O X QUINTUPLE POIKTS BY IYILDER D. B A N C R O F T
'
.
In a systeiii composed of two salts atid water tliere will lie i n equilibrium a t t h e quiiituple points, three solid phases, solutioii and vapor. All iioii\.ariaiit sj.steiiis, save oiie, if kept at coiistaiit pressure, will change oii addition of heat froiii t h e e solid phases into two pairs of solid phases a n d solutioii or into oiie pair of solid phases arid solutioii. if'ith certaiii liniitatiow-to be defiiied later-the inrersioii point will be, in t h e first case, a niiiiiiiiuiii teniperature for oiie of tlie solid phases iii eqtiililiriitni with solution aiitl vapor ; i i i tlie second case, a iiiaxiniuni teiiiperatui-e for soiiie solid phase under t h e saiiie conditions.' I n all cases tliere is disappearance of one or iiiore solid phases aiicl formation of solution. This is iii accortlaiice with t h e tlieoreiii of L e Chatelier that ntltlitioti of lieat caiises a n increase in tlie systeiii which is foriiietl witli tlie alisorptioii of heat. Keeping this in mind it is possillle, i i i iiianj. cases, to tell Ivliicli solid phase caii exist in eqiiililiriuiii with solution and 1.apor only above or bvlow the quiiituple point and whether it is ahore or lielow. T h e various quintuple points can lie classified under t l i r e p heads. I . T n ~ oof tlie solid phases can be iiiatle from tlie third with adtiitioii or subtraction of water. 11. One of tlie solid phases caii be traiisforiiied into one of t h e otliers addition or sulltractioii of water. 111. KO one of t h e solid phases caii be converted into either of t h e otliers by addition or sulitractioii of water. For quiiituple points o f ,tlie first tj.pe tlie following rule holds in all t h e instances >.et studied. Klieii oiie of tlie solid phases caii change into t h e other two with the acltlitioii or sulitl-action of water, t h e inversion point is a niiiiiriiuiii teniperature for that phase i f the 1 q r
__ 'If these conditions are not insisted upoii tlie onlj. geiieral statertient pOSS!lile i i i respect t o a hydrated double salt IIRS alrently Iieen irinde by Roozelioa~n. Zeit. phgs. Chein. 2, 51; (rSg;). ~~
LVilrc'er D. GmzcroJi
33s
water be added to complete the reaction and a tiiaximam temperature if the water be subtracted. Tlie following instances will illustrate this rule. A t - 3' one of the double sulfates of niagnesiiuii and potassiuni changes into the single sulfates with addition of water.' T h i s is, therefore, a mininium temperature for K2Mg(S0,)6H,0. K,Mg(S0,),6H,O
+ H,O 72K,SO, + RlgS0,7H,O.
T h e same change takes place at 2 1 . 5 ' with the double sulfate of sodium and niagiiesii~tii.~T h i s is a miiiiinum temperature for Naa2Mg( SO,),qH,O. Na,RIIg(S0,),4H2O
+ 13H,O ~2Na,SO,IoH,O + MgS047H,0.
Copper potassium chloricl changes at 56' into copper potassium chlorid antl hydrated cupric chlorid.8 T h i s is a niinimuni temperature for CuC1,KCl. 2CuCI,KCl+ 4H,O 72CuCl,zKCIzH,O
+ CuC1,2H,O
A t 92' copper dipotassium chlorid changes into copper potassium chlorid.3 T h i s is a niaxiniiini temperature for CuCl,zKClzH,O. CLIC~,~KC~ZH , zH,O O
y2 C U C I , K C ~ +KCl
A n analogous change occiirs a t 146' with copper tliamnionium chlorid.4 T h i s is a niaxinium temperature for CuC1,zNH4C12H0. CuC1,2NH,C1zH20 - zH,O
+
CLICI,NH,C~ NH,C1.
A t 15.5' one of the double salts of copper and tetrethSlatiimonium chloricls changes into another double salt antl hJdratec1 cupric chlorid.' T h i s is a niinitiium temperature for (CuCI,),.N(C,H,),Cl. ( CuC1,),2N(C,Hj),C1
+ SH,O 72CuC1,2N(C,H5),C1 + 4CuC1,2H20.
Tlie double salt of copper and calcium acetates changes at 76' into the single acetates." T h i s is a niaxiiiiiiiii temperature for CuCaAc,8H,O. CuCaAc,SH,O - 6H,O ~2 CuAc,H,O
+ CaAc,H,O.
'van der Heide. Zeit. phy% Clieni. 1 2 , 416 ( r S 9 3 ) . 't Hoff and van Deventer. Ibid. I , 165 (1887). ?Meyerhoffer. Ibid. 3, 336 (rSS9). 4Meyerhoffer. Ihid. 5 , 9s IrS9o). sbleyerhoffer. Sitzungsher. Akad. \Vis. Wien, 102, I I h 150 (1893). 6Reicher. Zeit. phys. Cheiii. I , 221 ( 1SS.i). %til
-
t
OlI i)l f
()/(I
PO (;il fS
,339
T h e double sodiuiii aiiiiiioiiiuiii raceiiiate clecoiiiposes at 27' into t h e dextrorotary aiid laevorotary sodium aiiiiiioiiiiitii tartrates.' This is a miniiiiuni temperature for (Nn?",C,H,O,H,O),. (NaNH,C,H,O,H,O),
-1 6H,O 72z(NaKH4C,H,O,4H,O).
Tliis saiiie salt cliaiiges at 35" into tlie single rnceiiiates.' tiiaxiiiiiiiii teiiiiierature for (NaNH,C,H,O,H,Oj,. 2 ( NaNH,C,H,0,jH,0)2-
4H,0.2
Tliis is a
+
( N a , C , H , 0 , i ) 2 ([NH,],C,H,O,;),.
T h e same cliaiiges take place with tlie doulile potassiuin sodium racemate a t tlie teiiiperatures of - G o aiid 41' respectivelj." tlie first heing a iiiiiiiiiiuiii atid tlie second a riiaxiiiiiiiii temperature for ( KNaC,H40,3H,O),.
+ aH,O yz zjK N n C , H 4 O , ~ H 2 0 ) 8H,O iKa,C,H,O,i)p+ (K,C,H,O,,?H,O,),
[ KN;aC,H,0,3H2O),
KNaC+H,0,3H20),For qiiiiituple points of t h e secoiitl t!.pe t h e follmviiig rule iiiajr be stated : If one solid phase can lie coii\.erted into oiie of the otliers ljj. addition of water t h e iiiversioii poiiit is a iiiaxiiiiiiiii or a iiiiiii i i i u i i i tetiiperature for oiie of those plinses and is neither a iiinxiiiiiiiii iior a iiiiniiiiuiii for t h e third solid phase. Tliis caii lie illustrated very readily by three iiistaiices froiii tlie s!.steni, potassiuni sulfate, magnesium sulfate atid water. At 47.2' two of tlie pliases are hlgSO,7H,O and MgS0,6H,O, t h e thirtl is K,\Ig(SO, ),GH,O. T h i s is a iiiiiiiiiiuiii reiiiperature for tlie l i e s a h ~ ~ d r a t e .Tlie Iildratecl douhle salt exists lioth above aticl lielow the teiiiperatiire of t h e i i i version point. A t 72' two of t h e solid phases are t h e h!~tlratetl doulile salts K,Rlg(SO,),/,H,O arid &hIg( SO,),4H,O while tlie third is magiiesiuiii sulfate heptahyclrate. X t 9 2 O t1vo of tlie solid phases are t h e sanie t\vo h > d r a t e d tlou1)le snlts n i i d t h e third is potassiuiii sulfate. T h e first temperature is a iiiiiiiiiiiiiii for t h e tlo~ible salt witli four iitiits of water aiitl t h e secotitl a iiiaxiiiiuiii for the oiie with six of water. If t h e teiiiperatures are not g-ir.eii it caii oiil?. lie told 1)). experiiiieiit wliicli poiiit is \vliicli. If tlie coiiipositioiis of tlie 2(
'van 't Hoff and van Deveiiter. Zeit. pliys. Clieiii. I , 165 ( ISST) Van ' t Hoff, Goldschniidt a n d Jorisseii. Ibirl. 17, 49 ( rSc)j). %an 't Hoff and Goltlscliniidt. I h i d 17, 505 ( rS95 1 .
solutioiis are kiio\vii, t h e tlirectioii of tlie teiiiperature change can be foretold froiii tlie tlieoreiii of vaii Xlkeiiiatle' that tlie teiiiperatiire rises aloiig t h e liouiidai-j. cur1.e iii the tlirectioii of t h e line coliiiectiii: t h e iiielting points o f tiie two solid phases, T h e higher teiiiperature will iiecessnril!. lie a iiiaxiiiiiiiii for tlie dotilile salt with a larger aiiioriiit of Ivnter of cr!.stnllizatioii. I t iiia!' not be cleai- \vli!. tlierc is nii uncertainty for qiiiiituple points of tlie second t!.p? ari:l iiot foi- those of t h e first type. For these latter the equation s1ion.s tlint tlie tloulile salt can iiot exist aliove tlie in\-ersion teiiipei-attire i i i eqiiililiriiiiii with solution and l'apor nor tlie t\vo siiigle salt.; lielow i t . Tliis necessitates tliat t h e two iiioiio\xriaiit s!.steiiis witli cloulile salt anti oiie compoiieiit, doulile salt niitl the other coiiiponeiit a s solid plinses, iiiust exist a t teiuperatiires below tlint of tlie qiiiiitiil'le poiiit arid thus there is coniplete iiiformntioii. so f:ir 3% teiii1)erature is conceriiecl. ip regard to tlie three solliliilitj, curves. IYitli qiiiiitiiple points of t h e second t!.pe t h e equatioii slimvs tile teiiipei-attire cliaiige for two of t h e curves h i t gi\.es 110 iiifci~ilatioiii i i i.egart1 to tlie third, along wliicli tlie solid pliases are tlie two coiiipotiiids eiitei-iiig iiito tlie equatioii. M'lieii no oiie of the tliree solid pliases can lie coiiveited into . prediction eitlier of t h e others, it is iiiiposs5ilJle to ilialie ~ 1 1 ~tlcfiiiite if t h e oiily (lata are t h e foriiiulas of tiie tliree solid pliases. A s an iristaiice, let lis take t h e t\vo qiiiiituple poiiits \rliere the solid phases are ice, liycli-atetl calciuiii acetate niitl copper calciuiii acetate ; ice, hydrated copper acetate ant1 cop1xr calcium acetate. Tlie two sets consist of ice. a Ii!~tlratctl salt ant1 a li!-drn:etl .tloulile snlt. T h e r e is iio \va!. of tlistiiiguisliiiig tlieni Ivitliout fiirtliei- iiiforiiiation. Here agaiii tlie tileorein of \.nil Alkeiiintle \vi11 Iielp 11s i f ' tlie conceiitratioiis o f t l i e tIvu soliitioii.; : i i ~k i i o \ v i i : i i i d i f tlie t l o i i l k salt is tlecoiiiposed I)!. \rater. Tliis lias 1)teii espressed i i i tlie following forin b y Sclireiiieiiinkers :' ( ( Tlie cr>mli!.tli.ic teiiiperature of a solutioli in eqiiililiritiiii n.itli tloii1)le salt aiitl the coiiipcmeiit which does not precipitate is lower t l i n i i t h e cr!.oli).dric teiiiperature of t h e solution i i i equ i liliri ti i i i \vi t h tloubl e salt a ntl t h e c-oiiiponeiit IV h icli. does precipitate ) ) . -~ ~
'Zeit. pIi~.s.Clieiii. 1 1 , 2S9 ( ~ ' $ 3 ) . 211iirl. 1 2 , Sgr ( 1Sy3I.
I f the double salt is stnllle in tile pwseiice (.if Ivater, there is no n firiori iiiethotl of telliiig ~vliicliCi.!'O!i!'dl-iC teiiilwrnture is the liiglier. It should lie clearl!. UlldeI-St~JUdtlint i i i nil tliesc c~isesn i i i n s i i i i i i i i i 01-n i i i i i i i i i i i i i i i teiiiperatiire ibr n gi\.eii siilistniice refus to t1i:it solid pliase i i i eqiiililiriiiiii Ivitli soltitioil aiid \ . n p o i ' . Fc ir iiistaiice. 56" is a iiiiiiiiiiiiiii teiiilwixtiire hI-colilwr p u t x s i i i i i i clilorid iii eciiiililiritiiii with solutioii arid vnpor : liut it is po55iliIe for copper tlipotassiiiiii clilorid, copper putnssiiiiii chloritl, pc:tn>>iuiii cliloritl niirl \.npur to lie i i i stalile equililiriuiii a t rooiii tei:ii)er:ltiire. IVlieii aii aiih>di.oiis antl a li!.tll-stetl clouhle salt c o i i i l h e to foriii a Ii!~tirntrtl cioul~lesnlt \.i,itli ntltlitioii or siil;tr:ictioii of Tvnter, tliere seeiiis, at first, 110 I-enmi \\.li>. tlieie :.l:ould iiot lie n quiiituple point at \vliicli tliese tiiree solid 1)liases c ~ J l l l t 1lie i i i eqiiililii-iiiiii Ivith r , tliis is iiot possililr. To take a coiicl-ete cnse solutio11 niid ~ ~ i i o!.et let its assiiiiie tliat lead aiitl potashiuiii ioclicls foi.iii iio niiliydrous doulile salt n i i t l oiil!. ~ i i eIi!~tlrated t!i~iiI~lc h a l t . I ~ l ~ I ~ I < I ~ IfI ~t h2e0 . iioiivxrixiit s!.steiii, li>,JrateJ lead iodid, pot.issiiiiii iotlitl, lead potnse 1inI.e siuiii iodid. solutioii niid ~.apoi..cnii exist i t rvill he ~ i o s s i l ~ lto tliesc tliree salts i i i eqiiililjl-i i i i i i \vitli ~ ~ i p uuTrw n series of' tciiipei-aturt2s X moiiieiit's coiisiclerntioii w i l l show t!i:&t tliere is 110 'ivn!. i i i Ivliicli this s!.hteiii c;iii t.lfloi.t?ce I v i t l i o i i t ,: ,riii:iig n lie\\. solid pliase aiitl t l i m n i i o : i \ x r i n i i t s: ,\teiii i , ~ ro r csisliiig c n w n i i iiitlefiiiite raiig-e of teiiiperature. Siiicc tlii:? i:i . i i 1 1 1 i i tic. it li11lon.stlint n q i i i i i tuple poiiit witli tliese tliI-ee salt:, :is holii: pl!:ixs c n i i iicit e s i s t and tlint aiiother solid phase iiiust nppear 1iefL.i.t. , I i i h lmiiit is I-eaclled. Yiider t h e coiitlitioiis nssiiiiiecl to exist, t h r lien. phase \vould lie lead iotlicl. either anli!.tlrous or l v i t l i uiie of'jvnter. X s a iiintter of fact, i t is prolialile that lead and pctassiuiii iodids i'oriii a secoiid Ii!.tII-nted tloii1)le snlt n i i d it is tliis p1i:isc: \vliicli appears.' The Ii!.drattd tloiil)le cliloritl of copper n i i t l lwtas,4uiii cnii lje made froiii potassiuiii cliloritl aiid li!drntetl ciipric elllorid \\.itliout ntltlitioii or su1,tractioil of v.ater. Here it is kiiuwii tlint t h e aiili),tlrous double salt, CiiCl,KCl, appenrs a s solid phase n t i t l tliat copper rlipotassiuiii cliloritl, potassiuiii cliloricl niitl Ii>.tlratt.tl cupric cliloiid caii not coexist i i i equililJriiiiii \vitli soltitioil antl \xpor. Tliere is a sugges1
1
tion of this relation in a paper by Pchreiiiemakers' in which h e iiiiplies that there caii tiot be t\vo 1ij.tiratetl double salts at tlie quintuple point with t h e same :iiiioniit of water of crj.stallization ; but h e offers no pi-oof for this, limits it to lijdrated clouble salts and does not take into account tlic tliirtl solid phase. In his paper on lead antl potassiuiii iotlids lie s r e s 110 theoretical impossibility in there being a temperature at \vliicli t h e hydrated double salt might cliatige into its conipoiieiits.2 T h e s e applicntioiis 'of tlic tlieoiwii of Le Chatelier ma). soiiietimes lie useful in throwiiig liglit 011 t h e possible coiistitution of a solid phase. Sclireineniakers tliiiiks tliat at I goo hydratecl lead iodic1 PI)I,zH,O, antl lead potnssiuiii iodide, Pb12K12H,0, are in equililii-imi \vitli solutioii, irapor ntitl a second hydrated double salt. When potassiuin iodic1 is sulistitutetl for hydrated lead ioclicl, t h e Assumresulting iion\.ariant system is supposed to exist at I 70'. ing that these two teiiiperatures are approximatelj. correct antl that t h e unknowii phase is the saiiie it1 both cases with the formula, PbI,.r-KIj~H,O,it is clear tliat 1709 is t h e lowest temperature a t wliicli tlie new clouble salt caii exist iii equililiriuiii with solution a n d vapor atid that 190' is tlie highest temperature possible for tlie orditiarj. t1oul)le salt under the same conditiotis. T h e two equations expressing these facts are :
PIiI,.cKIjnH,O i( 2 -JJ.)H~O72Pl)I,KIzH,O
+ (x.
-
/ ) K I a t 170'
s ( P b I , K I 2 H 2 O ) - ( 2 -jj)H,O ,-1 ( X - r)PbI,aH,O
f PIiI,xKIyH,O
at 190'.
In order that there sliall lie ti0 negative quantities aiitl that there shall be three solid phases a t I 70' we see that y must be less tliaii two aiid niay lie zero wliile .v caii not lie less tliaii unity nor equal to infiiiitj.. Since . I ' caiiiiot q u a l zero it follows that the new phase t e d iodid and is il double is neither anlij.drous tior ~ i i o n o l i ~ ~ d r a lead salt. If .x = I the two equations beconie indeterminate. Since t h e Iijdratecl douhle salt. PIiI,KIzH,O, is a1waj.s decomposed by mater n7itl1 precipitation of liytlrated lead iodid, t h e tlieol-eni of \.an Alke'Zeit. p1iJ.s. Clieni. 1 1 , gqr (rSg3). cIl)id. I O , 476 ( rS9a J.
343 macle requires that the quintuple point with hydrated lead iodid a s solid phase should occur at a higher teniperature t h a n the quintuple point with potassiuiii iodic1 as solid phase. Since 190' is higher than 170' tlie change may be oiie of delij~drationonlj.. W e can therefore draw tlie following coiiclnsioiis : T h e iiew solid phase must be a double salt ; it must contain less than two units of crystal water a n d may be anhydrous ; tlie ratio of potassiuni to lead can not be less than unity iior equal to infinity. I t niust he remembered that tliese conclusions rest upon the assumption that the same solid phase appears at tlie two quintuple points. T h e results of this paper may be assumed a s follows : I. Wlien one of the solid phases caii change into the other two n7ith a.tldition or subtraction of water, the inversion point is a minimum temperature for that pliase 'if tlie water lie added to complete the reactioii and a iiiaxiiiiuiii if the water be subtracted. If oiie of tlie solid phases caii be converted into one of tlie 2. others by addition of water, tlie in1,ersion point is a niaxiniuiii or a iiiiniiiiuni temperature for oiie of those phases and is neither a maxi i i i u n i iior a iiiiiiiiiium for the third solid phase. 3. \\'hen 110 one of t h e solid phases can be converted into either of tlie others by acltlitioii or sulitrnction uE water no prediction can lie made. 4. There can not be in equili1)riuni tliree solid phases such t h a t one can be made froiii tlie other t\vo without atlclion or subtraction of water 5 . If t h e same solid phase appears at 170' aiid 190' i n t h e system, lead iodid, potassium iodid and n a t e r , it must be a double salt and the ratio of potassium to lead iiiay exceed unity. CorjicII U ? i k r s i ~S6'pfcjji ~, Bcu rS96.
