BY 1YILDF.K D, B . l S C R O F T
Practically the only esteticled study of conjugate solutions is that made by TVright. alone and i n collaboratioii with other^.^ 'I'his work consisted in ;I determination of isotherms for systems composed of tn-o partially miscible metals and a third metal coiisoliite with each of the others. I t is easy to pick flaws in the eqieriniental work. Tl'right? himself, has pointed out its sliortcomings with great clearness arid his statement is recapitulated here solel!- to show that the conclusions to be deduced in this paper from t h a t work cannot be accepted as fiaal nritil the measurements ha\-e been repexted iiiider more fayorable circumstances. T h e metals used were not always pure, the aluminuin coiitaiiiiiig over four percent of iron and silicon.2 These inipurities were allon-ed for i n the ;analyses so that the tabulated data gil-e tlie gram percentages of each of tlie three metals forming the ternar!- mixture ; but we are not able in any n-a!- to foretell the effect of the impiirities upon the distribution ratios. T h e temperattires were iiot constant diiriiig tlie experiments, fluctuations of one hundred degrees iiot being excluded. From some esperiments that were made i t appears that tlie error due to tlie actiial temperatiire difference betn-eeii two ineasurenients XI-as probably not sc) serious as those cliie tCJ changes of temperature in a single experiment, the conr.ection currents thus generated pre\-enting the reaching of equilibrium. T h e most serious source of error, however, occurrecl iii the method adopted for separating tlie two phases. T h e two liqiiid layers were iiot drawn off at the temperature of the experiment and then anal)-zed. Instead of this,
' \T.right and
~hCJlllpSoll. Proc. Roy. s o c . 4 5 , 461 \ Iss9) ; 48, 2 j I s g O l : (1S91:I ; T\7rigl~t, Tlionipsoii atit1 Leon. Ibid. 49, 174 ( r S 9 r ; IVriglit, Ibid. 50, j ; ~ 1S91'1 ; 5 2 , I I (1S92, : 5 2 , j;o I rS93'1 ; 55, i j o I 1S94).
49, r j 6
\Vri,glit.
Ihid.
5 2 , 12
(1892 .
the whole mass \\-as cooled as rapidly as possible. the upper and lower portions of the ingot being then analyzed. IYlieii one recalls the difficulties to be o\-erconie in making a homogeneous casting with 0111~.two metals, one can easily see that this niethod of anal)-sis can he justified only on tlie ground taken by JYriglitthat h e could find no better metliod. -1s a matter of fact, attempts to draw off the molten sollitions pro\.ed unsatisfactory.1 T h a t the method of rapid cooling cannot gi\-e accurate results is sho\vn by two facts. JYe l;no\v from the phase rule that all inistiires correspoiiditig to points on a gi\.en tie-line must separate into the same t\vo liquid p1i:ises provided tlie system is allowed to reach eqiiilibrium. This was apparently not tlie case in the esperiiiieiits of K r i g l i t and Tlioiiipsoii.' T h e secoiid point is that Ivitli inistiires that did not separate into tIvo licliiid phases a n d which should therefore have been homogeneous, differences iii coiiipositioii between the upper and tlie lovier portions of tlie ingot w r e found, aniountiiig in one case to over tu-0 percent.' In 1-iew of the niiiiieroiis soiirces of error it is not surprising to find tliat increaking the aiiioiint of the consolute metal does not aln-a~.sproduce a:i increase in the soluhilitj. of the partially miscilile iiletals. Instead of this there are annoj.ing fluctuations \vliicli, though eL-idently dne to esperiniental error, are still sufficient to make tlie application of the mass law foriiiolas to the isotherm ail estreniel!. unsatisfactory proceeding. On the other Iiand these variations prodiice relatively less effect 011 the distribution ratio. For this reason I shall limit myself, in this paper, to a disciission of the equilibrium between the solntion plia:es. I t 113s been slio~viiithat, for tn-o lion-miscible liquids, -1a i d 13, and a third, C, consolute with the other two, the clistributioii of the third liquid between the other two can normally be represented b!. tlie foriiiiila
\\-riglit anti Thoiiip~oti. Proc. Roy. Sac. 45, 4;o jlS89:. . Ihid. 49, 192 i 1891) .
IVright and 'rlioinpsoii. Ihitl. 45, 463 ( 1SS9 ' . Jour. I%ys. Chetii. I , 471 (1S97).
' S. F.Taj-lor.
In this equation CIand C z refer to the aiiicunts of the consolute liciiiid in the two pliases while is the amount c:f tlie co~iipoiieiit -1in tlie pliase in n-liicli i t is tlie solvent niicl B2 is the amount of the component I: in the pliase in n-hicli it is sol\-erit. these amounts being e s p r e s e d in an!. iiiii ts n-liatsoei.er. T h e espoiieiitial factor I I is not necessarily a n integer. So far, 110 Iiypotliesis has yei been advanced eiiablirg 11s to predict tlie value of this exponential factor iii any one case. If tl:e logarithm of CI A I be measured along one axis and tlie logaritliiii of C?R? along tlie other, the resiiltiiig curve is a straight line provided the abo1.e equation describes the facts. T h i s grapliical method is the easiest and quickest metliod of determining. n-hetlier or not a given set of data conforins to the mass laivy and the direct iiieasiireiiient of the pitch of the curl-e is 1)). far the simplest method of getting a t the l.aliie of the espoiieiitial factor. T h e data of 'I'i'riglit and Tliompson are reproduced gi-apliicall!. in Fig.. I . T h e coordinates are the logarithnis of the concentrations, these latter lieiiig expressed in grains of tlie coiisolute metal per gram of tlie solvent tnetnl. In order to prei,ent overlapping, tlie origin is in a different place for each cii-1-e: but the scale is the zaiiie for all, each division being eqiial to o. 2 . Tlie curl-es are so labelled that the iiiidclle metal is the con.iolute one. T h e concentrations of the consolute metal in the first metal are measured along- the ordinates aiirl the concentratiotis iii the last metal of tlie three along tlie abscissas. Ciirl-es are gix-en for lead, silver a n d zinc1 : bisinuth, tin and zincp ; zinc, cadmium and bismutli3 ; cadniiuiii, tin and aliiiiiiiiiiiii4 ; aluiiiinuin, tiii and bismutlij ; altiiiiiiiiiiii, silver and leacP : alu:niiiuin, silver and hisiiiutli' : aluminuin, tin and leadS ; zinc, sill-er :ind I Proc. Roy So,, 50. j:)r : 1891) " I b i d . 50, 388 ( ~ S y r ) . Ihitl. 5 2 , j36 ( 1892 '. I Ihitl. 55, 132 (1894). ' Ihitl. 5 2 , 19 (1892). (' Iliicl. 5 2 , 2 2 ( ~ S y :I. z Ibitl. 5 2 , 24 ( 1892). Ihid. 5 2 , 16(1Sg2).
.
It must be reinembered in considering this diagram
Fig.
I
that a very slight error causes a large displaceiiient a t the lower ends of the curves. For instance a n error of less than one-half of one percent would make tlie aluminum, sill-er and lead curve a straight line. It is evident at once that all these systems are normal though there are soiiie curious variations to wliicli attention must be called. Tl-itli lead, silver and tin and with aluniin u m , till and bismuth, the curves sweep out and back jiist before the crest-point’ is reached. I t is probable that from such clisturbances conclusions might be drawii as to the relative positions of the bonndary curves : but I have not yet succeeded i n getting any satisfactor!. results in this way. T h e sudden apparent change of direction a t the upper end of the aluminum, tin and lead curve is quite unintelligible. T h e same data are tabulated it1 Tables I-SII. T h e figures are given for ail!- two of the metals in each phase, for the solvent metal and the consolute metal. Since the \-alues given are grains per hundred grams of the alloy the anioiuits of tlie third metal can readily be deteriiiiiied bj- subtraction. T h e subscripts one and two refer to the denser aiid the less dense phase respectisyly. In the sixth coluniu are the values of the coilstant as calculated from the formula at the head of each table. S o cor-
’ Proc. Roy. Soc. 50, 393 (1891). Snell.
Jour. Phys. Cllietn. 2, 470 ( rS98j.
rections have been made for the partial miscibility of the two hypotlietically non-miscible metals el-eii though bisinutli is soluble up to fifteen percent or thereabouts in zinc. S o formulas are given in the last three tables because it was ei.ident that the data were so abnorinal t h a t it was useless to tr!. to zpply the theory. The bracketed figures are the data for the crest-points. T h e y were not observed directlj. : but were obtained by estrapolation. TABLEI
Temperature about 6jo' Sll,
Bi,
Stl,
Sll, Sn,
Ztl?
0.00
8j.72
0.00
3.23
80.2 j
1.9s 3.97
I
6.35
.63 1.60 I .63
7.95
1.70 1.71
46.01
11.19 12.72
42.43
12.98
77.32
30.33 25.94
17.25 19.16
70.83 67.80
18.5
21.j
ho.o
,>.s2
r -
6.35 10.38 13.j 3
7 0 .j
19.09 20.80
jI.35
20.44 21.S9 22.37 r21.5
I.2j
1.54
2
66.33
1.64
]
57.97 5 5 .7 3
10.22
. j I .62 4s.gs 43. I I 40.S6 30.86
12.62
25.00
15.69
1.71
2.39
4. I8
5.jj
1.57 1.27 1.17 I .oo
4.19
31.1 26.6
34.8 36.0 44.0
26.3
5.9
4.2 5.1 3.8
19.j 1 29.53 29.90
16.49 13.92
3.8 3.3
11.23
2.1
11.53
2.0
1.0
I
z8.5
9.9
19.2;
1
2s
12.7
20.'7
