July, 1954
‘FHERMODYNAMIC
75 I
DATAFOR THE ZINC-INDIUM
557
SY8TEM
04
.-E! 4 .- 30 w&a a 15
I
I
I
01 0
I
20 40 60 80 100 Mole per cent. silver resin. Fig. 1.-Silver-hydrogen exchange in ethanol-water media. 0
effect is observed for this system in aqueous media when the ionic strength of the external solution is increased,6 thereby reducing the swollen volume of the resin. The selectivity coefficient is also increased a t all resin compositions4for resins of higher DVB content, in which the swelling is inhibited to a greater extent. Since little is known concerning (5) 0. D. Bonner, W. J. Argersinger and A. W. Davidson, J . A m . Chem. Soc., 74, 1044 (1952).
I
I
I
I
I
20 40 60 80 100 Mole per cent. silver resin. Fig. 2.-Silver-hydrogen exchange in dioxane-water media.
the behavior of silver ion in mixed solvents, it is difficult to predict the effect of the change in solvent composition in the resin phase with resin composition on the above activity coefficient ratio. The activity coefficient ratios of the ions in the external solution are likewise known only for aqueous media, and so the effect of this term on the selectivity coefficient cannot be quantitatively predicted. Theoretical considerations, other than those given above, therefore are not feasible.
THERMODYNAMIC DATA FOR THE ZINC-INDIUM SYSTEM OBTAINED FROM THE PHASE DIAGRAM BY W. J. SV~RBELY Department of Chemistry, University of Maryland, College Park, Maryland Received March 1. 1864
Integral heats of mixing and the relative partial molal heat contenta of zinc and indium in zinc-indium alloys a t 700°K. have been determined from solubility data for the system by means of semi-empirical equations proposed by Ifleppa. The relative partial molal heat contents of zinc have been used ‘in turn to calculate the activities and partial molal entropies of zinc in zinc-indium alloys a t 700’K. All calculated data have been compared with data in the literature. The results support Kleppa’s equations as well as can be expected.
Introduction Due t o experimental difficulties, it is frequently impossible t o apply either vapor pressure or electromotive force procedures to the determination of the thermodynamic properties of bimetallic systems. Consequently, attempts have been made to determine such properties through use of other available data, such as solubility data. Recently, Kleppa’ has criticized some of the earlier attempts and he has presented a method which permits the separation of the calculated partial molal free energies along the liquidus into approximate heat and entropy terms. The method is restricted to a simple eutectic phase diagram with a steep liquidus displaced toward one extreme in composition. The comparison of calculated heat data with experimental data made by Kleppa’ does not lead to (1) 0. J. Kleppa, J . Am. Chem. Soc., T4, 8047 (1952)
a satisfactory conclusion concerning the validity of Kleppa’s method because of the lack of sufficient experimental data for the systems considered. The phase diagram for the zinc-indium ~ y s t e m ~ * ~ indicates that this system is subject to the above restrictions. Furthermore, the thermodynamic properties of the zinc-indium system have been determined r e ~ e n t l y . ~There exist, therefore, in this case sufficient thermodynamic data for the checking of Kleppa’s method. Results Thermal Calculations.-The data of Valentiner2 and of Rhines and Grobe3 were used in the cal(2) 6. Valeotiner, 2. Melallkunde, 36, 250 (1943). (3) F. N. Rbines and A. H. Grobe, A m . Inst. Minine M e t . Ethers., I n s t . Metals Diu., 166, Tech. Pub. 1682 (1944). (4) W. J. Svirbely and 8. M. Selis, J . An. Cheni. Soc., 76, 1533 (1953).
W. J. SVIRBELY
558
Vol. 58
culations. Figure 1 shows a plot of log Nzncs, in In(1) vs. 1/T. From the slope and intercept of thg limiting straight line, one obtains values for AH, the heat of solution for zinc, and log Nzn at 1/T = 0, respectively. Through use of equations 1 and 2 = El = A f l - AHr (1)
tively, for the designated component. All quantities calculated by use of mole fraction expressions (equations 3,4,5) and by use of volume fraction expressions (equations 6, 7, 8) are shown in Fig. 2 along with the experimental values for the same quantities. I n the calculation of volume fractions, V1 and V2 were taken to be 9.2 and 15.7 cc. for zinc and indium, respecti~ely,~ over the complete tem2.3R log Nilr-o - ASr = A s i X o (2) perature range. It should be emphasized that in values of Elo, the relative partial molal heat con- this method of comparison one assumes that A H , tent of zinc a t high dilution, and ASlXo, the excess El and E2 are independent of the temperature not partial molal entropy of zinc a t high dilution, were only over the temperature range covered by the accalculated to be 2675 cal./mole and 1.94 e.u., re- tual phase diagram but actually to 700°K., the spectively. The heat of fusion of zinc was taken5 temperature at which the experimental values were to be 1765 cal./mole a t 692.7"K. obtained. 0.8
3200
--EXPERIMENTAL B---.-- MOLE FRACTION EQUATION5
~=-----uoLuME
P
I
11
0.4 2800 0
s!
2400
2 -0.4 -0.8
a6 \ a 2000
- 1.2
.-El
-8
1600 e
+ 0.8 1.2 1.6 2.0 l / T X 108. Fig. 1.-Solubility of Zn(s) in In(1). 0.4
2.4
!D 1200
Values of A H , the integral heating of mixing, E,, the relative partial molal heat content of zinc, and the relative partial molal heat content of indium, can be calculated by equations 3 , 4 and 5
800
z2,
N~N~T~~Q
(3)
f;, =
NZZE10
(4)
=
N12GO
(5)
AH =
400
0
0.2 0.4 0.6 0.8 if one assumes the validity of the Baud-Heitler617 NZ. equation for the heat of formation of one mole of solution. On the other hand, if oneassumes thevalid- Fig. 2.-Heat valuea for zinc and indium in Zn-In liquid alloys at 700" K. ity of the van Laars equation for the integral heat of mixing, then AH, El and 2 2 can be calculated' Activities.-In the calculation of the activities by equations 6, 7 and 8 of components in a homogeneous bimetallic mixture from solubility data, one must remember that inAH = N~5 e 1 2 ~ , o N t e 2 ~ 0 (6) formation obtained from the solubility diagram VI concerning equilibrium in the solid-liquid mixture Ll = ep2O (7) is restricted to the temperature and composition along the liquidus. I n such a case, N 1 is that mole I;Z = e12zlo (8) fraction of zinc a t each temperature in which I n these equations, N , e and p represent mole fracalo(s/l) = a*(l/l) (9) tion, volume fraction and molar volume, respecwhere alo(s/l)is the activity of pure solid zinc and (5) K. K. Kelley, Bureau of Mines, Bulletin 476, p. 203. al(l/l) is the activity of the zinc in the liquid alloy, ( 8 ) E. Baud, BUZZ. doc. chim., [4] 17, 324 (1915).
+
(7) W. Heitler,Ann.Phg/sik., [4] 80, 630 (1936).
(8) J. J. van Laar, "Thermodynamik der einheitlichen Stoffe und
biniier Gemitrche," Groningen, 1935.
(9) J. H.Hildebrand and R. L. Baott, "The Solubility of Noneleotrolytes," 3rd ed., Reinhold Publ. Corp., New York, N. Y.,1950, p. 323.
THERMODYNAMIC DATAFOR~THEZINC-INDIUMSYSTEM
July, 1954
both being referred to pure liquid zinc as the standard state. For the reaction Zn(s) -t Zn(l), one can express the variation of the activity of liquid zinc with temperature by the usual equation, namely R In UP(~/S)=
-++ c1
AH
(10)
Similarly, one uses for the variation of the activity of zinc with temperature in each liquid alloy the equation L R In al(l/l) = 2 (11) T +C Since alo(s/l) = l/alo(l/s), then on applying the equality expressed by equation 9 to equations 10 and 11 one obtains --Hi - LI = c1+ c (12)
tion 16, namely A& = G / T
559
- R In a,(l/l)
(16)
Using values of Zl and al obtained by both mole fraction and volume fraction relations, values of AS1 for zinc in the molten alloys were calculated at 700°K. and the results are shown in Fig. 4 along with the literature value^.^
T
- F,O = RT In a?(l/s), then AFo - AHi = (13)
Furthermore, since FIO by equation 10
c1
T
Combination of equations 12 and 13 yields
Thus one can obtain C for each alloy of a k e d composition on the liquidus if both the AFO value for the melting of pure zinc and the value for zinc in the alloy are available. Values of AFO at temperatures aIong the liquidus corresponding to the compositions for which values had been obtained by Kleppa's method were calculated through use of equation6 15 AFo = 852 - 4.951T log T f 0.0012T2 4-12.015T (15) The activity of zinc in an alloy of a fixed composition was next determined at 700°K. though use of and C over equation 11 assuming constancy for the temperature range. The results of the calculations for zinc using values of obtained by equations 4 and 7 are shown graphically in Fig. 3 along with the experimental values in the l i t e r a t ~ r e . ~
z1
a
1.0 0.8
*
2
0.2
0.4
0.6
0.8
Nzn.
Fig. 4.-Partial
molal entropy of zinc in Zn-In liquid alloys a t 700°K.
Discussion.-Reference to Fig. 2 shows that neither the mole fraction nor the volume fraction are completely satisexpressions for A H , El and factory for the accurate evaluation of those quantities over the entire concentration range of the zincindium system. However, the agreement is as good as can be expected considering the assumptions which were made in the derivation' of the equations. Moreover, consideration of the curves for all three quantities indicates that the mole fraction expressions lead to better agreement with experiment for the AH and E , calculations than do the volume fraction expressions. However, the opposite appears to be true concerning the results. Reference to Fig. 3 shows that the calculated activities of zinc in the liquid alloys obtained by are in good using the mole fraction values of agreement with the experimental activities. However, the calculated results obtained by using the volume fraction values of El are lower in the more dilute zinc alloys. Reference to Fig. 4 shows that the partial molal entropies of zinc in alloys are reproduced as well as can be expected by use of El values obtained by either method. In conclusion, it can be stated that while the results reported in this paper for the zinc-indium system support the semi-empirical relations proposed by Kleppa for certain restricted systems, nevertheless, one cannot choose definitely between the mole fraction or the volume fraction relations used.
z,
z2
0.6
z1
.eY 4 0.4 0.2
0 0.2
0.4
0.6
0.8
1.0
NZ. Fig. 3.-Activity of zinc in Zn-In liquid alloys a t 700°K.: 0 , experimental values; 0 , calculated values using mole fraction relations; O', calculated values using volume fraction relations.
Entropies.-In liquid alloy, the partial molal entropy of a component may be expressed by equa-
