,illu/ration3 ,,fig4 #id4 ,s9ce 9 ! cle> regions at ! corn]s ( ! triangle we h ?ree compon5ts 9 two phases1 liquid & vap\r1 ! sy/ems h ?ree degrees ( fre$om4 ,at con/ant temp]ature1 !re=e1 ! condition ( ! sy/em is n def9$ until ! conc5trations ( two ( ! compon5ts are fix$4 ,a sy/em belong+ to "o ( ! quadrilat]al spaces has1 z we h se51 two degrees ( fre$om2 besides ! temp]ature1 "o conc5tration mu/ be fix$4 ,la/ly1 a sy/em ! composition ( :i* falls )9 ! inn] triangle abc1 w =m ?ree lay]s1 & w !re=e possess only "o degree ( fre$om4 ,if ! temp]ature is fix$1 ! composition ( ! ?ree lay]s is also det]m9$1 viz4 t ( ! po9ts a1 b1 & c respectively2 & a *ange 9 ! composition ( ! orig9al mixture c lead only to a diff]5ce 9 ! relative am\nts ( ! ?ree lay]s1 n to a diff]5ce 9 _! composition4 ,an example ( a sy/em :i* c =m ?ree liquid phases is f\nd 9 wat]1 e!r1 & succ9ic nitrile4#ccj 99 99 99 99 99 #bec ,,*apt] ,,xv ,,pres5ce ,,( ,,solid ,,phases ,a4 ,! ,t]n>y ,eutectic ,po9t4--,9 pass+ to ! consid]ation ( ^? t]n>y sy/ems 9 :i* "o or m solid phases c exi/ toge!r ) "o liquid phase1 we %all fir/ discuss n ! solubility curves1 z 9 ! case ( two-compon5t sy/ems1 b ! simpl] relation%ips met ) at ! freez+ po9t4 ,t is1 we %all fir/ ( all exam9e ! freez+ po9t curves ( t]n>y sy/ems4 ,illu/ration3 ,,fig4 #ie4 ,s9ce x is necess>y to take into acc\nt n only ! *ang+ composition ( ! liquid phase1 b also ! v>iation ( ! temp]ature1 we %all employ ! "r prism = ! graphic repres5tation ( ! sy/ems1 z %[n 9 ,fig4 #ie4 ,a1 ,b1 & ,c 9 ?is figure1 !re=e1 d5ote ! melt+ po9ts ( ! pure compon5ts4 ,if we />t ) ! compon5t ,a at its melt+ po9t1 & add ,b1 :i* is capable ( dissolv+ 9 liquid ,a1 ! freez+ po9t ( ,a w be l[]$2 &1 simil>ly1 ! freez+ po9t ( ,b by addition ( ,a4 ,9 ?is way we get ! freez+ po9t curve ,ak#a;,b = ! b9>y sy/em2 k#a2 be+ an eutectic po9t4 ,?is curve w ( c\rse lie 9 ! plane =m$ by "o face ( ! prism4 ,9 a simil> mann] we obta9 ! freez+ po9t curves ,ak#b;,c & ,bk#c;,c4 ,^! curves give ! composition ( ! b9>y liquid phases 9 equilibrium #bed ) "o ( ! pure compon5ts1 or at ! eutectic po9ts1 ) a mixture ( two solid compon5ts4 ,if1 n[1 to ! sy/em repres5t$ say by ! po9t k#a1 a small quantity ( ! ?ird compon5t1 ,c1 is add$1 ! temp]ature at :i* ! two solid phases ,a & ,b c exi/ 9 equilibrium ) ! liquid phase is l[]$2 & ?is depression ( ! eutectic po9t is all ! great] ! l>g] ! addition ( ,c4 ,9 ?is way we obta9 ! curve k#a,k1 :i* slopes inw>ds & d[nw>ds1 & indicates ! v>y+ composition ( ! t]n>y liquid phase ) :i* a mixture ( solid ,a & ,b are 9 equilibrium4 ,simil>ly1 ! curves k#b,k & k#c,k are ! correspond+ eutectic curves = ,a & ,c1 & ,b & ,c 9 equilibrium ) t]n>y solutions4 ,at ! po9t ,k1 ! ?ree solid compon5ts are 9 equilibrium ) ! liquid phase2 & ?is po9t1 !re=e1 repres5ts ! l[e/ temp]ature atta9able ) ! ?ree compon5ts giv54 ,ea* ( ! t]n>y eutectic curves1 z !y may be call$1 is produc$ by ! int]section ( two surfaces1 :ile at ! t]n>y eutectic po9t1 ?ree surfaces1 viz4 ,ak#a,kk#b1 ,bk#a,kk#c1 & ,ck#a,kk#c int]sect4 ,any po9t on "o ( ^! surfaces repres5ts a t]n>y solution 9 equilibrium ) only "o compon5t 9 ! solid /ate2 ! l9es or curves ( int]section ( ^! repres5t equilibria ) two solid phases1 :ile at ! po9t ,k1 ! t]n>y eutectic po9t1 !re are ?ree solid phases 9 equilibrium ) a liquid & a vap\r phase4 ,! surfaces j m5tion$ repres5t biv>iant sy/ems4 ,"o compon5t 9 ! solid /ate c exi/ 9 equilibrium ) a t]n>y liquid phase "u v>y+ conditions ( temp]ature & conc5tration ( ! compon5ts 9 ! solution2 & be=e ! /ate ( ! sy/em is def9$1 ^! two v>iables1 temp]ature & composition ( ! liquid phase1 mu/ be fix$4 ,on ! o!r h&1 ! curves =m$ by ! int]section ( ^! planes repres5t univ>iant sy/ems2 at a giv5 temp]ature two solid phases c exi/ 9 equilibrium ) a t]n>y solution1 only :5 ! latt] has a def9ite composition4 ,la/ly1 ! t]n>y eutectic po9t1 ,k1 repres5ts an inv>iant sy/em2 ?ree solid phases c exi/ 9 equilibrium ) a t]n>y solution1 only :5 ! latt] has "o fix$ composition & :5 ! temp]ature has a def9ite value4 ,?is eutectic po9t1 !re=e1 #bee has a p]fectly def9ite position1 dep5d+ only on ! nature ( ! ?ree compon5ts4 ,in/ead ( employ+ ! prism1 ! *ange 9 ! composition ( ! t]n>y solutions c also be indicat$ by means ( ! projections ( ! curves k#a,k1 k#b,k1 & k#c,k on ! base ( ! prism1 ! p>ticul> temp]ature be+ writt5 beside ! diff]5t eutectic po9ts & curves4 ,?is is %[n 9 ,fig4 #if4 ,illu/ration3 ,,fig4 #if4 ,! numb]s :i* are giv5 9 ?is diagram ref] to ! eutectic po9ts = ! sy/em bismu?--lead--t91 ! data = :i* are z foll[s3--#cca ---------------------------------------- ---------------------------- ,melt+ po9t ( ,p]c5tage composition ( ,temp]ature ( b9>y pure metal4 b9>y eutectic mixture4 eutectic po9t4 ---------------------------------------- ---------------------------- ,bi ,pb ,sn ,bismu?1 #bfh;deg #ee #de -- ,bi--,pb1 #abg;deg ,lead1 #cbe;deg #eh -- #db ,bi--,sn1 #acc;deg ,t91 #bcb;deg -- #cg #fc ,pb--,sn1 #ahb;deg ---------------------------------------- ---------------------------- ---------------------------------------- ---------- ,p]c5tage composition ( ,temp]ature ( t]n>y t]n>y eutectic mixture4 eutectic po9t4 ---------------------------------------- ---------- ,bi ,pb ,sn #eb #cb #af #if;deg ---------------------------------------- ---------- ,=mation ( ,comp\nds4--,9 ! case j discuss$1 ! compon5ts cry/alliz$ out f solution 9 ! pure /ate4 ,if1 h[ev]1 comb9ation c take place betwe5 two ( ! compon5ts1 ! relation%ips w be some:at diff]5t2 ! curves :i* are obta9$ 9 su* a case be+ repres5t$ 9 ,fig4 #ig4 ,f ! figure1 we see t ! two compon5ts ,b #bef & ,c =m a comp\nd1 & ! freez+ po9t curve ( ! b9>y sy/em has !re=e ! =m %[n 9 ,fig4 #fd 7p4 #bji74 ,fur!r1 !re are two t]n>y eutectic po9ts1 ,k#a & ,k#b1 ! solid phases pres5t be+ ,a1 ,b1 & comp\nd1 & ,a1 ,c1 & comp\nd respectively4 ,illu/ration3 ,,fig4 #ig4 ,! p>ticul> po9t1 n[1 to :i* x is desir$ to draw att5tion is ?is4 ,suppose ! t]n>y eutectic curves project$ on a plane p>allel to ! face ( ! prism conta9+ ,b & ,c1 i4e4 suppose ! conc5trations ( ! two compon5ts ,b & ,c1 betwe5 :i* int]action c occur1 express$ 9 t]ms ( a con/ant am\nt ( ! ?ird compon5t ,a1#ccb curves w !n be obta9$ :i* are 9 e respect analog\s to ! freez+ po9t curves ( b9>y sy/ems4 ,?us1 suppose ! eutectic curves k#a,k & k#b,k 9 ,fig4 #ie project$ on ! face ,,bc ( ! prism1 !n evid5tly a curve w be obta9$ consi/+ ( two bran*es meet+ 9 an eutectic po9t4 ,on ! o!r h&1 ! projection ( ! t]n>y eutectic curves 9 ,fig4 #ig on ! face ,,bc ( ! prism1 w give a curve consi/+ ( ?ree portions1 z %[n by ! outl9e k#a,k#a,k#bk#b 9 ,fig4 #ig4 ,v>i\s examples ( ?is h be5 /udi$1 & ! foll[+ table conta9s "s ( ! data = ! sy/em e?yl5e bromide 7,a71 picric acid 7,b71 & beta-naph?ol 7,c71 obta9$ by ,bruni4#ccc #beg ---------------------------------------- --------------------------------- ,temp]ature ,solid phases pres5t4 ---------------------------------------- --------------------------------- ,po9t k#a #i4da;deg ,e?yl5e bromide1 picric acid4 ,curve k#a,k#a -- ,po9t ,k#a #i4cb;deg ,e?yl5e bromide1 picric acid1 & beta-naph?ol picrate4 ,curve ,k#a;,d',k#b -- ,e?yl5e bromide1 beta-naph?ol picrate4 ,po9t ,d' #i4ge;deg ,po9t ,k#b #h4hi;deg beta-naph?ol1 & picrate4 ,curve ,k#bk#b -- beta-naph?ol4 ,po9t k#b #i4jd;deg ---------------------------------------- --------------------------------- ,f :at has be5 said1 x w be app>5t t if ! t]n>y eutectic curve ( a ?ree-compon5t sy/em 79 :i* "o ( ! compon5ts is pres5t 9 con/ant am\nt7 is det]m9$1 x w be possible to /ate1 f ! =m ( curve obta9$1 :e!r or n ! two compon5ts pres5t 9 v>y+ am\nt cry/allize out pure or comb9e ) "o ano!r to =m a comp\nd4 ,x may be left to ! read] to "w out ! curves = ! o!r possible sy/ems2 b x w be app>5t1 t ! projections ( ! t]n>y eutectic curves 9 ! mann] giv5 w yield a s]ies ( curves alike 9 all po9ts to ! b9>y curves giv5 9 ,figs4 #fc-fe1 pp4 #bjh-baj4 ,s9ce1 f ! me?od ( inve/igation1 ! temp]atures ( ! eutectic curves w dep5d on ! melt+ po9t ( ! ?ird compon5t 7,a71 x is possible1 by employ+ sub/ances ) widely diff]+ melt+ po9ts1 to inve/igate ! int]action ( ! two compon5ts 7e4g4 two optical antipodes7 ,b & ,c ov] a range ( temp]ature2 & ?us det]m9e ! range ( /ability ( ! comp\nd1 if "o is =m$4 ,s9ce1 9 "s cases1 two sub/ances :i* at "o temp]ature =m mix$ cry/als comb9e at ano!r temp]ature to =m a def9ite comp\nd1 ! relation%ips :i* h j be5 describ$ c be employ$1 & inde$1 h be5 employ$1 to det]m9e ! temp]ature at :i* ?is *ange occurs4#ccd ,by means ( ?is me?od1 ,adriani f\nd t bel[ #ajc;deg i-camphoroxime exi/s z a racemic comp\nd1 :ile above #beh t temp]ature x occurs z a racemic mix$ cry/al#cce 7cf4 p4 #bai74 ,b4 ,equilibria at ,high] ,temp]atures4 ,=mation ( ,d\ble ,salts4--,aft] hav+ /udi$ ! relation%ips :i* are f\nd 9 ! neighb\rhood ( ! freez+ po9ts ( ! compon5ts1 we n[ pass to ! discussion ( ! equilibria :i* are met ) at high] temp]atures4 ,9 ?is connection we %all conf9e ! discussion entirely to ! sy/ems =m$ ( two salts & wat]1 deal+ m p>ticul>ly ) ^? cases 9 :i* ! wat] is pres5t 9 relatively l>ge am\nt & acts z solv5t4 ,fur!r1 9 /udy+ ^! sy/ems1 "o re/riction mu/ be made1 viz4 t ! s+le salts are salts ei!r ( ! same base or ( ! same acid2 or are1 9 o!r words1 capable ( yield+ a common ion 9 solution4 ,su* a re/riction is necess>y1 because o!rwise ! sy/em w\ld be "o n ( ?ree b ( f\r compon5ts4#ccf ,transition ,po9t4--,z is v well kn[n1 !re exi/ a numb] ( hydrat$ salts :i*1 on be+ heat$1 und]go app>5t p>tial fusion2 & 9 ,*apt] ,v4 ! behavi\r ( su* hydrates 0 m fully /udi$ 9 ! light ( ! ,phase ,rule4 ,glaub]'s salt1 or sodium sulphate decahydrate1 = example1 on be+ heat$ to a temp]ature ( ab\t #cb4e;deg1 p>tially liquefies1 ow+ to ! fact t ! wat] ( cry/allization is split (f & anhydr\s sodium sulphate =m$1 z %[n by ! equation-- ,na#b,,s#d1aj;,h#b,o ,na#b,,s#d #aj;,h#b,o ,! temp]ature ( #cb4e;deg1 x 0 le>n$1 con/itut$ a transition po9t = ! decahydrate & anhydr\s salt plus wat]2 decomposition ( ! hydrat$ salt occurr+ above ?is temp]ature1 comb9ation ( ! anhydr\s salt & wat] bel[ x4 ,analog\s ph5om5a are met ) 9 sy/ems con/itut$ ( two salts & wat] 9 :i* ! =mation ( d\ble salts c take place4 ,?us1 = example1 if d-sodium potassium #bei t>trate is heat$ to above #ee;deg1 app>5t p>tial fusion occurs1 & ! two s+le salts1 d-sodium t>trate & d-potassium t>trate1 are deposit$1 ! *ange :i* occurs be+ repres5t$ by ! 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 ! o!r h&1 if sodium & potassium t>trates are mix$ ) wat] 9 ! proportions %[n on ! "r side ( ! equation1 ! sy/em w rema9 p>tially liquid s long z ! temp]ature is ma9ta9$ above #ee;deg 79 a clos$ vessel to prev5t loss ( wat]71 b on all[+ ! temp]ature to fall bel[ ?is po9t1 complete solidification w ensue1 ow+ to ! =mation ( ! hydrat$ d\ble salt4 ,bel[ #ee;deg1 !re=e1 ! hydrat$ d\ble salt is ! /able sy/em1 :ile above ?is temp]ature ! two s+le salts plus saturat$ solution are /able4#ccg ,a simil> behavi\r is f\nd 9 ! case ( ! d\ble salt copp] dipotassium *loride 7,cu,cl#b1b,k,cl1#b;,h#b,o or ,cu,k#b;,cl#d1b;,h#b,o74#cch ,:5 ?is salt is heat$ to #ib;deg1 p>tial liquefaction occurs1 & ! orig9al blue plate-%ap$ cry/als give place to br[n cry/all9e ne$les & :ite cubes2 :ile on all[+ ! temp]ature to fall1 re-=mation ( ! blue d\ble salt ensues4 ,! temp]ature #ib;deg is1 !re=e1 a transition po9t at :i* ! rev]sible reaction-- ,cu,k#b;,cl#d1b;,h#b,o -- ,cu,k,cl#c ,k,cl #b;,h#b,o takes place4 ,! decomposition ( sodium potassium t>trate1 or ( copp] dipotassium *loride1 diff]s 9 s f> f t ( ,glaub]'s salt t two new solid phases are =m$2 & 9 ! case ( copp] dipotassium *loride1 "o ( ! decomposition products is itself a d\ble salt4 ,9 ! two examples ( d\ble salt decomposition :i* h j be5 m5tion$1 suffici5t wat] 0 yield$ to cause a p>tial liquefaction2 b o!r cases are kn[n :]e ?is is n s4 ,?us1 :5 copp] calcium acetate is heat$ to a #bfj temp]ature ( #ge;deg1 al?\gh decomposition ( ! d\ble salt into ! two s+le salts occurs z repres5t$ by ! 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 ! am\nt ( wat] split (f is insuffici5t to give ! appe>ance ( p>tial fusion1 &1 !re=e1 only a *ange 9 ! cry/als is obs]v$4 ,! prec$+ examples1 9 :i* decomposition ( ! d\ble salt 0 effect$ by a rise ( temp]ature1 7 *os5 = fir/ consid]ation z be+ m analog\s to ! case ( ,glaub]'s salt2 b n a few examples are kn[n :]e ! rev]se *ange takes place1 =mation ( ! d\ble salt occurr+ above ! transition po9t1 & decomposition into ! con/itu5t salts bel[ x4 ,in/ances ( ?is behavi\r are f\nd 9 ! case ( ! =mation ( a/racanite f sodium & magnesium sulphates1 & ( sodium ammonium racemate f ! two sodium ammonium t>trates1 to :i* ref]5ce w be made lat]4 ,betwe5 ^! v>i\s sy/ems1 h[ev]1 !re is no ess5tial diff]5ce2 & :e!r decomposition or =mation ( ! d\ble salt occurs at temp]atures above ! transition po9t1 w ( c\rse dep5d on ! heat ( *ange at t po9t4 ,=1 9 accordance ) van't ,h(f's law ( movable equilibrium 7p4 #eh71 t *ange w take place at ! high] temp]ature :i* is accompani$ by an absorption ( heat4 ,if1 !re=e1 ! =mation ( ! d\ble salt f ! s+le salts is accompani$ by an absorption ( heat1 ! d\ble salt w be =m$ f ! s+le salts on rais+ ! temp]ature2 b if ! rev]se is ! case1 !n ! d\ble salt on be+ heat$ w decompose into ! con/itu5t salts4#cdj ,9 ^? cases1 n[1 :i* h s f> be5 /udi$1 ! *ange at ! transition po9t is accompani$ by a tak+ up or a splitt+ (f ( wat]2 & 9 su* cases ! g5]al rule c be giv51 t if ! wat] ( cry/allization ( ! two con/itu5t #bfa salts toge!r is great] ?an t ( ! d\ble salt1 ! latt] w be produc$ f ! =m] on rais+ ! temp]ature 7e4g4 a/racanite f sodium & magnesium sulphates72 b if ! d\ble salt conta9s m wat] ( cry/allization ?an ! two s+le salts1 increase ( temp]ature w effect ! decomposition ( ! d\ble salt4 ,:5 we seek = ! connection betwe5 ?is rule & ! law ( van't ,h(f1 x is f\nd 9 ! fact t ! heat effect involv$ 9 ! hydration or dehydration ( ! salts is mu* great] ?an t ( ! o!r *anges :i* occur1 & det]m9es1 !re=e1 ! sign ( ! total heat effect4#cda ,vap\r ,pressure4 ,qu9tuple ,po9t4--,9 ! case ( ,glaub]'s salt1 we saw t at a c]ta9 temp]ature ! vap\r pressure curve ( ! hydrat$ salt cut t ( ! saturat$ solution ( anhydr\s sodium sulphate4 ,t po9t1 x w be rememb]$1 0 a quadruple po9t at :i* ! f\r phases sodium sulphate decahydrate1 anhydr\s sodium sulphate1 solution1 & vap\r1 c\ld co-exi/2 & 0 also ! po9t ( int]section ( ! curves = f\r univ>iant sy/ems4 ,9 ! case ( ! =mation ( d\ble salts1 simil> relation%ips are met )2 & also c]ta9 diff]5ces1 due to ! fact t we are n[ deal+ ) sy/ems ( ?ree compon5ts4 ,two cases w be *os5 "h = brief description1 "o 9 :i* =mation1 ! o!r 9 :i* decomposition ( ! d\ble salt occurs ) rise ( temp]ature4 ,on heat+ a mixture ( sodium sulphate decahydrate & magnesium sulphate heptahydrate1 x is f\nd t at #bb;deg p>tial liquefaction occurs ) =mation ( a/racanite4 ,at ?is temp]ature1 !re=e1 !re c coexi/ ! five phases-- ,na#b,,s#d1aj;,h#b,o2 ,mg,s,o#d1g;,h#b,o2 ,na#b,mg7,,s#d7b1d;,h#b,o2 solution2 vap\r4 ,?is con/itutes1 !re=e1 a qu9tuple po9t2 & s9ce !re are ?ree compon5ts pres5t 9 five phases1 ! sy/em is inv>iant4 ,?is po9t1 also1 w be ! po9t ( int]section ( curves = five univ>iant sy/ems1 :i*1 9 ?is case1 mu/ ea* be compos$ ( f\r phases4 ,^! sy/ems are-- #bfb ,i4 ,na#b,,s#d1aj;,h#b,o2 ,mg,s,o#d1g;,h#b,o2 ,na#b,mg7,,s#d7b1d;,h#b,o2 vap\r4 ,,ii4 ,na#b,,s#d1aj;,h#b,o2 ,mg,s,o#d1g;,h#b,o2 solution2 vap\r4 ,,iii4 ,mg,s,o#d1g;,h#b,o2 ,na#b,mg7,,s#d7b1d;,h#b,o2 solution2 vap\r4 ,,iv4 ,na#b,,s#d1aj;,h#b,o2 ,na#b,mg7,,s#d7b1d;,h#b,o2 solution2 vap\r4 ,v4 ,na#b,,s#d1aj;,h#b,o2 ,mg,s,o#d1g;,h#b,o2 ,na#b,mg7,,s#d7b1d;,h#b,o2 solution4 ,illu/ration3 ,,fig4 #ih4 ,on repres5t+ ! vap\r pressures ( ^! diff]5t sy/ems graphically1 a diagram is obta9$ su* z is %[n 9 ,fig4 #ih1cdb ! curves be+ numb]$ 9 accordance ) ! above li/4 ,:5 ! sy/em ,i4 is heat$1 ! vap\r pressure increases until at ! qu9tuple po9t ! liquid phase 7solution7 is =m$1 & x w !n dep5d on ! relative am\nts ( ! diff]5t phases :e!r on fur!r heat+ !re is =m$ sy/em ,,iii41 ,,iv41 or ,v4 ,if ei!r ( ! fir/ two is produc$1 we %all obta9 ! vap\r pressure ( ! solutions saturat$ ) respect to bo? d\ble salt & "o ( ! s+le salts2 :ile if ! vap\r phase disappe>s1 !re w be obta9$ ! pressure ( ! cond5s$ sy/ems =m$ ( d\ble salt1 two s+le salts & solution4 ,?is curve1 !re=e1 indicates ! *ange ( ! transition po9t ) pressure2 & s9ce 9 ! ord9>y det]m9ations ( ! transition po9t 9 op5 vessels1 we are 9 reality deal+ ) cond5s$ sy/ems "u ! pressure ( #a atm41 x w be evid5t t ! transition po9t does n accurately co9cide ) ! qu9tuple po9t 7at :i* ! sy/em is "u ! pressure ( its own vap\r74 ,z 9 ! case ( o!r cond5s$ sy/ems1 h[ev]1 pressure has only a slight influ5ce on ! temp]ature ( ! transition po9t4 ,:e!r or n pressure raises or l[]s ! transition po9t w dep5d on :e!r trans=mation is accompani$ by an increase or #bfc dim9ution ( volume 7!orem ( ,le ,*ateli]1 p4 #eh74 ,9 ! case ( ! =mation ( a/racanite1 expansion occurs1 & ! transition po9t w !re=e be rais$ by increase ( pressure4 ,al?\gh measurem5ts h n be5 made 9 ! case ( ?is sy/em1 ! exi/5ce ( su* a curve has be5 exp]im5tally v]ifi$ 9 ! case ( copp] & calcium acetates & wat] 7v4 infra74#cdc ,illu/ration3 ,,fig4 #ii4 ,! vap\r pressure diagram 9 ! case ( copp] calcium acetate & wat] 7,fig4 #ii71 is almo/ ! rev]se ( t already discuss$4 ,9 ?is case1 ! d\ble salt decomposes on heat+1 & ! decomposition is accompani$ by a contraction4 ,curve ,i4 is ! vap\r pressure curve = d\ble salt1 two s+le salts 7p4 #bfj71 & vap\r2 curves ,,ii4 & ,,iii4 give ! vap\r pressures ( solutions saturat$ ) respect to d\ble salt & "o ( ! s+le salts2 curve ,,iv4 is ! curve ( pressures = ! solutions saturat$ ) respect to ! two s+le salts2 :ile curve ,v4 aga9 repres5ts ! *ange ( ! transition po9t ) pressure4 ,on exam9+ ?is diagram1 x is se5 t :]eas #bfd a/racanite c\ld exi/ bo? above & bel[ ! qu9tuple po9t1 copp] calcium acetate c exi/ only bel[ ! qu9tuple po9t4 ,?is behavi\r is f\nd only 9 ^? cases 9 :i* ! d\ble salt is decompos$ by rise ( temp]ature1 & :]e ! decomposition is accompani$ by a dim9ution ( volume4#cdd ,z already m5tion$1 ! decomposition ( copp] calcium acetate into ! s+le salts & saturat$ solution is accompani$ by a contraction1 & x 0 !re=e to be expect$ t increase ( pressure w\ld l[] ! transition po9t4 ,?is expectation ( !ory 0 confirm$ by exp]im5t1 = van't ,h(f & ,spr+ f\nd t al?\gh ! transition po9t "u atmosph]ic pressure is ab\t #ge;deg1 decomposition ( ! d\ble salt took place ev5 at ! ord9>y temp]ature :5 ! pressure 0 increas$ to #fjjj atm4#cde ,solubility ,curves at ! ,transition ,po9t4--,at ! transition po9t1 z has already be5 %[n1 ! d\ble salt & ! two con/itu5t salts c exi/ 9 equilibrium ) ! same solution4 ,! transition po9t1 !re=e1 mu/ be ! po9t ( int]section ( two solubility curves2 ! solubility curve ( ! d\ble salt & ! solubility curve ( ! mixtures ( ! two con/itu5t salts4 ,x %\ld be not$ "h t we are n deal+ ) ! solubility curves ( ! s+le salts sep>ately1 = s9ce ! sy/ems are compos$ ( ?ree compon5ts1 a s+le solid phase c1 at a giv5 temp]ature1 be 9 equilibrium ) solutions ( diff]5t composition1 & two solid phases 9 contact ) solution 7& vap\r7 are !re=e necess>y to give an univ>iant sy/em4 ,! same applies1 ( c\rse1 to ! solubility ( ! d\ble salt2 = a d\ble salt also con/itutes a s+le phase1 & c !re=e exi/ 9 equilibrium ) solutions ( v>y+ composition4 ,if1 h[ev]1 we make ! re/riction 7:i* we d = ! pres5t7 t ! d\ble salt is n decompos$ by wat]1 !n ! solution w conta9 ! con/itu5t salts 9 ! same relative proportions z !y are conta9$ 9 ! d\ble salt1 & ! sy/em may !re=e be reg>d$ z "o ( two compon5ts1 viz4 d\ble salt & wat]4 ,9 ?is case "o solid phase is suffici5t1 ) solution & #bfe vap\r1 to give an univ>iant sy/em2 & at a giv5 temp]ature1 !re=e1 ! solubility w h a p]fectly def9ite value4 ,s9ce 9 almo/ all cases ! solubility is det]m9$ 9 op5 vessels1 we %all 9 ! foll[+ discussion consid] t ! vap\r phase is abs5t1 & t ! sy/em is "u a con/ant pressure1 t ( ! atmosph]e4 ,) ?is re/riction1 !re=e1 f\r phases w con/itute an inv>iant sy/em1 ?ree phases an univ>iant1 & two phases a biv>iant sy/em4 ,x has already be5 le>n$ t 9 ! case ( sodium sulphate & wat]1 ! solubility curve ( ! salt und]goes a sudd5 *ange 9 direction at ! transition po9t1 & t ?is is accompani$ by a *ange 9 ! solid phase 9 equilibrium ) ! solution4 ,! same behavi\r is also f\nd 9 ! case ( d\ble salts4 ,to illu/rate ?is1 we %all briefly discuss ! solubility relations ( a few d\ble salts1 beg9n+ ) "o ( ! simple/ cases1 t ( ! =mation ( rubidium racemate f rubidium d- & l-t>trates4 ,! solubilities are repres5t$ diagrammatically 9 ,fig4 #ajj1 ! num]ical data be+ conta9$ 9 ! foll[+ table1 9 :i* ! solubility is express$ z ! numb] ( gram-molecules ,rb#b;,c#d;,h#d,o#f 9 #ajj gm4-molecules ( wat]4#cdf ---------------------------------------- ----------------------- ,temp]ature4 ,solubility ( t>trate ,solubility ( racemate4 mixture4 ---------------------------------------- ----------------------- #be;deg #ac4jc #aj4ia #ce;deg -- #ab4fc #dj4d;deg -- #ac4dh #dj4g;deg #ac4df -- #ed;deg #ac4hc -- ---------------------------------------- ----------------------- ,9 ,fig4 #ajj ! curve ,,ab repres5ts ! solubility ( ! racemate1 :ile ,a',,bc repres5ts ! solubility ( ! mix$ t>trates4 ,bel[ ! transition po9t1 !re=e1 ! solubility ( ! racemate is less ?an t ( ! mix$ t>trates4 ,! solution1 saturat$ ) respect to ! latt]1 w be sup]saturat$ ) respect to ! racemate2 & if a nucleus ( ?is is pres5t1 racemate w be deposit$1 & ! mix$ t>trates1 if pres5t 9 equimolecul> am\nts1 w ultimately #bff entirely disappe>1 & only racemate w be left z solid phase4 ,! solution w !n h ! composition repres5t$ by a po9t on ! curve ,,ab4 ,conv]sely1 above ! transition po9t1 ! saturat$ solution ( ! racemate w\ld be sup]saturat$ ) respect to ! two t>trates1 & trans=mation into ! latt] w\ld ensue4 ,if1 !re=e1 a solution ( equimolecul> proportions ( rubidium d- & l-t>trates is all[$ to evaporate at a temp]ature above #dj;deg1 a mixture ( ! two t>trates w be deposit$2 :ile at temp]atures bel[ #dj;deg ! racemate w sep>ate out4 ,illu/ration3 ,,fig4 #ajj4 ,simil> relation%ips are met ) 9 ! case ( sodium ammonium d- & l-t>trate & sodium ammonium racemate2 b 9 ?is case ! racemate is ! /able =m 9 contact ) solution above ! transition po9t 7#bg;deg74#cdg ,bel[ ! transition po9t1 !re=e1 ! solubility curve ( ! mix$ t>trates w lie bel[ ! solubility curve ( ! racemate4 ,bel[ ! transition po9t1 !re=e1 sodium ammonium racemate w break up 9 contact ) solution into a mixture ( sodium ammonium d- & l-t>trates4 ,at a high] temp]ature1 #ce;deg1 sodium ammonium racemate und]goes decomposition into sodium racemate & ammonium racemate4#cdh ,! behavi\r ( sodium ammonium racemate is ( int]e/ f ! fact t x 0 ! fir/ racemic sub/ance to be resolv$ into its optically active =ms by a process ( cry/allization4 ,on neutraliz+ a solution ( racemic t>t>ic acid1 half ) soda & half ) ammonia1 & all[+ ! solution to evaporate1 ,pa/eur#cdi obta9$ a mixture ( sodium ammonium #bfg d- & l-t>trates4 ,s9ce ,pa/eur 0 unaw>e ( ! exi/5ce ( a transition po9t1 ! success ( 8 exp]im5t 0 due to ! happy *ance t he all[$ ! solution to evaporate at a temp]ature bel[ #bg;deg2 = _h he employ$ a temp]ature above ?is1 sep>ation ( ! racemate into ! two enantiomorph\s =ms w\ld n h occurr$4 ,= ?is reason ! attempt ( ,/a$el to p]=m ! same resolution met only ) failure4#cej ,decomposition ( ! ,d\ble ,salt by ,wat]4--,9 ! two cases j describ$1 ! solubility relation%ips at ! transition po9t are ( a simpl] "* ?an 9 ! case ( mo/ d\ble salts4 ,if1 at a temp]ature above ! transition po9t1 a mixture ( rubidium d- & l-t>trates 9 equimolecul> proportions is br\ght 9 contact ) wat] a solution w be obta9$1 :i* is saturat$ ) respect to bo? enantiomorph\s =ms2 & s9ce ! solubility ( ! two optical antipodes is id5tical1 & ! effect ( "o on ! solubility ( ! o!r also ! same1 ! solution w conta9 equimolecul> am\nts ( ! d- & l-salt4 ,if1 n[1 ! solution is cool$ d[n 9 contact ) ! solid salts to j bel[ ! transition po9t1 x becomes sup]saturat$ ) respect to ! racemate1 & ?is w be deposit$4 ,! solution !reby becomes unsaturat$ ) respect to ! mixture ( ! active salts1 & ^! mu/ !re=e pass into solution4 ,z ! latt] are equally soluble1 equal am\nts ( ea* w dissolve1 & a fur!r quantity ( ! racemate w be deposit$4 ,^! processes ( solution & deposition w cont9ue until ! s+le t>trates h completely disappe>$1 & only racemate is left z solid phase4 ,z a consequ5ce ( ! id5tical solubility ( ! two t>trates1 !re=e1 no excess ( ei!r =m w be left on pass+ ?r\gh ! transition po9t4 ,f ?is x w be evid5t t ! racemate c exi/ z s+le solid phase 9 contact ) its saturat$ solution at ! transition po9t2 or1 9 o!r words1 ! racemate is n decompos$ by wat] at ! transition po9t4 ,! same behavi\r w evid5tly be exhibit$ by sodium ammonium racemate at #bg;deg1 = ! two enantiomorph\s sodium ammonium t>trates h also id5tical solubility4 #bfh ,v diff]5t1 h[ev]1 is ! behavi\r (1 say1 a/racanite1 or ( ! majority ( d\ble salts2 = ! solubility ( ! con/itu5t salts is n[ no long] ! same4 ,if1 = example1 excess ( a mixture ( sodium sulphate & magnesium sulphate1 9 equimolecul> proportions1 is br\ght 9 contact ) wat] bel[ ! transition po9t 7#bb;deg71 m magnesium sulphate ?an sodium sulphate w dissolve1 ! solubility ( ^! two salts 9 a common solution be+ giv5 by ! foll[+ figures1 :i* express numb] ( molecules ( ! salt 9 #ajj molecules ( wat]4#cea ,,composition ,,( ,,solutions ,,saturat$ ,,) ,,respect ,,to ,na#b,,s#d1aj;,h#b,o ,,& ,mg,s,o#d1g;,h#b,o4 ---------------------------------------- ,temp]ature4 ,na#b,,s#d4 ,mg,s,o#d4 ---------------------------------------- #ah4e;deg #b4af #d4eg #bd4e;deg #c4dc #d4fh ---------------------------------------- ,at ! transition po9t1 !n1 x is evid5t t ! solution conta9s m magnesium sulphate ?an sodium sulphate3 & ?is mu/ /ill be ! case :5 a/racanite1 :i* conta9s sodium sulphate & magnesium sulphate 9 equimolecul> proportions1 sep>ates out4 ,if1 !re=e1 ! temp]ature is rais$ slightly above ! transition po9t1 magnesium sulphate & sodium sulphate w pass into solution1 ! =m]1 h[ev]1 9 l>g] quantities ?an ! latt]1 & a/racanite w be deposit$2 & ?is w g on until all ! magnesium sulphate has disappe>$1 & a mixture ( a/racanite & sodium sulphate decahydrate is left z solid phases4 ,s9ce !re are n[ ?ree phases pres5t1 ! sy/em is univ>iant 7by reason ( ! re/riction previ\sly made t ! vap\r phase is abs5t71 & at a giv5 temp]ature ! solution w h a def9ite composition2 z giv5 9 ! foll[+ table3-- ,,composition ,,( ,,solutions ,,saturat$ ,,) ,,respect ,,to ,na#b,mg7,,s#d7b1d;,h#b,o ,,& ,na#b,,s#d1aj;,h#b,o4 ---------------------------------------- ,temp]ature4 ,na#b,,s#d4 ,mg,s,o#d4 ---------------------------------------- #bb;deg #b4ie #d4gj #bd4e;deg #c4de #c4fb ---------------------------------------- #bfi ,f ! above figures1 !re=e1 x w be se5 t at a temp]ature j above ! transition po9t a solution 9 contact ) ! two solid phases1 a/racanite & ,glaub]'s salt1 conta9s a relatively small] am\nt ( sodium sulphate ?an a pure solution ( a/racanite w\ld2 = 9 ?is case !re w\ld be equal molecul> am\nts ( ,na#b,,s#d & ,mg,s,o#d4 ,a solution :i* is saturat$ ) respect to a/racanite alone1 w conta9 m sodium sulphate ?an ! solution saturat$ ) respect to a/racanite plus ,glaub]'s salt1 & ! latt] w !re=e be deposit$4 ,f ?is1 !re=e1 x is cle> t if a/racanite is br\ght 9 contact ) wat] at ab\t ! transition po9t1 x w und]go decomposition ) sep>ation ( ,glaub]'s salt 7sup]saturation be+ exclud$74 ,illu/ration3 ,,fig4 #aja4 ,?is w p]haps be made cle>] by consid]+ ,fig4 #aja4 ,9 ?is diagram ! ord9ates repres5t ! ratio ( sodium sulphate to magnesium sulphate 9 ! solutions1 & ! abscissae repres5t ! temp]atures4 ,! l9e ,,ab repres5ts solutions saturat$ ) respect to a mixture ( ! s+le salts 7p4 #bfh72 ,,bc ref]s to solutions 9 equilibrium ) a/racanite & magnesium sulphate2 :ile ,,bx repres5ts ! composition ( solutions 9 contact ) ! solid phases a/racanite & ,glaub]'s salt4 ,! values ( ! solubility are conta9$ 9 ! foll[+ table1 & 9 t on p4 #bfh1 & are1 z be=e1 express$ 9 gm4-molecules ( salt 9 #ajj gm4-molecules ( wat]4#ceb #bgj ---------------------------------------- --------------------------------- ,a/racanite ,a/racanite ,temp]ature4 sodium sulphate4 magnesium sulphate4 ---------------------------------------- ------------------ ,na#b,,s#d4 ,mg,s,o#d4 ,na#b,,s#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 ! transition po9t ! ratio ( sodium sulphate to magnesium sulphate is approximately #a 3 #a4f4 ,9 ! case ( solutions saturat$ ) respect to bo? a/racanite & ,glaub]'s salt1 ! relative am\nt ( sodium sulphate increases z ! temp]ature rises1 :ile 9 ! solutions saturat$ = a/racanite & magnesium sulphate1 ! ratio ( sodium sulphate to magnesium sulphate decreases4 ,if1 n[1 we consid] only ! temp]atures above ! transition po9t1 we see f ! figure t solutions repres5t$ by po9ts above ! l9e ,,bx conta9 relatively m sodium sulphate ?an solutions 9 contact ) a/racanite & ,glaub]'s salt2 & solutions ly+ bel[ ! l9e ,,bc conta9 relatively m magnesium sulphate ?an solutions saturat$ ) ?is salt & a/racanite4 ,^! solutions w !re=e n be /able1 b w deposit 9 ! "o case1 a/racanite & ,glaub]'s salt1 & 9 ! o!r case1 a/racanite & magnesium sulphate1 until a po9t on ,,bx or ,,bc is rea*$4 ,all solutions1 h[ev]1 ly+ to ! "r ( ,,cbx1 w be unsaturat$ ) respect to ^! two pairs ( salts1 & only ! solutions repres5t$ by ! l9e ,,xy 7& :i* conta9 equimolecul> am\nts ( sodium & magnesium sulphates7 w be saturat$ ) respect to ! pure d\ble salt4 ,transition ,int]val4--,fig4 #aja w also r5d] intelligible a po9t ( great importance 9 connection ) a/racanite1 & ( d\ble salts g5]ally4 ,at temp]atures betwe5 ^? repres5t$ by ! po9ts ,b & ,x1 ! d\ble salt :5 br\ght 9 contact ) wat] w be decompos$ ) sep>ation ( sodium sulphate4 ,above ! temp]ature ( ! po9t #bga ,x1 h[ev]1 ! solution ( ! pure d\ble salt is /able1 because x c /ill take up a little ( ei!r ( ! compon5ts4 ,at temp]atures1 !n1 above t at :i* ! solution 9 contact ) ! d\ble salt & ! less soluble s+le salt1 conta9s ! s+le salts 9 ! ratio 9 :i* !y are pres5t 9 ! d\ble salt1 solution ( ! latt] w take place )\t decomposition4 ,! range ( temp]ature betwe5 t at :i* d\ble salt c beg9 to be =m$ 7! transition po9t7 & t at :i* x ceases to be decompos$ by wat] is call$ ! transition int]val4#cec ,if ! two s+le salts h id5tical solubility at ! transition po9t1 ! transition int]val dim9i%es to n\ght4 ,9 ^? cases :]e ! d\ble salt is ! /able =m bel[ ! transition po9t1 ! transition int]val w ext5d d[nw>ds to a l[] temp]ature4 ,fig4 #aja w !n h ! rev]se =m4 ,summ>y4--,) reg>d to d\ble salts we h le>n$ t _! =mation f & _! decomposition into ! s+le salts1 is connect$ ) a def9ite temp]ature1 ! transition temp]ature4 ,at ?is transition temp]ature two vap\r pressure curves cut1 viz4 a curve ( dehydration ( a mixture ( ! s+le salts & ! solubility curve ( ! d\ble salt2 or ! dehydration curve ( ! d\ble salt & ! solubility curve ( ! mix$ s+le salts4 ,! solubility curves1 also1 ( ^! two sy/ems int]sect at ! transition po9t1 b al?\gh ! =mation ( ! d\ble salt comm5ces at ! transition po9t1 complete /ability 9 contact ) wat] may n be atta9$ till "s temp]ature above 7or bel[7 t po9t4 ,only :5 ! temp]ature is beyond ! transition int]val1 w a d\ble salt dissolve 9 wat] )\t decomposition 7e4g4 ! alums74 99 99 99 99 99 #bgb ,,*apt] ,,xvi ,,iso!rmal ,,curves ,,& ,,! ,,space ,,model ,9 ! prec$+ *apt] we consid]$ ! *anges 9 ! solubility ( d\ble salts & ( mixtures ( _! con/itu5t salts ) ! temp]ature2 not+1 m especially1 ! relation%ips betwe5 ! two sy/ems at ! transition po9t4 ,x is n[ propos$ to conclude ! /udy ( ! ?ree-compon5t sy/ems by discuss+ v briefly ! solubility relations at con/ant temp]ature1 or ! iso!rmal solubility curves4 ,9 ?is way fre% light w be ?r[n on ! *ange 9 ! solubility ( "o compon5t by ! addition ( ano!r compon5t1 & also on ! conditions ( =mation & /able exi/5ce ( d\ble salts 9 solution4 ,) ! help ( ^! iso!rmal curves1 also1 ! ph5om5a ( cry/allization at con/ant temp]ature--ph5om5a :i* h n only a sci5tific int]e/ b also an important be>+ on ! indu/rial prep>ation ( d\ble salts--w be m cle>ly und]/ood4#ced ,a brief description w also be giv5 ( ! me?od ( repres5t+ ! v>iation ( ! conc5tration ( ! two salts 9 ! solution ) ! temp]ature4 ,non-=mation ( ,d\ble ,salts4--,9 ,fig4 #ajb are %[n ! solubility curves ( two salts1 ,a & ,b1 :i* at ! giv5 temp]ature d n =m a d\ble salt4#cee ,! ord9ates repres5t ! am\nt ( ,a1 ! abscissae ! am\nt ( ,b 9 a con/ant am\nt ( ! ?ird compon5t1 ! solv5t4 ,! #bgc po9t ,a1 !re=e1 repres5ts ! solubility ( ! salt ,a at ! giv5 temp]ature2 & simil>ly1 po9t ,b repres5ts ! solubility ( ,b4 ,s9ce we are deal+ ) a ?ree-compon5t sy/em1 "o solid phase 9 contact ) solution w con/itute a biv>iant sy/em 79 ! abs5ce ( ! vap\r phase & "u a con/ant pressure74 ,at any giv5 temp]ature1 !re=e1 ! conc5tration ( ! solution 9 equilibrium ) ! solid c und]go *ange4 ,if1 n[1 to a pure solution ( ,a a small quantity ( ,b is add$1 ! solubility ( ,a w 9 g5]al be alt]$2 z a rule x is dim9i%$1 b sometimes x is increas$4#cef ,! curve ,,ac repres5ts ! v>y+ composition ( ! solution 9 equilibrium ) ! solid compon5t ,a4 ,simil>ly1 ! curve ,,bc repres5ts ! composition ( ! solutions 9 contact ) pure ,b z solid phase4 ,at ! po9t1 ,c1 :]e ^! two curves int]sect1 !re are two solid phases1 viz4 pure ,a & pure ,b1 9 equilibrium ) solution1 & ! sy/em becomes inv>iant4 ,at ?is po9t ! solution is saturat$ ) respect to bo? ,a & ,b1 & at a giv5 temp]ature mu/ h a p]fectly def9ite composition4 ,to take an example1 if we suppose ,a to repres5t sodium sulphate decahydrate1 & ,b1 magnesium sulphate heptahydrate1 & ! temp]ature to be #ah4e;deg 7i4e4 bel[ ! transition po9t71 ! po9t ,c w\ld repres5t a solution conta9+ #b4af gm4-molecules ,na#b,,s#d & #d4eg gm4-molecules ,mg,s,o#d p] #ajj gm4-molecules ( wat] 7p4 #bfh74 ,! curve ,,acb is ! b\nd>y curve = saturat$ solutions2 solutions ly+ outside ?is curve are sup]saturat$1 ^? ly+ )9 ! area ,,acbo1 are unsaturat$4 ,illu/ration3 ,,fig4 #ajb4 ,illu/ration3 ,,fig4 #ajc4 ,illu/ration3 ,,fig4 #ajd4 ,=mation ( ,d\ble ,salt4--,we h already le>n$ 9 ! prec$+ *apt] t if ! temp]ature is outside#ceg ! #bgd transition int]val1 x is possible to prep>e a pure saturat$ solution ( ! d\ble salt4 ,if1 n[1 we suppose ! d\ble salt to conta9 ! two con/itu5t salts 9 equimolecul> proportions1 its saturat$ solution mu/ be repres5t$ by a po9t ly+ on ! l9e :i* bisects ! angle ,,aob2 e4g4 po9t ,d1 ,fig4 #ajc4 ,b a d\ble salt con/itutes only a s+le phase1 & c exi/1 !re=e1 9 contact ) solutions ( v>y+ conc5tration1 z repres5t$ by ,,edf4 ,let u comp>e1 n[1 ! relations betwe5 ! solubility curve = ! d\ble salt1 & ^? = ! two con/itu5t salts4 ,we %all suppose t ! d\ble salt is =m$ f ! s+le salts :5 ! temp]ature is rais$ above a c]ta9 po9t 7z 9 ! =mation ( a/racanite74 ,at a temp]ature bel[ ! transition po9t1 z we h already se51 ! solubility ( ! d\ble salt is great] ?an t ( a mixture ( ! s+le salts4 ,! curve ,,edf1 !re=e1 mu/ lie above ! po9t ,c1 9 ! region repres5t+ solutions sup]saturat$ ) respect to ! s+le salts 7,fig4 #ajd74 ,su* a solution1 h[ev]1 w\ld be meta/able1 & on be+ br\ght 9 contact ) ! s+le salts w\ld deposit ^! & yield a solution repres5t$ by ! po9t ,c4 ,at ?is p>ticul> temp]ature1 !re=e1 ! iso!rmal solubility curve w consi/ ( only two bran*es4 ,illu/ration3 ,,fig4 #aje4 ,suppose1 n[1 t ! temp]ature is t ( ! transition po9t4 ,at ?is po9t1 ! d\ble salt c exi/ toge!r ) ! s+le salts 9 contact ) solution4 ,! solubility curve #bge ( ! d\ble salt mu/1 !re=e1 pass ?r\gh ! po9t ,c1 z %[n 9 ,fig4 #aje4 ,f ?is figure1 n[1 x is se5 t a solution saturat$ ) respect to d\ble salt alone 7po9t ,d71 is sup]saturat$ ) respect to ! compon5t ,a4 ,if1 !n1 at ! temp]ature ( ! transition po9t1 excess ( ! d\ble salt is br\ght 9 contact ) wat]1#ceh & if sup]saturation is exclud$1 ! d\ble salt w und]go decomposition & ! compon5t ,a w be deposit$4 ,! relative conc5tration ( ! compon5t ,b 9 ! solution w1 !re=e1 increase1 & ! composition ( ! solution w be !reby alt]$ 9 ! direction ,,dc4 ,:5 ! solution has ! composition ( ,c1 ! s+le salt ceases to be deposit$1 = at ?is po9t ! solution is saturat$ = bo? d\ble & s+le salt2 & ! sy/em becomes inv>iant4 ,?is diagram expla9s v cle>ly ! ph5om5on ( ! decomposition ( a d\ble salt at ! transition po9t4 ,z is evid5t1 ?is decomposition w occur :5 ! solution :i* is saturat$ at ! temp]ature ( ! transition po9t1 ) respect to ! two s+le salts 7po9t ,c71 does n conta9 ^! salts 9 ! same ratio 9 :i* !y are pres5t 9 ! d\ble salt4 ,if po9t ,c lay on ! dott$ l9e bisect+ ! "r angle1 !n ! pure saturat$ solution ( ! d\ble salt w\ld n be sup]saturat$ ) respect to ei!r ( ! s+le salts1 & ! d\ble salt w\ld1 !re=e1 n be decompos$ by wat]4 ,z has already be5 m5tion$1 ?is behavi\r is f\nd 9 ! case ( optically active isom]ides1 ! solubilities ( :i* are id5tical4 ,at ! transition po9t1 !re=e1 ! iso!rmal curve also consi/s ( two bran*es2 b ! po9t ( int]section ( ! two bran*es n[ repres5ts a solution :i* is saturat$ n #bgf only ) respect to ! s+le salts1 b also = ! d\ble salt 9 pres5ce ( ! s+le salts4 ,we h j se5 t by a *ange ( temp]ature ! two solubility curves1 t = ! two s+le salts & t = ! d\ble salt1 7 made to approa* "o ano!r 7cf4 ,figs4 #ajd & #aje74 ,9 ! previ\s *apt]1 h[ev]1 we f\nd t on pass+ ! transition po9t to ! region ( /ability = ! d\ble salt1 ! solution :i* is saturat$ = a mixture ( ! two con/itu5t salts1 is sup]saturat$ = ! d\ble salt4 ,9 ?is case1 !re=e1 po9t ,c mu/ lie above ! solubility curve ( ! pure d\ble salt 7,fig4 #ajf71 & a solution ( ! composition ,c1 if br\ght 9 contact ) d\ble salt1 w deposit ! latt]4 ,if ! s+le salts 7 also pres5t1 !n z ! d\ble salt sep>at$ out1 ! s+le salts w\ld pass into solution1 because s long z ! two s+le salts are pres5t1 ! composition ( ! solution mu/ rema9 unalt]$4 ,if "o ( ! s+le salts disappe> be=e ! o!r1 !re w be left d\ble salt plus ,a or d\ble salt plus ,b1 accord+ to :i* 0 9 excess2 & ! composition ( ! solution w be ei!r t repres5t$ by ,d 7saturat$ = d\ble salt plus ,a71 or t ( ! po9t ,f 7saturat$ = d\ble salt plus ,b74 ,illu/ration3 ,,fig4 #ajf4 ,9 connection ) ! iso!rmal repres5t$ 9 ,fig4 #ajf1 x %\ld be not$ t at ?is p>ticul> temp]ature a solution saturat$ ) respect to ! pure d\ble salt is no long] sup]saturat$ = "o ( ! s+le salts 7po9t ,d72 s t at ! temp]ature ( ?is iso!rmal ! d\ble salt is n decompos$ by wat]4 ,at ?is temp]ature1 fur!r1 ! b\nd>y curve consi/s ( ?ree bran*es ,,ad1 ,,df1 & ,,fb1 :i* give ! composition ( ! solutions 9 equilibrium ) pure ,a1 d\ble salt1 & pure ,b respectively2 :ile ! po9ts ,d & ,f repres5t solutions saturat$ = d\ble salt plus ,a & d\ble salt plus ,b4 ,on cont9u+ to alt] ! temp]ature 9 ! same direction #bgg z be=e1 ! relative %ift+ ( ! solubility curves becomes m m>k$1 z %[n 9 ,fig4 #ajg4 ,at ! temp]ature ( ?is iso!rmal1 ! solution saturat$ = ! d\ble salt n[ lies 9 a region ( di/9ct unsaturation ) respect to ! s+le salts2 & ! d\ble salt c n[ exi/ z solid phase 9 contact ) solutions conta9+ bo? relatively m ( ,a 7curve ,,ed71 & relatively m ( ,b 7curve ,,df71 ?an is conta9$ 9 ! d\ble salt itself4 ,illu/ration3 ,,fig4 #ajg4 ,transition ,int]val4--,f :at has be5 said1 & f an exam9ation ( ! iso!rmal diagrams1 ,figs4 #ajd-ajg1 x w be se5 t by a v>iation ( ! temp]ature we c pass f a condition :]e ! d\ble salt is q incapable ( exi/+ 9 contact ) solution 7sup]saturation be+ exclud$71 to a condition :]e ! exi/5ce ( ! d\ble salt 9 pres5ce ( solution becomes possible2 only 9 ! pres5ce1 h[ev]1 ( "o ( ! s+le salts 7transition po9t1 ,fig4 #aje74 ,a fur!r *ange ( temp]ature leads to a condition :]e ! /able exi/5ce ( ! pure d\ble salt 9 contact ) solution j becomes possible 7,fig4 #ajf72 & f ?is po9t onw>ds1 pure saturat$ solutions ( ! d\ble salt c be obta9$ 7,fig4 #ajg74 ,at any temp]ature1 !re=e1 betwe5 t repres5t$ by ,fig4 #aje1 & t repres5t$ by ,fig4 #ajf1 ! d\ble salt und]goes p>tial decomposition1 ) deposition ( "o ( ! con/itu5t salts4 ,! temp]ature range betwe5 ! transition po9t & ! temp]ature at :i* a /able saturat$ solution ( ! pure d\ble salt j beg9s to be possible1 is kn[n z ! transition int]val 7p4 #bgj74 ,z ! figures %[1 ! transition int]val is limit$ on ! "o side by ! transition temp]ature1 & on ! o!r by ! temp]ature at :i* ! solution saturat$ = d\ble salt & ! less soluble ( ! s+le salts1 conta9s ! compon5t salts 9 ! same ratio z !y are pres5t 9 ! d\ble salt4 ,! great] ! diff]5ce 9 ! solubility ( ! s+le salts1 ! l>g] w be ! transition int]val4 #bgh ,iso!rmal ,evaporation4--,! iso!rmal solubility curves are ( great importance = obta9+ an insight into ! behavi\r ( a solution :5 subject$ to iso!rmal evaporation4 ,to simplify ! discussion ( ! relation%ips f\nd "h1 we %all /ill suppose t ! d\ble salt conta9s ! s+le salts 9 equimolecul> proportions2 & we %all1 9 ! fir/ in/ance1 suppose t ! unsaturat$ solution ) :i* we comm5ce1 also conta9s ! s+le salts 9 ! same ratio4 ,! composition ( ! solution mu/1 !re=e1 be repres5t$ by "s po9t ly+ on ! l9e ,,od1 ! bisectrix ( ! "r angle4 ,f :at has be5 said1 x is evid5t t :5 ! =mation ( a d\ble salt c occur1 ?ree temp]ature int]vals c be di/+ui%$1 viz4 ! s+le-salt int]val1 ! transition int]val1 & ! d\ble-salt int]val4#cei ,:5 ! temp]ature lies 9 ! fir/ int]val1 evaporation leads fir/ ( all to ! cry/allization ( "o ( ! s+le salts1 & !n to ! sep>ation ( bo? ! s+le salts toge!r4 ,9 ! second temp]ature int]val1 evaporation aga9 leads1 9 ! fir/ place1 to ! deposition ( "o ( ! s+le salts1 & aft]w>ds to ! cry/allization ( ! d\ble salt4 ,9 ! ?ird temp]ature int]val1 only ! d\ble salt cry/allizes out4 ,?is w become cle>] f :at foll[s4 ,illu/ration3 ,,fig4 #ajh4 ,illu/ration3 ,,fig4 #aji4 ,if an unsaturat$ solution ( ! two s+le salts 9 equimolecul> proportion 7e4g4 po9t x1 ,fig4 #ajh7 is evaporat$ at a temp]ature at :i* ! =mation ( d\ble salt is impossible1 ! compon5t ,a1 ! solubility curve ( :i* is #bgi cut by ! l9e ,,od1 w fir/ sep>ate out2 ! solution w !reby become ri*] 9 ,b4 ,on cont9u$ evaporation1 m ,a w be deposit$1 & ! composition ( ! solution w *ange until x atta9s ! composition repres5t$ by ! po9t ,c1 :5 bo? ,a & ,b w be deposit$1 & ! composition ( ! solution w rema9 un*ang$4 ,! result ( evaporation w !re=e be a mixture ( ! two compon5ts4 ,if ! =mation ( d\ble salt is possible1 b if ! temp]ature lies )9 ! transition int]val1 ! relations w be repres5t$ by a diagram l ,fig4 #aji4 ,iso!rmal evaporation ( ! solution ,x w lead to ! deposition ( ! compon5t ,a1 & ! composition ( ! solution w alt] 9 ! direction ,,de2 at ! latt] po9t ! d\ble salt w be =m$1 & ! composition ( ! solution w rema9 un*ang$ s long z ! two solid phases are pres5t4 ,z c be se5 f ! diagram1 h[ev]1 ! solution 9 ,e conta9s less ( compon5t ,a ?an is conta9$ 9 ! d\ble salt4 ,deposition ( ! d\ble salt at ,e1 !re=e1 w\ld lead to a relative decrease 9 ! conc5tration ( ,a 9 ! solution1 & to c\nt]balance ?is1 ! salt :i* sep>at$ out at ! comm5cem5t mu/ r$issolve4 ,s9ce ! salts 7 orig9ally pres5t 9 equimolecul> proportions1 ! f9al result ( evaporation w be ! pure d\ble salt4 ,if :5 ! solution has rea*$ ! po9t ,e ! salt ,a :i* _h sep>at$ out is remov$1 d\ble salt only w be left z solid phase4 ,at a giv5 temp]ature1 h[ev]1 a s+le solid phase c exi/ 9 equilibrium ) solutions ( diff]5t composition4 ,if1 !re=e1 iso!rmal evaporation is cont9u$ aft] ! removal ( ! salt ,a1 d\ble salt w be deposit$1 & ! composition ( ! solution w *ange 9 ! direction ,,ef4 ,at ! po9t ,f ! salt ,b w sep>ate out1 & on evaporation bo? d\ble salt & ! salt ,b w be deposit$4 ,9 ! =m] case 7:5 ! salt ,a disappe>s on evaporation7 we are deal+ ) an incongru5tly saturat$ solution2 b 9 ! latt] case1 :]e bo? solid phases cont9ue to be deposit$1 ! solution is said to be congru5tly saturat$4#cfj ,a congru5tly saturat$ solution is "o f :i* ! #bhj solid phases are cont9u\sly deposit$ dur+ iso!rmal evaporation to dryness1 :]eas 9 ! case ( incongru5tly saturat$ solutions1 at lea/ "o ( ! solid phases disappe>s dur+ ! process ( evaporation4 ,illu/ration3 ,,fig4 #aaj4 ,la/ly1 if ! temp]ature lies outside ! transition int]val1 iso!rmal evaporation ( an unsaturat$ solution ( ! composition ,x 7,fig4 #aaj7 w lead to ! deposition ( pure d\ble salt f beg9n+ to end4 ,if a solution ( ! composition ,y is evaporat$1 ! compon5t ,a w fir/ be deposit$ & ! composition ( ! solution w alt] 9 ! direction ( ,e1 at :i* po9t d\ble salt w sep>ate out4 ,s9ce ! solution at ?is po9t conta9s relatively m ( ,a ?an is pres5t 9 ! d\ble salt1 bo? ! d\ble salt & ! s+le salt ,a w be deposit$ on cont9u$ evaporation1 9 ord] t ! composition ( ! solution %all rema9 un*ang$4 ,9 ! case ( solution ,z1 fir/ compon5t ,b & aft]w>ds ! d\ble salt w be deposit$4 ,! result w1 !re=e1 be a mixture ( d\ble salt & ! salt ,b 7congru5tly saturat$ solutions71 ,x may be /at$ "h t ! same relation%ips z h be5 expla9$ above = d\ble salts are also f\nd 9 ! resolution ( racemic comp\nds by means ( optically active sub/ances 7?ird me?od ( ,pa/eur74 ,9 ?is case ! s+le salts are d\bly active sub/ances 7e4g4 /ry*n9e-d-t>trate & /ry*n9e-l-t>trate71 & ! d\ble salt is a p>tially racemic comp\nd4#cfa ,cry/allization ( ,d\ble ,salt f ,solutions conta9+ ,excess ( ,"o ,compon5t4--,"o m case ( iso!rmal cry/allization may be discuss$4 ,x is well kn[n t a d\ble salt :i* is decompos$ by pure wat] c nev]!less be obta9$ pure by cry/allization f a solution conta9+ excess ( "o ( ! s+le salts 7e4g4 9 ! case ( c>nallite74 ,s9ce ! d\ble salt is p>tially decompos$ by wat]1 ! temp]ature ( ! exp]im5t mu/ be )9 ! transition #bha int]val1 & ! relations w1 !re=e1 be repres5t$ by a diagram l ,fig4 #aji4 ,if1 n[1 in/ead ( />t+ ) an unsaturat$ solution conta9+ ! s+le salts 9 equimolecul> proportions1 we comm5ce ) "o 9 :i* excess ( "o ( ! salts is pres5t1 z repres5t$ by ! po9t ,y1 iso!rmal evaporation w cause ! composition to alt] 9 ! direction ,,yd'1 ! relative am\nts ( ! s+le salts rema9+ ! same ?r\gh\t4 ,:5 ! composition ( ! solution rea*es ! po9t ,d'1 pure d\ble salt w be deposit$4 ,! sep>ation ( d\ble salt w1 h[ev]1 cause a relative decrease 9 ! conc5tration ( ! salt ,a1 & ! composition ( ! solution w1 !re=e1 alt] 9 ! direction ,d',f4 ,if ! evaporation is discont9u$ be=e ! solution has atta9$ ! composition ,f1 only d\ble salt w h sep>at$ out4 ,ev5 )9 ! transition int]val1 !re=e1 pure d\ble salt c be obta9$ by cry/allization1 provid$ ! orig9al solution has a composition repres5t$ by a po9t ly+ betwe5 ! two l9es ,,oe & ,,(4 ,s9ce1 z already %[n1 ! composition ( ! solution alt]s on evaporation 9 ! direction ,,ef1 x w be be/ to employ a solution hav+ a composition ne> to ! l9e ,,oe4 ,=mation ( ,mix$ ,cry/als4--,if ! two s+le salts ,a & ,b d n cry/allize out pure f solution1 b =m an unbrok5 s]ies ( mix$ cry/als1 x is evid5t t an inv>iant sy/em _c be produc$4 ,! solubility curve w !re=e be cont9u\s f ,a to ,b2 ! liquid solutions ( v>y+ composition be+ 9 equilibrium ) solid solutions also ( v>y+ composition4 ,if1 h[ev]1 ! s]ies ( mix$ cry/als is n cont9u\s1 !re w be a break 9 ! solubility curve at :i* two solid solutions ( diff]5t composition w be 9 equilibrium ) liquid solution4 ,?is1 ( c\rse1 w con/itute an inv>iant sy/em1 & ! po9t w correspond to ! po9t ,c 9 ,fig4 #ajh4 ,a full discussion ( ^! sy/ems w\ld1 h[ev]1 lead u too f>1 & ! above indication ( ! behavi\r mu/ suffice4#cfb #bhb ,application to ! ,*>act]ization ( ,racemates4--,! =m ( ! iso!rmal solubility curves is also ( great value = det]m9+ :e!r an inactive sub/ance is a racemic comp\nd or a conglom]ate ( equal proportions ( ! optical antipodes4#cfc ,z has already be5 po9t$ out1 ! =mation ( racemic comp\nds f ! two enantiomorph\s isom]ides1 is analog\s to ! =mation ( d\ble salts4 ,! iso!rmal solubility curves1 also1 h a simil> =m4 ,9 ! case ( ! latt]1 inde$1 ! relation%ips are simplifi$ by ! fact t ! two enantiomorph\s =ms h id5tical solubility1 & ! solubility curves are !re=e symmetrical to ! l9e bisect+ ! angle ( ! co-ord9ates4 ,fur!r1 ) ! exception ( ! p>tially racemic comp\nds to be m5tion$ lat]1 !re is no transition int]val4 ,9 ,fig4 #aaa1 are giv5 diagrammatically two iso!rmal solubility curves = optically active sub/ances4 ,f :at has be5 said 9 ! imm$iately prec$+ pages1 ! figure ought really to expla9 itself4 ,! upp] iso!rmal acb repres5ts ! solubility relations :5 ! =mation ( a racemic comp\nd is exclud$1 z1 e4g4 9 ! case ( rubidium d- & l-t>trates above ! transition po9t 7p4 #bfe74 ,! solution at ! po9t c is1 ( c\rse1 inactive1 & is unaffect$ by addition ( ei!r ! d- or l- =m4 ,! l[] iso!rmal1 on ! o!r h&1 w\ld be obta9$ at a temp]ature at :i* ! racemic comp\nd c\ld be =m$4 ,! curve a'e is ! solubility curve = ! l- =m2 b'f1 t = ! d- =m2 & edf1 t = ! racemic comp\nd 9 pres5ce ( solutions ( v>y+ conc5tration4 ,! po9t d corresponds to saturation = ! pure racemic comp\nd4 ,illu/ration3 ,,fig4 #aaa4 ,f ^! curves n[1 x w be evid5t t x w be possible1 9 any giv5 case1 to decide :e!r or n an inactive body is a mixture or a racemic comp\nd4 ,= ?is purpose1 #bhc two solubility det]m9ations are made1 fir/ ) ! inactive mat]ial alone 79 excess71 & !n ) ! inactive mat]ial plus excess ( "o ( ! optically active =ms4 ,if we are deal+ ) a mixture1 ! two solutions ?us obta9$ w be id5tical2 bo? w h ! composition correspond+ to ! po9t c1 & w be inactive4 ,if1 h[ev]1 ! inactive mat]ial is a racemic comp\nd1 !n two diff]5t solutions w be obta9$2 namely1 an inactive solution correspond+ to ! po9t d 7,fig4 #aaa71 & an active solution correspond+ ei!r to e or to f1 accord+ to :i* enantiomorph\s =m 0 add$4 ,p>tially racemic comp\nds4#cfd ,9 ?is case we are no long] deal+ ) enantiomorph\s =ms1 & ! solubility ( ! two oppositely active isom]ides is no long] ! same4 ,! symmetry ( ! solubility curves !re=e disappe>s1 & a figure is obta9$ :i* is id5tical 9 its g5]al =m ) t f\nd 9 ! case ( ord9>y d\ble salts 7,fig4 #aab74 ,9 ?is case !re is a transition int]val4 ,illu/ration3 ,,fig4 #aab4 ,! curves acb belong to a temp]ature at :i* ! p>tially racemic comp\nd _c be =m$2 a'dfb'1 to ! temp]ature at :i* ! comp\nd j beg9s to be /able 9 contact ) wat]1 & aed'f'b belongs to a temp]ature at :i* ! p>tially racemic comp\nd is q /able 9 contact ) wat]4 ,suppose n[ solubility det]m9ations1 made 9 ! fir/ case ) ! orig9al mat]ial alone1 & !n ) ! orig9al body plus ea* ( ! two comp\nds1 =m$ f ! enantiomorph\s sub/ances sep>ately1 !n if ! orig9al body 0 a mixture1 id5tical solutions w be obta9$ 9 all ?ree cases 7po9t c72 if x 0 a p>tially racemic comp\nd1 ?ree diff]5t solutions 7e1 d'1 & f'7 w be obta9$ if ! temp]ature 0 outside ! transition int]val1 & two solutions1 d & f1 if ! temp]ature belong$ to ! transition int]val4 #bhd ,repres5tation 9 ,space4 ,space ,model = ,c>nallite4--,int]e/+ & important z ! iso!rmal solubility curves are1 !y are insuffici5t = ! purpose ( obta9+ a cle> insight into ! complete behavi\r ( ! sy/ems ( two salts & wat]4 ,a %ort description w1 !re=e1 be giv5 "h ( ! repres5tation 9 space ( ! solubility relations ( potassium & magnesium *lorides1 & ( ! d\ble salt :i* !y =m1 c>nallite4#cfe ,illu/ration3 ,,fig4 #aac4 ,fig4 #aac is a diagrammatic sket* ( ! model = c>nallite look$ at sideways f above4 ,along ! ,x-axis is measur$ ! conc5tration ( magnesium *loride 9 ! #bhe solution2 along ! ,y-axis1 ! conc5tration ( potassium *loride2 :ile along ! ,t-axis is measur$ ! temp]ature4 ,! ?ree axes are at "r angles to "o ano!r4 ,! ,,xt-plane1 !re=e1 conta9s ! solubility curve ( magnesium *loride2 ! ,,yt-plane1 ! solubility curve ( potassium *loride1 & 9 ! space betwe5 ! two planes1 !re are repres5t$ ! composition ( solutions conta9+ bo? magnesium & potassium *lorides4 ,any surface betwe5 ! two planes w repres5t ! v>i\s solutions 9 equilibrium ) only "o solid phase1 & w !re=e indicate ! area or field ( exi/5ce ( biv>iant t]n>y sy/ems4 ,a l9e or curve =m$ by ! int]section ( two surfaces w repres5t solutions 9 equilibrium ) two solid phases 7viz4 ^? belong+ to ! int]sect+ surfaces71 & w %[ ! conditions = ! exi/5ce ( univ>iant sy/ems4 ,la/ly1 po9ts =m$ by ! int]section ( ?ree surfaces w repres5t inv>iant sy/ems1 9 :i* a solution c exi/ 9 equilibrium ) ?ree solid phases 7viz4 ^? belong+ to ! ?ree surfaces74 ,we %all fir/ consid] ! solubility relations ( ! s+le salts4 ,! complete equilibrium curve = magnesium *loride & wat] is repres5t$ 9 ,fig4 #aac by ! s]ies ( curves ,,abf#a ,g#a ,h#a ,j#a ,l#a ,n#a4 ,,ab is ! freez+-po9t curve ( ice 9 contact ) solutions conta9+ magnesium *loride1 & ,b is ! cryohydric po9t at :i* ! solid phases ice & ,mg,cl#b1ab;,h#b,o c co-exi/ ) solution4 ,,bfg is ! solubility curve ( magnesium *loride dodecahydrate4 ,?is curve %[s a po9t ( maximum temp]ature at ,f#a1 & a retr(lex portion ,f#a;,g#a4 ,! curve is !re=e ( ! =m exhibit$ by calcium *loride hexahydrate1 or ! hydrates ( f]ric *loride 7,*apt] ,,viii474 ,g#a is a transition po9t at :i* ! solid phase *anges f dodecahydrate to octahydrate1 ! solubility ( :i* is repres5t$ by ! curve ,g#a;,h#a4 ,at ,h#a ! octahydrate gives place to ! hexahydrate1 :i* is ! solid phase 9 equilibrium ) ! solutions repres5t$ by ! curve ,h#a;,j#a4 ,j#a & ,l#a are also transition po9ts at :i* ! solid phase und]goes *ange1 9 ! =m] case f hexahydrate to tetrahydrate2 & 9 ! latt] case1 #bhf f tetrahydrate to dihydrate4 ,! complete curve ( equilibrium = magnesium *loride & wat] is1 !re=e1 some:at complicat$1 & is a good example ( ! solubility curves obta9$ ) salts capable ( =m+ sev]al hydrates4 ,! solubility curve ( potassium *loride is ( ! simple/ =m1 consi/+ only ( ! two bran*es ,,ac1 ! freez+-po9t curve ( ice1 & ,,co1 ! solubility curve ( ! salt4 ,c is ! cryohydric po9t4 ,?is po9t & ! two curves lie 9 ! ,,yt-plane4 ,on pass+ to ! t]n>y sy/ems1 ! composition ( ! solutions mu/ be repres5t$ by po9ts or curves situat$ betwe5 ! two planes4 ,we %all n[ turn to ! consid]ation ( ^!4 ,,bd & ,,cd are t]n>y eutectic curves 7p4 #bhd74 ,!y give ! composition ( solutions 9 equilibrium ) ice & magnesium *loride dodecahydrate 7,,bd71 & ) ice & potassium *loride 7,,cd74 ,d is a t]n>y cryohydric po9t4 ,if ! temp]ature is rais$ & ! ice all[$ to disappe>1 we %all pass to ! solubility curve = ,mg,cl#b1ab;,h#b,o ,k,cl 7curve ,,de74 ,at ,e c>nallite is =m$ & ! potassium *loride disappe>s2 ,,efg is !n ! solubility curve = ,mg,cl#b1ab;,h#b,o c>nallite 7,k,mg,cl#c1f;,h#b,o74 ,?is curve also %[s a po9t ( maximum temp]ature 7,f7 & a retr(lex portion4 ,,gh & ,,hj repres5t ! solubility curves ( c>nallite ,mg,cl#b1h;,h#b,o & c>nallite ,mg,cl#b1f;,h#b,o1 ,g & ,h be+ transition po9ts4 ,,jk is ! solubility curve = c>nallite ,mg,cl#b1d;,h#b,o4 ,at ! po9t ,k we h ! highe/ temp]ature at :i* c>nallite c exi/ ) magnesium *loride 9 contact ) solution4 ,above ?is temp]ature decomposition takes place & potassium *loride sep>ates out4 ,if at ! po9t ,e1 at :i* ! two s+le salts & ! d\ble salt are pres5t1 excess ( potassium *loride is add$1 ! magnesium *loride w all disappe> ow+ to ! =mation ( c>nallite1 & !re w be left c>nallite & potassium *loride4 ,! solubility curve = a mixture ( ^! two salts is repres5t$ by ,,emk2 a simple curve exhibit+1 h[ev]1 a temp]ature maximum at ,m4 ,?is maximum po9t corresponds ) ! fact t dry c>nallite melts at ?is temp]ature ) sep>ation ( potassium *loride4 ,at all temp]atures #bhg above ?is po9t1 ! =mation ( d\ble salt is impossible4 ,! retr(lex portion ( ! curve repres5ts solutions 9 equilibrium ) c>nallite & potassium *loride1 b 9 :i* ! ratio ,mg,cl#b 3 ,k,cl is great] ?an 9 ! d\ble salt4 ,?r\gh\t its :ole c\rse1 ! curve ,,emk repres5ts solutions 9 :i* ! ratio ( ,mg,cl#b 3 ,k,cl is great] ?an 9 ! d\ble salt4 ,z ?is is a po9t ( "s importance1 x w be well1 p]haps1 to make x cle>] by giv+ "o ( ! iso!rmal curves1 e4g4 ! curve = #aj;deg1 :i* is repres5t$ diagrammatically 9 ,fig4 #aad4 ,e & ,f "h repres5t solutions saturat$ = c>nallite plus magnesium *loride hydrate1 & = c>nallite plus potassium *loride4 ,z is evid5t1 ! po9t ,f lies above ! l9e repres5t+ equimolecul> proportions ( ! salts 7,,od74 ,illu/ration3 ,,fig4 #aad4 ,summ>y & ,num]ical ,data4--,we may n[ sum up ! diff]5t sy/ems :i* c be =m$1 & give ! num]ical data f :i* ! model is con/ruct$4#cff ,i4 ,biv>iant ,sy/ems4 -------------------------------------- ,solid phase4 ,area ( exi/5ce4 -------------------------------------- ,ice ,,abdc ,k,cl ,,cdemklno ,c>nallite ,,efghjkm ,mg,cl#b1ab;,h#b,o ,,bf#a;,g#a;,,gf$ ,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 ,univ>iant ,sy/ems4--,! diff]5t univ>iant sy/ems h already be5 describ$4 ,! c\rse ( ! curves w be suffici5tly indicat$ if ! temp]ature & composition ( ! solutions = ! diff]5t inv>iant sy/ems are giv54 #bhh ,,iii4--,inv>iant ,sy/ems--,b9>y & ,t]n>y4 ---------------------------------------- --------------------------------- ,composition ( solution4 ,po9t4 ,solid ,phases4 ,temp]- ,gram-molecules ( salt ature4 p] #ajjj gram-mol4 wat]4 ---------------------------------------- --------------------------------- ,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 c>nallite ,f#a ,mg,cl#b1ab;,h#b,o -#af4d;deg #hc4cc ,mg,cl#b ,f ,mg,cl#b1ab;,h#b,o2 -#af4f;deg ,almo/ same z ,f#a2 c>nallite conta9s small am\nt ( ,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 ,almo/ same z ,g#a1 ,mg,cl#b1h;,h#b,o2 b conta9s small c>nallite quantity ( ,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 ,almo/ same z ,h#a1 ,mg,cl#b1f;,h#b,o2 b conta9s small c>nallite am\nt ( ,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 c>nallite ,k ,mg,cl#b1d;,h#b,o2 ,k,cl2 #aeb4e;deg #bjj ,mg,cl#b2 #bd ,k,cl c>nallite ,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 ,c>nallite2 ,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 ---------------------------------------- --------------------------------- ,) ! help ( ! data 9 ! prec$+ table & ( ! solid model x w be possible to /ate 9 any giv5 case :at w be ! behavi\r ( a sy/em compos$ ( magnesium *loride1 potassium *loride & wat]4 ,"o or two diff]5t cases w be v briefly describ$2 & ! read] %\ld h no difficulty 9 work+ out ! behavi\r "u o!r conditions ) ! help ( ! model & ! num]ical data j giv54 #bhi ,9 ! fir/ place x may be aga9 not$ t at a temp]ature above #afg4e;deg 7po9t ,m7 c>nallite _c exi/4 ,if1 !re=e1 a solution ( magnesium & potassium *lorides is evaporat$ at a temp]ature above ?is po9t1 ! result w be a mixture ( potassium *loride & ei!r magnesium *loride tetrahydrate or magnesium *loride dihydrate1 accord+ z ! temp]ature is bel[ or above #agf;deg4 ,! iso!rmal curve "h consi/s ( only two bran*es4 ,fur!r1 ref]5ce has already be5 made to ! fact t all po9ts ( ! c>nallite area correspond to solutions 9 equilibrium ) c>nallite1 b 9 :i* ! ratio ( ,mg,cl#b to ,k,cl is great] ?an 9 ! d\ble salt4 ,a solution :i* is saturat$ ) respect to d\ble salt alone w be sup]saturat$ ) respect to potassium *loride4 ,at all temp]atures1 !re=e1 c>nallite is decompos$ by wat] ) sep>ation ( potassium *loride2 h5ce all solutions obta9$ by add+ excess ( c>nallite to wat] w lie on ! curve ,,em4 ,a pure saturat$ solution ( c>nallite _c be obta9$4 ,if an unsaturat$ solution ( ! two salts 9 equimolecul> am\nts is evaporat$1 potassium *loride w fir/ be deposit$1 because ! plane bisect+ ! "r angle =m$ by ! ,x & ,y axes cuts ! area = t salt4 ,deposition ( potassium *loride w lead to a relative increase 9 ! conc5tration ( magnesium *loride 9 ! solution2 & on cont9u$ evaporation a po9t 7on ! curve ,,em7 w be rea*$ at :i* c>nallite w sep>ate out4 ,s long z ! two solid phases are pres5t1 ! composition ( ! solution mu/ rema9 un*ang$4 ,s9ce ! sep>ation ( c>nallite causes a decrease 9 ! relative conc5tration ( ! potassium *loride 9 ! solution1 ! portion ( ?is salt :i* 0 deposit$ at ! comm5cem5t mu/ r$issolve1 & c>nallite w be left on evaporat+ to dryness4 7,incongru5tly saturat$ solution47 ,al?\gh c>nallite is decompos$ by pure wat]1 x w be possible to cry/allize x f a solution hav+ a composition repres5t$ by any po9t 9 ! c>nallite area4 ,s9ce dur+ ! sep>ation ( ! d\ble salt ! relative am\nt ( magnesium *loride increases1 x is mo/ advantage\s to #bij comm5ce ) a solution ! composition ( :i* is repres5t$ by a po9t ly+ j above ! curve ,,em 7cf4 p4 #bha74 ,f ! above description ( ! behavi\r ( c>nallite 9 solution1 ! processes usually employ$ = obta9+ potassium *loride w be readily intelligible4#cfg ,f]ric ,*loride--,hydrog5 ,*loride--,wat]4--,9 ! case ( ano!r sy/em ( ?ree compon5ts :i* we %all n[ describe1 ! relation%ips are consid]ably m complicat$ ?an 9 ^? already discuss$4 ,!y des]ve discussion1 h[ev]1 on acc\nt ( ! fact t !y exhibit a numb] ( new ph5om5a4 ,9 ! sy/em =m$ by ! ?ree compon5ts1 f]ric *loride1 hydrog5 *loride1 & wat]1 n only c v>i\s comp\nds ( f]ric *loride & wat] 7p4 #aeb71 & ( hydrog5 *loride & wat] be =m$1 ea* ( :i* possesses a def9ite melt+ po9t1 b v>i\s t]n>y comp\nds are also kn[n4 ,?us we h ! foll[+ 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 ,f ?is x w be readily und]/ood t ! complete /udy ( ! conditions ( temp]ature & conc5tration "u :i* solutions c exi/1 ei!r ) "o solid phase or ) two or ?ree solid phases1 are exce$+ly complicat$2 &1 z a matt] ( fact1 only a few ( ! possible equilibria h be5 inve/igat$4 ,we %all attempt "h only a brief description ( ! mo/ important ( ^!4#cfh ,if we aga9 employ rectangul> co-ord9ates = ! graphic #bia repres5tation ( ! results1 we h ! two planes ,,xot & ,,yot 7,fig4 #aae73 ! conc5tration ( f]ric *loride be+ measur$ along ! ,x-axis1 ! conc5tration ( hydrog5 *loride along ! ,y-axis1 & ! temp]ature along ! ,t-axis4 ,! curve ,,abcdefghjk is1 !re=e1 ! solubility curve ( f]ric *loride 9 wat] 7p4 #aeb71 & ! curve ,a',b',c',d',e',f' ! solubility curve ( hydrog5 *loride & its hydrates4 ,b' & ,d' are ! melt+ po9ts ( ! hydrates ,h,cl1#c;,h#b,o & ,h,cl1#b;,h#b,o4 ,9 ! space betwe5 ^! two planes are repres5t$ ^? sy/ems 9 :i* all ?ree compon5ts are pres5t4 ,z already /at$1 only a few ( ! possible t]n>y sy/ems h be5 inve/igat$1 & ^! are repres5t$ 9 ,fig4 #aaf4 ,! figure %[s ! model re/+ on ! ,,xot-plane1 s t ! l[] edge repres5ts ! solubility curve ( f]ric *loride1 ! conc5tration increas+ f "r to left4 ,! conc5tration ( hydrog5 *loride is measur$ upw>ds1 & ! temp]ature =w>ds4 ,! fur!r end ( ! model repres5ts ! iso!rmal surface = -#cj;deg4 ,! surface ( ! model on ! left does n correspond ) ! plane ,,yot 9 ,fig4 #aae1 b ) a p>allel plane :i* cuts ! conc5tration axis = f]ric *loride at a po9t repres5t+ #fe gm4-molecules ,fe,cl#c 9 #ajj gm4-molecules ( wat]4 ,! upp] surface corresponds ) a plane p>allel to ! axis ,,xot1 at a di/ance correspond+ ) ! conc5tration ( #ej gm4-molecules ,h,cl 9 #ajj gm4-molecules ( wat]4 ,illu/ration3 ,,fig4 #aae4 ,t]n>y ,sy/ems4--,we pass ov] ! b9>y sy/em ,fe,cl#c--;,h#b,o1 :i* has already be5 discuss$ 7p4 #aeb71 & ! simil> sy/em ,h,cl--,h#b,o 7see ,fig4 #aae71 & turn to ! discussion ( "s ( ! t]n>y sy/ems repres5t$ by #bib po9ts on ! surface ( ! model betwe5 ! planes ,,xot & ,,yot4 ,z 9 ! case ( c>nallite1 a plane repres5ts ! conditions ( conc5tration ( solution & temp]ature "u :i* a t]n>y solution c be 9 equilibrium ) a s+le solid phase 7biv>iant sy/ems71 a l9e repres5ts ! conditions = ! coexi/5ce ( a solution ) two solid phases 7univ>iant sy/ems71 & a po9t ! conditions = equilibrium ) ?ree solid phases 7inv>iant sy/ems74 ,illu/ration3 ,,fig4 #aaf4 ,9 ! case ( a b9>y sy/em1 9 :i* #b;,fe,cl#c1ab;,h#b,o is 9 equilibrium ) a solution ( ! same composition1 addition ( hydrog5 *loride mu/ evid5tly l[] ! temp]ature at :i* equilibrium c exi/2 & ! same holds1 ( c\rse1 #bic = all o!r b9>y solutions 9 equilibrium ) ?is solid phase4 ,9 ?is way we obta9 ! surface ,i41 :i* repres5ts ! temp]atures & conc5trations ( solutions 9 :i* #b;,fe,cl#c1ab;,h#b,o c be 9 equilibrium ) a t]n>y solution conta9+ f]ric *loride1 hydrog5 *loride1 & wat]4 ,?is surface is analog\s to ! curv$ surface ,k#a,k#bk#dk#c 9 ,fig4 #ig 7p4 #bef74 ,simil>ly1 ! surfaces ,,ii41 ,,iii41 ,,iv41 & ,v4 repres5t ! conditions = equilibrium betwe5 ! 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 & t]n>y solutions respectively4 ,! l9es ,,cl1 ,,em1 ,,gn1 & ,,io on ! model repres5t univ>iant sy/ems 9 :i* a t]n>y solution is 9 equilibrium ) two solid phases1 viz4 ) ^? repres5t$ by ! adjo9+ fields4 ,^! l9es correspond ) ! t]n>y eutectic curves k#c,k#a & k#d,k#b 9 ,fig4 #ig4 ,besides ! surfaces already m5tion$1 !re are /ill ?ree o!rs1 ,,vi41 ,,vii41 & ,,viii41 :i* also repres5t ! conditions = equilibrium betwe5 "o solid phase & a t]n>y solution2 b 9 ^! cases1 ! solid phase is n a b9>y comp\nd or an anhydr\s salt1 b a t]n>y comp\nd conta9+ all ?ree compon5ts4 ,! solid phases :i* are 9 equilibrium ) ! t]n>y solutions repres5t$ by ! surfaces ,,vi41 ,,vii41 & ,,viii41 are #b;,fe,cl#c1b;,h,cl1#d;,h#b,o2 #b;,fe,cl#c1b;,h,cl1#h;,h#b,o2 & #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o respectively4 ,! model = ,fe,cl#c--;,h,cl--,h#b,o exhibits c]ta9 o!r peculi>ities n f\nd 9 ! case ( ,mg,cl#b--,k,cl--,h#b,o4 ,on exam9+ ! model m closely1 x is f\nd t ! field ( ! t]n>y comp\nd #b;,fe,cl#c1b;,h,cl1#h;,h#b,o 7,,vii47 resembles ! surface ( a sug> cone1 & has a project+ po9t1 ! end ( :i* corresponds ) a high] temp]ature ?an does any o!r po9t ( ! surface4 ,at ! po9t ( maximum temp]ature ! composition ( ! liquid phase is ! same z t ( ! solid4 ,?is po9t1 !re=e1 repres5ts ! melt+ po9t ( ! d\ble salt ( ! above composition4 ,! curves repres5t+ univ>iant sy/ems are ( two k9ds4 ,9 ! "o case1 ! two solid phases pres5t are bo? b9>y comp\nds2 or "o is a b9>y comp\nd & ! o!r is "o ( ! compon5ts4 ,9 ! o!r case1 ei!r "o or bo? solid phases are t]n>y comp\nds4 ,curves belong+ #bid to ! =m] class 7s-call$ bord] curves7 />t f b9>y eutectic po9ts1 & _! c\rse is always t[>ds l[] temp]atures1 e4g4 ,,cl1 ,,em1 ,,gn1 ,,io4 ,curves belong+ to ! latt] class 7s-call$ m$ial curves7 w\ld1 9 a triangul> diagram1 lie entirely )9 ! triangle4 ,su* curves are ,,yv1 ,,wv1 ,,vl1 ,,lm1 ,,mv1 ,,ns1 ,,/1 ,,s1 ,,oz4 ,^! curves d n always run f high] to l[] temp]atures1 b may ev5 exhibit a po9t ( maximum temp]ature4 ,su* maxima are f\nd1 = example1 at ,u 7,fig4 #aaf71 & also on ! curves ,,/ & ,,lv4 ,f9ally1 :]eas all ! o!r t]n>y univ>iant curves run 9 valleys betwe5 ! adjo9+ surfaces1 we f9d at ! po9t ,x a simil> appe>ance to t f\nd 9 ! case ( c>nallite1 z ! univ>iant curve "h rises above ! surr\nd+ surface4 ,! po9t ,x1 !re=e1 does n correspond ) a eutectic po9t1 b ) a transition po9t4 ,at ?is po9t ! t]n>y comp\nd #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o melts ) sep>ation ( #b;,fe,cl#c1ab;,h#b,o1 j z c>nallite melts at #afh;deg ) sep>ation ( potassium *loride4 ,! ,iso!rmal ,curves4--,a deep] insight into ! behavi\r ( ! sy/em ,fe,cl#c--;,h,cl--,h#b,o is obta9$ f a /udy ( ! iso!rmal curves1 ! complete s]ies ( :i*1 s f> z !y h be5 /udi$1 is giv5 9 ,fig4 #aag4cfi ,9 ?is figure ! lightly drawn curves repres5t iso!rmal solubility curves1 ! p>ticul> temp]ature be+ pr9t$ beside ! curve4#cgj ,! d>k l9es give ! composition ( ! univ>iant sy/ems at diff]5t temp]atures4 ,! po9t ( int]section ( a d>k ) a light curve gives ! composition ( ! univ>iant solution at ! temp]ature repres5t$ by ! light curve2 & ! po9t ( int]section ( two d>k l9es gives ! composition ( ! inv>iant solution 9 equilibrium ) ?ree solid phases4 ,! dott$ l9es repres5t meta/able sy/ems1 & ! po9ts ,p1 ,q1 & ,r repres5t solutions ( #bie ! composition ( ! t]n>y salts1 #b;,fe,cl#c1b;,h,cl1#d;,h#b,o2 #b;,fe,cl#c1b;,h,cl1#h;,h#b,o2 & #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o4 ,illu/ration3 ,,fig4 #aag4 ,! f>!r end ( ! model 7,fig4 #aaf7 corresponds1 z already m5tion$1 to ! temp]ature -#cj;deg1 s t ! outl9e evid5tly repres5ts ! iso!rmal curve = t temp]ature4 ,fig4 #aag does n %[ ?is4 ,we c1 h[ev]1 foll[ ! iso!rmal = -#bj;deg1 :i* is ! extreme curve on ! "r 9 ,fig4 #aag4 ,po9t ,a repres5ts ! solubility ( #b;,fe,cl#c1ab;,h#b,o 9 wat]4 ,if hydrog5 *loride is add$1 ! conc5tration ( f]ric *loride 9 ! solution fir/ decreases & !n increases1 until at po9t #cd ! t]n>y d\ble salt #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o is =m$4 ,if ! addition ( hydrog5 *loride is cont9u$1 ! f]ric *loride disappe>s ultimately1 & only ! t]n>y d\ble salt rema9s4 ,?is salt c coexi/ ) solutions ( ! composition repres5t$ by ! curve :i* passes ?r\gh ! po9ts #agc1 #agd1 #age4 ,at ! la/-m5tion$ po9t1 ! t]n>y salt ) #h;,h#b,o is =m$4 ,! composition ( ! solutions ) :i* ?is salt is 9 equilibrium at -#bj;deg is repres5t$ by ! curve :i* passes ?r\gh a po9t ( maximal conc5tration ) respect to ,h,cl1 & cuts ! curve ,,sn at ! po9t #aab1 at :i* ! solution is 9 equilibrium ) ! two solid phases #b;,fe,cl#c1d;,h#b,o & #b;,fe,cl#c1b;,h,cl1#h;,h#b,o4 ,! succe$+ portion ( ! iso!rm repres5ts ! solubility curve at -#bj;deg ( #b;,fe,cl#c1d;,h#b,o1 :i* cuts ! d>k l9e ,,os at po9t #aac1 at :i* ! solution is 9 equilibrium ) ! two solid phases #b;,fe,cl#c1d;,h#b,o & #b;,fe,cl#c1b;,h,cl1#d;,h#b,o4 ,!reaft] comes ! solubility curve ( ! latt] comp\nd4 ,! o!r iso!rmal curves c be foll[$ 9 a simil> mann]4 ,if ! temp]ature is rais$1 ! region ( exi/5ce ( ! t]n>y d\ble salts becomes small] & small]1 & at temp]atures above #cj;deg ! t]n>y salts ) #ab;,h#b,o & #h;,h#b,o are no long] capable ( exi/+4 ,if ! temp]ature is rais$ above #df;deg1 only ! b9>y comp\nds ( f]ric *loride & wat] & ! anhydr\s salt c exi/ z solid phases4 ,! iso!rmal curve = #j;deg repres5ts ! solubility curve = #b;,fe,cl#c1ab;,h#b,o2 #b;,fe,cl#c1g;,h#b,o2 #b;,fe,cl#c1e;,h#b,o2 & #b;,fe,cl#c1d;,h#b,o4 #bif ,f9ally1 9 ! case ( ! sy/em ,fe,cl#c--;,h,cl--,h#b,o1 we f9d clos$ iso!rmal curves4 ,s9ce1 z already /at$1 ! salt #b;,fe,cl#c1b;,h,cl1#h;,h#b,o has a def9ite melt+ po9t1 ! temp]ature ( :i* is !re=e high] ?an t at :i* ?is comp\nd is 9 equilibrium ) solutions ( o!r composition1 x foll[s t ! l9e ( int]section ( an iso!rmal plane correspond+ ) a temp]ature imm$iately bel[ ! melt+ po9t ( ! salt ) ! cone-%ap$ surface ( its region ( exi/5ce1 w =m a clos$ curve4 ,?is is %[n by ! iso!rm = -#d4e;deg1 :i* surr\nds ! po9t ,q1 ! melt+ po9t ( ! t]n>y salt4 ,! foll[+ table gives "s ( ! num]ical data f :i* ! curves & ! model h be5 con/ruct$3-- ---------------------------------------- --------------------------------- ,composition ( ! sol- ution 9 gm4-mols4 salt ,po9t4 ,solid phases4 ,temp]- to #ajj gm4-mols4 wat]4 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 7melt+ po9t7 ---------------------------------------- --------------------------------- ,basic ,salts4--,ano!r class ( sy/ems 9 ! /udy ( #big :i* ! ,phase ,rule has p]=m$ exceptional s]vice1 is t ( ! basic salts4 ,9 _m cases x is impossible1 by ! ord9>y me?ods ( analysis1 to decide :e!r "o is deal+ ) a def9ite *emical individual or ) a mixture4 ,! "q :e!r a solid phase is a *emical individual c1 h[ev]1 be answ]$1 9 mo/ cases1 ) ! help ( ! pr9ciples :i* we h already le>nt4 ,let u consid]1 = example1 ! =mation ( basic salts f bismu? nitrate1 & wat]4 ,9 ?is case we c *oose z compon5ts ,bi#b,o#c1 ,n#b,o#e1 & ,h#b,o2 s9ce all ! sy/ems consi/ ( ^! 9 v>y+ am\nts4 ,if we are deal+ ) a condition ( equilibrium at con/ant temp]ature betwe5 liquid & solid phases1 ?ree cases c be di/+ui%$1#cga viz4-- #a4 ,! solutions 9 diff]5t exp]im5ts h ! same composition1 b ! composition ( ! precipitate alt]s4 ,9 ?is case !re mu/ be two solid phases4 #b4 ,! solutions 9 diff]5t exp]im5ts c h v>y+ composition1 :ile ! composition ( ! precipitate rema9s un*ang$4 ,9 ?is case only "o solid phase exi/s1 a def9ite comp\nd4 #c4 ,! composition bo? ( ! solution & ( ! precipitate v>ies4 ,9 ?is case ! solid phase is a solid solution or a mix$ cry/al4 ,9 ord]1 !re=e1 to decide :at is ! nature ( a precipitate produc$ by ! hydrolysis ( a normal salt1 x is only necess>y to asc]ta9 :e!r & h[ ! composition ( ! precipitate alt]s ) alt]ation 9 ! composition ( ! solution4 ,if ! composition ( ! solution is repres5t$ by abscissae1 & ! composition ( ! precipitate by ord9ates1 ! =m ( ! curves obta9$ w\ld enable u to answ] our "q2 = v]tical l9es w\ld indicate ! pres5ce ( two solid phases 7#a/ case71 horizontal l9es ! pres5ce ( only "o solid phase 7#bnd case71 & slant+ l9es ! pres5ce ( mix$ cry/als 7#crd case74 ,?is me?od ( repres5tation _c1 h[ev]1 be c>ri$ out 9 mo/ cases4 ,x is1 h[ev]1 #bih g5]ally possible to f9d "o pair or sev]al pairs ( compon5ts1 ! relative am\nts ( :i* 9 ! solution or 9 ! precipitate und]go *ange :51 & only :51 ! composition ( ! solution or ( ! precipitate *anges4 ,?us1 9 ! case ( bismu?1 nitrate1 & wat]1 we c repres5t ! ratio ( ,bi#b,o#c 3 ,n#b,o#e 9 ! precipitate z ord9ates1 & ,n#b,o#e 3 ,h#b,o 9 ! solution z abscissae4 ,a horizontal l9e !n indicates a s+le solid phase1 & a v]tical l9e two solid phases4 ,an example ( ?is is giv5 9 ,fig4 #aah4cgb ,illu/ration3 ,,fig4 #aah4 ,bi#b,o#c--,n#b,o#e--;,h#b,o4--,al?\gh v>i\s sy/ems h be5 /udi$ 9 :i* !re is =mation ( basic salts1#cgc we %all cont5t ourselves "h ) ! description ( "s ( ! conditions = ! =mation ( basic salts ( bismu? nitrate1 & = _! equilibrium 9 contact ) solutions4#cgd ,?ree normal salts ( bismu? oxide & nitric acid are kn[n1 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 & ,bi#b,o#c1c,n#b,o#e1c;,h#b,o7,s#c74 ,besides ^! normal salts1 !re are ! foll[+ basic salts3-- #bii ,bi#b,o#c1,n#b,o#e1b;,h#b,o 7repres5t$ 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 "s o!rs also exi/4 ,! problem n[ is to f9d ! conditions "u :i* ^! diff]5t normal & basic salts c be 9 equilibrium ) solutions ( v>y+ conc5tration ( ! ?ree compon5ts4 ,hav+ det]m9$ ! equilibrium conditions = ! diff]5t salts1 x is !n possible to con/ruct a model simil> to t = ,mg,cl#b--,k,cl--,h#b,o or = ,fe,cl#c--;,h,cl--,h#b,o1 f :i* x w be possible to det]m9e ! limits ( /ability ( ! diff]5t salts1 & to pr$ict :at w occur :5 we br+ ! salts 9 contact ) solutions ( nitric acid ( diff]5t conc5trations & at diff]5t temp]atures4 ,= our pres5t purpose x is suffici5t to pick out only "s ( ! equilibria :i* h be5 /udi$1 & :i* are repres5t$ 9 ! model 7,fig4 #aai74 ,9 ?is case use has be5 made ( ! triangul> me?od ( repres5tation1 s t ! surface ( ! model lies )9 ! prism4 ,illu/ration3 ,,fig4 #aai4 ,?is model %[s ! ?ree surfaces1 ,a1 ,b1 & ,c1 :i* repres5t ! conditions = ! /able exi/5ce ( ! salts ,b#a-a-a1 ,s#aj1 & ,s#c 9 contact ) solution at diff]5t #cjj temp]atures4 ,! front surface ( ! model repres5ts ! temp]ature #i;deg1 & ! f>!r end ! temp]ature #ge4e;deg4 ,! dott$ curve repres5ts ! iso!rm = #bj;deg4 ,! prom95ces betwe5 ! surfaces repres5t1 ( c\rse1 solutions :i* are saturat$ 9 respect ( two solid phases4 ,?us1 = example1 pabc repres5ts solutions 9 equilibrium ) ,b#a-a-a & ,s#aj2 & ! ridge qdc1 solutions 9 equilibrium ) ,s#aj & ,s#c4 ,! po9t b1 :i* lies at #ge4e;deg1 is ! po9t ( maximum temp]ature = ,s#aj4 ,if ! temp]ature is rais$ above ?is po9t1 ,s#aj decomposes into ! basic salt ,b#a-a-a & solution4 ,?is po9t is !re=e analog\s to ! po9t ,m 9 ! c>nallite model1 at :i* ?is salt decomposes into potassium *loride & solution 7p4 #bhd72 or to ! po9t at :i* ! salt #b;,fe,cl#c1b;,h,cl1#ab;,h#b,o decomposes into #b;,fe,cl#c1ab;,h#b,o & solution 7p4 #bid74 ,! curve pab has be5 foll[$ to ! temp]ature ( #gb;deg 7po9t c74 ,! end ( ! model is incomplete1 b x is probable t 9 ! neighb\rhood ( ! po9t c !re exi/s a qu9tuple po9t at :i* ! basic salt ,b#a-b-b appe>s4 ,9 ! neighb\rhood ( e also !re probably exi/s ano!r qu9tuple po9t at :i* ,s#d is =m$4 ,^! sy/ems h1 h[ev]1 n be5 /udi$4 ,! foll[+ tables give "s ( ! num]ical data3-- ,,iso!rm ,,= #bj;deg4 ---------------------------------------- ------------------------------ ,composition ( ! solution4 ,gram-mols4 9 #ajjj gm4-mols4 ( wat]4 ,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 ---------------------------------------- ------------------------------ ,,sy/ems ,,9 ,,equilibrium ,,) ,b#a-a-a ,,& ,s#aj 7,,curve pabc74 ---------------------------------------- -------------------- ,composition ( ! solution4 ,gram-mols4 9 #ajjj gm4-mols4 ( wat]4 ,temp]ature4 ---------------------------------------- ,bi#b,o#c ,n#b,o#e ---------------------------------------- ------------------ #i;deg #bf4g #hh4b #bj;deg 7po9t a7 #cj4ae #ig4ig #cj;deg #cc4f #aab4c #ej;deg #da4h #adh4d #fe;deg #eg4ba #aij4h #ge4e;deg 7po9t b7 #hg4i #bhh4d #gb;deg 7po9t c7 #if4j #cbg4j ---------------------------------------- -------------------- ,,sy/ems ,,9 ,,equilibrium ,,) ,s#aj ,,& ,s#c 7,,curve qde74 ---------------------------------------- ---------------- ,composition ( ! solution4 ,gram-mols4 9 #ajjj gm4-mols4 ( wat]4 ,temp]ature4 ---------------------------------------- - ,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 ,m]cury ,salts4--,! ,phase ,rule has also be5 appli$ by ,a4 ,j4 ,cox#cge 9 an inve/igation ( ! basic salts ( m]cury1 ! result ( :i* has be5 to %[ t1 ( ! salts m5tion$ 9 text-books1 q a numb] are incorrectly /at$ to be *emical comp\nds or *emical individuals 7p4 #ib74 ,! inve/igation1 :i* 0 c>ri$ out ess5tially 9 ! mann] describ$ above1 includ$ ! salts m5tion$ 9 ! foll[+ table2 & ( ! basic salts said to be d]iv$ f !m1 only ^? m5tion$ really exi/4 ,9 ! foll[+ table1 ! numb]s 9 ! second column give ! m9imum values ( ! conc5tration ( ! acid1 express$ 9 equival5t normality1 necess>y = ! exi/5ce ( ! #cja correspond+ salts 9 contact ) solution at ! temp]ature giv5 9 ! ?ird column3-- ---------------------------------------- --------------------- ,salt4 ,normality ( ,temp]ature4 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,,s#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,,s#d #d4b x #aj-c #be;deg #b;,hg#b,o4,,s#c4;,h#b,o #e4f x #aj-d #be;deg ---------------------------------------- --------------------- ,m]curic fluoride does n =m any basic salt4 ,s9ce two succe$+ memb]s ( a s]ies c coexi/ only 9 contact ) a solution ( def9ite conc5tration1 we c prep>e acid solutions ( def9ite conc5tration by br++ an excess ( two su* salts 9 contact ) wat]4 ,indirect ,det]m9ation ( ! ,composition ( ! ,solid ,phase4--,x has already be5 %[n 7p4 #bbh7 h[ ! composition ( ! solid phase 9 a sy/em ( two compon5ts c be det]m9$ )\t analysis1 & we %all n[ describe h[ ?is c be done 9 a sy/em ( ?ree compon5ts4#cgf ,we %all assume t we are deal+ ) ! aque\s solution ( two salts :i* c give rise to a d\ble salt1 9 :i* case we c repres5t ! solubility relations 9 a sy/em ( rectangul> co-ord9ates4 ,9 ?is case we %\ld obta91 z be=e 7,fig4 #abj71 ! iso!rm adcb1 if we express ! #cjb composition ( ! solution 9 gram-molecules ( ,a or ( ,b to #ajj gram-molecules ( wat]4 ,illu/ration3 ,,fig4 #abj4 ,let u suppose1 n[1 t ! d\ble salt is 9 equilibrium ) ! solution at a def9ite temp]ature1 & t ! composition ( ! solution is repres5t$ by ! po9t e4 ,! great] "p ( ! solution is n[ sep>at$ f ! solid phase1 & ! latt]1 toge!r ) ! adh]+ "m liquor1 is analyz$4 ,! composition 7express$1 z be=e1 9 gram-molecules ( ,a & ,b to #ajj gram molecules ( wat]7 w be repres5t$ by a po9t 7e4g4 f7 on ! l9e e,s1 :]e ,s repres5ts ! composition ( ! d\ble salt4 ,t ?is is s w be evid5t :5 "o consid]s t ! composition ( ! :ole mass mu/ lie betwe5 ! composition ( ! solution & t ( ! d\ble salt1 no matt] :at ! relative am\nts ( ! solid phase & ! "m liquor4 ,if1 9 a simil> mann]1 we analyze a solution ( a diff]5t composition 9 equilibrium ) ! same d\ble salt 7n necess>ily at ! same temp]ature z be=e71 & also ! mixture ( solid phase & solution1 we %all obta9 two o!r po9ts1 z1 = example1 g & h1 & ! l9e jo9+ ^! mu/ likewise pass ?r\gh ,s4 ,! me?od ( f9d+ ! #cjc composition ( an unkn[n d\ble salt consi/s1 !re=e1 9 f9d+1 9 ! mann] j describ$1 ! position ( two l9es su* z ef & gh4 ,! po9t ( int]section ( ^! l9es !n gives ! composition ( ! d\ble salt4 ,if ! d\ble salt is anhydr\s1 ! po9t ,s lies at inf9ity1 & ! l9es ef & gh are p>allel to ea* o!r4 ,! same result is arriv$ at by means ( ! triangul> me?od ( repres5tation4#cgg ,if we />t ) ! ?ree compon5ts 9 kn[n am\nts1 & repres5t ! initial composition ( ! :ole by a po9t 9 ! triangle1 & !n asc]ta9 ! f9al composition ( ! solution 9 equilibrium ) ! solid phase at a def9ite temp]ature1 ! l9e jo9+ ! po9ts repres5t+ ! initial & end conc5tration passes ?r\gh ! po9t repres5t+ ! composition ( ! solid phase4 ,if two det]m9ations are made ) solutions hav+ diff]5t initial & f9al conc5trations 9 equilibrium ) ! same solid phase1 !n ! po9t ( int]section ( ! two l9es s obta9$ gives ! composition ( ! solid phase4 99 99 99 99 99 #cjd ,,*apt] ,,xvii ,,abs5ce ,,( ,a ,,liquid ,,phase ,9 ! prec$+ *apt]s deal+ ) equilibria 9 ?ree-compon5t sy/ems1 our att5tion 0 direct$ only to ^? cases 9 :i* liquid solutions =m$ "o or m phases4 ,m5tion mu/1 h[ev]1 be made ( c]ta9 sy/ems :i* conta9 no liquid phase1 & 9 :i* only solids & gases are 9 equilibrium4 ,s9ce1 9 all cases1 !re c be b "o gas phase1 f\r solid phases w be necess>y 9 ord] to =m an inv>iant sy/em4 ,:5 only ?ree solid phases are pres5t1 ! sy/em is univ>iant2 & :5 only two solid phases coexi/ ) gas1 x is biv>iant4 ,if1 h[ev]1 we make ! re/riction t ! gas pressure is con/ant1 we dim9i% ! v>iability by "o4 ,on acc\nt ( _! great indu/rial importance1 we %all describe briefly "s ( ! sy/ems belong+ to ?is class4 ,iron1 ,c>bon ,monoxide1 ,c>bon ,dioxide4--,"s ( ! mo/ important sy/ems ( ?ree compon5ts 9 :i* equilibrium exi/s betwe5 solid & gas phases are ^? =m$ by ! ?ree compon5ts--iron1 c>bon monoxide1 & c>bon dioxide--& !y are ( importance especially = ! /udy ( ! processes occurr+ 9 ! bla/ furnace4 ,if c>bon monoxide is pass$ ov] r$uc$ iron p[d] at a temp]ature ( ab\t #fjj;deg1 ! iron is oxidiz$ & ! c>bon monoxide r$uc$ ) sep>ation ( c>bon 9 accordance ) ! equation ,fe ,,co ,fe,o ,c ,?is reaction is succe$$ by ! two reactions ,fe,o ,,co ,fe ,,co#b ,,co#b ,c #b;,,co #cje ,illu/ration3 ,,fig4 #aba4 ,! =m] ( ^! reactions is n complete1 b leads to a def9ite equilibrium4 ,! result ( ! diff]5t reactions is !re=e an equilibrium betwe5 ! ?ree solid phases1 c>bon1 iron1 & f]r\s oxide1 & ! gas phase consi/+ ( c>bon monoxide & dioxide4 ,we h "h f\r phases2 & if ! total pressure is ma9ta9$ con/ant1 equilibrium c occur only at a def9ite temp]ature4 ,s9ce1 "u c]ta9 conditions1 we c also h ! reaction ,fe#c,o#d ,,co #c;,fe,o ,,co#b #cjf a second s]ies ( equilibria c be obta9$ ( a "* simil> to ! =m]4 ,^! v>i\s equilibria h be5 inve/igat$ by ,baur & ,glaessn]1#cgh & ! foll[+ is a %ort acc\nt ( ! results ( _! "w4 ,mixtures ( ! solid phases 9 equilibrium ) c>bon monoxide & dioxide 7 heat$ 9 a porcela9 tube at a def9ite temp]ature until equilibrium 0 produc$1 & ! gas 0 !n pump$ (f & analyz$4 ,! results :i* 7 obta9$ are giv5 9 ! foll[+ tables1 & repres5t$ graphically 9 ,fig4 #aba4 ,,solid ,,phases3 ,fe#c,o#d2 ,fe,o4 ---------------------------------------- ------------------------- ,duration ( ,p]c5tage ( ,no4 ,tube fill$ ! exp]im5t ,temp]ature4 ) 9 h\rs4 ,,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 ( ,p]c5tage ( ,no4 ,tube fill$ exp]im5t ,temp]ature4 ) 9 h\rs4 ,,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 ---------------------------------------- -------------------- ,z is evid5t f ! above tables & f ! curves 9 ,fig4 #aba1 ! curve ( equilibrium 9 ! case ( ! reaction ,fe#c,o#d ,,co #c;,fe,o ,,co#b exhibits a maximum = ! ratio ,,co 3 ,,co#b1 at #dij;deg1 :ile1 = ! reaction ,fe,o ,,co ,fe ,,co#b ?is ratio has a m9imum value at #fhj;deg4 ,f ^! curves c be d]iv$ ! conditions "u :i* ! diff]5t solid phases c exi/ 9 contact ) gas4 ,?us1 = example1 at a temp]ature ( #fij;deg1 ,fe,o & ,fe#c,o#d c coexi/ ) a mixture ( #fe4e p] c5t4 ( ,,co#b & #cd4e p] c5t4 ( ,,co4 ,if ! p>tial pressure ( ,,co#b is increas$1 !re occurs ! reaction #c;,fe,o ,,co#b ,fe#c,o#d ,,co & if c>bon dioxide is add$ 9 suffici5t am\nt1 ! f]r\s oxide f9ally disappe>s completely4 ,if1 on ! o!r h&1 ! p>tial pressure ( ,,co is increas$1 !re occurs ! reaction ,fe#c,o#d ,,co #c;,fe,o ,,co#b & all ! f]ric oxide c be made to disappe>4 ,we see1 !re=e1 t ,fe#c,o#d c only exi/ at temp]atures & 9 #cjh contact ) mixtures ( c>bon monoxide & dioxide1 repres5t$ by ! area :i* lies bel[ ! "u curve 9 ,fig4 #aba4 ,simil>ly1 ! region ( exi/5ce ( ,fe,o is t repres5t$ by ! area betwe5 ! two curves2 :ile metallic iron c exi/ "u ! conditions ( temp]ature & composition ( gas phase repres5t$ by ! area above ! upp] curve 9 ,fig4 #aba4 ,if1 !re=e1 f]ric oxide or metallic iron is heat$ = a suffici5tly long "t at temp]atures above #gjj;deg 7to ! "r ( ! dott$ l9e2 vide infra71 complete trans=mation to f]r\s oxide f9ally occurs4 ,9 ano!r s]ies ( equilibria :i* c be obta9$1 c>bon is "o ( ! solid phases4 ,9 ,fig4 #aba ! equilibria betwe5 c>bon1 c>bon monoxide1 & c>bon dioxide "u pressures ( "o & ( a qu>t] atmosph]e1 are repres5t$ by dott$ l9es4#cgi ,if we consid] only ! dott$ l9e on ! "r1 repres5t+ ! equilibria "u atmosph]ic pressure1 we see t ! po9ts 9 :i* ! dott$ l9e cuts ! o!r two curves mu/ repres5t sy/ems 9 :i* c>bon monoxide & c>bon dioxide are 9 equilibrium ) ,fe,o ,fe#c,o#d ,c1 on ! "o h&1 & ) ,fe ,fe,o ,c on ! o!r4 ,^! sy/ems c only exi/ at "o def9ite temp]ature1 if we make ! re/riction t ! pressure is ma9ta9$ con/ant 7atmosph]ic pressure74 ,/>t+1 !re=e1 ) ! equilibrium ,fe,o ,fe#c,o#d ,,co ,,co#b at a temp]ature ( ab\t #fgj;deg1 & !n add c>bon to ! sy/em1 ! reaction ,c ,,co#b #b;,,co w occur1 because ! conc5tration ( ,,co#b is great] ?an :at corresponds ) ! sy/em ,fe,o ,fe#c,o#d ,c 9 equilibrium ) c>bon monoxide & dioxide4 ,9 consequ5ce ( ?is reaction1 ! equilibrium betwe5 ,fe,o ,fe#c,o#d & ! gas phase is di/urb$1 & ! *ange 9 ! composition ( ! gas phase is oppos$ by ! reaction ,fe#c,o#d ,,co #c;,fe,o ,,co#b1 :i* cont9ues until ei!r all ! c>bon #cji or all ! f]ric oxide is us$ up4 ,if ! f]ric oxide fir/ disappe>s1 ! equilibrium corresponds ) a po9t on ! dott$ l9e 9 ! middle area ( ,fig4 #aba1 :i* repres5ts equilibria betwe5 ,fe,o ,c z solid phases1 & a mixture ( c>bon monoxide & dioxide z gas phase4 ,if ! temp]ature is high] ?an #fhe;deg1 at :i* temp]ature ! curve = ,c--,,co--,,co#b cuts t = ,fe--,fe,o--,,co--,,co#b2 !n1 :5 all ! f]ric oxide has disappe>$1 ! conc5tration ( ,,co#b is /ill too great = ! coexi/5ce ( ,fe,o & ,c4 ,consequ5tly1 !re occurs ! reaction ,c ,,co#b #b;,,co1 & ! composition ( ! gas phase alt]s until a po9t on ! upp] curve is rea*$4 ,a fur!r increase 9 ! conc5tration ( ,,co is oppos$ by ! reaction ,fe,o ,,co ,fe ,,co#b1 & ! pressure rema9s con/ant until all ! f]r\s oxide is r$uc$ & only iron & c>bon rema9 9 equilibrium ) gas4 ,if ! quantities ( ! sub/ances h be5 rightly *os51 we ultimately rea* a po9t on ! dott$ curve 9 ! upp] "p ( ,fig4 #aba4 ,fig4 #aba %[s u1 also1 :at are ! conditions "u :i* ! r$uction ( f]ric to f]r\s oxide by c>bon c occur4 ,let u suppose1 = example1 t we />t ) a mixture ( c>bon monoxide & dioxide at ab\t #fjj;deg 7! l[e/ po9t on ! dott$ l9e71 & ma9ta9 ! total pressure con/ant & equal to "o atmosph]e4 ,if ! temp]ature is increas$1 ! conc5tration ( ! c>bon dioxide w dim9i%1 ow+ to ! reaction ,c ,,co#b #b;,,co1 b ! f]ric oxide w und]go no *ange until ! temp]ature rea*es #fdg;deg1 ! po9t ( int]section ( ! dott$ curve ) ! curve = ,fe,o & ,fe#c,o#d4 ,at ?is po9t fur!r increase 9 ! conc5tration ( c>bon monoxide is oppos$ by ! r$uction ( f]ric oxide 9 accordance ) ! equation ,fe#c,o#d ,,co #c;,fe,o ,,co#b4 ,! pressure1 !re=e1 rema9s con/ant until all ! f]ric oxide has disappe>$4 ,if ! temp]ature is /ill fur!r rais$1 we aga9 obta9 a univ>iant sy/em1 ,fe,o ,c1 9 equilibrium ) gas 7univ>iant because ! total pressure is con/ant72 & if ! temp]ature is rais$ ! composition ( ! gas mu/ und]go *ange4 ,?is is effect$ by ! reaction ,c ,,co#b #b;,,co4 ,:5 ! #caj temp]ature rises to #fhe;deg1 at :i* ! dott$ curve cuts ! curve = ,fe--,fe,o1 fur!r *ange is prev5t$ by ! reaction ,fe,o ,,co ,fe ,,co#b4 ,:5 all ! f]r\s oxide is us$ up1 we obta9 ! sy/em ,fe ,c 9 equilibrium ) gas4 ,if ! temp]ature is n[ rais$1 ! composition ( ! gas und]goes *ange1 z %[n by ! dott$ l9e4 ,! two temp]atures1 #fdg;deg & #fhe;deg1 give1 evid5tly1 ! limits )9 :i* f]ric or f]r\s oxide c be r$uc$ directly by c>bon4 ,x is fur!r evid5t t at any temp]ature to ! "r ( ! dott$ l9e1 c>bon is un/able 9 pres5ce ( iron or its oxides2 :ile at temp]atures l[] ?an ^? repres5t$ by ! dott$ l9e1 x is /able4 ,9 ! bla/ furnace1 !re=e1 sep>ation ( c>bon c occur only at l[] temp]atures1 & ! c>bon mu/ disappe> on rais+ ! temp]ature4 ,f9ally1 x may be rem>k$ t ! equilibrium curves %[ t f]r\s oxide is mo/ easily r$uc$ at #fhj;deg1 s9ce ! conc5tration ( ! c>bon monoxide requir$ at ?is temp]ature is a m9imum4 ,on ! o!r h&1 f]ric oxide is r$uc$ ) greate/ difficulty at #dij;deg1 s9ce at ?is temp]ature ! requisite conc5tration ( c>bon monoxide is a maximum4 ,o!r equilibria betwe5 solid & gas phases are3 ,equilibrium betwe5 iron1 f]ric oxide1 wat] vap\r1 & hydrog51#chj & ! equilibria betwe5 c>bon1 c>bon monoxide1 c>bon dioxide1 wat] vap\r1 & hydrog51#cha :i* is ( importance = ! manufacture ( wat] gas4 99 99 99 99 99 #caa ,,*apt] ,,xviii ,,sy/ems ,,( ,,f\r ,,compon5ts ,9 ! sy/ems :i* h s f> be5 /udi$1 we h met ) cases :]e two or ?ree compon5ts c\ld ent] into comb9ation2 b 9 no case did we f9d d\ble decomposition occurr+4 ,! reason ( ?is is t 9 ! sy/ems previ\sly /udi$1 9 :i* d\ble decomposition might h be5 possible1 namely 9 ^? sy/ems 9 :i* two salts act$ z compon5ts1 ! re/riction 0 impos$ t ei!r ! basic or ! acid con/itu5t ( ^! salts mu/ be ! same2 a re/riction impos$1 inde$1 = ! v purpose ( exclud+ d\ble decomposition4 ,n[1 h[ev]1 we %all all[ ?is re/riction to fall1 !reby ext5d+ ! range ( /udy4 ,hi!rto1 9 connection ) f\r-compon5t sy/ems1 ! att5tion has be5 direct$ solely to ! /udy ( aque\s solutions ( salts1 & m especially ( ! salts :i* occur 9 sea-wat]1 i4e4 *iefly1 ! sulphates & *lorides ( magnesium1 potassium1 & sodium4 ,! importance ( ^! inve/igations w be recogniz$ :5 "o recollects t by ! evaporation ( sea-wat] !re h be5 =m$ ! enorm\s salt-b$s at ,/assfurt1 :i* con/itute at pres5t ! *ief s\rce ( ! sulphates & *lorides ( magnesium & potassium4 ,! inve/igations1 !re=e1 are n only ( great geological int]e/ z t5d+ to elucidate ! conditions "u :i* ^! salt-b$s h be5 =m$1 b are ( no less importance = ! indu/rial work+ ( ! deposits4 ,x is1 h[ev]1 n ! int5tion to ent] "h into any detail$ description ( ! diff]5t sy/ems :i* h s f> be5 /udi$1 & ( ! sometimes v complex relation%ips #cab met )1 b m]ely to ref] briefly to "s po9ts ( m g5]al import 9 connection ) ^! sy/ems4#chb ,reciprocal ,salt-,pairs4 ,*oice ( ,compon5ts4--,:5 two salts und]go d\ble decomposition1 ! int]action c be express$ by an equation su* z ,,nh#d;,cl ,na,n,o#c ,na,cl ,,nh#d,,no#c ,s9ce "o pair ( salts--,na,cl ,,nh#d,,no#c--;is =m$ f ! o!r pair--,,nh#d;,cl ,na,n,o#c--;by d\ble decomposition1 ! two pairs ( salts are kn[n z reciprocal salt-pairs4#chc ,x is ) sy/ems 9 :i* ! compon5t salts =m reciprocal salt-pairs t we h to deal "h4 ,x mu/ be not$1 h[ev]1 t ! f\r salts =m$ by two reciprocal salt-pairs d n con/itute a sy/em ( f\r1 b only ( ?ree compon5ts4 ,?is w be und]/ood if x is recall$ t only s _m con/itu5ts are tak5 z compon5ts z are necess>y to express ! composition ( all ! phases pres5t 7p4 #ab74 ,x w be se51 n[1 t ! composition ( ea* ( ! f\r salts :i* c be pres5t toge!r c be express$ 9 t]ms ( ?ree ( !m4 ,?us1 = example1 9 ! case ( ,,nh#d;,cl1 ,na,n,o#c1 ,,nh#d,,no#c1 ,na,cl1 we c express ! composition ( ,,nh#d;,cl by ,,nh#d,,no#c ,na,cl - ,na,n,o#c2 or ( ,na,n,o#c by ,,nh#d,,no#c ,na,cl - ,,nh#d;,cl4 ,9 all ^! cases x w be se5 t negative quantities ( "o ( ! compon5ts mu/ be employ$2 b t we h se5 to be q p]missible 7p4 #ab74 ,! numb] ( compon5ts is1 !re=e1 ?ree2 b any ?ree ( ! f\r salts c be *os54 ,s9ce1 !n1 two reciprocal salt-pairs con/itute only ?ree #cac compon5ts or indep5d5tly v>iable con/itu5ts1 ano!r compon5t is necess>y 9 ord] to obta9 a f\r-compon5t sy/em4 ,z su*1 we %all *oose wat]4 ,transition ,po9t4--,9 ! case ( ! =mation ( d\ble salts f two s+le salts1 we saw t !re 0 a po9t--! qu9tuple po9t--at :i* five phases c\ld coexi/4 ,?is po9t we also saw to be a transition po9t1 on "o side ( :i* ! d\ble salt1 on ! o!r side ! two s+le salts 9 contact ) solution1 7 f\nd to be ! /able sy/em4 ,a simil> behavi\r is f\nd 9 ! case ( reciprocal salt-pairs4 ,! f\r-compon5t sy/em1 two reciprocal salt-pairs & wat]1 c give rise to an inv>iant sy/em 9 :i* ! six phases1 f\r salts1 solution1 vap\r1 c coexi/2 ! temp]ature at :i* ?is is possible con/itutes a sextuple po9t4 ,n[1 ?is sextuple po9t is also a transition po9t1 on ! "o side ( :i* ! "o salt-pair1 on ! o!r side ! reciprocal salt-pair1 is /able 9 contact ) solution4 ,! sextuple po9t is ! po9t ( int]section ( ! curves ( six univ>iant sy/ems1 viz4 f\r solubility curves ) ?ree solid phases ea*1 a vap\r-pressure curve = ! sy/em3 two reciprocal salt-pairs--vap\r2 & a transition curve = ! cond5s$ sy/em3 two reciprocal salt-pairs--solution4 ,if we omit ! vap\r phase & "w "u atmosph]ic pressure 79 op5 vessels71 we f9d t ! transition po9t is ! po9t ( int]section ( f\r solubility curves4 ,j z 9 ! case ( ?ree-compon5t sy/ems we saw t ! pres5ce ( "o ( ! s+le salts along ) ! d\ble salt 0 necess>y 9 ord] to give a univ>iant sy/em1 s 9 ! f\r-compon5t sy/ems ! pres5ce ( a ?ird salt is necess>y z solid phase along ) "o ( ! salt-pairs4 ,9 ! case ( ! reciprocal salt-pairs m5tion$ above1 ! transition po9t w\ld be ! po9t ( int]section ( ! solubility curves ( ! sy/ems ) ! foll[+ gr\ps ( salts z solid phases3 ,bel[ ! transition po9t3 ,,nh#d;,cl ,na,n,o#c ,na,cl2 ,,nh#d;,cl ,na,n,o#c ,,nh#d,,no#c2 above ! transition po9t3 ,na,cl ,,nh#d,,no#c ,na,n,o#c2 ,na,cl ,,nh#d,,no#c ,,nh#d;,cl4 ,f ?is we see t ! two salts ,,nh#d;,cl & ,na,n,o#c w\ld be able to exi/ toge!r ) solution bel[ ! transition po9t1 b n above x4 ,?is transition po9t has n be5 det]m9$4 #cad ,=mation ( ,d\ble ,salts4--,9 all cases ( f\r-compon5t sy/ems s f> /udi$1 ! transition po9ts h n be5 po9ts at :i* "o salt-pair pass$ into its reciprocal1 b at :i* a d\ble salt 0 =m$4 ,?us1 at #d4d;deg ,glaub]'s salt & potassium *loride =m glas]ite & sodium *loride1 accord+ to ! equation #b,na#b,,s#d1aj;,h#b,o #c,k,cl ,k#c,na7,,s#d7b #c,na,cl #bj;,h#b,o ,above ! transition po9t1 !re=e1 !re w\ld be ,k#c,na7,,s#d7b1 ,na,cl & ,k,cl2 & x may be consid]$ t at a high] temp]ature ! d\ble salt w\ld int]act ) ! potassium *loride accord+ to ! equation ,k#c,na7,,s#d7b ,k,cl #b,k#b,,s#d ,na,cl ?us giv+ ! reciprocal ( ! orig9al salt-pair4 ,?is po9t has1 h[ev]1 n be5 exp]im5tally realiz$4#chd ,transition ,int]val4--,a d\ble salt1 we le>n$ 7p4 #bgg71 :5 br\ght 9 contact ) wat] at ! transition po9t und]goes p>tial decomposition ) sep>ation ( "o ( ! con/itu5t salts2 & only aft] a c]ta9 range ( temp]ature 7transition int]val7 has be5 pass$1 c a pure saturat$ solution be obta9$4 ,a simil> behavi\r is also f\nd 9 ! case ( reciprocal salt-pairs4 ,if "o ( ! salt-pairs is br\ght 9 contact ) wat] at ! transition po9t1 int]action w occur & "o ( ! salts ( ! reciprocal salt-pair w be deposit$2 & ?is w be ! case ?r\gh\t a c]ta9 range ( temp]ature1 aft] :i* x w be possible to prep>e a solution saturat$ only = ! "o salt-pair4 ,9 ! case ( ammonium *loride & sodium nitrate ! l[] limit ( ! transition int]val is #e4e;deg1 s t above ?is temp]ature & up to t ( ! transition po9t 7unkn[n71 ammonium *loride & sodium nitrate 9 contact ) wat] w\ld give rise to a ?ird salt by d\ble decomposition1 9 ?is case to sodium *loride4#che #cae ,graphic ,repres5tation4--,= ! graphic repres5tation ( sy/ems ( f\r compon5ts1 f\r axes may be *os5 int]sect+ at a po9t l ! edges ( a regul> octah$ron 7,fig4 #abb74chf ,along ^! diff]5t axes ! equival5t molecul> am\nts ( ! diff]5t salts are measur$4 ,illu/ration3 ,,fig4 #abb4 ,illu/ration3 ,,fig4 #abc4 ,to repres5t a giv5 sy/em consi/+ ( x,b1 y,c1 & z,d 9 a giv5 am\nt ( wat] 7:]e ,b1 ,c1 & ,d repres5t equival5t molecul> am\nts ( ! salts71 measure (f on ,,ob & ,,oc l5g?s equal to x & y respectively4 ,! po9t ( int]section a 7,fig4 #abb7 repres5ts a solution conta9+ x,b & y,c 7ab x2 ac y74 ,f a a l9e a,p is drawn p>allel to ,,od & equal to z4 ,p !n repres5ts ! solution ( ! above composition4 ,x is usual1 h[ev]1 n to employ ! ?ree-dim5sional figure1 b its horizontal & v]tical projections4 ,fig4 #abb1 if project$ on ! base ( ! octah$ron1 w\ld yield a diagram su* z is %[n 9 ,fig4 #abc4 ,! projection ( ! edges ( ! octah$ron =m two axes at "r angles & give rise to f\r quadrants simil> to ^? employ$ = ! repres5tation ( t]n>y solutions 7p4 #bgc74 ,"h1 ! po9t a repres5ts a t]n>y solution saturat$ ) respect to ,b & ,c2 & a,p1 quat]n>y solutions 9 equilibrium ) ! same two salts z solid phases4 ,su* a diagram repres5ts ! conditions ( equilibrium only = "o def9ite temp]ature1 & corresponds1 !re=e1 to ! iso!rmal diagrams = t]n>y sy/ems 7p4 #bgc74 ,9 su* a diagram1 s9ce ! temp]ature & #caf pressure are con/ant 7vessels op5 to ! air71 a surface w repres5t a solution 9 equilibrium ) only "o solid phase2 a l9e1 a solution ) two solid phases1 & a po9t1 "o 9 equilibrium ) ?ree solid phases4 ,illu/ration3 ,,fig4 #abd4 ,example4--,z an example ( ! complete iso!rmal diagram1 !re may be giv5 "o repres5t+ ! equilibria 9 ! sy/em compos$ ( wat] & ! reciprocal salt-pair sodium sulphate--potassium *loride = ! temp]ature #j;deg 7,fig4 #abd74chg ,! am\nts ( ! diff]5t salts are measur$ along ! f\r axes1 & ! composition ( ! solution is #cag express$ 9 equival5t gram-molecules p] #ajjj gram-molecules ( wat]4#chh ,! outl9e ( ?is figure repres5ts f\r t]n>y solutions 9 :i* ! compon5t salts h a common acid or basic con/itu5t2 viz4 sodium *loride--sodium sulphate1 sodium sulphate--potassium sulphate1 potassium sulphate--potassium *loride1 potassium *loride--sodium *loride4 ,^! f\r sets ( curves are !re=e simil> to ^? discuss$ 9 ! previ\s *apt]4 ,9 ! case ( sodium & potassium sulphate1 a d\ble salt1 glas]ite ,k#c,na7,,s#d7b is =m$4 ,:e!r glas]ite is really a def9ite comp\nd or n is /ill a matt] ( d\bt1 s9ce isomorphic mixtures ( ,na#b,,s#d & ,k#b,,s#d h be5 obta9$4 ,accord+ to van't ,h(f & ,b>s*oll1#chi glas]ite is an isomorph\s mixture2 b ,gossn]#cij consid]s x to be a def9ite comp\nd hav+ ! =mula ,k#c,na7,,s#d7b4 ,po9ts ,,viii4 & ,,ix4 repres5t solutions saturat$ ) respect to glas]ite & sodium sulphate1 & glas]ite & potassium sulphate respectively4 ,! l9es :i* pass inw>ds f ^! b\nd>y curves repres5t solutions conta9+ ?ree salts1 b 9 contact ) only two solid phases2 & ! po9ts :]e ?ree l9es meet1 or :]e ?ree fields meet1 repres5t solutions 9 equilibrium ) ?ree solid phases2 ) ! phases1 namely1 belong+ to ! ?ree concurr5t fields4 ,if x is desir$ to repres5t a solution conta9+ ! salts say 9 ! proportions1 #ea,na#b;,cl#b1 #i4e,k#b;,cl#b1 #c4e,k#b,,s#d1 ! difficulty is met ) t two ( ! salts1 sodium *loride & potassium sulphate1 lie on opposite axes4 ,to ov]come ?is difficulty ! diff]5ce #ea - #c4e #dg4e is tak5 & measur$ (f along ! sodium *loride axis2 & ! solution is !re=e repres5t$ by ! po9t #dg4e,na#b;,cl#b1 #i4e,k#b;,cl#b4 ,9 ord]1 !re=e1 to f9d ! am\nt ( potassium sulphate pres5t #cah f su* a diagram1 x is necess>y to "k ! total numb] ( salt molecules 9 ! solution4 ,:5 ?is is kn[n1 x is only necess>y to subtract f x ! sum ( ! molecules ( sodium & potassium *loride1 & ! result is equal to twice ! numb] ( potassium sulphate molecules4 ,?us1 9 ! above example1 ! total numb] ( salt molecules is #fd4 ,! numb] ( molecules ( sodium & potassium *loride is #eg2 #fd - #eg #g1 & !re=e ! numb] ( potassium sulphate molecules is #c4e4 ,ano!r me?od ( repres5tation employ$ is to indicate ! am\nts ( only two ( ! salts 9 a plane diagram1 & to measure (f ! total numb] ( molecules along a v]tical axis4 ,9 ?is way a solid model is obta9$4 ,! num]ical data f :i* ,fig4 #abd 0 con/ruct$ are conta9$ 9 ! foll[+ table1 :i* gives ! composition ( ! diff]5t solutions at #j;deg3--#cia ---------------------------------------- ,po9t4 ,solid phases4 ---------------------------------------- ,i4 ,na,cl ,,ii4 ,k,cl ,,iii4 ,na#b,,s#d1aj;,h#b,o ,,iv4 ,k#b,,s#d ,v4 ,na,cl2 ,k,cl ,,vi4 ,na,cl2 ,na#b,,s#d1aj;,h#b,o ,,vii4 ,k,cl2 ,k#b,,s#d ,,viii4 ,glas]ite2 ,na#b,,s#d1aj;,h#b,o ,,ix4 ,glas]ite2 ,k#b,,s#d ,x4 ,na#b,,s#d1aj;,h#b,o2 ,k,cl2 ,na,cl ,,xi4 ,na#b,,s#d1aj;,h#b,o2 ,k,cl2 glas]ite ,,xii4 ,k#b,,s#d2 ,k,cl2 glas]ite ---------------------------------------- ,transcrib]'s note3 table cont9u$ bel[444 ---------------------------------------- --------------------------------- ,composition ( solution 9 gram-mols4 ,total p] #ajjj gram-mols4 wat]4 numb] ---------------------------------------- --------------------- ( salt ,na#b;,cl#b4 ,k#b;,cl#b4 ,na#b,,s#d4 ,k#b,,s#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 ---------------------------------------- --------------------------------- ,f ! aspect ( ^! diagrams ! conditions "u :i* ! salts c coexi/ c be read at a glance4 ,?us1 #cai = example1 ,fig4 #abd %[s t at #j;deg ,glaub]'s salt & potassium *loride c exi/ toge!r ) solution2 namely1 9 contact ) solutions hav+ ! composition ,x--,,xi4 ,?is temp]ature mu/ !re=e be bel[ ! transition po9t ( ?is salt-pair 7p4 #cad74 ,on rais+ ! temp]ature to #d4d;deg1 x is f\nd t ! curve ,,viii4--,,xi4 moves s t ! po9t ,,xi4 co9cides ) po9t ,x4 ,at ?is po9t1 !re=e1 !re w be f\r concurr5t fields1 viz4 ,glaub]'s salt1 potassium *loride1 glas]ite1 & sodium *loride4 ,b ^! f\r salts c coexi/ ) solution only at ! transition po9t2 s t #d4d;deg is ! transition temp]ature ( ! salt-pair3 ,glaub]'s salt--potassium *loride4 ,at high] temp]atures ! l9e ,,viii4--,,xi4 moves /ill fur!r to ! left1 s t ! field = ,glaub]'s salt becomes entirely sep>at$ f ! field = potassium *loride4 ,?is %[s t at temp]atures above ! transition po9t ! salt-pair ,glaub]'s salt--potassium *loride _c coexi/ 9 pres5ce ( solution4 ,illu/ration3 ,,fig4 #abe4 ,if x is only desir$ to indicate ! mutual relation%ips ( ! diff]5t compon5ts & ! conditions = _! coexi/5ce 7p>ag5esis71 a simpl] diagram ?an ,fig4 #abd c be employ$4 ,?us if ! b\nd>y curves ( ,fig4 #abd are s drawn t !y cut "o ano!r at "r angles1 a figure su* z ,fig4 #abe is obta9$1 ! ,roman num]als "h correspond+ ) ^? 9 ,fig4 #abd4 ,ammonia-,soda ,process4--,"o ( ! mo/ important applications ( ! ,phase ,rule to sy/ems ( f\r compon5ts ) reciprocal salt-pairs has rec5tly be5 made by ,f$otieff#cib 9 8 inve/igations ( ! conditions = ! =mation ( sodium c>bonate by ! s-call$ ammonia-soda 7,solvay7 #cbj process4#cic ,?is process consi/s1 z is well kn[n1 9 pass+ c>bon dioxide ?r\gh a solution ( common salt saturat$ ) ammonia4 ,:atev] diff]5ces ( detail !re may be 9 ! process z c>ri$ out 9 diff]5t manufactories1 ! reaction :i* =ms ! basis ( ! process is t repres5t$ by ! equation ,na,cl ,,nh#d;,,hco#c ,na,h,c,o#c ,,nh#d;,cl ,we are deal+ "h1 !re=e1 ) reciprocal salt-pairs1 ! behavi\r ( :i* has j be5 discuss$ 9 ! prec$+ pages4 ,! pres5t case is1 h[ev]1 simpl] ?an t ( ! salt-pair ,na#b,,s#d4aj;,h#b,o ,k,cl1 inasmu* z "u ! conditions ( exp]im5t nei!r hydrates nor d\ble salts are =m$4 ,s9ce ! /udy ( ! reaction is r5d]$ m difficult on acc\nt ( ! fact t ammonium bic>bonate 9 solution1 :5 "u atmosph]ic pressure1 und]goes decomposition at temp]atures above #ae;deg1 ?is temp]ature 0 ! "o *os5 = ! detail$ inve/igation ( ! conditions ( equilibrium4 ,s9ce1 fur!r1 x has be5 %[n by ,bodla5d]#cid t ! bic>bonates possess a def9ite solubility only :5 ! pressure ( c>bon dioxide 9 ! solution has a def9ite value1 ! measurem5ts 7 c>ri$ out 9 solutions saturat$ ) ?is gas4 ,?is1 h[ev]1 does n con/itute ano!r compon5t1 because we h made ! re/riction t ! sum ( ! p>tial pressures ( c>bon dioxide & wat] vap\r is equal to #a atmosph]e4 ,! conc5tration ( ! c>bon dioxide is1 !re=e1 n indep5d5tly v>iable 7p4 #aj74 ,illu/ration3 ,,fig4 #abf4 ,9 ord] to obta9 ! data necess>y = a discussion ( ! conditions ( soda =mation by ! ammonia-soda process1 solubility det]m9ations ) ! f\r salts1 ,na,cl1 ,,nh#d;,cl1 ,,nh#d;,,hco#c1 & ,na,h,c,o#c 7 made1 fir/ ) ! s+le salts & !n #cba ) ! salts 9 pairs4 ,! results obta9$ are repres5t$ graphically 9 ,fig4 #abf1 :i* is an iso!rmal diagram simil> to t giv5 by ,fig4 #abd4 ,! po9ts ,i41 ,,ii41 ,,iii41 ,,iv41 repres5t ! composition ( solutions 9 equilibrium ) two solid salts4 ,we h1 h[ev]1 se5 7p4 #cad7 t ! transition po9t1 :5 ! exp]im5t is c>ri$ out "u con/ant pressure 7atmosph]ic pressure71 is ! po9t ( int]section ( f\r solubility curves1 ea* ( :i* repres5ts ! composition ( solutions 9 equilibrium ) ?ree salts1 viz4 "o ( ! reciprocal salt-pairs along ) a ?ird salt4 ,s9ce1 n[1 x 0 f\nd t ! /able salt-pair at temp]atures betwe5 #j;deg & #cj;deg is sodium bic>bonate & ammonium *loride1 det]m9ations 7 made ( ! composition ( solutions 9 equilibrium ) ,na,h,c,o#c ,,nh#d;,cl ,,nh#d;,,hco#c & ) ,na,h,c,o#c ,,nh#d;,cl ,na,cl z solid phases4 ,"u ! #cbb conditions ( exp]im5t 7temp]ature #ae;deg7 sodium *loride & ammonium bic>bonate _c coexi/ 9 contact ) solution4 ,^! det]m9ations gave ! data necess>y = ! con/ruction ( ! complete iso!rmal diagram 7,fig4 #abg74 ,! mo/ important ( ^! data are giv5 9 ! foll[+ table 7temp]ature1 #ae;deg73-- ---------------------------------------- --------------------------------- ,composition ( ! solution 9 gram-molecules to #ajjj gram-molecules ,po9t4 ,solid phases4 ( wat]4 ---------------------------------------- ------ ,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 ---------------------------------------- --------------------------------- ,) ref]5ce to ! solution repres5t$ by ! po9t ,p#a1 x may be rem>k$ t x is an incongru5tly saturat$ solution 7p4 #bgi74 ,if sodium *loride is add$ to ?is solution1 ! composition ( ! latt] und]goes *ange2 & if a suffici5t am\nt ( ! salt is add$1 ! solution ,p#b is obta9$4 ,turn+ n[ to ! practical application ( ! data s obta9$1 consid] fir/ :at is ! influ5ce ( conc5tration on ! yield ( soda4 ,s9ce ! reaction consi/s ess5tially 9 a d\ble decomposition betwe5 sodium *loride & ammonium bic>bonate1 !n1 aft] ! deposition ( ! sodium bic>bonate1 we obta9 a solution conta9+ sodium *loride1 ammonium *loride1 & sodium bic>bonate4 ,9 ord] to asc]ta9 to :at ext5t ! sodium *loride has be5 conv]t$ into solid sodium bic>bonate1 x is necess>y to exam9e ! composition ( ! solution :i* is obta9$ #cbc ) def9ite am\nts ( sodium *loride & ammonium bic>bonate4 ,illu/ration3 ,,fig4 #abg4 ,consid]1 9 ! fir/ place1 ! solutions repres5t$ by ! curve ,p#b,p#a4 ,) ! help ( ?is curve we c /ate ! conditions "u :i* a solution1 saturat$ = ammonium *loride1 is obta9$1 aft] deposition ( sodium bic>bonate4 ,9 ! foll[+ table ! composition ( ! solutions is giv5 :i* are obta9$ ) diff]5t initial am\nts ( sodium *loride & ammonium bic>bonate4 ,! la/ two columns give ! p]c5tage am\nt ( ! sodium us$1 :i* is deposit$ z solid sodium bic>bonate 7,u,na72 & likewise ! p]c5tage am\nt ( ammonium bic>bonate :i* is usefully conv]t$ into sodium bic>bonate1 t is to say1 ! am\nt ( ! radical ,,hco#c deposit$ 7,u,,nh#d73-- #cbd --------------------------- ,initial composition ( ! solutions3 grams ( salt to #ajjj ,po9t4grams ( wat]4 -------------------- ,na,cl ,,nh#d;,,hco#c -------------------------- ,p#b #dgi #bie -- #ddh #cfj -- #dag #dca ,p#a #cig #dif -------------------------- ,transcrib]'s note3 table cont9u$ bel[444 ---------------------------------------- ------------- ,composition ( solutions obta9$3 gram-equival5ts p] #ajjj grams ,u,na ,u,,nh#d ( wat]4 p] c5t4p] c5t4 ------------------------------- ,,hco#c ,cl ,na ,,nh#d ---------------------------------------- ---------- #j4ah #h4ag #d4fb #c4gc #dc4d #ie4a #j4ca #g4fe #c4ci #d4ef #ee4g #ic4d #j4ea #g4ac #b4ai #e4de #fi4b #ij4e #j4ib #f4gi #a4dd #f4bh #gh4h #he4a ---------------------------------------- ---------- ,?is table %[s t ! great] ! excess ( sodium *loride1 ! great] is ! p]c5tage utilization ( ammonia 7,po9t ,p#b72 & ! m ! am\nt ( sodium *loride decreases1 ! great] is ! p]c5tage am\nt ( sodium *loride conv]t$ into bic>bonate4 ,9 ! latt] case1 h[ev]1 ! p]c5tage utilization ( ! ammonium bic>bonate decreases2 t is to say1 less sodium bic>bonate is deposit$1 or m ( x rema9s 9 solution4 ,consid]1 9 ! same mann]1 ! relations = solutions repres5t$ by ! curve ,p#b;,,iv1 :i* gives ! composition ( solutions saturat$ ) respect to sodium bic>bonate & ammonium bic>bonate4 ,9 ?is case we obta9 ! foll[+ results3-- --------------------------- ,initial composition ( ! solutions3 grams ( salt to #ajjj ,po9t4grams ( wat]4 -------------------- ,na,cl ,,nh#d;,,hco#c -------------------------- ,p#a #cig #dif -- #cea #ddf -- #caf #dab -- #bid #chi -- #bcd #cbg -------------------------- ,transcrib]'s note3 table cont9u$ bel[444 ---------------------------------------- ---------- ,composition ( solutions obta9$3 9 gram-equival5ts p] #ajjj grams,u,na,u,,nh#d ( wat]4 ------------------------------- ,,hco#c ,cl ,na ,,nh#d ---------------------------------------- ------- #j4ib #f4gi #a4dd #f4bh #gh4h #he4a #j4ii #f4jj #a4cd #e4fe #gg4g #hb4e #a4jg #e4da #a4bg #e4ba #gf4d #gi4e #a4ab #e4jc #a4bc #d4ib #ge4e #ge4a #a4cj #d4jj #a4af #d4ad #ga4j #fh4f ---------------------------------------- ------- ,z is evid5t f ?is table1 dim9ution 9 ! relative am\nt ( sodium *loride ex]cises only a slight influ5ce #cbe on ! utilization ( ?is salt1 b is accompani$ by a rapid dim9ution ( ! effective trans=mation ( ! ammonium bic>bonate4 ,s f> z ! effici5t conv]sion ( ! sodium is conc]n$1 we see t x rea*es its maximum at ! po9t ,p#a1 & t x decreases bo? ) increase & ) decrease ( ! relative am\nt ( sodium *loride employ$2 & fa/]1 inde$1 9 ! =m] ?an 9 ! latt] case4 ,on ! o!r h&1 ! effective trans=mation ( ! ammonium bic>bonate rea*es its maximum at ! po9t ,p#b1 & dim9i%es ) increase 9 ! relative am\nt ( ammonium bic>bonate employ$4 ,s9ce sodium *loride is1 9 comp>ison ) ammonia--ev5 :5 ?is is reg5]at$--a *eap mat]ial1 x is evid5tly m advantage\s to "w ) solutions :i* are relatively ri* 9 sodium *loride 7solutions repres5t$ by ! curve ,p#a,p#b74 ,?is fact has also be5 e/abli%$ empirically4 ,:51 z is ! case 9 indu/rial practice1 we are deal+ ) solutions :i* are saturat$ n = two salts b only = sodium bic>bonate1 x is evid5t t we h !n to d ) solutions ! composition ( :i* is repres5t$ by po9ts 9 ! area ,p#a,p#b;,i1,,iv4 ,s9ce 9 ! comm]cial manufacture1 ! aim mu/ be to obta9 z complete a utilization ( ! mat]ials z possible1 ! solutions employ$ indu/rially mu/ lie 9 ! neighb\rhood ( ! curves ,p#b,p#a;,,iv1 z is indicat$ by ! %ad$ portion 9 ,fig4 #abg4 ,! be/ results1 f ! manufactur]'s /&po9t1 w be obta9$1 z already /at$1 :5 ! composition ( ! solutions approa*es t giv5 by a po9t on ! curve ,p#b,p#a4 ,consid]$ f ! *emical /&po9t1 ! results ( ! exp]im5ts lead to ! conclusion t ! ,solvay process1 i4e4 passage ( c>bon dioxide ?r\gh a solution ( sodium *loride saturat$ ) ammonia1 is n s good z ! new] me?od ( ,s*loes+1 :i* consi/s 9 br++ toge!r sodium *loride & ammonium bic>bonate ) wat]4#cie #cbf ,prep>ation ( ,b>ium ,nitrite4--,m5tion may also be made "h ( ! prep>ation ( b>ium nitrite by d\ble decomposition ( b>ium *loride & sodium nitrite4#cif ,! reaction ) :i* we are deal+ "h is repres5t$ by ! equation ,ba,cl#b #b,na,n,o#b #b,na,cl ,ba7,,no#b7b ,x 0 f\nd t at ! ord9>y temp]ature ,na,cl & ,ba7,,no#b7b =m ! /able salt-pair4 ,if1 !re=e1 b>ium *loride & sodium nitrite are br\ght toge!r ) an am\nt ( wat] insuffici5t = complete solution1 trans=mation to ! /able salt-pair occurs1 & sodium *loride & b>ium nitrite are deposit$4 ,:51 h[ev]1 a /able salt-pair is 9 its transition int]val 7p4 #cae71 a ?ird salt--9 ?is case b>ium *loride--w be deposit$1 z we h already le>n$4 ,on br++ b>ium *loride & sodium nitrite toge!r ) wat]1 !re=e1 ?ree solid phases are obta9$1 viz4 ,ba,cl#b1 ,na,cl1 ,ba7,,no#b7b4 ,^! ?ree phases1 toge!r ) solution & vap\r1 con/itute a univ>iant sy/em1 s t at ea* temp]ature ! composition ( ! solution mu/ be con/ant4 ,witt & ,ludwig f\nd t ! pres5ce ( solid b>ium *loride c be prev5t$ by add+ an excess ( sodium nitrite1 z c be readily =ese5 f :at has be5 said4 ,s9ce ! solution 9 pres5ce ( ! ?ree solid phases mu/ h a def9ite composition at a def9ite temp]ature1 ! addition ( sodium nitrite to ! solution mu/ h1 z its consequ5ce1 ! solution ( an equival5t am\nt ( b>ium *loride1 & ! deposition ( an equival5t am\nt ( sodium *loride & b>ium nitrite4 ,by suffici5t addition ( sodium nitrite1 ! complete disappe>ance ( ! solid b>ium *loride c be effect$1 & !re w rema9 only ! /able salt-pair sodium *loride & b>ium nitrite4 ,z 0 po9t$ out by ,mey]h(f]1 h[ev]1 ! disappe>ance ( ! b>ium *loride is effect$1 n by a *ange 9 ! #cbg composition ( ! solution1 b by ! necessity = ! composition ( ! solution rema9+ con/ant4 ,illu/ration3 ,,fig4 #abh4 ,b>ium ,c>bonate & ,potassium ,sulphate4--,z has be5 f\nd by ,mey]h(f]1#cig ^! two salts =m ! /able pair1 n only at ! ord9>y temp]ature1 b also at ! melt+ po9t4 ,= ! ord9>y temp]atures ?is 0 prov$ 9 ! foll[+ mann]3 ,a solution ) ! solid phases ,k#b,,s#d & ,k#b;,,co#c4b;,h#b,o 9 excess c only coexi/ 9 contact ei!r ) ,ba,c,o#c or ) ,ba,s,o#d1 s9ce1 evid5tly1 9 "o ( ! two gr\ps ! /able sy/em mu/ be pres5t4 ,two solutions 7 prep>$1 ea* ) excess ( ,k#b,,s#d ,k#b;,,co#c4b;,h#b,o1 #cbh & to "o 0 add$ ,ba,c,o#c & to ! o!r ,ba,s,o#d4 ,aft] /irr+ = a few days1 ! b>ium sulphate 0 completely trans=m$ to ,ba,c,o#c1 :]eas ! b>ium c>bonate rema9$ un*ang$4 ,consequ5tly1 ,ba,c,o#c ,k#b,,s#d ,k#b;,,co#c4b;,h#b,o is /able1 &1 !re=e1 s also is ,ba,c,o#c ,k#b,,s#d4 ,t ,ba,c,o#c ,k#b,,s#d is ! /able pair also at ! melt+ po9t 0 prov$ by a special analytical me?od :i* all[s ( ! detection ( ,k#b;,,co#c 9 a mixture ( ! f\r solid salts4 ,?is analysis %[$ t a mixture ( ,ba,c,o#c ,k#b,,s#d1 aft] be+ fus$ & all[$ to solidify1 conta9s only small am\nts ( ,k#b;,,co#c2 & ?is is due entirely to ! fact t ,ba,c,o#c ,k#b,,s#d on fusion deposits a little ,ba,s,o#d1 !reby giv+ rise at ! same "t to ! sep>ation ( an equival5t am\nt ( ,k#b;,,co#c4 ,! diff]5t solubilities are %[n 9 ,fig4 #abh4 ,9 ?is diagram ! solubility ( ! two b>ium salts has be5 neglect$4 ,a is ! solubility ( ,k#b;,,co#c4b;,h#b,o2 addition ( ,ba,c,o#c does n alt] ?is4 ,b is ! solubility ( ,k#b;,,co#c4b;,h#b,o ,k#b,,s#d ,ba,c,o#c4 ,a & ,b almo/ co9cide1 s9ce ! potassium sulphate is v slightly soluble 9 ! conc5trat$ solution ( potassium c>bonate4 ,d gives ! conc5tration ( ! solution 9 equilibrium ) ,k#b,,s#d ,ba,s,o#d4 ,! mo/ int]e/+ po9t is ,c4 ,?is solution is obta9$ by add+ a small quantity ( wat] to ,ba,c,o#c ,k#b,,s#d1 :]eupon1 be+ 9 ! transition int]val1 ,ba,s,o#d sep>ates out & an equival5t am\nt ( ,k#b;,,co#c goes into solution4 ,c is ! end po9t ( ! curve ,,co1 :i* is call$ ! ,guldb]g-,waage curve1 because ^! inve/igators det]m9$ sev]al po9ts on x4 ,9 _! exp]im5ts1 ,guldb]g & ,waage f\nd ! ratio ,k#b;,,co#c 3 ,k#b,,s#d 9 solution to be con/ant & equal to #d4 ,?is result is1 h[ev]1 n exact1 = ! curve ,,co is n a /raight l9e1 z x %\ld be if ! above ratio 7 con/ant2 b x is concave to ! abscissa axis1 & m s at l[] ?an at high] temp]atures4 ,! foll[+ table ref]s to ! temp]ature ( #be;deg4 ,! ,roman numb]s 9 ! fir/ column ref] to ! po9ts 9 ,fig4 #abh4 ,! numb]s 9 ! column ,sigmak#b give ! am\nt1 #cbi 9 gram-molecules1 ( ,k#b;,,co#c ,k#b,,s#d conta9$ 9 #ajjj gram-molecules ( wat]3-- ,,solubility ,,det]m9ations ,,at #be;deg4 ---------------------------------------- ------------------------- #ajj gms4 ( ! solution conta91 ,no4 ,solid phases4 9 grams1 ,k#b;,,co#c,k#b,,s#d ---------------------------------------- ------------------------ ,i4 ,k#b;,,co#c4b;,h#b,o ,ba,c,o#c #ec4b -- ,,ii4 ,k#b;,,co#c4b;,h#b,o ,k#b,,s#d #ec4j #j4jbc ,ba,c,o#c ,,iii4 ,k#b,,s#d ,ba,c,o#c #bh4e #j4hhf ,,iv4 #bb4a #a4gb ,v4 ,ba,c,o#c ,k#b,,s#d ,ba,s,o#d #ag4ha #b4dhe ,,vi4 ,k#b,,s#d ,ba,s,o#d #ab4f #c4ib ,,vii4 #e4he #f4gf ,,viii4 ,k#b,,s#d -- #aj4gf ,,ix4 ,ba,c,o#c ,ba,s,o#d #g4ce #j4fjb ,x4 #b4he #j4agc ---------------------------------------- ------------------------ ,transcrib]'s note3 table cont9u$ bel[444 ---------------------------------------- ---------------- #ajjj moles ( wat] conta91 ,k#b;,,co#c ,no4 9 moles1 ,sigmak#b ----------- ,k#b,,s#d ,k#b;,,co#c,k#b,,s#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 ---------------------------------------- --------------- ,! ,guldb]g-,waage curve at #ajj;deg 0 also det]m9$1 & x 0 f\nd t ! ratio ,k#b;,,co#c3 ,k#b,,s#d is also n con/ant1 al?\gh ! v>iations are n s great z at #be;deg4 ,,guldb]g-,,waage ,,curve ,,at #ajj;deg4 ---------------------------------------- ----------------------------- #ajj moles ( wat] ,k#b;,,co#c ,solid phases4 conta91 9 moles1 ,sigmak#b ----- ,k#b,,s#d ,k#b;,,co#c,k#b,,s#d ---------------------------------------- ---------------------------- ,ba,c,o#c ,k#b,,s#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 ,,app5dix ,,exp]im5tal ,,det]m9ation ,,( ,,! ,,transition ,,po9t ,= ! purpose ( det]m9+ ! transition temp]ature1 a numb] ( me?ods h be5 employ$1 & ! mo/ important ( ^! w be briefly describ$ "h4 ,9 any giv5 case x is sometimes possible to employ m ?an "o me?od1 b all are n equally suitable1 & ! values ( ! transition po9t obta9$ by ! diff]5t me?ods are n always id5tical4 ,inde$1 a diff]5ce ( sev]al degrees 9 ! value f\nd may q well occur4#cih ,9 ea* case1 !re=e1 "s c>e mu/ be tak5 to select ! me?od mo/ suitable = ! purpose4 ,i4 ,! ,dilatometric ,me?od4--,s9ce1 9 ! majority ( cases1 trans=mation at ! transition po9t is accompani$ by an appreciable *ange ( volume1 x is only necess>y to asc]ta9 ! temp]ature at :i* ?is *ange ( volume occurs1 9 ord] to det]m9e ! transition po9t4 ,= ?is purpose ! dilatomet] is employ$1 an app>atus :i* consi/s ( a bulb ) capill>y tube atta*$1 & :i* con/itutes a sort ( l>ge !rmomet] 7,fig4 #abi74 ,"s ( ! sub/ance to be exam9$ is pass$ into ! bulb ,a ?r\gh ! tube ,b1 :i* is !n seal$ (f4 ,! re/ ( ! bulb & a small portion ( ! capill>y tube is !n fill$ ) "s liquid1 :i*1 ( c\rse1 mu/ be )\t *emical action on ! sub/ance "u inve/igation4 ,a liquid1 h[ev]1 may be employ$ :i* dissolves ! sub/ance1 =1 z we h se5 7p4 #gj71 ! trans=mation at ! transition po9t is1 z a rule1 accel]at$ by ! pres5ce ( a solv5t4 ,on ! o!r h&1 ! liquid mu/ n dissolve 9 ! sub/ance "u exam9ation1 = ! temp]ature ( trans=mation w\ld be !reby alt]$4 #cca ,9 us+ ! dilatomet]1 two me?ods ( proc$ure may be foll[$4 ,accord+ to ! fir/ me?od1 ! dilatomet] conta9+ ! =m /able at l[] temp]atures is plac$ 9 a !rmo/at1 ma9ta9$ at a con/ant temp]ature1 until x has tak5 ! temp]ature ( ! ba?4 ,! height ( ! m5iscus is !n read on a millimetre scale atta*$ to ! capill>y4 ,! temp]ature ( ! !rmo/at is !n rais$ degree by degree1 & ! height ( ! m5iscus at ea* po9t asc]ta9$4 ,if1 n[1 no *ange takes place 9 ! solid1 ! expansion w be practically uni=m1 or ! rise 9 ! level ( ! m5iscus p] degree ( temp]ature w be practically ! same at ! diff]5t temp]atures1 z repres5t$ diagrammatically by ! l9e ,,ab 9 ,fig4 #acj4 ,on pass+ ?r\gh ! transition po9t1 h[ev]1 !re w be a m or less sudd5 increase 9 ! rise ( ! m5iscus p] degree 7l9e ,,bc7 if ! specific volume ( ! =m /able at high] temp]atures is great] ?an t ( ! orig9al modification2 !reaft]1 ! expansion w aga9 be uni=m 7l9e ,,cd74 ,simil>ly1 on cool+1 contraction w at fir/ be uni=m & !n at ! transition po9t !re w be a relatively l>ge dim9ution ( volume4 ,illu/ration3 ,,fig4 #abi4 ,illu/ration3 ,,fig4 #acj4 ,if1 n[1 trans=mation occurr$ imm$iately ! transition po9t 0 rea*$1 ! sudd5 expansion & contraction w\ld take place at ! same temp]ature4 ,x is1 h[ev]1 g5]ally f\nd t !re is a lag1 & t ) ris+ temp]ature ! relatively l>ge expansion does n take place until a temp]ature some:at high] ?an ! transition po9t2 & ) fall+ temp]ature ! contraction occurs at a temp]ature some:at bel[ ! transition po9t4 ,?is is repres5t$ 9 ,fig4 #acj by ! l9es ,,bc & ,,ef4 ,! am\nt ( lag w v>y f case to case1 & w #ccb also dep5d on ! l5g? ( "t dur+ :i* ! dilatomet] is ma9ta9$ at con/ant temp]ature4 ,z an example1 !re may be giv5 ! results obta9$ 9 ! det]m9ation ( ! transition po9t at :i* sodium sulphate & magnesium sulphate =m a/racanite 7p4 #bfh74cii ,! dilatomet] 0 *>g$ ) a mixture ( ! two sulphates4 ---------------------------------------- ---------------- ,temp]ature4 ,level ( oil 9 capill>y4 ,rise p] #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 ---------------------------------------- ---------------- ,! transition po9t1 !re=e1 lies ab\t #ba4f;deg 7p4 #bfh74 ,! second me?od ( manipulation dep5ds on ! fact t1 :ile above or bel[ ! transition po9t trans=mation ( "o =m into ! o!r c take place1 at ! transition po9t ! two =ms und]go no *ange4 ,! bulb ( ! dilatomet] is1 !re=e1 *>g$ ) a mixture ( ! /able & meta/able =ms & a suitable liquid1 & is !n imm]s$ 9 a ba? at con/ant temp]ature4 ,aft] ! temp]ature ( ! ba? has be5 acquir$1 read+s ( ! height ( ! m5iscus are made f "t to "t to asc]ta9 :e!r expansion or contraction occurs4 ,if expansion is f\nd1 ! temp]ature ( ! !rmo/at is alt]$ until a temp]ature is obta9$ at :i* a gradual contraction takes place4 ,! transition po9t mu/ !n lie betwe5 ^! two temp]atures2 & by repeat+ ! det]m9ations x w be possible to r$uce ! diff]5ce betwe5 ! temp]atures at :i* expansion & contraction take place to1 say1 #a;deg1 & to fix ! temp]ature ( ! transition po9t1 !re=e1 to )9 half a degree4 ,by ?is me?od ! transition po9t1 = example1 ( sulphur 0 f\nd to be #ie4f;deg "u a pressure ( #d atm4#djj ,! foll[+ are ! figures obta9$ by ,rei*]1 :o us$ a mixture #ccc ( #a "p ( c>bon disulphide 7solv5t = sulphur7 & #e p>ts ( turp5t9e z ! measur+ liquid4 ,,temp]ature #ie4a;deg4 ----------------------------------- ,"t 9 m9utes4 ,level ( liquid4 ----------------------------------- #e #cdc4e #cj #cdj4e #ee #cce4ge #fe #ccc ----------------------------------- ,,temp]ature #if4a;deg4 ----------------------------------- ,"t 9 m9utes4 ,level ( liquid4 ----------------------------------- #e #cdb4ge #cj #ced4ge #ee #cfj4e #fj #cfa4e ----------------------------------- ,,temp]ature #ie4f;deg4 ----------------------------------- ,"t 9 m9utes4 ,level ( liquid4 ----------------------------------- #e #cfh4ge #ajj #cfh #aaj #cfh4ge ----------------------------------- ,at a temp]ature ( #ie4a;deg !re is a contraction1 i4e4 monocl9ic sulphur passes into ! rhombic1 ! specific volume ( ! =m] be+ great] ?an t ( ! latt]4 ,at #if4a;deg1 h[ev]1 !re is expansion1 %[+ t at ?is temp]ature rhombic sulphur passes into monocl9ic2 :ile at #ie4f;deg !re is nei!r expansion nor contraction4 ,?is is1 !re=e1 ! transition temp]ature2 & s9ce ! dilatomet] 0 seal$ up to prev5t evaporation ( ! liquid1 ! pressure )9 x 0 #d atm4 ,,ii4 ,measurem5t ( ! ,vap\r ,pressure4--,9 ! prec$+ pages x has be5 se5 repeat$ly t ! vap\r pressures ( ! two sy/ems und]go+ reciprocal trans=mation become id5tical at ! transition po9t 7m /rictly1 at ! triple or #ccd multiple po9t71 & ! latt] c !re=e be det]m9$ by asc]ta9+ ! temp]ature at :i* ?is id5tity ( vap\r pressure is e/abli%$4 ,! app>atus usually employ$ = ?is purpose is ! ,brem]-,fr[e9 t5simet] 7p4 #ia74 ,al?\gh ?is me?od has n z yet be5 appli$ to sy/ems ( "o compon5t1 x has be5 us$ to a consid]able ext5t 9 ! case ( sy/ems conta9+ wat] or o!r volatile compon5t4 ,an example ( ?is has already be5 giv5 9 ,glaub]'s salt 7p4 #aci74 ,,iii4 ,solubility ,measurem5ts4--,! temp]ature ( ! transition po9t c also be fix$ by means ( solubility measurem5ts1 = at t po9t ! solubility ( ! two sy/ems becomes id5tical4 ,ref]5ce has already be5 made to sev]al cases 9 :i* ?is me?od 0 employ$1 e4g4 ammonium nitrate 7p4 #aab71 ,glaub]'s salt 7p4 #acd71 a/racanite & sodium & magnesium sulphates 7p4 #bfh74 ,! det]m9ations ( ! solubility c be c>ri$ out 9 v>i\s ways4 ,"o ( ! simple/ me?ods1 :i* also gives suffici5tly accurate results :5 ! temp]ature is n high or :5 ! solv5t is n v volatile1 c be c>ri$ out 9 ! foll[+ mann]4 ,! solid sub/ance is f9ely p[d]$ 79 ord] to accel]ate ! process ( solution71 & plac$ 9 suffici5t quantity along ) ! solv5t 9 a tube c>efully clos$ by a glass /opp]2 ! latt] is protect$ by a rubb] cap1 su* z a rubb] f+]-/all4 ,! tube is !n rotat$ 9 a !rmo/at1 ! temp]ature ( :i* does n v>y m ?an "o or two t5?s ( a degree1 until saturation is produc$4 ,! solution is )drawn by means ( a pipette to :i* a small glass tube1 fill$ ) cotton wool to act z a filt]1 is atta*$4 ,! solution is !n run into a weigh+ bottle1 & weigh$2 aft] :i* ! am\nt ( solid 9 solution is det]m9$ 9 a suitable mann]4 ,= m accurate det]m9ations ( ! solubility1 especially :5 ! solv5t is appreciably volatile at ! temp]ature ( exp]im5t1 o!r me?ods are pref]able4 ,9 ,fig4 #aca is %[n ! app>atus employ$ by ,h4 ,golds*midt1#dja & us$ to a consid]able ext5t 9 ! laboratory ( van't ,h(f4 ,?is consi/s ess5tially ( ?ree p>ts3 a1 a tube 9 :i* ! solv5t & salt are plac$2 ?is is clos$ at ! foot by an india-rubb] /opp]4 ,?r\gh ?is /opp] !re passes ! b5t tube cb1 :i* connects ! tube a ) ! weigh+-tube d4 ,at c !re is a plug ( cotton wool4 ,tube e is op5 to ! air4 ,! wid] portion ( ! tube cb1 :i* passes ?r\gh ! rubb] /opp] 9 a1 c be clos$ by a plug #cce atta*$ to a glass rod ff1 :i* passes up ?r\gh a holl[ ,witt /irr]1 g4 ,aft] be+ fitt$ toge!r1 ! :ole app>atus is imm]s$ 9 ! !rmo/at4 ,aft] ! solution has become saturat$1 ! /opp] ( ! b5t tube is rais$ by means ( ! rod ff & a suction-pump atta*$ to ! end ( e4 ,! solution is !reby drawn into ! weigh+-tube d1 ! undissolv$ salt be+ reta9$ by ! plug at c4 ,! app>atus is !n remov$ f ! !rmo/at1 tube d deta*$ & imm$iately clos$ by a gr\nd /opp]4 ,x is !n c>efully dri$ & weigh$4 ,illu/ration3 ,,fig4 #aca4 ,ano!r =m ( solubility vessel1 due to ,mey]h(f] & ,saund]s1 is %[n 9 ,fig4 #acb4djb ,?is consi/s ( a s+le tube1 & ! /irr+ is effect$ by means ( a glass screw4 ,illu/ration3 ,,fig4 #acb4 ,! progress ( ! solution t[>ds saturation c be v well te/$ by det]m9+ ! d5sity ( ! solution f "t to #ccf "t4 ,?is is mo/ conv5i5tly c>ri$ out by means ( ! pipette %[n 9 ,fig4 #acc4djc ,) ?is pipette ! solution c n only be remov$ = weigh+1 b ! volume c be det]m9$ at ! same "t4 ,x consi/s ( ! wide tube a1 to :i* ! graduat$ capill>y b1 furni%$ ) a cap c1 is atta*$4 ,to ! l[] end ( ! pipette ! tube e1 ) plug ( cotton wool1 c be fix$4 ,aft] ! pipette has be5 fill$ by suck+ at ! end ( b1 ! /op-cock d is clos$ & ! cap c plac$ on ! capill>y4 ,! app>atus c !n be weigh$1 & ! volume ( ! solution be asc]ta9$ by means ( ! graduations4 ,z has already be5 insi/$1 p>ticul> c>e mu/ be paid to ! *>act]ization ( ! solid 9 contact ) ! solution4 ,illu/ration3 ,,fig4 #acc4 ,,iv4 ,!rmometric ,me?od4--,if a sub/ance is heat$1 its temp]ature w gradually rise until ! melt+ po9t is rea*$1 & ! temp]ature w !n rema9 con/ant until all ! solid has pass$ into liquid4 ,simil>ly1 if a sub/ance :i* c und]go trans=mation is heat$1 ! temp]ature w rise until ! transition po9t is rea*$1 & w !n rema9 con/ant until complete trans=mation has tak5 place4 ,?is me?od1 x w be rememb]$1 0 employ$ by ,ri*>ds = ! det]m9ation ( ! transition po9t ( sodium sulphate decahydrate 7p4 #acf74 ,! foll[+ figures give ! results obta9$ by ,mey]h(f] 9 ! case ( ! trans=mation3-- ,cu,k#b;,cl#d1b;,h#b,o -- ,cu,k,cl#c ,k,cl #b;,h#b,o ! temp]ature be+ not$ f m9ute to m9ute3 #ie;deg1 #ic;deg1 #ia4h;deg1 #ia4g;deg1 #ib;deg1 #ib4c;deg1 #ib4d;deg1 #ib4b;deg1 #ib4b;deg1 #ib;deg1 #ij4e;deg1 #hi;deg1 & !n a rapid fall 9 ! temp]ature4 ,f ?is we see t ! transition po9t is ab\t #ib4b;deg4 ,x is also evid5t t a slight sup]cool+ took place 7#ia4g;deg71 ow+ to a delay 9 ! trans=mation1 b t !n ! temp]ature rose to ! transition po9t4 ,?is is analog\s to ! sup]cool+ ( a liquid4 ,a simil> halt 9 ! temp]ature w\ld be obs]v$ on pass+ f l[] to high] temp]atures2 b ow+ to a lag 9 ! trans=mation1 ! same temp]ature is n always obta9$4 #ccg ,v4 ,optical ,me?od4--,! transition po9t c sometimes be det]m9$ by not+ ! temp]ature at :i* "s alt]ation 9 ! appe>ance ( ! sub/ance occurs1 su* z a *ange ( col\r or ( ! cry/all9e =m4 ,?us m]curic iodide *anges col\r f r$ to yell[1 & ! blue quadratic cry/als ( copp] calcium acetate *ange1 on pass+ ! transition po9t1 into gre5 rhombs ( copp] acetate & :ite ne$les ( calcium acetate 7p4 #bfj74 ,or aga91 *anges 9 ! d\ble refraction ( ! cry/als may be also employ$ to asc]ta9 ! temp]ature ( ! transition po9t4 ,^! *anges are be/ obs]v$ by means ( a microscope4 ,= ! purpose ( regulat+ ! temp]ature ( ! sub/ance a small copp] air-ba? is employ$4#djd ,,vi4 ,electrical ,me?ods4--,electrical me?ods = ! det]m9ation ( ! transition po9t are ( two k9ds1 bas$ on measurem5ts ( conductivity or ( electromotive =ce4 ,bo? me?ods are re/rict$ 9 _! application1 b :]e applicable give v exact results4 ,! =m] me?od1 :i* has be5 employ$ 9 sev]al cases1 ne$ n be describ$ "h4 ,! second me?od1 h[ev]1 is ( consid]able int]e/ & importance1 & calls = special ref]5ce4#dje ,if two pieces1 say1 ( z9c1 connect$ toge!r by a conduct+ wire1 are plac$ 9 a solution ( a z9c salt1 e4g4 z9c sulphate1 ! pot5tial ( ! two electrodes w be ! same1 & no curr5t w be produc$ 9 ! connect+ wire4 ,if1 h[ev]1 ! z9c electrodes are imm]s$ 9 two solutions ( diff]5t conc5tration conta9$ 9 sep>ate vessels1 b plac$ 9 connection ) "o ano!r by means ( a b5t tube fill$ ) a conduct+ solution1 ! pot5tials at ! electrodes w no long] be ! same1 & a curr5t w n[ fl[ ?r\gh ! connect+ wire4 ,! direction ( ?is curr5t 9 ! cell w be f ! weak] to ! m conc5trat$ solution4 ,! great] ! diff]5ce 9 ! conc5tration ( ! solutions ) respect to z9c1 ! great] w be ! diff]5ce ( ! pot5tial at ! two electrodes1 or ! great] w be ! ,e4,m4,f4 ( ! cell4 ,:5 ! conc5tration ( ! two solutions becomes ! same1 ! ,e4,m4,f4 w become z]o1 & no curr5t w pass4 ,x w be und]/ood n[ h[ ?is me?od c be made use ( #cch = det]m9+ ! transition po9t ( a salt1 :5 we be> 9 m9d t at ! transition po9t ! solubility ( ! two =ms becomes id5tical4 ,?us1 = example1 ! transition po9t ( z9c sulphate heptahydrate into hexahydrate c\ld be det]m9$ 9 ! foll[+ mann]4 ,tube ,a 7,fig4 #acd7 conta9s1 say1 a saturat$ solution ( ! heptahydrate along ) "s ( ! solid salt2 tube ,b1 a saturat$ solution ( ! hexahydrate along ) ! solid salt4 ,! tube ,c is a connect+ tube b5t d[nw>ds s z to prev5t ! mix+ ( ! solutions by convection curr5ts4 ,,zz are two z9c electrodes imm]s$ 9 ! solution2 ! cell is plac$ 9 a !rmo/at & ! z9c electrodes connect$ ) a galvanomet]4 ,s9ce1 n[1 at temp]atures bel[ ! transition po9t ! solubility ( ! hexahydrate 7! meta/able =m7 is great] ?an t ( ! heptahydrate1 a curr5t w be produc$1 fl[+ 9 ! cell f heptahydrate to hexahydrate4 ,z ! temp]ature is rais$ t[>ds ! transition po9t1 ! solubilities ( ! two hydrates also approa*1 & ! curr5t produc$ w !re=e become weak]1 because ! ,e4,m4,f4 ( ! cell becomes less2 & :5 ! transition po9t is atta9$1 ! ,e4,m4,f4 becomes z]o1 & ! curr5t ceases4 ,if ! temp]ature is rais$ above ?is1 ! solubility ( ! heptahydrate becomes great] ?an t ( ! hexahydrate1 & a curr5t w aga9 be produc$1 b 9 ! opposite direction4 ,by not+ ! temp]ature1 !re=e1 at :i* ! curr5t ceases1 or ! ,e4,m4,f4 becomes z]o1 ! transition temp]ature c be asc]ta9$4#djf ,illu/ration3 ,,fig4 #acd4 ,9 ! case j describ$1 ! electrodes consi/$ ( ! same metal z 0 conta9$ 9 ! salt4 ,b 9 "s cases1 e4g4 sodium sulphate1 electrodes ( ! metal conta9$ 9 ! salt _c be employ$4 ,nev]!less1 ! above electrical me?od c be us$ #cci ev5 9 ^? cases1 if a suitable non-pol>izable m]cury electrode is employ$4#djg ,al?\gh1 z we saw1 no curr5t 0 produc$ :5 two pieces ( z9c 7 imm]s$ 9 ! same solution ( z9c salt1 a curr5t w be obta9$ if two diff]5t metals1 or ev5 two diff]5t modifications ( ! same metal1 are employ$4 ,?us an ,e4,m4,f4 w be e/abli%$ :5 electrodes ( grey & ( :ite t9 are imm]s$ 9 ! same solution ( z9c salt1 b at ! transition po9t ?is ,e4,m4,f4 w become z]o4 ,by ?is me?od ,coh5 det]m9$ ! transition po9t ( grey & :ite t9 7p4 #db74 99 99 99 99 99 #cdj ,,"n ,,index ,a ,abegg1 #eb ,adriani1 #ahf1 #bag1 #bbj ,alexejeff1 #ig1 #abe ,allan1 #bih ,all51 ,l4 ,e41 #aji ,all51 ,r4 ,w41 #fc ,ampolla1 #bac ,&reae1 #aji ,ari/otle1 #da ,arm/rong1 ,e4 ,f41 #cac ,arm/rong1 ,h4 ,e41 #aif ,arzruni1 #cc ,at51 #adg1 #afc ,au]ba*1 #cbf ,b ,babo1 #abf ,bancr(t1 #ajb1 #ajd1 #afa1 #agf1 #aif1 #bjb1 #bbi1 #bdf1 #bfj1 #bfa1 #bgb1 #bha1 #cjb ,b>nes1 #cca1 #cci ,b>s*all1 #cah ,b>us1 #fg ,battelli1 #bc ,baur1 #bcc1 #cjg ,beckmann1 #di ,bell1 #bbi ,b]?ollet1 #g ,bodla5d]1 #aha1 #bdg1 #caa1 #cba ,bogojawl5ski1 #gb ,b\d\>d1 #cji1 #caa ,braun1 #ajg ,brauns1 #dj1 #ea1 #gd ,br$ig1 #eb ,brem]1 #ia ,brodie1 #cd1 #dg ,brun]1 #abf ,bruni1 #aha1 #ahb1 #bef1 #beg ,buns51 #fg ,c ,cady1 #aib ,calv]t1 #acj ,cam]on1 #bjc ,c>nelley1 #dg ,c>p5t]1 #bbe ,c>ve?1 #bjd1 #bee ,c5tn]szw]1 #aeh ,*apman1 #dg ,*appuis1 #ea1 #agf ,*>py1 #bee ,*ur*ill1 #adj ,coehn1 #eb ,coh51 #da1 #gb1 #acf1 #aci1 #adj ,cooke1 #cca1 #cci ,cox1 #cja ,d ,dawson1 #bfc ,debray1 #gd1 #ha1 #aci ,deville1 #di1 #gd ,dew>1 #bf1 #ea1 #agh ,dietz1 #aeg #cda ,doelt]1 #bcc ,donnan1 #h1 #ah ,drey]1 #gc ,duhem1 #ef1 #aea ,dutoit1 #bjd ,e ,et>d1 #aae1 #ace ,f ,fahr5heit1 #cj ,f>aday1 #hb1 #hi ,fa?1 #bjd ,f$otieff1 #cae1 #cbj ,f9dlay1 #aaa1 #bjd1 #bjf1 #bai ,foote1 #fi ,fri$la5d]1 #gb ,frits*e1 #da ,fr[e91 #ia ,fue*tbau]1 #ge ,fyffe1 #adc ,g ,gatt]mann1 #ea1 #eb ,gauti]1 #bbb1 #bbc ,gay-,lussac1 #ace ,g]nez1 #gb ,gibbs1 #g1 #h1 #aea1 #bcf ,glaessn]1 #cjg ,golds*midt1 ,e41 #da ,golds*midt1 ,h41 #cce ,golds*midt1 ,v41 #cb ,gooss5s1 #bf ,gossn]1 #cah ,graham1 #agh ,gu]tl]1 #gc ,guldb]g1 #g ,gu?rie1 #ig1 #ajd1 #aag1 #aah1 #aai1 #bcc ,h ,hab]1 #caa ,hahn1 #cji1 #caa ,hallock1 #ce ,hamm]l1 #ade ,hautefeuille1 #df1 #di1 #ej1 #ea1 #agh ,hell]1 #caa ,h5ry1 #id ,h]old1 #cba ,h]tz1 #di ,heycock1 #aid1 #bba1 #bbc ,heyn1 #bbe1 #bbh ,hickmans1 #bai ,hiorns1 #bbh ,hiss9k1 #aae1 #aij ,hoitsema1 #ad1 #ij1 #agg1 #agh1 #bih ,hollmann1 #bjd ,holsbo]1 #aaj ,hor/mann1 #h1 #hc1 #hi ,hudson1 #ajb ,hulett1 #aj1 #dh1 #eb1 #ed1 #fg1 #aji ,i ,isaac1 #aad ,isamb]t1 #hj1 #hb1 #hd ,j ,jaffe1 #gd1 #aad ,j\l91 #agf ,juhl91 #bc1 #bd1 #cj von ,jueptn]1 #bbe ,k ,ka/le1 #ga ,kaufl]1 #di ,kaufmann1 #aab ,kays]1 #agf ,keel+1 #bbe ,kelv91 #be ,k5rick1 #bfc1 #big ,kipp+1 #bai ,kir*h(f1 #cb ,knorr1 #bjc de ,kock1 #ec1 #ahb1 #aid ,kon[al(f1 #ajb1 #ajc1 #ajd ,krasnicki1 #add ,kremann1 #adg1 #bab ,ku551 #aje ,kultas*eff1 #bcc #cdb ,kuril(f1 #baf ,kurnak(f1 #bba1 #bbb1 #bcj ,kue/]1 #gb1 #aha1 #ahc ,l ,la>1 #aie ,lab5burg1 #baf ,lattey1 #aja ,le ,*ateli]1 #eh1 #ha1 #bcc ,lehfeldt1 #cch1 #cdj ,lehmann1 #cc1 #eb1 #ec ,lidbury1 #adg ,loewel1 #acd1 #ace ,loew5h]z1 #acd1 #caf ,l[ry1 #aif1 #aih ,ludwig1 #cbg ,lumsd51 #hj1 #aji1 #aaj ,lussana1 #fh ,lu!r1 #bb ,m ,mack1 #fg ,magnus1 #bb ,ma!ws1 #bba ,mellor1 #hj ,meuss]1 #adb ,mey]1 ,j41 #ga ,mey]1 ,v41 #dg ,mey]h(f]1 #aeh1 #bcc1 #bei1 #bfh1 #bga1 #bgh1 #bgi1 #bhj1 #bhd1 #cac1 #cae1 #cag1 #cai1 #cbg1 #cbh1 #ccf1 #ccg ,middelb]g1 #aaf ,mi]s1 #aad ,mill]1 #big ,mits*]li*1 #cc1 #di ,mond1 #agh ,moore1 #gb ,moss1 #ff ,muell]1 #aab1 #bfe ,mylius1 #aji1 #adb1 #aeg ,n ,naumann1 #di ,neville1 #aid1 #bba1 #bbc ,o ,(f]1 #aai ,o/wald1 #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 ,p>sons1 #bih ,pa/eur1 #bff ,pat]no1 #bac ,pay51 #gd ,p$l]1 #dg ,pfaundl]1 #aai ,philip1 #bac1 #bad von ,pick>dt1 #gc ,planck1 #fh ,pope1 #bai ,poynt+1 #fh ,preun]1 #caa ,pus*91 #bbb ,q ,qu9cke1 #eb ,r ,rabe1 #aac ,ramsay1 #c1 #bb1 #bc1 #bd1 #cj1 #cb1 #fc1 #fd1 #ff1 #gi1 #ij1 #afe1 #agh ,ra\lt1 #ahj ,re$1 #ga ,regnault1 #bb ,rei*]1 #cf1 #cg1 #aaj1 #bfj1 #ccc ,re9d]s1 #ga1 #ahe1 #ahh ,re9itz]1 #ea1 #eb ,ri*>ds1 #acf1 #adj ,riddle1 #dg ,riecke1 #dh1 #ee ,rob]ts-,au/51 #fc1 #aid1 #bba1 #bbc1 #bbe ,rol(f1 #aag ,roozeboom1 #aj1 #ch1 #de1 #dg1 #di1 #ej1 #ea1 #ed1 #ef1 #eg1 #fb1 #fc1 #fh1 #hh1 #ajc1 #abf1 #ade1 #adg1 #aej1 #aea1 #aeg1 #afb1 #agj1 #agd1 #agh1 #ahb1 #aif1 #bja1 #baa1 #bag1 #bbj1 #bbe1 #bcf1 #bch1 #bfb1 #bfd1 #bfi1 #bgb1 #bgc1 #bha1 #bhb1 #bij1 #cca #cdc ,rose1 #bbc ,rot>ski1 #eb ,ro?mund1 #ig1 #ih1 #ajj ,rutt51 #bih ,s ,sapos*nik(f1 #bab ,saund]s1 #cac1 #cag1 #cai1 #ccf1 #ccg ,saurel1 #aea ,s*aum1 #di1 #ge ,s*eel1 #bb1 #bc1 #cj ,s*5ck1 #di1 #eb1 #ed1 #caa ,s*neid]1 #eb ,s*o5beck1 #ge ,s*re9emak]s1 #abb1 #abf1 #bdf1 #bdh1 #bej1 #beb1 #bij1 #cjb ,s*roett]1 #df ,s*uk[sky1 #eb ,s*w>z1 #cca ,seitz1 #eb ,%5/one1 #aji1 #aae1 #ace ,%eph]d1 #bba1 #bee ,%ields1 #agh ,skirr[1 #acj ,spr+1 #fc von ,/ackelb]g1 #ajg1 #aaj ,/a$el1 #bfg ,/ansfield1 #aid1 #bba ,/okes1 #bcf ,/ort5bek]1 #dd1 #adg1 #afa1 #afd1 #bha ,t ,tab]1 #bbi ,tammann1 #bf1 #cb1 #cc1 #cg1 #ch1 #ci1 #dh1 #eb1 #fe1 #fg1 #fh1 #gb1 #gc1 #adj1 #aea1 #agf1 #bba1 #bcj ,?ies51 #bb1 #bc1 #cj ,?omson1 ,j41 #be1 #bh1 #cb ,?omson1 ,w41 #be ,tild51 #aji1 #aae1 #ace ,trevor1 #af ,troo/1 #df1 #di1 #ej1 #ea ,tumlirz1 #gb ,v ,van ,bemmel51 #ahj ,van ,dev5t]1 #aaj1 #aci1 #bff1 #bfg1 #ccc ,van ,eyk1 #da1 #fc1 #aib1 #cch ,van't ,h(f1 #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 ,leeuw51 #bei ,van ,wyk1 #ahe ,vogt1 #e1 #bcc ,w ,waage1 #g ,wald1 #ib ,wald51 #aeh ,walk]1 #hj1 #aje1 #abb1 #abf1 #adc ,wegs*eid]1 #aj1 #di1 #bjb ,wells1 #acf ,w5zel1 #g ,wiebe1 #bb ,witt1 #cbg ,wright1 #bda1 #bdf1 #bdg von ,wro*em1 #aji1 #adb ,y ,"y1 #c1 #bb1 #bc1 #bd1 #cj1 #cb1 #fc1 #fd1 #ff1 #gi1 #aje1 #afe ,z ,za*>ias1 #ahj ,zawidski1 #fc ,z5ghelis1 #ce ,zimm]mann1 #caa ,z9cke1 #dd ,ziz1 #ada 99 99 99 99 99 #cdd ,,subject ,,index ,a ,acetaldehyde & p>aldehyde1 #bjd ,acetic acid1 *lor(orm1 wat]1 #bda ,acetone1 ph5ol1 wat]1 #bdh ,adsorption1 #agf ,alcohol1 *lor(orm1 wat]1 #bdf ----1 e!r1 wat]1 #bdf ,alloys1 equilibrium curves (1 #bba ---- ( copp] & t91 liquefaction (1 by cool+1 #aid ---- ( iron & c>bon1 #bbc ---- ( ?allium & m]cury1 #bbb ----1 t]n>y1 #bdf ,ammonia comp\nds ( metal *lorides1 #hb ,ammonia silv] *lorides1 #hb ---- ---- ----1 dissociation pressures (1 #hd ,ammonia-soda process1 #cbj ,ammonium *loride1 dissociation (1 #c1 #gi ---- cyanide1 dissociation (1 #hj ---- hydrosulphide1 dissociation (1 #hj ---- nitrate1 solubility (1 #aac ,anil9e1 ph5ol1 wat]1 #bej ,a/racanite1 #bfj1 #bfa1 #bfh1 #bgd ,b ,babo1 law (1 #abf ,b>ium acetate1 solubility (1 #adc ,b>ium c>bonate & potassium sulphate1 #cbh ---- nitrite1 prep>ation (1 #cbg ,basic salts1 #bif ,b5zaldoximes1 #bjc ,b5z5e & picric acid1 #baf ,bismu?1 effect ( pressure on ! melt+ po9t (1 #fg ----1 lead1 t91 #bee ---- nitrates1 basic1 #bih ,biv>iant sy/ems1 #af ,bromoc9namic aldehyde & *loroc9namic aldehyde1 #ahc ,c ,calcium c>bonate1 dissociation (1 #c1 #aa1 #ha ---- *loride hexahydrate1 solubility (1 #adf ---- ----1 solubility ( hydrates (1 #adh ---- ----1 vap\r-pressure ( hydrates (1 #hh ,camphor oximes1 #bai1 #beg ,c>nallite1 #bhd ,c>voximes1 #ahf1 #bai ,cem5tite1 #bbd ,*lor9e & iod9e1 #afa ,*loroc9namic aldehyde & bromoc9namic aldehyde1 #ahc ,*lor(orm1 acetic acid1 wat]1 #bda ----1 alcohol1 wat]1 #bdf #cde ,classification ( sy/ems1 #ag ,compon5t1 #h1 #aj1 #ab ----1 sy/ems ( "o1 #ba1 #ee ,compon5ts1 *oice (1 #ab1 #ac1 #ad1 #gf1 #cac ----1 det]m9ation ( numb] (1 #ac ----1 sy/ems ( f\r1 #cab ----1 ---- ( ?ree1 #bcd ----1 ---- ( two1 #gf1 #bjg ----1 v>iation 9 numb] (1 #aa1 #ad ,composition1 det]m9ation (1 )\t analysis1 #bbh1 #cjb ,conc5tration-temp]ature curve = two liquids1 #aja ,cond5s$ sy/ems1 #cf ,con/itu5t1 #aj ,cool+ curve1 #bcj ,copp] calcium acetate1 #bfj ---- *loride1 heat ( solution (1 #aaj ---- dipotassium *loride1 #bei ---- sulphate1 #he ,critical conc5tration1 #ih1 #bdb ---- pressure ( wat]1 #bc ---- solution temp]ature1 #ih ---- temp]ature ( wat]1 #bc ,cryohydrates1 #aag1 #aah ,cryohydric po9t1 #aag ---- ----1 *anges at !1 #aai ---- ---- = silv] nitrate & ice1 #aaf ,cry/als1 liquid1 #ea ----1 ----1 equilibria (1 #ec ----1 ----1 li/ (1 #ed ----1 ----1 nature (1 #eb ----1 mix$1 #ahj ,cry/allization1 velocity (1 #gb1 #gd ----1 spontane\s1 #aad ,d ,deliquesc5ce1 #acj ,devitrification1 #gc ,die?ylam9e & wat]1 solubility (1 #aja ,dilatomet]1 det]m9ation ( transition po9ts by1 #cca ,d9]ic surface1 #bdg ,dissociation equilibrium1 effect ( addition ( dissociation products on1 #d ---- ( ammonia comp\nds ( metal *lorides1 #hb1 #hd ---- ( ammonium *loride1 #c1 #gi ---- ---- cyanide1 #hj ---- ---- hydrosulphide1 #hj ---- ( calcium c>bonate1 #c1 #ha ---- ( comp\nds1 degree (1 #adg ---- ( phosphonium bromide1 #hj ---- ( salt hydrates1 #he ----1 ph5om5a (1 #gi ,dissociation pressure1 #ha ,di/illation ( sup]cool$ liquid to solid1 #cb1 #ej ,d\ble salt int]val1 #bgh ---- salts1 cry/allization f solution1 #bhj ---- ----1 decomposition by wat]1 #bfg ---- ----1 =mation (1 #beh1 #bgc1 #cae ,e ,effloresc5ce1 #hf ,electrical me?ods ( det]m9+ transition po9ts1 #cch ,enantiotropy1 #dd1 #ea ,equilibria1 ,gibbs's !ory (1 #h ----1 meta/able1 #fi ,equilibrium app>5t 7false71 #e1 #f ---- betwe5 ice & solution1 #aaf ---- betwe5 ice & wat]1 #be ---- betwe5 ice1 wat]1 vap\r1 #bg ---- betwe5 wat] & vap\r1 #ba ----1 *emical1 #c1 #af ----1 het]og5e\s1 #e ----1 homog5e\s1 #e ----1 indep5d5ce (1 on am\nts ( phases1 #i ----1 law ( movable1 #eh #cdf ----1 physical1 #c1 #af ---- real 7true71 #e1 #f ,e!r1 alcohol1 wat]1 #bdf ----1 succ9ic nitrile1 wat]1 #beb ,e?yl5e bromide1 picric acid1 beta-naph?ol1 #bef ,eutectic mixtures1 #aag1 #aia1 #bji1 #bee1 #beg ---- po9t1 #aag1 #bji1 #bac1 #bec ,f ,f]ric *loride1 evaporation ( solutions (1 #aee ---- ----1 hydrates (1 #aea1 #aec ---- ----1 hydrog5 *loride & wat]1 sy/ems (1 #bij ,f]rite1 modifications (1 #bbd ,fre$om1 degree (1 #ad ,freez+ mixtures1 #abj ---- po9t1 natural1 #aih ,fusion curve1 #ff ---- ---- ( ice1 #be ---- ( ice1 influ5ce ( pressure on1 #bf ----1 p>tial1 #aci ,g ,glas]ite1 #cae1 #cag ,glasses1 #agf ,glaub]'s salt1 #ac1 #acd ---- ----1 transition curve (1 #fh1 #adj ,graphic repres5tation 9 space1 #gg1 #bhd ,h ,hydrates1 range ( exi/5ce (1 #hi ---- *loride & wat]1 #agd ,hydrog5 bromide & wat]1 #agd ,hylotropic sub/ances1 #aih ,i ,ice ,i41 #cb ---- ,,ii41 #cb ---- ,,iii41 #cb ----1 equilibrium betwe5 wat] &1 #be ----1 influ5ce ( pressure on melt+ po9t (1 #be1 #bf ----1 sublimation curve (1 #bd ----1 vap\r pressure (1 #be1 #ca ,indiff]5t po9t1 #aej ,individual1 *emical1 #ib ,inv]sion temp]ature1 #cf ,iod9e & *lor9e1 #afa ,iron--c>bon alloys1 #bbc ----1 c>bon monoxide & c>bon dioxide1 #cje ,isom]ides1 dynamic1 #aie1 #aif ----1 ----1 equilibrium betwe51 #aie1 #aif ----1 ----1 equilibrium po9t (1 #aih ----1 trans=mation ( un/able into /able1 #bja ,isom]ism1 dynamic1 #aif ,iso!rmal evaporation1 #bgh ---- solubility curves1 #bgb ,l ,lead1 bismu?1 t91 #bee ----1 desilv]ization (1 #bdg ----1 silv]1 z9c1 #bdf ,le ,*ateli]1 !orem (1 #eg ,lime1 burn+ (1 #c ,liquidus curve1 #ahb ,m ,m&elic acid1 #bag ,m>t5site1 #bbd ,mass action1 law (1 #g ,melt+ po9t1 influ5ce ( pressure on1 #ff #cdg ---- ----1 congru5t1 #adf ---- ----1 incongru5t1 #aci ---- "u ! solv5t1 #abb ,m5?yl m&elates1 #bai ,m]curic bromide & iodide1 #ahh ,m]cury salts1 basic1 #cja ,meta/able equilibria1 #fi ---- region1 #cj ---- /ate1 #cj ,me?yle?yl ketone & wat]1 #ajj ,m9]als1 =mation (1 #bcb ,miscibility ( liquids1 complete1 #ie1 #ajd1 #aad ---- ----1 p>tial1 #ie1 #if1 #aba ,mix$ cry/als1 #ahj1 #bha ---- ----1 *anges 91 ) temp]ature1 #aib ---- ----1 examples (1 #ahc1 #ahf1 #ahg1 #aij1 #aib1 #bai1 #bbc ---- ----1 =mation (1 #aha1 #ahb ---- ----1 fractional cry/allization (1 #ahh ---- ----1 freez+ po9ts (1 #ahb ---- ----1 melt+ po9ts (1 #ahb1 #ahd ---- ----1 pseudoracemic1 #bai ,mixtures1 isomorph\s1 #aha ---- ( con/ant boil+ po9t1 #aje ---- ( con/ant melt+ po9t1 #aag1 #ahf1 #ahg1 #aib1 #bji1 #bee1 #beg ,monotropy1 #dd1 #ea ,multiv>iant sy/ems1 #af ,n ,naph?al5e & mono*loracetic acid1 #aib ---- & beta-naph?ol1 mix$ cry/als (1 #ahc beta-,naph?ol1 e?yl5e bromide1 picric acid1 #bef alpha-,naph?ylam9e & ph5ol1 #bac ,nickel iodate1 solubility (1 #adb o-,nitroph5ol & p-toluid9e1 #bac ,o ,occlusion ( gases1 #agf ,optical me?od ( det]m9+ transition po9ts1 #cch ,optically active sub/ances1 freez+-po9t curves (1 #baf ,ord] ( a sy/em1 #ac ,organic comp\nds1 application ( ,phase ,rule to1 #bab ,p ,palladium & hydrog51 #ij1 #agh ,p>ag5esis1 #cbj ,p>aldehyde & acetaldehyde1 #bjd ,p>tial pressures ( two compon5ts1 #ajb ,pe>lite1 #bbd ,phase1 #h ---- ,rule1 #h1 #af ---- ----1 d$uction (1 #ah ---- ----1 scope (1 #a ,phases1 =mation ( new1 #fi ----1 numb] (1 #i ,ph5ol1 acetone1 wat]1 #bdh ----1 anil9e1 wat]1 #bej ---- & alpha-naph?ylam9e1 #bac ---- & p-toluid9e1 #bad ---- & wat]1 solubility (1 #ig ,phosphonium bromide1 dissociation (1 #hj ---- *loride1 #fe ,phosphorus1 #df ----1 di/illation ( :ite to r$1 #ej ----1 melt+ po9t ( r$1 #dg ----1 ---- ---- ( :ite1 #dh ----1 solubility ( :ite & r$1 #dg ----1 vap\r pressure ( :ite & r$1 #df ,picric acid & b5z5e1 #baf ---- ----1 e?yl5e bromide1 & beta-naph?ol1 #bef ,polymorphic =ms1 solubility (1 #aab #cdh ---- sub/ances1 li/ (1 #fc ,polymorphism1 #cc ,potassium nitrate & ?allium nitrate1 #aib ,pot5tial1 *emical1 #ai ,pressure-conc5tration diagram = two liquids1 #ajb ,pressure-temp]ature diagram = solutions1 #abf ,pseudomonotropy1 #de ,pseudo-racemic mix$ cry/als1 #ba ,pyrid9e & me?yl iodide1 #adg ,pyromet]1 regi/]+1 #bcj ,q ,quadruple po9t1 #aaf ,qu9tuple po9t1 #bcd1 #bfa ,r ,racemates1 *>act]ization (1 #bag1 #bhb ,reactions1 law ( successive1 #gc ,reciprocal salt-pairs1 #cac ---- ----1 transition po9t (1 #cad ,rubidium t>trates1 #bfe ,s ,salt hydrates1 #he ---- ----1 indef9it5ess ( vap\r pressure (1 #hg ---- ---- ) def9ite melt+ po9t1 #ade ,sep>ation ( salt on evaporation1 #acj ,silicates1 hydrat$1 #agf ,silv]1 lead1 z9c1 #bdf ,silv] nitrate1 solubility (1 #aad ---- ---- & sodium nitrate1 #aij ,s+le salt int]val1 #bgh ,sodium ammonium t>trates1 #bff ---- nitrate & silv] nitrate1 #aij ---- sulphate & wat]1 equilibria betwe51 #acd ,sodium sulphate & wat]1 vap\r pressures (1 #ach1 #adj ---- ----1 anhydr\s1 dehydration by1 #ach ---- ----1 solubility (1 #ace ---- ---- decahydrate1 solubility (1 #acd ---- ---- ----1 transition po9t (1 #acf1 #aci ---- ---- heptahydrate1 solubility (1 #acf ---- ---- ----1 transition po9t (1 #acg ,solidus curve1 #ahb ,solubility curve at high] temp]atures1 #aad ---- ----1 =m (1 #ajh ---- ---- ( anhydr\s salts1 #aaa ---- ----1 retr(lex1 #adf1 #aea1 #afb ---- curves1 int]polation & extrapolation (1 #aaa ---- ---- ( ?ree compon5t sy/ems1 #bfd ----1 det]m9ation ( transition po9ts by1 #cce ----1 influ5ce ( pressure on1 #ajg ----1 ---- ( subdivision on1 #aj ----1 ---- ( temp]ature on1 #aji ---- ( meta/able =ms1 #dg1 #aab1 #acg ,solubility ( polymorphic =ms1 #aab ---- ( salt hydrates1 #acc1 #ade ---- ( sup]cool$ liquids1 #abe ----1 retrograde1 #bde ,solute1 #ic ,solution1 def9ition (1 #ib ----1 heat (1 #aji1 #aaj ----1 saturat$1 #ajf1 #ajh ----1 sup]saturat$1 #ajh ---- temp]ature1 critical1 #ih ----1 unsaturat$1 #ajh ,solutions1 biv>iant sy/ems1 #abi ----1 congru5tly saturat$1 #bgi ---- conjugate1 #ig1 #bda #cdi ----1 incongru5tly saturat$1 #bgi1 #bhi ----1 inevaporable1 #aeg ---- ( gases 9 liquids1 #ic ---- ---- 9 solids1 #agf ---- ( liquids 9 liquids 7b9>y71 #ie ---- ---- ---- 7t]n>y71 #bdj ---- ----1 influ5ce ( temp]ature on1 #bdg ---- ( solids 9 liquids1 #ajf ---- ---- 9 solids1 #ahj ----1 solid1 #age1 #ahj ----1 univ>iant sy/ems1 #abg ,space model = c>nallite1 #bhd ,/ability limit1 #bjb ,/eel1 =mation (1 #bbc ,sublimation curve1 #fc ---- ---- ( ice1 #bd ---- )\t fusion1 #fe ,succ9ic nitrile & wat]1 #abb ---- e!r1 wat]1 #beb ,sulphur1 #cc1 #cd ---- dioxide & wat]1 #afi ---- ---- & potassium iodide1 #aeh ----1 transition po9t ( rhombic & monocl9ic1 #cf ,sup]saturation1 #aac1 #aad1 #abd ----1 limits (1 #aad ,sy/ems1 cond5s$1 #cf ---- ( "o compon5t1 #ba ---- ( two compon5ts1 #gf1 #gg1 #bjg ,t ,ta*ydrite1 influ5ce ( pressure on ! transition po9t (1 #bfc ,t>trate1 dime?yl1 #bag ----1 sodium potassium1 #bei ,tautom]ic sub/ances1 #aie ,t5simet]1 #ia ,?allium nitrate & potassium nitrate1 #aib ,!orem ( van't ,h(f & ,le ,*ateli]1 #eg ,!rmometric det]m9ation ( transition po9t1 #ccg ,t91 #da ----1 lead1 bismu?1 #bee ---- plague1 #dc ----1 transition po9t ( :ite & grey1 #da p-,toluid9e & o-nitroph5ol1 #bac ---- & ph5ol1 #bad ,trans=mation ( optically active sub/ances1 #bbj ----1 susp5d$1 #cg1 #fi1 #hi1 #aac1 #acg1 #aee ----1 velocity (1 #gj ,transition curve1 #ff ---- ---- ( ,glaub]'s salt1 #fh1 #adj ---- ---- ( rhombic & monocl9ic sulphur1 #cg ---- int]val1 #bgj1 #bgg1 #cae ---- po9t1 #cd ---- ---- = d\ble salts1 #beh ---- ----1 influ5ce ( pressure on !1 #fh ---- po9ts1 z fix$ po9ts 9 !rmometry1 #adj ---- ----1 me?ods ( det]m9+1 #cca ---- ---- ( polymorphic sub/ances1 #fc ,triangle1 graphic repres5tation by1 #bce ,trie?ylam9e & wat]1 #aja ,triple po9t1 #bg1 #ee ---- ----1 arrangem5t ( curves r\nd1 #ef ---- ----1 *anges at1 #eh ---- ----1 ice1 wat]1 vap\r1 #bg ---- ----1 ice ,,ii41 ice ,,iii41 & wat]1 #cc ---- ----1 meta/able1 #ch ---- ----1 monocl9ic sulphur1 liquid1 vap\r1 #ch ---- ----1 monocl9ic & rhombic sulphur1 liquid1 #ch ---- ----1 monocl9ic & rhombic sulphur1 vap\r1 #cd #cej ---- ----1 r$ phosphorus1 liquid1 vap\r1 #dg ---- ----1 rhombic sulphur1 liquid1 vap\r1 #ch ---- ---- solid1 solid1 vap\r1 #fb ---- ----1 :ite phosphorus1 liquid1 vap\r1 #dh ,u ,univ>iant sy/ems1 #af ,v ,van't ,h(f1 !orem (1 #eg ,vaporization curve1 #fc ---- ----1 int]polation & extrapolation (1 #ff ---- ---- ( wat]1 #ba1 #bc ,vap\r pressure1 con/ancy (1 & =mation ( comp\nds1 #ij ---- ----1 dep5d5ce (1 on solid phase1 #hh ---- ----1 influ5ce ( surface t5sion on1 #b ---- ---- 9 ?ree-compon5t sy/ems1 #bfa ---- ----1 measurem5t (1 #ia1 #ccd ---- ---- ( calcium *loride solutions1 #aej ---- ---- ( ice1 #be1 #ca ---- ---- ( small drops1 #aj ---- ---- ( sodium sulphate & wat]1 #ach ,vap\r pressure ( solid1 solution1 vap\r1 #abf ---- ---- ( wat]1 #ba1 #ca ,v>iability ( a sy/em1 #ad1 #af ,v>iance ( a sy/em1 #af ,volatile compon5ts1 two1 #afa ,w ,wat]1 #ba ----1 acetic acid1 *lor(orm1 #bda ----1 acetone1 ph5ol1 #bdh ----1 alcohol1 e!r1 #bdf ----1 ----1 *lor(orm1 #bdf ----1 anil9e1 ph5ol1 #bej ----1 biv>iant sy/ems (1 #bi ----1 critical pressure (1 #bc ----1 critical temp]ature (1 #bc ----1 equilibrium betwe5 ice &1 #be ----1 ---- betwe5 vap\r &1 #ba ----1 e!r1 succ9ic nitrile1 #beb ----1 sup]cool$1 #cj ----1 ----1 vap\r pressure (1 #ca ----1 vaporization curve (1 #ba ----1 vap\r pressure (1 #bc ,z ,zeolites1 #agf ,z9c1 lead1 silv]1 #bdf ---- *loride 9 wat]1 solubility (1 #aeg ,,! ,,end ,,pr9t$ ,,by ,,william ,,cl[es ,,& ,,sons1 ,,limit$1 ,,london ,,& ,,beccles4 99 99 99 99 99 ,,notes #a ,except :5 ! volume ( ! liquid becomes exce$+ly small1 9 :i* case ! surface t5sion ex]ts an influ5ce on ! vap\r pressure4 #b ,= reasons :i* w appe> lat] 7,*ap4 ,,iv471 ! volume ( ! vap\r is suppos$ to be l>ge 9 comp>ison ) t ( ! solid & liquid4 #c ,ramsay & ,"y1 ,phil4 ,trans41 #ahhf1 #agg4 #hg4 #d ,see1 m especially1 ,vogt1 ,die ,silikats*melzloesung54 7,*ri/iania1 #aijc1 #aijd47 #e ,trans4 ,connecticut ,acad41 #ahgd-ahgh4 #f ,lehre von d] *emis*5 ,v]w&ts*aft d] ,ko]p]1 #aggg4 #g ,see ,o/wald's ,klassik]1 ,no4 #gd4 #h ,etudes sur les aff9ites *imiques1 #ahfg2 ,o/wald's ,klassik]1 ,no4 #ajd4 #i ,di$ ,april1 #aijc4 #aj ,= a ma!matical treatm5t ( ! ,phase ,rule ! read] is ref]r$ to ! volume 9 ?is s]ies on ,!rmodynamics1 by ,f4 ,g4 ,donnan4 #aa ,liebig's ,annal51 #ahgc1 #agj1 #aib2 ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #aaa4 #ab ,! action ( gravity & o!r =ces be+ exclud$ 7see p4 #e74 #ac ,x may seem z if ?is 7 a contradiction to :at 0 said on p4 #d z to ! effect ( ! addition ( ammonia or hydrog5 *loride to ! sy/em con/itut$ by solid ammonium *loride 9 contact ) its products ( dissociation4 ,!re is1 h[ev]1 no contradiction1 because 9 ! case ( ammonium *loride ! gase\s phase consi/s ( ammonia & hydrog5 *loride 9 equal proportions1 & 9 add+ ammonia or hydrog5 *loride alone we are n add+ ! gase\s phase1 b only a con/itu5t ( x4 ,addition ( ammonia & hydrog5 *loride toge!r 9 ! proportions 9 :i* !y are comb9$ to =m ammonium *loride w\ld cause no *ange 9 ! equilibrium4 #ad ,! vap\r pressure ( wat] 9 small drops is great] ?an t ( wat] 9 mass1 & ! solubility ( a solid is great] :5 9 a /ate ( f9e subdivision ?an :5 9 l>ge pieces 7cf4 ,hulett1 ,zeits*r4 physikal4 ,*em41 #aija1 #cg4 #che74 #ae ,see ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #dgf1 #icd2 ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahid1 #ae4 #aej2 ,het]og5e ,glei*gewi*te1 ,i4 p4 #af2 ,wegs*eid]1 ,zeits*r4 physikal4 ,*em41 #aijc1 #dc4 #hi4 #af ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #dgh4 #ag ,see also ,hoitsema1 ,zeits*r4 physikal4 ,*em4 #ahie1 #ag4 #fea4 #ah ,! t]m degree ( fre$om employ$ "h mu/ n be confus$ ) ! same t]m us$ to d5ote ! v>i\s movem5ts ( a gas molecule accord+ to ! k9etic !ory4 #ai ,trevor1 ,j\r4 ,physical ,*em41 #aijb1 #f4 #acf4 #bj ,o/wald1 ,pr9ciples ( ,inorganic ,*emi/ry1 translat$ by ,a4 ,f9dlay1 #bnd edit41 p4 #g4 7,macmillan1 #aijd47 #ba ,see ! volume 9 ?is s]ies on ,!rmodynamics by ,f4 ,g4 ,donnan4 #bb ,pogg4 ,annal51 #ahdd1 #fa4 #bbe4 #bc ,memoires de l',acad41 #bf4 #gea4 #bd ,phil4 ,trans4 #ahhd1 #age4 #dfa2 #ahib1 ,a1 #ahc4 #ajg4 #be ,bihang ,sv5ska ,akad4 ,h&l4 #ahia1 #ag4 ,i4 #a4 #bf ,abh&l4 physikal4-te*4 ,rei*san/alt1 #aijj1 #c4 #ga4 #bg ,o/wald-,lu!r1 ,physiko-*emis*e ,messung51 #bnd edit41 p4 #aef4 #bh ,annales *im4 et phys41 #ahib #f1 #bf4 #dbe4 #bi ,! vap\r pressure ( wat] at #j;deg has rec5tly be5 v accurately det]m9$ by ,?ies5 & ,s*eel 7loc4 cit471 & f\nd to be #d4egi _/- #j4jja mm4 ( m]cury 7at #j;deg71 or equal to #j4jjfjbe atm4 #cj ,juhl91 ,bihang ,sv5ska ,akad4 ,h&l41 #ahia1 #ag4 ,i4 #eh4 ,see also ,ramsay & ,"y1 loc4 cit4 #ca ,trans4 ,roy4 ,soc4 ,ed941 #ahdi1 #af4 #ege4 #cb ,proc4 ,roy4 ,soc4 ,ed941 #ahej1 #b1 #bfg4 #cc ,annal5 d] ,physik1 #ahii #c1 #fh4 #efd2 #aijj #d1 #b4 #a1 #dbd4 ,see also ,dew>1 ,proc4 ,roy4 ,soc41 #ahhj1 #cj4 #ecc4 #cd ,! pressure ( #a atmosph]e is equal to #a4jcc kilogm4 p] sq4 cm42 or ! pressure ( #a kilogm4 p] sq4 cm4 is equal to #j4ifh atm4 #ce ,tammann1 loc4 cit41 #aijj1 #b4 #a1 #dbd2 cf4 ,gooss5s1 ,ar*4 ne]l&1 #ahhf1 #bj4 #ddi4 #cf ,j4 ,?omson1 ,proc4 ,roy4 ,soc41 #ahgd1 #bb4 #bh4 #cg ,a field is enclos$ by two curves :5 ^! cut at an angle less ?an two "r angles4 ,x may be useful to rememb] t an inv>iant sy/em is repres5t$ by a po9t1 a univ>iant sy/em by a l9e1 & a biv>iant sy/em by an area4 #ch ,phil4 ,trans41 #agbd1 #ci4 #gh4 #ci ,juhl91 loc4 cit41 p4 #fa2 cf4 ,ramsay & ,"y1 loc4 cit43 ,?ies5 & ,s*eel1 loc4 cit4 #dj ,?is small diff]5ce is due to exp]im5tal errors 9 ! det]m9ation ( ! vap\r pressures2 a diff]5tial me?od betray$ no diff]5ce betwe5 ! vap\r pressure ( ice & ( wat] at #j;deg4 #da ,phil4 ,mag41 #ahgd #d1 #dg4 #ddg2 ,proc4 ,roy4 ,soc41 #ahgc1 #bb4 #bg4 #db ,pogg4 ,annal51 #aheh1 #ajc1 #bjf4 #dc ,see ,phil4 ,trans41 #ahhd1 #age1 #dfa4 #dd ,?is ph5om5on ( di/illation f ! sup]cool$ liquid to ! solid has be5 v cle>ly obs]v$ 9 ! case ( furfuraldoxime 7,v4 ,golds*midt1 ,zeits*r4 f4 ,kry/allographie1 #ahig1 #bh4 #afi74 #de ,annal5 d] ,physik1 #aijj #d1 #b4 #a1 #dbd4 #df ,a simil> triple po9t has be5 det]m9$ by ,tammann 9 ! case ( ph5ol 7,annal5 d] ,physik1 #aijb #d1 #i4 #bdi74 #dg ,annales *im4 et phys41 #ahba1 #ai4 #dad4 #dh ,lehmann1 ,molekul>physik1 ,i4 #aec42 ,arzruni1 ,physikalis*e ,*emie d] ,kry/alle4 7,graham-,otto1 ,lehrbu* d] ,*emie1 ,i4 #c47 #di ,brodie1 ,proc4 ,roy4 ,soc41 #ahee1 #g4 #bd4 #ej ,t solid sulphur does possess a c]ta9 vap\r pressure has be5 %[n by ,hallock1 :o obs]v$ ! =mation at ! ord9>y temp]ature ( copp] sulphide 9 a tube conta9+ copp] & sulphur 7,am]4 ,j\r4 ,sci41 #ahhi #c1 #cg4 #dje74 ,see also ,z5ghelis1 ,zeits*r4 physikal4 ,*em41 #aijd1 #ej4 #bai4 #ea ,zeits*r4 fu] ,kry/allographie1 #ahhd1 #h4 #eic4 #eb ,van't ,h(f1 ,/udies on ,*emical ,dynamics1 p4 #afc4 #ec ,rei*]1 loc4 cit4 ,see also ,tammann1 ,annal5 d] ,physik1 #ahii #c1 #fh4 #ffc4 #ed ,tammann1 ,annal5 d] ,physik1 #ahii #c1 #fh4 #fcc4 #ee ,rec4 ,trav4 ,*im4 ,pays-,bas1 #ahhg1 #f4 #cad4 #ef ,cf4 van't ,h(f1 ,lectures on ,physical ,*emi/ry1 ,i41 p4 #bg 7,arnold74 #eg ,annal5 d] ,physik1 #ahii #c1 #fh4 #ffc4 #eh ,brauns1 ,jahrbu* fu] ,m9]alogie1 #ahii-aija1 #ac4 ,beilage1 p4 #ci4 #ei ,frits*e1 ,b]41 #ahfi1 #b4 #aab1 #edj4 #fj ,de mirabilibus ,auscultationibus1 ,cap4 #ea 7v4 ,coh51 ,zeits*r4 physikal4 ,*em41 #aija1 #cf4 #eac74 #fa ,e4 ,coh5 & ,c4 van ,eyk1 ,zeits*r4 physikal4 ,*em41 #ahii1 #cj4 #fja2 ,coh51 ibid41 #aijj1 #cc4 #ei2 #ce4 #ehh2 #aija1 #cf4 #eac2 ,coh5 & ,e4 ,golds*midt1 ibid41 #aijd1 #ej4 #bbe4 #fb ,zeits*r4 physikal4 ,*em41 #aijj1 #cc1 #eh4 #fc ,/ort5bek]1 ,zeits*r4 physikal4 ,*em41 #ahhi1 #c4 #aa2 ,rec4 ,trav4 ,*im4 ,pays-,bas1 #ahhh1 #g4 #aeb4 #fd ,z9cke1 ,b]41 #ahga1 #d4 #egf4 #fe ,o/wald1 ,zeits*r4 physikal4 ,*em41 #ahig1 #bb4 #cac4 #ff ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #agg4 #fg ,roozeboom1 ibid41 p4 #agi4 #fh ,s*roett]1 ,pogg4 ,annal51 #ahej1 #ha4 #bgf2 ,troo/ & ,hautefeuille1 ,annales de ,*im4 et ,phys4 #ahgd #e1 #b4 #aec2 ,ann4 ,sci5t4 ,ecole ,norm4 #ahfh #b1 ,,ii4 #bff4 #fi ,p$l]1 ,trans4 ,*em4 ,soc41 #ahij1 #eg4 #eii4 #gj ,brodie1 ,trans4 ,*em4 ,soc41 #ahec1 #e1 #bhi4 #ga ,?is is a famili> fact 9 ! case ( ! solubility 9 c>bon disulphide4 #gb ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #agj4 #gc ,trans4 ,*em4 ,soc41 #ahii1 #eg4 #gcd4 #gd ,c>nelley1 ,trans4 ,*em4 ,soc41 #ahgf1 #bi4 #dhi2 #ahgh1 #cc4 #bge4 ,v4 ,mey] & ,riddle1 ,b]41 #ahic1 #bf4 #bddc4 #ge ,riecke1 ,zeits*r4 physikal4 ,*em41 #ahij1 #f4 #daa4 #gf ,annal5 d] ,physik41 #ahih #c1 #ff4 #dib4 #gg ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #fff4 #gh ,see ,naumann1 ,b]41 #ahgb1 #d4 #fdf2 ,troo/ & ,hautefeuille1 ,compt4 r5d41 #ahfh1 #ff4 #gie2 #ahfh1 #fg4 #acde2 ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 pp4 #fb1 #aga4 #gi ,mits*]li*1 ,lieb4 ,annal51 #ahcd1 #ab4 #acg2 ,deville & ,troo/1 ,compt4 r5d41 #ahfc1 #ef4 #hia4 #hj ,beckmann1 ,zeits*r4 physikal4 ,*em41 #ahij1 #e4 #gi2 ,h]tz1 ibid41 #f4 #ceh4 #ha ,b]41 #aijb1 #ce4 #cea4 ,cf4 also1 ,k4 ,s*aum1 ,annal5 d] ,*em41 #ahih1 #cjj4 #bba2 ,r4 ,wegs*eid] & ,kaufl]1 ,sitzungsb]4 kais]l4 ,akad4 ,wiss5s*4 9 ,wi51 #aija1 #aaj1 ,,ii4 #fjf4 #hb ,see also ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #agg4 #hc ,annales de ,*im4 et ,phys41 #ahgd #e1 #b4 #aed4 #hd ,compt4 r5d41 #ahhg1 #ajd4 #aeje4 #he ,compt4 r5d41 #ahfh1 #ff4 #gie4 #hf ,phil4 ,mag41 #ahhd #e1 #ah4 #baj4 ,see also ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #agg4 #hg ,brauns1 ,neues ,jahrbu* fu] ,m9]alogie1 #aijj1 #ac4 ,beilage-,b&1 p4 #ci2 ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #aha4 #hh ,monat%efte1 #ahhh1 #i4 #dce4 #hi ,gatt]mann1 ,b]41 #ahij1 #ec4 #agch4 #ij ,zeits*r4 physikal4 ,*em41 #ahhi1 #d4 #dfh2 ,annal5 d] ,physik1 #aijj #d1 #b4 #fdi4 #ia ,qu9cke1 ,annal5 d] ,physik1 #ahid #c1 #ec4 #fac2 ,tammann1 ,annal5 d] ,physik1 #aija #d1 #d4 #ebd2 #aijb1 #h4 #ajc2 ,rot>ski1 ibid41 #d4 #ebh4 #ib ,annal5 d] ,physik1 #aijj #d1 #b4 #fdi4 #ic ,annal5 d] ,physik1 #aijb #d1 #h4 #iaa4 #id ,see1 m especially1 ,o4 ,lehmann1 ,annal5 d] ,physik1 #aijj #d1 #b4 #fdi2 ,re9itz]1 ,sitzungsb]4 kais]l4 ,akad4 zu ,wi541 #ahhh1 #id4 7#b71 #gai2 #ig4 7#a71 #afg2 ,gatt]mann1 loc4 cit42 ,s*5ck1 ,zeits*r4 physikal4 ,*em41 #ahig1 #bc4 #gjc2 #ahih1 #be4 #ccg2 #bg4 #agj2 #ahii1 #bh4 #bhj2 ,s*5ck & ,s*neid]1 ibid41 #ahii1 #bi4 #edf2 ,abegg & ,seitz1 ibid41 #ahii1 #bi4 #dia2 ,hulett1 ibid41 #ahii1 #bh4 #fbi2 ,coehn1 ,zeits*r4 ,elektro*em41 #aijd1 #aj4 #hef3 ,br$ig & ,s*uk[sky1 ibid41 #cdai4 ,= a full acc\nt ( ! subject1 ! read] is ref]r$ to ! "w by ,lehmann1 ,fluessige ,kri/alle 7,engelmann1 #aijd71 or ! small] monograph by ,s*5ck1 ,kri/all9is*e ,fluessigkeit5 und fluessige ,kri/alle 7,engelmann1 #aije74 #ie ,a4 ,c4 de ,kock1 ,zeits*r4 physikal4 ,*em41 #aijd1 #dh4 #abi4 #if ,on acc\nt ( ! fact t all grades ( rigidity h be5 realiz$ betwe5 ! ord9>y solid & ! liquid /ate1 9 ! case bo? ( cry/all9e & amorph\s sub/ances1 x has be5 propos$ to ab&on ! t]ms solid & liquid1 & to class bodies z cry/all9e or amorph\s1 ! passage f ! "o condition to ! o!r be+ discont9u\s2 cry/all9e bodies possess a c]ta9 regul> ori5tation ( _! molecules & a directive =ce1 :ile 9 amorph\s bodies ^! are want+ 7see ,lehmann1 ,annal5 d] ,physik1 #aijj #d1 #b4 #fif74 #ig ,hulett1 loc4 cit4 #ih ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #add4 ,see also ,s*5ck1 ,kri/all9is*e ,fluessigkeit5 und fluessige ,kri/alle1 p4 #h 7,engelmann1 #aijd74 #ii ,! possible numb] ( triple po9ts 9 a "o-compon5t sy/em is giv5 by ! expression 7n7n - #a77n - #b77_/a4b4c1 :]e n is ! numb] ( phases 7,riecke1 ,zeits*r4 physikal4 ,*em41 #ahij1 #f1 #daa74 ,! numb] ( triple po9ts1 !re=e1 increases v rapidly z ! numb] ( possible phases increases4 #ajj ,duhem1 ,zeits*r4 physikal4 ,*em41 #ahia1 #h4 #cga4 ,cf4 ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 p4 #id ff4 #aja ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #ii4 #ajb ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahhh1 #b4 #dgd4 #ajc ,^! *anges c be pr$ict$ quantitatively by means ( ! !rmodynamic equation1 dp_/dt ,q_/7,t7v#b - v#a771 provid$ ! specific volumes ( ! phases are kn[n1 & ! heat effect :i* accompanies ! trans=mation ( "o phase into ! o!r4 #ajd ,/udies on ,*emical ,dynamics1 translat$ by ,ewan1 p4 #bah4 #aje ,le ,*ateli]1 ,compt4 r5d41 #ahhd1 #ii4 #ghf4 #ajf ,see ,pr9ciples ( ,inorganic ,*emi/ry1 translat$ by ,f9dlay1 #bnd edit41 p4 #acc4 7,macmillan1 #aijd47 #ajg ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahhh1 #b4 #dgd4 #ajh ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #ahi4 #aji ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #abe4 ,see also ,zawidski1 ,zeits*r4 physikal4 ,*em41 #aijd1 #dg4 #gbg2 van ,eyk1 ibid41 #aije1 #ea4 #gbj4 #aaj ,rob]ts-,au/51 ,proc4 ,roy4 ,soc41 #fc4 #ded2 ,spr+1 ,zeits*r4 physikal4 ,*em41 #ahid1 #ae4 #fe4 ,see also p4 #ce4 #aaa ,ramsay & ,"y1 ,phil4 ,trans41 #ahhd1 #age4 #dfa2 ,all51 ,trans4 ,*em4 ,soc41 #aijj1 #gg4 #dac4 #aab ,ramsay & ,"y1 ,phil4 ,trans4 #ahhf1 #agg4 #hg4 #aac ,?is is exemplifi$ 9 ! well-kn[n exp]im5t ) ! cryophorus4 #aad ,tammann has1 h[ev]1 f\nd t ! fusion curve 7solid 9 contact ) liquid7 ( phosphonium *loride c be foll[$ up to temp]atures above ! critical po9t 7,ar*4 ne]41 #aija #b1 #f4 #bdd74 #aae ,phil4 ,mag41 #ahhf1 #ba4 #cc4 ,see also ,s4 ,a4 ,moss1 ,physical ,review1 #aijc1 #af4 #cef4 #aaf ,?is is f\nd also 9 ! case ( bismu?4 ,see ,tammann1 ,zeits*r4 anorgan4 ,*em41 #aijd1 #dj4 #ed4 #aag ,see p4 #eg1 footnote4 #aah ,pogg4 ,annal51 #ahej1 #ha4 #efb4 #aai ,b>us1 ,am]4 ,j\r4 ,sci41 #ahib1 #db4 #abe2 ,mack1 ,compt4 r5d41 #ahih1 #abg4 #cfa2 ,hulett1 ,zeits*r4 physikal4 ,*em41 #ahii1 #ch4 #fbi4 #abj ,annal5 d] ,physik1 #ahii #c1 #fh4 #eec1 #fbi2 #aijj #d1 #a4 #bge2 #b4 #a2 #c4 #afa4 ,see also ,tammann1 ,kri/allisi]5 und ,s*melz5 7,leipzig1 #aijc74 #aba ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #cgc2 ,poynt+1 ,phil4 ,mag41 #ahha #e1 #ab4 #b2 ,planck1 ,wi$4 ,annal51 #ahhb1 #ae4 #ddf4 #abb ,bakhuis ,roozeboom1 ,das ,het]og5e ,glei*gewi*t1 ,i4 p4 #ia4 #abc ,lussana1 ,il nuovo ,cim5to1 #ahie #d1 #a4 #aje4 #abd ,tammann1 ,zeits*r4 physikal4 ,*em41 #aijc1 #df4 #hah4 #abe ,foote1 ,zeits*r4 physikal4 ,*em41 #aijj1 #cc4 #gdj4 #abf ,o/wald1 ,zeits*r4 physikal4 ,*em41 #ahig1 #bb4 #bhi4 #abg ,van't ,h(f1 ,ar*1 ne]41 #aija1 #f4 #dga4 #abh ,see1 = example1 ! det]m9ations ( ! solubility ( rhombic & monocl9ic sulphur1 by ,j4 ,mey]1 ,zeits*r4 anorg4 ,*em41 #aijb1 #cc4 #adj4 #abi ,zeits*r4 physikal4 ,*em41 #ahii1 #cb4 #ejf4 #acj ,ka/le & ,re$1 ,am]4 ,*em4 ,j\r41 #aijb1 #bg4 #bji4 #aca ,zeits*r4 physikal4 ,*em41 #aijj1 #ce4 #eha4 #acb ,compt4 r5d41 #ahhb1 #ie4 #abgh2 #ahhd1 #ig4 #abih1 #acff1 #adcc4 #acc ,zeits*r4 physikal4 ,*em41 #ahic1 #ab4 #ede4 #acd ,sitzungsb]4 ,wi5] ,akad41 #ahid1 #ajc4 ,i,ia4 #bbf4 #ace ,zeits*r4 physikal4 ,*em41 #bc-bi4 ,see also ,kue/]1 ibid41 #be-bh4 #acf ,zeits*r4 physikal4 ,*em41 #ahig1 #bd4 #aeb4 #acg ,ibid41 #ahih1 #bg4 #ehe4 #ach ,see ,w4 ,gu]tl]1 ,zeits*r4 anorgan4 ,*em41 #aijd1 #dj4 #bfh2 ,tammann1 ,zeits*r4 ,elektro*em41 #aijd1 #aj4 #ecb4 #aci ,e4 von ,pick>dt1 ,zeits*r4 physikal4 ,*em41 #aijb1 #db4 #ag4 #adj ,zeits*r4 physikal4 ,*em41 #aijd1 #dh4 #dfg4 #ada ,m4 ,padoa1 ,accad4 ,l9cei1 ,atti1 #aijd1 #ac4 #cbi4 #adb ,deville1 ,compt4 r5d41 #aheb1 #cd4 #efa2 ,pay51 ibid41 #aheb1 #cd4 #ejh2 ,debray1 ibid41 #aheh1 #df4 #egf4 ,x has also be5 f\nd by ,jaffe 7,zeits*r4 physikal4 ,*em41 #aijc1 #dc4 #dfe7 t :5 spontane\s cry/allization f solution occurs1 ! less /able =m always sep>ates fir/ :5 purification has be5 c>ri$ suffici5tly f>4 #adc ,brauns1 ,neues ,jahrbu* fu] ,m9]alogie1 #ahii1 #ac4 7,beilage ,b&7 #hd4 #add ,lehrbu*1 ,,ii4 #b4 #dde4 ,see also ,pr9ciples ( ,inorganic ,*emi/ry1 #bnd edit41 p4 #baj ff4 #ade ,s*aum & ,s*o5beck1 ,annal5 d] ,physik1 #aijb #d1 #h4 #feb4 ,see also ,*r4 ,fue*tbau]1 ,zeits*r4 physikal4 ,*em41 #aijd1 #dh4 #edi4 #adf ,ramsay & ,"y1 ,phil4 ,trans41 #ahhf1 #agg4 #hg4 #adg ,see volume 9 ?is s]ies on ,*emical ,dynamics1 by ,dr4 ,j4 ,w4 ,mellor4 #adh ,isamb]t1 ,compt4 r5d41 #ahha1 #ib4 #iai2 #ahhb1 #id4 #ieh2 #ahhc1 #if4 #fdc4 ,walk] & ,lumsd51 ,j\r4 ,*em4 ,soc41 #ahig1 #ga4 #dbh4 #adi ,compt4 r5d41 #ahfg1 #fd4 #fjc4 #aej ,compt4 r5d41 #ahhc1 #ajb4 #abdc4 #aea ,compt4 r5d41 #ahfh1 #ff1 #abei4 #aeb ,hor/mann1 ,b]41 #ahgf1 #i4 #gdi4 #aec ,loc4 cit4 #aed ,= ! reasons = *oos+ anhydr\s salt & wat] in/ead ( salt hydrate & wat] z compon5ts1 see p4 #ad4 #aee ,see ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #ebg4 #aef ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #ech4 #aeg ,zeits*r4 physikal4 ,*em41 #ahhi1 #d4 #dc4 #aeh ,b]41 #ahgf1 #i4 #gdi4 #aei ,see1 = example1 van't ,h(f1 ,lectures on ,!oretical & ,physical ,*emi/ry1 ,i4 p4 #fb 7,arnold74 #afj ,j\r4 ,*em4 ,soc41 #ahgg1 #cb4 #cie4 #afa ,hoitsema1 ,zeits*r4 physikal4 ,*em41 #ahie1 #ag4 #a4 #afb ,zeits*r4 physikal4 ,*em41 #ahhg1 #a4 #e2 #ahie1 #ag4 #eb4 #afc ,x is important to p[d] ! salt1 s9ce o!rwise ! dehydration ( ! hydrate & ! production ( equilibrium occurs ) comp>atively great t>d9ess4 #afd ,a *emical individual is a sub/ance :i* p]si/s z a phase ( con/ant composition :5 ! conditions ( temp]ature1 pressure1 & composition ( ! o!r phases pres5t1 und]go cont9u\s alt]ation )9 c]ta9 limits--! limits ( exi/5ce ( ! sub/ance 7,wald1 ,zeits*r4 physikal4 ,*em41 #ahig1 #bd4 #fdh74 #afe ,van't ,h(f1 ,zeits*r4 physikal4 ,*em41 #ahij1 #e4 #cbc2 ,o/wald1 ,lehrbu*1 ,i4 #fjf4 #aff ,t m]cury does dissolve 9 wat] c be argu$ f analogy1 say1 ) m]cury & bromonaph?al5e4 ,at ! ord9>y temp]ature ^! two liquids appe> to be q insoluble 9 "o ano!r1 b at a temp]ature ( #bhj;deg ! m]cury dissolves 9 appreciable quantity2 = on heat+ a tube conta9+ bromonaph?al5e ov] m]cury ! latt] sublimes ?r\gh ! liquid bromonaph?al5e & cond5ses on ! upp] surface ( ! tube4 #afg ,phil4 ,mag41 #ahhd1 #e1 #ah4 #bb2 #die4 #afh ,wi$4 ,annal51 #ahhf1 #bh4 #cje4 #afi ,zeits*r4 physikal4 ,*em41 #ahih1 #bf4 #dcc4 #agj ,ro?mund1 loc4 cit4 #aga ,ro?mund1 loc4 cit4 #agb ,a simil> behavi\r is f\nd 9 ! case ( die?ylam9e & wat] 7,r4 ,t4 ,lattey1 ,phil4 ,mag41 #aije1 #f1 #aj1 #cig74 #agc ,c4 ,s4 ,hudson1 ,zeits*r4 physikal4 ,*em41 #aijd1 #dg4 #aac4 #agd ,kon[al(f1 ,wi$4 ,annal51 #ahha1 #ad4 #bai4 ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #fhg4 ,bancr(t1 ,phase ,rule1 p4 #if4 #age ,kon[al(f1 loc4 cit4 #agf ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahia1 #h4 #ebf2 ,rec4 ,trav4 ,*im4 ,pays-,bas1 #ahhd1 #c4 #ch4 #agg ,kon[al(f1 loc4 cit4 ,cf4 ,bancr(t1 ,phase ,rule1 p4 #ajj4 #agh ,phil4 ,mag41 #ahhd #e1 #ah4 #ejc4 #agi ,see1 = example1 ,walk]1 ,introduction to ,physical ,*emi/ry1 #crd edit41 p4 #hf 7,macmillan1 #aijc74 ,consult also ,"y1 ,fractional ,di/illation 7,macmillan1 #aijc71 or ,ku551 ,v]dampfung und ,v]fluessigung von ,gemis*5 7,b>?1 #aijf71 :]e ! subject is fully treat$4 #ahj ,s9ce ?is is ! only phase ( v>iable composition pres5t4 #aha ,e4 von ,/ackelb]g1 ,zeits*r4 physikal4 ,*em41 #ahif1 #bj4 #ccg4 ,if ! *ange ( volume :i* accompanies solution1 & ! heat effect are kn[n1 ! quantitative *ange ( ! solubility ) ! pressure c be calculat$ 7,braun1 ,zeits*r4 physikal4 ,*em41 #ahhg1 #a4 #bei74 #ahb ,van't ,h(f1 ,ar*4 ne]l&4 #aija #b1 #f4 #dga4 #ahc ,tild5 & ,%5/one1 ,phil4 ,trans4 #ahhd1 #age4 #bc2 ,hulett & ,all51 ,j\r4 ,am]4 ,*em4 ,soc4 #aijb1 #bd4 #ffg2 ,&reae1 ,j\r4 prak4 ,*em4 #acg4 #dgd2 ,lumsd51 ,j\r4 ,*em4 ,soc41 #aijb1 #ha4 #cej2 ,mylius & v4 ,wro*em1 ,b]4 #aijj1 #cc4 #cfhi4 #ahd ,e4 von ,/ackelb]g1 ,zeits*r4 physikal4 ,*em4 #ahif1 #bj4 #aei2 #ahih1 #bf4 #ecc2 ,lumsd51 ,j\r4 ,*em4 ,soc41 #aijb1 #ha4 #cej2 ,holsbo]1 ,zeits*r4 physikal4 ,*em41 #aijb1 #ci4 #fia4 #ahe ,rei*] & van ,dev5t]1 ,zeits*r4 physikal4 ,*em4 #ahij1 #e4 #eei2 cf4 ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #hjc4 #ahf ,x has be5 %[n t ! =mula ( ,ramsay & ,"y 7p4 #ff7 c be appli$ 7) c]ta9 re/rictions7 to ! int]polation & extrapolation ( ! solubility curve ( a sub/ance provid$ two 7or ?ree7 po9ts on ! curve are kn[n4 ,9 ?is case ,t1 ,t#a1 etc41 ref] to ! temp]atures at :i* ! two sub/ances--"o ! solubility curve ( :i* is kn[n1 ! o!r ! solubility curve ( :i* is to be calculat$--h equal solubilities1 in/ead (1 z 9 ! previ\s case1 equal vap\r pressures4 7,f9dlay1 ,proc4 ,roy4 ,soc41 #aijb1 #fi4 #dga2 ,zeits*r4 physikal4 ,*em41 #aijc1 #db4 #aaj47 #ahg ,w4 ,muell] & ,p4 ,kaufmann1 ,zeits*r4 physikal4 ,*em4 #aijc1 #db4 #dig4 #ahh ,w4 ,o4 ,rabe1 ,zeits*r4 physikal4 ,*em41 #aija1 #ch4 #age4 #ahi ,) reg>d to ! limits ( sup]saturation & ! spontane\s cry/allization ( ! solute f sup]saturat$ solutions1 see ,jaffe1 ,zeits*r4 physikal4 ,*em41 #aijc1 #dc4 #efe1 & ! v int]e/+ pap] by ,mi]s & ,isaac1 ,trans4 ,*em4 ,soc41 #aijf1 #hi4 #dac4 #aij ,annales *im4 phys41 #ahid #g1 #b4 #ebd4 #aia ,phil4 ,trans41 #ahhd1 #age4 #bc4 #aib ,hiss9k1 ,zeits*r4 physikal4 ,*em41 #aijj1 #cb4 #edc4 #aic ,zeits*r4 physikal4 ,*em41 #aijc1 #dc4 #cac4 #aid ,gu?rie1 ,phil4 ,mag41 #ahge1 #d1 #di4 #a2 #ahhd1 #e1 #ag4 #dfb4 #aie ,see ,rol(f1 ,zeits*r4 physikal4 ,*em41 #ahie1 #ag4 #cbe2 ,gu?rie1 loc4 cit4 #aif ,gu?rie1 ,phil4 ,mag41 loc4 cit4 ,cf4 ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #hdc4 #aig ,gu?rie1 ,phil4 ,mag41 #ahge #d1 #di4 #bfi4 #aih ,b]41 #ahgg1 #bj4 #bbbc4 #aii ,silz-,b]4 ,wi54 ,akad41 #ahhj1 #ha4 ,,ii4 #ajeh4 #bjj ,gu?rie1 ,phil4 ,mag41 #ahge #d1 #di4 #bjf4 #bja ,if 9 ! neighb\rhood ( ! cryohydric po9t solution %\ld be accompani$ by an evolution ( heat1 !n z ! solubility w\ld 9 t case increase ) fall ( temp]ature1 salt w\ld pass into solution4 #bjb ,walk]1 ,zeits*r4 physikal4 ,*em41 #ahij1 #e4 #aic4 #bjc ,zeits*r4 physikal4 ,*em41 #ahig1 #bc4 #dah4 #bjd ,provid$ ! solid nitrile is n pres5t 9 too great excess4 #bje ,wi$4 ,annal51 #ahhf1 #bh4 #cbh4 ,cf4 ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #hgb4 #bjf ,walk]1 ,zeits*r4 physikal4 ,*em41 #ahij1 #e4 #aic4 ,s*re9emak]s1 ibid41 #ahig1 #bc4 #dag4 ,roozeboom1 ,rec4 trav4 *im4 ,pays-,bays1 #ahhi1 #h4 #beg4 ,brun]1 ,zeits*r4 physikal4 ,*em41 #ahig1 #bc4 #edb4 #bjg ,van't ,h(f1 ,lectures on ,!oretical ,*emi/ry1 ,i4 p4 #db4 ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #hbd4 #bjh ,o/wald1 ,pr9ciples ( ,inorganic ,*emi/ry1 translat$ by ,a4 ,f9dlay1 #bnd edit41 p4 #dec 7,macmillan1 #aijd72 ,skirr[ & ,calv]t1 ,zeits*r4 physikal4 ,*em41 #aija1 #cg4 #bag4 #bji ,vide ,loewel1 ,annales *im4 phys41 #aheg #c1 #di4 #cb4 ,cf4 ,loew5h]z1 ,zeits*r4 physikal4 ,*em41 #ahie1 #ah4 #hb4 #baj ,loewel1 loc4 cit4 ,gay-,lussac1 ,annales *im4 phys41 #ahai1 #aa4 #bif4 ,= ! solubility at high] temp]atures1 see ,tild5 & ,%5/one1 ,phil4 ,trans41 #ahhd1 #age4 #bc4 ,et>d1 ,annales *im4 phys41 #ahid #g1 #b4 #edh4 #baa ,ri*>ds1 ,zeits*r4 physikal4 ,*em41 #ahih1 #bf4 #fij2 ,ri*>ds & ,wells1 ibid41 #aijc1 #dc4 #dfe4 ,?is temp]ature is n q ! same z t ( ! quadruple po9t anhydr\s salt--hydrat$ salt--solution--vap\r1 because ! latt] is ! temp]ature at :i* ! sy/em is "u ! pressure ( its own vap\r4 ,s9ce1 h[ev]1 ! influ5ce ( pressure on ! solubility is v slight 7p4 #ajg71 ! position ( ! two po9ts w n be greatly diff]5t4 ,! quadruple po9t 0 f\nd by ,coh5 7,zeits*r4 physikal4 ,*em41 #ahid1 #ad4 #ij7 to be #cb4f;deg & #cj4h mm4 ( m]cury4 #bab ,van't ,h(f & van ,dev5t]1 ,zeits*r4 physikal4 ,*em41 #ahhg1 #a4 #ahe4 ,cf4 ,coh51 ibid41 #ahid1 #ad4 #hh4 #bac ,debray1 ,compt4 r5d41 #ahfh1 #ff4 #aid4 #bad ,ri*>ds1 ,zeits*r4 physikal4 ,*em41 #ahih1 #bf4 #fij4 ,a numb] ( o!r salt hydrates1 hav+ transition-po9ts rang+ f #bj;deg to #gh;deg1 :i* might be us$ = ! same purpose1 h be5 giv5 by ,ri*>ds & ,*ur*ill1 ibid41 #ahii1 #bh4 #cac4 #bae ,zeits*r4 physikal4 ,*em41 #aijc1 #df4 #hah4 #baf ,van't ,h(f1 ,lectures on ,physical ,*emi/ry1 ,i4 p4 #fg4 #bag ,coh51 ,zeits*r4 physikal4 ,*em41 #ahid1 #ad4 #ij4 #bah ,ziz1 ,s*weigg]'s ,j\rnal1 #ahae1 #ae4 #aff4 ,see ,o/wald1 ,lehrbu*1 ,,ii4 #b4 #gag4 #bai ,see1 = example1 ! solubility det]m9ations publi%$ 9 ,wiss5s*aftli*e ,abh&l4 d] physikalis*-te*nis*5 ,rei*san/alt1 ,vol4 ,,iii41 or 9 ! ,b]i*te1 = ! ye>s #ahig-aija4 #bbj ,meuss]1 ,b]41 #aija1 #cd4 #bddj4 #bba ,mylius & von ,wro*em1 ,b]41 #aijj1 #cc4 #cfic4 #bbb ,walk] & ,fyffe1 ,j\r4 ,*em4 ,soc41 #aijc1 #hc4 #ahj4 #bbc ,monat%efte1 #ahhg1 #h4 #fja4 #bbd ,! equilibria betwe5 calcium *loride & wat] h be5 mo/ completely /udi$ by ,roozeboom 7,zeits*r4 physikal4 ,*em41 #ahhi1 #d4 #ca74 #bbe ,hamm]l1 ,sitzungsb]4 ,wi54 ,akad41 #bte ,abteil1 #ahgh1 #gh4 #ei4 ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahhi1 #d4 #ca4 #bbf ,lidbury1 ,zeits*r4 physikal4 ,*em41 #aijb1 #ci4 #dec4 ,! curvature at ! melt+ po9t is all ! great] ! m ! comp\nd is dissociat$ into its compon5ts 9 ! liquid /ate4 ,if ! comp\nd is completely undissociat$1 ev5 9 ! vap\r phase1 ! two bran*es ( ! curve w int]sect1 7e4g4 pyrid9e & me?yl iodide2 ,at51 ,v]sl4 ,kon9k4 ,akad4 ,wet5s*4 ,am/]dam1 #aije1 #ac4 #dfb74 ,! small] ! degree ( dissociation1 !re=e1 ! %>p] w be ! b5d4 7,see ,/ort5bek]1 ,zeits*r4 physikal4 ,*em41 #ahib1 #aj4 #aid47 ,f ! ext5t ( flatt5+ ( ! curve1 x is also possible1 ) "s degree ( approximation1 to calculate ! degree ( dissociation ( ! sub/ance 9 ! fus$ /ate4 7,see ,roozeboom & ,at51 ,zeits*r4 physikal4 ,*em41 #aije1 #ec4 #dfc2 ,kremann1 ,zeits*r4 ,elektro*em41 #aijf1 #ab4 #bei47 #bbg ,see ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahhi1 #d4 #ca4 #bbh ,tammann1 ,wi$4 ,annal51 #ahii1 #fh4 #egg4 #bbi ,duhem1 ,j\rn4 ,physical ,*em41 #ahih1 #b4 #ca4 #bcj ,gibbs1 ,trans4 ,conn4 ,acad41 #c4 #aee2 ,saurel1 ,j\rn4 ,phys4 ,*em41 #aija1 #e4 #ce4 #bca ,9 ! case ( ! fusion ( a comp\nd ( two compon5ts ) =mation ( a liquid phase ( ! same composition1 ! temp]ature is a maximum2 9 ! case ( liquid mixtures ( con/ant boil+-po9t1 ! temp]ature may be a m9imum 7p4 #aje74 #bcb ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahib1 #aj4 #dgg4 ,! =mula ( f]ric *loride has be5 d\bl$1 9 ord] to avoid fractions 9 ! expression ( ! wat] ( cry/allization4 #bcc ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahib1 #aj4 #dgg4 #bcd ,a simil> s]ies ( hydrates is =m$ by z9c *loride & wat] 7,dietz & ,mylius1 ,zeits*r4 anorg4 ,*em41 #aije1 #dd4 #bji74 #bce ,mey]h(f]1 ,b]41 #ahig1 #cj4 #ahaj4 #bcf ,wald51 ,b]41 #ahii1 #cb4 #bhfc4 #bcg ,zeits*r4 physikal4 ,*em41 #aijc1 #db4 #dcb4 #bch ,?is composition 0 also confirm$ by measurem5ts ( ! vap\r pressure 7cf4 p4 #ij74 #bci ,s9ce all sub/ances are no d\bt volatile to a c]ta9 ext5t at "s temp]ature1 x is to be und]/ood "h t ! sub/ances are appreciably volatile at ! temp]ature ( ! exp]im5t4 #bdj ,= a g5]al discussion ( ! p>tial pressures 9 a sy/em ( two compon5ts1 see ,bancr(t1 ,j\rn4 ,physical ,*em41 #ahii1 #c4 #a4 #bda ,zeits*r4 physikal4 ,*em41 #ahhi1 #c4 #aa2 ,rec4 trav4 *im4 ,pays-,bas1 #ahhh1 #g4 #aeb4 #bdb ,! composition ( a solution is repres5t$ symbolically by plac+ a d\ble wavy l9e betwe5 ! symbols ( ! compon5ts1 & indicat+ ! numb] ( atoms pres5t 9 ! ord9>y mann]3 ?us1 ,i wavy ,clx repres5ts a solution conta9+ x atoms ( *lor9e to "o atom ( iod9e 7,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahhh1 #b4 #dej74 #bdc ,s9ce iod9e mono*loride 9 ! liquid /ate is only v slightly dissociat$1 ! b5d at ,c is v %>p 7see p4 #adg1 footnote74 ,see also ! inve/igation ( ! sy/em pyrid9e & me?yl iodide 7,at51 ,v]sl4 ,kon9k4 ,akad4 ,wet5s*4 ,am/]dam1 #aije1 #ac4 #dfb74 #bdd ,?is upp] bran* ( ! curve is n %[n 9 ! figure1 z ! ord9ate correspond+ to #cj;deg w\ld be v great4 #bde ,/ort5bek]1 ,zeits*r4 physikal4 ,*em41 #ahhi1 #c4 #bb4 #bdf ,ramsay & ,"y1 ,j\rn4 ,*em4 ,soc41 #ahhf1 #di4 #deh4 #bdg ,van't ,h(f1 ,lectures on ,physical ,*emi/ry1 ,i4 p4 #gg 7,arnold74 #bdh ,?is is diff]5t f :at we f\nd 9 ! case ( non-volatile solutes 7p4 #abf74 ,9 ! pres5t case1 ! p>tial pressure ( ! iod9e 9 ! vap\r w be l[]$ by addition ( *lor9e1 b ! total pressure is increas$4 #bdi ,! dim9ution ( volume is suppos$ to be c>ri$ out at con/ant temp]ature4 ,! pressure & ! composition ( ! phases mu/1 !re=e1 rema9 un*ang$1 & only ! relative am\nts ( ^! c und]go alt]ation4 #bej ,at po9t b ! ratio ( *lor9e to iod9e 9 ! solution is less ?an 9 ! mono*loride1 s t by ! sep>ation ( ?is ! excess ( *lor9e yield$ by ! cond5sation ( ! vap\r is remov$4 #bea ,roozeboom1 ,rec4 trav4 *im4 ,pays-,bas1 #ahhd1 #c4 #bi2 #ahhe1 #d4 #fe2 ,zeits*r4 physikal4 ,*em41 #ahhh1 #b4 #dej4 #beb ,two curves enclose a field :5 !y =m ) "o ano!r an angle less ?an two "r angles4 #bec ,roozeboom1 ,zeits*r4 physikal4 ,*em41 loc4 cit4 #bed ,van't ,h(f1 ,zeits*r4 physikal4 ,*em41 #ahij1 #e4 #cbc4 #bee ,bancr(t has propos$ to re/rict ! t]m occlusion to ! =mation ( solid solutions1 & to apply adsorption only to effects :i* are prim>ily due to surface t5sion4 ,su* a di/9ction1 h[ev]1 w\ld probably be v difficult to c>ry ?r\gh1 = al?\gh adsorption may1 9 l>ge measure1 be due to surface t5sion1 ! behavi\r ( adsorb$ sub/ances is simil> to t ( sub/ances exi/+ 9 solid solutions4 #bef ,tammann1 ,wi$4 ,annal51 #ahig1 #fc4 #af2 ,zeits*r4 physikal4 ,*em41 #ahih1 #bg4 #cbc4 #beg ,see1 = example1 ,*appuis1 ,wi$4 ,annal51 #ahha1 #ab4 #afa2 ,j\l91 ,annal4 *im4 phys41 #ahha1 #e1 #bb4 #cih2 ,kays]1 ,wi$4 ,annal51 #ahha1 #ab4 #ebf4 #beh ,hoitsema1 ,zeits*r4 physikal4 ,*em41 #ahie1 #ag4 #a4 #bei ,annales *im4 phys41 #ahgd1 #e1 #b4 #bgi4 #bfj ,hoitsema1 ,zeits*r4 physikal4 ,*em41 #ahie1 #ag4 #a2 ,dew>1 ,phil4 ,mag41 #ahgd1 #d1 #dg1 #cbd1 #cdb2 ,mond1 ,ramsay & ,%ields1 ,proc4 ,royal ,soc41 #ahig1 #fb4 #bij4 #bfa ,loc4 cit4 #bfb ,x is notewor?y t ! =m ( curve obta9$ = hydrog5 & palladium be>s a /rik+ resemblance to t = ! dehydration ( colloids conta9+ absorb$ wat]1 e4g4 silicic acid 7vide van ,bemmel51 ,zeits*r4 anorg4 ,*em41 #ahig-aijj4 ,cf4 ,za*>ias1 ,zeits*r4 physikal4 ,*em41 #aijb1 #ci4 #dhj74 #bfc ,zeits*r4 physikal4 ,*em41 #ahij1 #e4 #cbb4 #bfd ,kue/]1 ,zeits*r4 physikal4 ,*em41 #ahie1 #ag4 #cfg4 ,bodla5d]1 ,neues ,jahrbu* f4 ,m9]alogie1 #ahih-ii1 ,beilage ,b&1 #ab4 #ib4 #bfe ,bruni & ,padoa1 ,atti ,accad4 ,l9cei1 #aijb #e1 #aa4 #a2 #efe4 #bff ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahii1 #cj4 #che2 ,bruni1 ,r5d4 ,accad4 ,l9cei1 #ahih1 #b4 #ach1 #cdg4 ,= a g5]al acc\nt ( solid solutions ! read] is ref]r$ to ,bruni1 ,ueb] fe/e ,loesung5 7,ahr5s's*e ,sammlung71 & to ,bodla5d]1 loc4 cit4 ,= ! =mation & trans=mation ( liquid mix$ cry/als1 see ,a4 ,c4 de ,kock1 ,zeits*r4 physikal4 ,*em41 #aijd1 #dh4 #abi4 #bfg ,9 discuss+ ! v>i\s sy/ems :i* may be obta9$ "h1 ,roozeboom 7loc4 cit47 made use ( ! v>iation ( ! !rmodynamic pot5tial 7p4 #bi7 ) ! conc5tration4 ,9 spite ( ! advantages :i* su* a treatm5t af=ds1 ! temp]ature-conc5tration diagram has be5 adopt$ z be+ m readily und]/ood & z m suitable = an elem5t>y discussion ( ! subject4 #bfh ,^! curves are also call$ ! liquidus & ! solidus curve respectively4 #bfi ,kue/]1 ,zeits*r4 physikal4 ,*em41 #ahie1 #ag4 #cfj4 #bgj ,kue/]1 ibid41 #ahia1 #h4 #ehi4 #bga ,x %\ld be rem>k$ t ! behavi\r describ$ "h w hold /rictly only :5 ! solid mix$ cry/als und]go *ange suffici5tly rapidly to be always 9 equilibrium ) ! liquid4 ,?is1 h[ev]1 is n always ! case 7see ,re9d]s1 ,zeits*r4 physikal4 ,*em41 #aijj1 #cb4 #did2 van ,wyk1 ,zeits*r4 anorg4 ,*em41 #aije1 #dh4 #be71 & complete solidification w n 9 ?is case take place at ! temp]ature correspond+ ) ! l9e dc 9 ,fig4 #ej1 b only at a l[] temp]ature4 #bgb ,adriani1 ,zeits*r4 physikal4 ,*em41 #aijj1 #cc4 #dfi4 #bgc ,re9d]s1 ,zeits*r4 physikal4 ,*em41 #aijj1 #cb4 #did4 #bgd ,hiss9k1 ,zeits*r4 physikal4 ,*em41 #aijj1 #cb4 #edb4 #bge ,van ,eyk1 ,zeits*r4 physikal4 ,*em41 #ahii1 #cj4 #dcj4 #bgf ,cady1 ,j\rn4 ,physical4 ,*em41 #ahii1 #c4 #abg4 #bgg ,see ,rob]ts-,au/5 & ,/ansfield1 ,rapports du congres int]national de physique1 #aijj1 ,i4 #cfc4 #bgh ,heycock & ,neville1 ,proc4 ,roy4 ,soc41 #aijc1 #ga4 #dji4 ,= ! p>tial liquefaction ( mix$ cry/als on cool+1 see also ,a4 ,c4 de ,kock 7,zeits*r4 physikal4 ,*em41 #aijd1 #dh4 #abi74 #bgi ,arm/rong1 ,watt's ,diction>y ( ,*emi/ry 7,morley & ,muir71 ,,iii41 p4 #hh4 ,see also ,l[ry1 ,j\r4 ,*em4 ,soc41 #ahii1 #ge4 #baa4 #bhj ,see ,bancr(t1 ,j\rn4 ,physical ,*em41 #ahih1 #b4 #adc2 ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #bhh4 #bha ,hylotropic sub/ances are su* z c und]go trans=mation into o!r sub/ances ( ! same composition 7,o/wald1 ,lehrbu*1 ,,ii4 #b4 #bih74 #bhb ,also call$ ,equilibrium ,po9t 7,l[ry74 #bhc ,= a discussion ( ^! sy/ems1 see ,roozeboom1 ,zeits*r4 physikal4 ,*em41 loc4 cit4 #bhd ,see ,bancr(t1 loc4 cit41 p4 #adg2 ,wegs*eid]1 ,sitzungsb]4 ,wi5] ,akad41 #aijb1 #aaj4 #ijh4 #bhe ,ref]5ce may be made "h to ! t]m /ability limit1 introduc$ by ,knorr 7,annal51 #ahif1 #bic4 #hh7 to indicate t temp]ature above :i* liquefaction & isom]ic *ange takes place4 ,z employ$ by ,knorr & o!rs1 ! t]m does n appe> to h a v precise mean+1 s9ce x is us$ to d5ote1 n ! temp]ature at :i* ^! *anges c occur1 b ! temp]ature at :i* ! *ange is rapid 7vide ,annal51 #ahif1 #bic4 #ia2 #ahii1 #cjf4 #ccd72 & ! introduction ( an indef9ite velocity ( *ange r5d]s ! temp]ature ( ! /ability limit also some:at indef9ite4 ,! def9it5ess ( ! t]m is also n a little dim9i%$ by ! fact t ! limit c be alt]$ by means ( catalytic ag5ts4 ,s9ce1 z we h se51 ! /able modification c always und]go isom]ic *ange & liquefy at temp]atures above ! natural freez+ po9t1 b n bel[ t po9t2 &1 fur!r1 ! less /able modification c und]go isom]ic trans=mation & liquefy at temp]atures above ! eutectic po9t1 b w n liquefy at temp]atures bel[ t2 x seems to ! au?or t x w\ld be m precise to id5tify ^! two po9ts--! natural freez+ po9t & ! eutectic po9t--:i* are n alt]$ by catalytic ag5ts1 ) ! /ability limits ( ! /able & un/able modification respectively4 ,a p]fectly def9ite mean+ w\ld !reby be giv5 to ! t]m4 ,9 ! case ( ^? sub/ances :i* d n und]go appreciable isom]ic *ange at ! temp]ature ( ! melt+ po9t1 ! /ability limits w\ld be ! po9ts ,g & ,h1 ,fig4 #fj4 #bhf ,cam]on1 ,j\rn4 ,physical ,*em41 #ahih1 #b4 #dji4 #bhg ,c>ve?1 ,j\rn4 ,phys4 ,*em41 #ahih1 #b4 #aei4 ,see also ,dutoit & ,fa?1 ,j\rn4 *im4 phys41 #aijc1 #a4 #ceh2 ,f9dlay1 ,trans4 ,*em4 ,soc41 #aijd1 #he4 #djc4 #bhh ,hollmann1 ,zeits*r4 physikal4 ,*em41 #aijc1 #dc4 #abi4 #bhi ,= o!r examples ( ! application ( ! ,phase ,rule to isom]ic sub/ances1 see ,j\rn4 ,physical ,*em41 vols4 #b4 et seq42 ,f9dlay1 ,trans4 ,*em4 ,soc41 #aijd1 #he4 #djc4 #bij ,see ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahii1 #cj4 #daj4 #bia ,see also ,sapos*nik(f1 ,zeits*r4 physikal4 ,*em41 #di4 #fhh2 ,kremann1 ,monat%efte1 #aijd1 #be4 #abae1 #abga1 #acaa4 #bib ,j4 ,c4 ,philip1 ,j\rn4 ,*em4 ,soc41 #aijc1 #hc4 #hba4 #bic ,cf4 also ,pat]no & ,ampolla1 ,gazzetta *im4 ital41 #ahig1 #bg4 #dha4 #bid ,philip1 loc4 cit41 p4 #hbf4 #bie ,philip1 loc4 cit41 p4 #hbi4 ,comp>e curves = iod9e mono*loride1 ,fig4 #db1 p4 #afb4 #bif ,kuril(f1 ,zeits*r4 physikal4 ,*em41 #ahig1 #bc4 #fgf4 #big ,lad5burg1 ,b]41 #ahie1 #bh4 #afc2 #aiia4 #bih ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #did2 ,adriani1 ibid41 #aijj1 #cc4 #dec4 #bii ,adriani1 ,zeits*r4 physikal4 ,*em41 #aijj1 #cc4 #dec4 #cjj ,a4 ,f9dlay & ,miss ,e4 ,hickmans4 #cja ,kipp+ & ,pope1 ,j\rn4 ,*em4 ,soc41 #ahig1 #ga4 #iic4 #cjb ,see ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #eab2 ,adriani1 ibid41 #aijj1 #cc4 #dgc2 #aija1 #cf4 #afh4 #cjc ,9 ?is connection ref]5ce %\ld be made m especially to ! pap] by ,rob]ts-,au/5 & ,/ansfield1 ,sur la con/itution des alliages metalliques1 9 ! ,rapports du congres int]national de physique1 #aijj1 ,i4 #cfc2 ,j4 ,a4 ,ma!ws1 ,j\rn4 ( ! ,frankl9 ,in/41 #aijb2 ,gauti]1 ,compt4 r5d41 #ahif1 #abc4 #aji2 ,rob]ts-,au/51 ,reports ( ! ,alloys ,rese>* ,committee1 9 ,j\rn4 ,in/4 ,me*an4 ,eng9e]s1 f #ahia to #aijd2 & ! pap]s by ,heycock & ,neville1 publi%$ 9 ! ,j\rn4 ,*em4 ,soc41 & ! ,trans4 ,roy4 ,soc4 s9ce #ahig2 also ,neville1 ,reports ( ! ,briti% ,association1 #aijj1 p4 #aca4 ,ref]5ce mu/ also be made to ! important metallographic inve/igations by ,tammann & 8 pupils1 & ( ,kurnak(f 7,zeits*r4 anorgan4 ,*em41 vol4 #dj & onw>ds71 & also to ^? ( ,%eph]d1 ,j\rn4 ,physical ,*em41 #h4 ,a bibliography ( ! alloys is giv5 9 ,zeits*r4 anorgan4 ,*em41 #aijc1 #ce4 #bdi4 #cjd ,kurnak(f & ,pus*91 ,zeits*r4 anorgan4 ,*em41 #aijb1 #cj4 #ajd4 #cje ,gauti]1 ,bull4 ,soc4 d',enc\ragem5t1 #ahif #e1 #a4 #acab4 #cjf ,heycock & ,neville1 ,phil4 ,trans41 #aijj1 #aid4 #bja4 #cjg ,gauti]1 loc4 cit4 ,see also ,rob]ts-,au/5 & ,rose1 ,proc4 ,roy4 ,soc41 #aijc1 #ga4 #afa4 #cjh ,heycock & ,neville1 ,j\rn4 ,*em4 ,soc41 #ahig1 #ga4 #dad4 #cji ,see ,rob]ts-,au/51 ,introduction to ,metallurgy1 #e? edit41 p4 #ajb2 ,bakhuis ,roozeboom1 ,j\rn4 ,iron & ,/eel ,in/41 #aijj1 ,,ii4 #caa2 ,zeits*r4 physikal4 ,*em41 #aijj1 #cd4 #dcg2 von ,jueptn]1 ,sid]ology1 p4 #bbc 7translation by ,c4 ,salt]72 van't ,h(f1 ,z9n1 ,gips1 und ,/ahl1 p4 #bd1 or ,a*t ,vortraege ueb] physikalis*e ,*emie1 p4 #cg4 ,fur!r1 ,roozeboom1 ,zeits*r4 ,elektro*em41 #aijd1 #aj4 #dhi2 ,e4 ,heyn1 ibid41 p4 #dia2 ,c>p5t] & ,keel+1 ,j\rn4 ,iron & ,/eel ,in/41 #aijd1 #fe4 #bbd4 #caj ,! melt+ po9t ( pure iron is giv5 by ,c>p5t] & ,keel+ 7,j\rn4 ,iron & ,/eel ,in/41 #aijd1 #fe4 #bbd7 z #aeje;deg4 #caa ,zeits*r4 fu] ,elektro*em41 #aijd1 #aj4 #dia4 #cab ,see also ,hiorns1 ,j\rn4 ,soc4 ,*em4 ,ind41 #aijf1 #be4 #ej4 #cac ,bancr(t1 ,j\r4 ,physical ,*em41 #aijb1 #f4 #agh2 ,bell & ,tab]1 ibid41 #aijf1 #aj4 #abj4 #cad ,! me?od to be foll[$ :5 ! ?ird compon5t ent]s into ! solid phase w be expla9$ lat]4 #cae ,tammann1 ,zeits*r4 anorg4 ,*em41 #aijc1 #cg4 #cjc2 #aije1 #de4 #bd4 ,ref]5ce may be made "h to ! regi/]+ pyromet] ( ,kurnak(f1 ,zeits*r4 anorg4 ,*em41 #aijd1 #db4 #ahd4 #caf ,9 ?is connection1 see ,doelt]1 ,physikalis*-*emis* ,m9]alogie 7,b>?1 #aija72 ,mey]h(f]1 ,zeits*r4 f4 ,kri/allographie1 #aijb1 #cf4 #eic2 ,gu?rie1 ,phil4 ,mag41 #ahhd #e1 #ag4 #dgi2 ,le ,*ateli]1 ,compt4 r5d41 #aijj1 #acj4 #he2 & especially ,e4 ,baur1 ,zeits*r4 physikal4 ,*em41 #aijc1 #db4 #efg2 ,j4 ,h4 ,l4 ,vogt1 ,zeits*r4 ,elektro*em41 #aijc1 #i4 #heb1 & ,die ,silikats*melzloesung51 ,p>ts ,i4 & ,,ii4 7,*ri/iania1 #aijc1 #aijd74 ,see also ,n4 ,v4 ,kultas*eff1 ,zeits*r4 anorg4 ,*em41 #aijc1 #ce4 #ahg4 #cag ,g4 ,g4 ,/okes1 ,proc4 ,roy4 ,soc41 #ahia1 #di4 #agd2 ,gibbs1 ,trans4 ,conn4 ,acad41 #ahgf1 #c4 #agf2 ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahid1 #ae4 #adg4 #cah ,?is figure has be5 tak5 f ,o/wald's ,lehrbu*1 ,,ii4 #b4 #ihd4 #cai ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahic1 #ab4 #cfi4 #cbj ,c4 ,r4 ,a4 ,wright1 ,proc4 ,roy4 ,soc41 #ahia1 #di4 #agd2 #ahib1 #ej4 #cge4 #cba ,! di/ribution coeffici5t w n rema9 con/ant because1 ap>t f o!r reasons1 ! mutual solubility ( *lor(orm & wat] is alt]$ by ! addition ( ! acid4 #cbb ,bancr(t1 ,physical ,review1 #ahie1 #c4 #ba2 ,s*re9emak]s1 ,zeits*r4 physikal4 ,*em41 #ahig1 #bc4 #feb1 & subsequ5t volumes4 #cbc ,c4 ,r4 ,a4 ,wright1 ,proc4 ,roy4 ,soc41 #ahhi-ahic4 #cbd ,c4 ,r4 ,a4 ,wright1 ,proc4 ,roy4 ,soc41 #ahib1 #ej4 #cij4 #cbe ,bodla5d]1 ,b]g- und ,huett5ma5n4 ,ztg41 #ahig1 #ef4 #cca4 #cbf ,c4 ,r4 ,a4 ,wright1 ,proc4 ,roy4 ,soc41 loc4 cit4 #cbg ,s*re9emak]s1 ,zeits*r4 physikal4 ,*em41 #aijj1 #cc4 #gh4 #cbh ,s*re9emak]s1 ,zeits*r4 physikal4 ,*em41 #ahih1 #bg4 #ie4 #cbi ,s*re9emak]s1 ,zeits*r4 physikal4 ,*em41 #ahii1 #bi4 #egg4 #ccj ,s*re9emak]s1 ,zeits*r4 physikal4 ,*em41 #ahih1 #be4 #edc4 #cca ,*>py1 ,compt4 r5d41 #ahih1 #abf4 #aefi4 ,comp>e ! curves = ! sy/em ,,kno#c--,na,n,o#c--,li,n,o#c 7,h4 ,r4 ,c>ve?1 ,j\rn4 ,physical ,*em41 #ahih1 #b4 #bji74 ,also alloys ( ,pb--,sn--,bi 7,e4 ,s4 ,%eph]d1 ,j\rn4 ,physical ,*em41 #aijb1 #f4 #ebg74 #ccb ,x %\ld be rememb]$ t 9 ! triangul> diagram a l9e p>allel to "o ( ! sides indicates1 at a giv5 temp]ature1 a con/ant am\nt ( ! compon5t repres5t$ by ! opposite corn] ( ! triangle2 &1 h5ce1 po9ts 9 a plane1 p>allel to "o face ( a "r prism1 w indicate = diff]5t temp]atures1 v>iation 9 ! am\nts ( two compon5ts1 b con/ancy 9 ! am\nt ( ! ?ird4 #ccc ,gazzetta *im4 ital41 #ahih1 #bh4 ,,ii4 #ebj4 #ccd ,bruni1 ,gazzetta *im4 ital41 #ahih1 #bh4 ,,ii4 #ejh2 #aijj1 #cj4 ,i4 #ce4 #cce ,zeits*r4 physikal4 ,*em41 #aijj1 #cf4 #afh4 #ccf ,= a discussion ( ^! sy/ems1 see van't ,h(f1 ,bildung und ,spaltung von ,doppelsalz5 7,leipzig1 #ahig74 #ccg ,van ,leeuw51 ,zeits*r4 physikal4 ,*em41 #ahig1 #bc4 #ce4 #cch ,mey]h(f]1 ,zeits*r4 physikal4 ,*em41 #ahhi1 #c4 #ccf2 #ahij1 #e4 #ig4 #cci ,rei*]1 ,zeits*r4 physikal4 ,*em41 #ahhg1 #a4 #bbj4 #cdj ,= o!r examples ( ! =mation & decomposition ( d\ble salts at a transition po9t1 ! read] is ref]r$ to ! "w by van't ,h(f1 already cit$1 on ! ,bildung und ,spaltung von ,doppelsalz52 or to ,bancr(t1 ,phase ,rule1 p4 #ahj4 #cda ,bancr(t1 ,phase ,rule1 p4 #ahc4 #cdb ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahhh1 #b4 #ead4 #cdc ,! influ5ce ( pressure on ! transition po9t 9 ! case ( ta*ydrite has be5 det]m9$ by van't ,h(f1 ,k5rick1 & ,dawson 7,zeits*r4 physikal4 ,*em41 #aija1 #ci4 #bg1 #cd2 van't ,h(f1 ,zur ,bildung d] ozeanis*5 ,salzablag]ung51 ,i4 p4 #ff--;,brunswick1 #aije74 ,?is salt is =m$ f magnesium *loride & calcium *loride at #bb;deg1 9 accordance ) ! 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 ( pressure raises ! transition po9t1 because ! =mation ( ta*ydrite is accompani$ by increase ( volume2 ! elevation be+ #j4jaf;deg = an increase ( pressure ( #a atm4 ,! numb] calculat$ f ! !oretical =mula 7p4 #eg7 is #j4jac;deg = #a atm4 ,if "o calculates ! influ5ce ( ! pressure ( sea-wat] on ! temp]ature ( =mation ( ta*ydrite 7:i* is ( int]e/ on acc\nt ( ! natural occurr5ce ( ?is salt71 x is f\nd t a dep? ( wat] ( #aejj metres1 ex]t+ a pressure ( #ahj atm41 w\ld alt] ! temp]ature ( =mation ( ta*ydrite by only #c;deg4 ,! effect is1 !re=e1 comp>atively unimportant4 #cdd ,roozeboom1 ,zeits*r4 physical4 ,*em41 #ahhg1 #a4 #bbg4 #cde ,zeits*r4 physical4 ,*em41 #ahhg1 #a4 #bbg4 #cdf ,van't ,h(f & ,muell]1 ,b]41 #ahih1 #ca4 #bbjf4 #cdg ,van't ,h(f & van ,dev5t]1 ,zeits*r4 physikal4 ,*em41 #ahhg1 #a4 #afe4 #cdh ,= a full discussion ( ! solubility relations ( sodium ammonium racemate1 see van't ,h(f1 ,bildung und ,spaltung von ,doppelsalz51 p4 #ha4 #cdi ,annales *im4 phys41 #ahdh #c1 #bd4 #ddb4 #cej ,see ,van't ,h(f & van ,dev5t]1 ,zeits*r4 phys4 ,*em41 #ahhg1 #a4 #afe4 #cea ,mey]h(f]1 ,zeits*r4 physikal4 ,*em41 #ahij1 #e4 #aba4 #ceb ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahhh1 #b4 #eah4 #cec ,mey]h(f]1 ,zeits*r4 physikal4 ,*em41 #ahij1 #e4 #aji4 ,on ! importance ( ! transition int]val 9 ! case ( optically active sub/ances1 see ,mey]h(f]1 ,b]41 #aijd1 #cg4 #bfjd4 #ced ,9 connection ) ?is *apt]1 see1 m especially1 van't ,h(f1 ,bildung und ,spaltung von ,doppelsalz51 p4 #c1 ff42 ,roozeboom1 ,zeits*r4 physikal ,*em41 #ahib1 #aj4 #aeh2 ,bancr(t1 ,phase ,rule1 p4 #bja2 #bji4 #cee ,! same re/riction mu/ be made "h z 0 impos$ 9 ! prec$+ *apt]1 namely1 t ! two salts 9 solution give a common ion4 #cef ,= example1 addition ( ammonium *loride to solutions ( f]ric *loride 7,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahib1 #aj4 #adi74 #ceg ,x mu/1 ( c\rse1 be und]/ood t ! temp]ature is on t side ( ! transition po9t on :i* ! d\ble salt is /able4 #ceh ,excess ( ! d\ble salt mu/ be tak51 because o!rwise an unsaturat$ solution might be =m$1 & ?is w\ld1 ( c\rse1 n deposit any salt4 #cei ,mey]h(f]1 ,b]41 #aijd1 #cg4 #bfje4 #cfj ,mey]h(f]1 ,b]41 #ahig1 #cj4 #ahji4 #cfa ,mey]h(f]1 ,b]41 #aijd1 #cg4 #bfjd4 #cfb ,bancr(t1 ,phase ,rule1 p4 #bjc2 ,roozeboom1 ,zeits*r4 physikal4 ,*em41 #ahia1 #h4 #ejd1 #eca2 ,/ort5bek]1 ibid41 #ahie1 #ag4 #fdc2 #ahig1 #bb4 #fj2 #aijj1 #cd4 #ajh4 #cfc ,roozeboom1 ,zeits*r4 phys4 ,*em41 #ahii1 #bh4 #did2 ,b]41 #ahii1 #cb4 #ecg4 #cfd ,z1 = in/ance1 /ry*n9e racemate1 a comp\nd ( racemic acid ) ! optically active /ry*n9e4 ,?is w\ld be resolv$ into /ry*n9e d-t>trate & /ry*n9e l-t>trate1 :i* are n enantiomorph\s =ms4 #cfe ,van't ,h(f & ,mey]h(f]1 ,zeits*r4 physikal ,*em41 #ahih1 #bg4 #ge2 #ahii1 #cj4 #hf4 ,fig4 #aac is tak5 f ! latt] pap]4 #cff ,solid models con/ruct$ ( pla/] ( ,p>is c be obta9$ f ,max ,kaehl] & ,m>t9i1 ,b]l94 #cfg ,in/ead ( ! pres5t me?od ( obta9+ potassium *loride by decompos+ c>nallite ) wat]1 advantage might be tak5 ( ! fact t c>nallite :5 heat$ to #afh;deg und]goes decomposition ) sep>ation ( ?ree-f\r?s ( ! potassium *loride 7van't ,h(f1 ,a*t ,vortraege ueb] physikalis*e ,*emie1 #aijb1 p4 #cb74 #cfh ,roozeboom & ,s*re9emak]s1 ,zeits*r4 physikal4 ,*em41 #ahid1 #ae4 #ehh4 #cfi ,^! curves repres5t only portions ( ! iso!rms1 s9ce ! sy/ems 9 :i* a t]n>y solution is 9 equilibrium ) solid hydrog5 *loride or a hydrate1 h n be5 inve/igat$4 #cgj ,! numb]s pr9t$ beside ! po9ts on ! curves ref] to ! numb] ( ! exp]im5t 9 ! orig9al pap]4 #cga ,la%1 ,mill] & ,k5rick1 ,j\rn4 ,physical4 ,*em41 #aijc1 #g4 #bei2 ,allan1 ,am]4 ,*em4 ,j\rn41 #aija1 #be4 #cjg4 #cgb ,allan1 ,am]4 ,*em4 ,j\rn41 #aija1 #be4 #cjg4 #cgc ,hoitsema1 ,zeits*r4 physikal4 ,*em41 #ahie1 #ag4 #fea2 ,allan1 loc4 cit4 #cgd ,rutt51 ,zeits*r4 anorgan4 ,*em41 #aijb1 #cj4 #cdb4 ,comp>e ! sy/em ,be,o--,,s#c--;,h#b,o2 ,p>sons1 ,zeits*r4 anorgan4 ,*em41 #aijd1 #db4 #bej4 #cge ,zeits*r4 anorgan4 ,*em41 #aijd1 #dj4 #adf4 #cgf ,s*re9emak]s1 ,zeits*r4 physikal4 ,*em41 #ahic1 #aa4 #gf2 ,bancr(t1 ,j\rn4 ,physical ,*em41 #aijb1 #f4 #agi4 #cgg ,zeits*r4 anorgan4 ,*em41 #aijd1 #dj4 #adh4 #cgh ,zeits*r4 physikal4 ,*em41 #aijc1 #dc4 #ced4 #cgi ,^! equilibria 7 obta9$ by ,b\d\>d1 ,annales *im4 phys41 #aija #g1 #bd4 #e4 ,see also ,hahn1 ,zeits*r4 physikal4 ,*em41 #aijc1 #db4 #gje2 #dd4 #eac4 #chj ,g4 ,preun]1 ,zeits*r4 physikal4 ,*em41 #aijc1 #dg4 #che4 #cha ,see ,hahn1 ,zeits*r4 physikal4 ,*em41 #aijc1 #db4 #gje2 #dd4 #eac2 ,b\d\>d1 ,bull4 ,soc4 *im41 #c1 #be4 #dhd2 ,bodla5d]1 ,zeits*r4 f4 ,elektro*em41 #aijb1 #h4 #hcc2 ,r4 ,s*5ck & ,zimm]mann1 ,b]41 #aijc1 #cf4 #abca1 #cffc2 ,s*5ck & ,hell]1 ibid41 #aije1 #ch4 #bacb2 ,zeits*r4 f4 ,elektro*em41 #aijc1 #i4 #fia2 ,hab]1 ,!rmodynamik te*nis*] ,gasreaktion51 p4 #bic 7,muni*1 #aijc74 #chb ,a v useful summ>y ( ! inve/igations c>ri$ out by van't ,h(f & 8 pupils on ! =mation ( ! ,/assfurt salt-b$s is giv5 by ,e4 ,f4 ,arm/rong1 9 ! ,reports ( ! ,briti% ,association = #aija1 p4 #bfb4 ,see also van't ,h(f1 ,zur ,bildung d] ozeanis*5 ,salzablag]ung5 7,brunswick1 #aije74 #chc ,see especially ,mey]h(f]1 ,silzungsb]4 ,wi54 ,akad41 #ahie1 #ajd4 ,,ii4 b1 #hdj2 ,mey]h(f] & ,saund]s1 ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #dec2 #ca4 #cgj4 ,! inve/igation ( ! equilibria betwe5 reciprocal salt-pairs alone 7?ree-compon5t sy/ems7 is ( great importance = ! artificial prep>ations ( m9]als1 z also 9 analytical *emi/ry = ! prop] und]/&+ ( ! me?ods ( conv]sion ( insoluble sy/ems into soluble by fusion 7see ,mey]h(f]1 ,zeits*r4 physikal4 ,*em41 #aija1 #ch4 #cjg74 #chd ,see ,mey]h(f]1 ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #dei4 #che ,comp>e ! reciprocal salt-pair ,na,cl--,,nh#d;,,hco#c 7p4 #cba74 ,9 ?is case ! upp] limit ( ! transition int]val 0 f\nd by extrapolation ( ! solubility curve = ,na,h,c,o#c ,,nh#d;,cl ,,nh#d;,,hco#c & ,na,h,c,o#c ,,nh#d;,cl ,na,cl to be #cb;deg 7,f$otieff1 ,zeits*r4 phys4 ,*em41 #aijd1 #di4 #agi74 #chf ,loew5h]z1 ,zeits*r4 physikal4 ,*em41 #ahid1 #ac4 #dfd4 #chg ,mey]h(f] & ,saund]s1 ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #dgi4 #chh ,z ! quantities ( ! salts are express$ 9 equival5t gram-molecules1 ! molecule ( sodium & potassium *loride mu/ be d\bl$ 9 ord] to be equival5t to sodium sulphate & potassium sulphate4 #chi ,sitz-,b]4 d] kgl4 preuss4 ,akad4 d] ,wiss41 #aijc1 p4 #cei4 ,van't ,h(f1 ,zur ,bildung d] ozeanis*5 ,salzablag]ung51 ,i4 p4 #cd 7,brunswick1 #aije74 #cij ,zeits*r4 fu] ,kri/allographie1 #aijd1 #ci4 #aee4 #cia ,mey]h(f] & ,saund]s1 ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #dgi4 #cib ,zeits*r4 physikal4 ,*em41 #aijd1 #di4 #afb4 #cic ,ano!r comm]cial process1 9 ! /udy ( :i* good s]vice is done by ! ,phase ,rule1 is ! cau/ification ( ! alkali salts 7,g4 ,bodla5d]1 ,zeits*r4 fu] ,elektro*em41 #aije1 #aa4 #ahf2 ,j4 ,h]old1 ibid41 #dah74 #cid ,zeits*r4 physikal4 ,*em41 #aijj1 #ce4 #cb4 #cie ,m5tion may also be made "h ( ! equilibria betwe5 magnesium c>bonate & potassium c>bonate1 al?\gh ^! d n =m a reciprocal salt-pair 7,au]ba*1 ,zeits*r4 fu] ,elektro*em41 #aijd1 #aj4 #afa74 #cif ,o4 ,n4 ,witt & ,k4 ,ludwig1 ,b]41 #aijc1 #cf4 #dchd2 ,mey]h(f]1 ibid41 #aijd1 #cg4 #bfa1 #aaaf4 #cig ,zeits*r4 physikal4 ,*em41 #aije1 #ec4 #eac4 ,comp>e also1 ibid41 #aijc1 #ch4 #cjg4 #cih ,see ,s*w>z1 ,beitraege zur ,k5ntnis d] umkehrb>5 ,umw&lung5 polymorph] ,korp] 7,goett+51 #ahib72 or1 ,roozeboom1 ,het]og54 ,glei*gewi*t1 ,i4 p4 #abe4 ,also ,b>nes & ,cooke1 ,j\rn4 ,physical ,*em41 #aijb1 #f4 #agb4 #cii ,van't ,h(f & van ,dev5t]1 ,zeits*r4 physikal4 ,*em41 #ahhg1 #a4 #agc4 #djj ,rei*]1 ,zeits*r4 fu] ,kry/allographie1 #ahhd1 #h4 #eic4 #dja ,zeits*r4 physikal4 ,*em41 #ahie1 #ag4 #aec4 #djb ,zeits*r4 physikal4 ,*em41 #ahii1 #bh4 #dfd4 #djc ,mey]h(f] & ,saund]s1 ibid41 p4 #dff4 #djd ,see ,van ,eyk1 ,zeits*r4 physikal4 ,*em41 #ahii1 #cj4 #ddf4 #dje ,see 9 ?is connection ! volume 9 ?is s]ies on ,electro-*emi/ry1 by ,dr4 ,r4 ,a4 ,lehfeldt4 #djf ,b>nes & ,cooke1 ,j\rn4 ,physical ,*em41 #aijb1 #f4 #agb4 #djg ,= a description & explanation ( ^!1 ! read] %\ld consult ! volume 9 ?is s]ies by ,dr4 ,lehfeldt on ,electro-*emi/ry2 & van't ,h(f1 ,bildung und ,spaltung von ,doppelsalz51 p4 #dh ff4 99 99 99 99 99 ,*anges made to ! pr9t$ orig9al4 ,pages #cj-ca4 ,fig4 #c1 p4 #bg43 'p4 #be4 9 orig9al4 ,s also page #cc1 ,fig4 #b1 p4 #bg4 ,page #eg4 pp4 #bi & #ce3 'pp4 #be & #ch 9 orig9al4 ,page #fe4 p4 #eg43 'p4 #fj 9 orig9al 7twice74 ,page #aff4 !re is ! po9t ,c#a3 ,c' 9 orig9al4 ,page #bbe4 ,c is an eutectic po9t3 'eutetic' 9 orig9al4 ,page #bbh4 ,al?\gh ?is view put =w>d by ,heyn3 ',a?\gh' 9 orig9al4 ,page #bcb4 ! p]iod ( con/ant temp]ature = ! eutectic po9t c3 '! eutectic po9t e' 9 orig9al4 ,page #bdi4 two liquid lay]s betwe5 #ac;deg & #ca;deg3 'betw5' 9 orig9al4 ,page #beg4 ,tables entries #d & #g4 naph?ol3 'nap?ol' 9 orig9al4 ,page #bhg4 f :i* ! model is con/ruct$3 'he model' 9 orig9al4