658
W. J. SVIRBELY AND SHIRLEY 11.R~3.41)
another argument in favor of an E2 process for the debromination of tetrabromoethane.
Vol. 66
Acknowledgment.--We wish to thank the Research Corporation for its financial support.
THE THERMODYKAMIC PROPERTIES OF LIQUID TERSARY ZINC, INDIUM, AKD GALLIUNI SOLUTIONS BY Jv. J. SVIRBELY AKD
SHIRLEY
M. REBD1
Department of Chemistry, University of Maruland, College Park, M d . Received J u l y .9& 1961
The ternary system zinc-indium-gallium and the binary systems zinc-indium and zinc-gallium have been investigated by electrode-potential methods over the temperature range of 420 to 520'. The properties, AFx, A H x , ASx! APix, L, and activities were calculated from the experimental data for the systems at 470'. The corresponding properties of the gallium-indium binary system were obtained by calculation by means of Darken's procedure utilizing the experimental data.
Introduction At the time this research was started, thermodynamic studies of liquid alloys involving more than two components were limited. The studies on the cadmium-lead-bismuth, cadmium-lead-tin, and the cadmium-lead-antimony systems had been reported by Elliott and Chipman2 and the cadmium-bismuth-tin system by Mellgren. 8 Both papers made use of Darken's equations4 developed for a single phase ternary system in which the composition of the third component is varied in a constant ratio mixture of the other two components. In our Laboratory, attempts had been made to study the gallium-indium binary system directly by use of the electrode-potential method. We were not successful. However, values of this binary may be calculated4 from experimental measurements on a ternary system involving gallium, indium, and some other more electropositive metal, for example, zinc. Consequently, the present research was undertaken in order to determine: (1) the thermodynamic properties of the zinc-indium-gallium system; (2) the thermodynamic properties of the gallium-indium binary system. Materials.-The sources of indium,6 zinc, and galliumG already have been described. However, gallium of 99.99% purity, obtained from the Aluminum Co. of America, also was used in some of the runs. Spectrographic analyses indicated the complete absence of foreign elements in all three metals. Apparatus.-The apparatus was essentially the same as before.6 Cells of the type Zn(1)I ZnClz in KC1-LiCl(1) I Zn(a1loy) were used. Details concerning the preparation of the cells already have been described.6
Experimental A series of measurements of the e.m.f. of cells of the abovt type were made over a temperature range of 420 t o 520 using zinc-gallium, zinc-indium, and zinc-indium-gallium alloys. I n the latter series, the measurements were performed on alloys having constant atomic ratios of Naa/"iu (1) Abstraoted in part from a thesis submitted by Shirley M. Read to the Graduate Sohool of the University of Maryland in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (2) J. F. Elliott and J. Chipman, J . Am. Chem. SOC.,7S, 2682 (1951). (3) S. Mellgren, zbzd., 74, 5037 (1952). (4) L. S. Darken, zbzd., 71,2909 (1950). ( 5 ) W.J. Svirbely and S. M. Sella, zbzd , 75, 1532 (1953). (6) W. J. Svirbely and S. M. Sells. J . P h w . Chem., 58, 33 (1954).
equal to 3/17, 1/3, 1/1, and 3/1. The mole fraction of zinc was varied from 0.100 to 0.900 in each of the binary and ternary systems. The experimental e.m.f. for each alloy was plotted against the temperature. Linear plots were obtained. The temperature gradient and the e.m.f. for each alloy at the arbitrarily selected temperature of 470' were determined from the plots. These data are given in Table I.
TABLE I
CELLCOXPOSITION ANI POTENTIALS AT 470' Ne"
E.m.f. (mv.)
dE/dT mv./degree
Zinc-gallium series 61.45 0.11532 0.100 41.25 ,08188 .200 ,06400 ,300 30.26 24.97 .05425 .370 22.76 ,04888 .400 17.45 .03838 .500 12.91 ,02722 .600 9.26 ,01916 .700 6.08 .01195 ,800 2.89 ,00505 .900 Zinc-indium series 38.92 0.11600 0.100 21.91 ,08333 .ZOO 11.90 ,05525 .350 7.54 .03573 ,500 6.74 .0308 ,548 6.06 .02669 .600 4.92 .01961 ,700 4.18 .01331 ,749 3.70 ,01013 ,800 2.26 ,00386 ,900
E.m.f.
Nzn
mv./dedE/dT,
(mv.)
gree
Zinc--induim-gallium series N G & / N I=~ 113 0.100 47.75 0.11333 .200 29.63 ,08275 ,300 20.37 .06133 ,400 15.05 ,04762 .03538 ,500 11.04 8.29 ,02434 ,600 ,01750 ,700 6.42 .SO0 4.45 ,00974 .00403 ,900 2.44 NGa/l\'l
0.100 .200 .300 .400
,500 .600 .io0 .SO0 .goo
n
=
54.11 35.23 25.18 18.84 13.99 10.45 7.48 5.06 2.74
NGs/hTln
0.100 ,200 ,300 ,400 .500 ,600 ,700 .SO0 ,900
58.43 39.47 28.63 21.32 15.99 12.12 9.08 5.96 2.98
1/1 0.11300 ,08000 .06300 .04938 .03644 ,02663 .01815 .01030 ,00425
3/1 0.11375 ,08289 ,06257 .04863 ,03675 ,02738 ,01976 .01254 .00504
Zinc-indium-gallium series .VGJ.VI~ = 3/17 43.28 0.11422 0.100 ,0838 ,200 26.88 18.93 .06371 .300 13.19 .04788 .400 10.0 ,0361 ,500 7.49 ,02556 ,600 5.90 ,01825 ,700 4.09 .01044 .800 2.50 ,00454 ,900 When an alloy of a particular composition was chosen for analysis, part of the original sample was saved. After completion of a run, appropriate amounts of the used alloy
April, 1962,
‘~“GRMODYSAMIC
h m m ” I E S OF T E R N A R Y ZINC-INDIvlLr-GnLLIuM
and the original sample were dissolved and analyzed by a comparative fluorescent X-ray spectrographic procedure.’ Within the limits of accuracy of the method no significant changes in composition of the alloys were observed. Eight different alloys were analyzed between the mole fraction limits from 0.100 to 0.900 for each of the three metals. Thus the experimental method w-as found to cause no loss of material. Check runs were made on twelve alloys. The number of runs made is designated by 2 and 4 on Fig. 2 and 3 . Agreement between the E470 values is within 0.75% for all but one case (2.3%). The zinc-gallium system har been studied previously.* At Ne,, = 0.370, I‘ = 761.4”K., the agrcement betwcen 1.: and dE/dT values in the two studios is within 2% deviation from the mean. At iVzn = 0.700, the agreement is less satisfactory, 3.6% for E and 15.8% for dE/dT. Our check run on this particular alloy is within 0.37% for E and identical for dE/d?’with its duplicate. The zinc-indium system also has been studied prev i o u ~ l y . While ~ ~ ~ compositions are not exaetly alike, a comparison with the data of this research indicates average deviations of 5.5% for &‘K and 3.4% for d E l d T with those of Bohl and Hildebrandt and Z.l%.for ~%00”K and 5.1% for dE/dT with those of Svirbcly arid Sells. In all of our calculations involving the data of thc above two binary systems, we have chosen to use the results of this research.
Calculations.-In all equations, the subscripts associated with a property refer to definite eleInents: 1 refers to gallium, 2 refers to zinc, and 3 refers to indium. The various coiistants in the equations have the following values: n = 2, R = 1.986 cal./mole-degree, T = 743.2’K. and 5 = 23061.6 eal./volt-degree.10 The cell reaction is
0
0.2
SOLUTIONS
659
0.6 0.8 Nz.. Fig. 1.-Activities of zinc at 470’ in zinc-indium, zincgallium and in zinc-indium-gallium systems. Note: Symbolism on Fig. 2, 3, 4, and 5 is the same as above. 5 c
0.4
b
Zn(1) -+ Zn(in liquid alloy solution)
The partial molal free energy, the activity, the activity coefficient, the partial molal entropy, and the relative partial molal heat content of zinc in-the alloys (the standard state in all eases is the pure metal) are obtained directly from the data by use of the equations
-
AFz = &(l) P z 0 ( l ) = -n5E -n W log a2 = -2.3026 RT
0.4 0.6 0.8 XZ ”. of solution fuuctions of zinc in the binary and ternary solutions. 0.2
Fig. 2.-Heat
(4)
The activities of zinc in tho binary and ternary syskms are shown in k’ig. 1. Excess thermodynamic quantities are dcfined as thc difference between the actual values and the values for an ideal solution of the same concentration. The excess partial molal properties of einc were calculated by means of the equations AE?,. = 2.3026RT log
zz2 = zz = A& -~
012
(6)
- Values of the quantities AFzz/(l - N J 2 and Lzz/(l - N z ) were ~ calculated a t each mole fraction for use in the graphical integrations of Darken’s procedure. Graphs of such data us. N P are shown in Fig. 2 and 3 for the two biliary systems and the four ternary systems investigated. Graphical integrations of thc resulting plots were made and thc results were used in the calculation of the values of the integral cxccss thermodynamic properties of the ternary systems in accordance4 with eq. 9, namcly
(7)
(7) We acknowledge our indebtedness to Dr. W. J. Campbell and Mr. J. D. Brown, U. 6 . Bureau of Mines, College Park, RId., for the analyses. (8) V. Gents, M. Fiorani, and V. Valanti, Gum. chim. itul., 86, 103
(1965).
The binary constants, [Ci.],~*=1 and were evaluated by the equations
(9) R. W. Bohl and V. D. Hildebrandt, J . Am. Chem. Soc., 79, 2711 (1957). (10) D. N. Craig, J. I. Hoffman, C. A. Law, and W. J. IIamer,’J. Research Nall. Bur. fiiandarda, M A , 381 (1900).
and
[(?3z],vz-1
W. J. SVIRBELY AND SIIII~LEY M. KEAD
660
7l
Vol. GG
800 A I
I
I
6
GOO
-2 400 E
\
v
0.4 0.6 0.8 Nz~. Fig. 5.-Integral heata of mixing per mole of solution 470' for binary and ternary solutions. 0.2
0
600 -
0.6
2e 3 v
Oa4
0.2
0
0.2
Fig. 3.-Excess I
0.4
0.6
0
0.8
Nzn. free energy functions of zinc in the binary and ternary solutions.
-0.2 0
0.2
0.4
0.6
0.8
Nos. Fig. &-Integral thermodynamic functions of mixing per mole of solution at 470' for gallium-indium solutions.
500
The values obtained from the graphical integrations were multiplied by (1 - X z ) , X I , or Na as appropriate in each case in accordance with eq. 9. The sum of the resulting three quantities is G", or more specifically, the excess integral molal free energy of solution AF", and the integral molal heat of solution A H = AH". Excess integral molal entropies of solution, ASz, were calculated by eq. 12 100
0
0.2
0.4 0.6 0.8 Nz,. Fig. 4.-Int~gral cxcess free energies of mixirig per rriole of solution at 470" for binary and ternary solutions.
in which the values of the integrals are the total areas under the appropriate binary curves of Pig. 2 and 3. The values of the binary constants arc = 1177 cal./mole;
[ z , z ] ~=t -2308 ~ cal./mole
[ A R z ] ~ w l = 312Ucal./moh;
[G]= N3286 ~~ cal./mole
[A@]N+I
For the ternary curves of Fig, 2 and 3, graphical integrations were performed in 0.1 mole fraction intervals from N s = 1 to N z = 0.
The values of the excess integral free energies and enthalpies of solution for the ternary systems are plotted us. Nz in Fig. 4 and 5 . The excess partial molal properties of gallium and indium in their respective binary systems with zinc were calculated from the experimental data by means of eq. 13.
where & is an excess partial molal property of zinc and i refers to either gallium or indium. The integral in eq. 13 was evaluated graphically in each case at intervals corresponding to 0.1 mole fraction unit of zinc from 0 to 0.900. The excess integral molal free energy and excess heat of solution for both binary systems were calculated by means of eq. 14 using these calculated excess partial molal
April, 1982
THERMODYNAMIC PROPERTIES OF TERRARY ZINC-IXDIUM-GALLI~M SOLIJTIONS 661 Zn
In
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Ga No.. Fig. 7.-Excess integral free energy of mixing per mole of solution surface in 100-cal. steps at 470".
In
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Ga NO.. Fig. 9.-Excess integral entropy of mixing per mole of Eolution surface in 0.1-e.u. steps at 470'.
Zn
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Ga No.. Fig. S.--Integral heat of mixing per mole of solution surface in 100-cal. steps a t 470". In
solution, and excess entropy of solution for the gallium-indium binary system are plotted us. N G ~ on Fig. 6. Values of A P and AHx in 100-cal. steps were Gz Nisi' N&az (14) In the calculation of the excess thermodynamic picked from their respective curves and values of properties of the gallium-indium binary system ASz in 0.1-e.u. steps were picked from similar from the ternary data, use is made of eq. 9. The plots. All such data are plotted in Fig. 7, 8, and 9. gallium-indium (binary 1-3 system) may be con- These ternary molal surface plots reprcscnt the excess integral thermodynamic properties of mixsidered as the limiting case of the ternary 1-2-3 system in which AT2 = 0. Thus eq. 9 becomes eq. ing per mole of solution for the zinc-indium-gallium ternary system a t 470'. The values of the 15. exress properties may be obtained at any composition by interpolation of the data shown on these triangular plots. In the calculation of the excrss partial properties The hinary constants remain the same as before, of gallium and indium in the gallium-indium binary but AT1and N s are the mole fraction values for the system, usc was made of the plots shown on Fig. 6 binary 1-3 system. The first term on the right for the excess molal solution properties. Tangents is now the total area under the curve for a dcfinite were dr:iwn to the curves at 0.1 mole fraction iniVl/NZ ratio ternary system of plots of the type tcrvds. The extension of these tangents to give ~ 1 and N I = ~ 1 axes yields shown in Fig. 2 and 3. The values of the excess intercepts on the N G = integral molal free energy of solution, heat of the values of the excess partial molal proprrties
values. The final results also are shown on Fig. 4 and 5 .
+
662
W. J. SVIRBELY AND SHIRLEY M. READ
of gallium and indium, respectively, in the binary solution of the selected concentration a t the poigt of tangency. The application of eq. 6 to the AFi" values yielded the corresponding a1 values which in turn yielded the activities of gallium and indium in the gallium-indium binary system. These final results are shown graphically in Fig. 10. Discussion The Method.-The functions plotted as ordinates in Fig. 2 and 3 are very sensitive to experimental error, particularly as N Z n --t 1. Reference to Table I shows that at Nzn = 0.9, the e.m.f. of all systems 'was between 2 and 3 mv. Since we believed that data obtained in the Nz, region of 0.9 to 1.0 mould lead to unreliable calculations for these functions and consequently influence the drawing of the whole curve, experimental data were not gathered in that region. Consequently, the extrapolation of these curves to Nzn = 1.0 must be based on the available data. Since the required area under the curves are from Nz, = 1.0, it follows that such areas must be subject to some uncertainty. Chipman and Elliott2 were able to check the reliability of the extrapolation method by ultimately calculating values of AF" and AH" for the lead-bismuth binary from measurements made on the cadmium-lead-bismuth ternary and comparing the predicted results with experimentally determined values. Their results for two different binary compositions indicated deviations between 5 and 7% for AF" and AH", respectively. The agreement was considered excellent. Assuming that our derived results are no worse than those of Chipman and Elliott, the values of AFa and AH. shown on Fig. 6 would be in error by 5 and 7%. Tn the determination of the intercepts of the tangents to the curves, a very large difference in any intercept could result from just a small change in the shape of the curve. Thus no more than a semi-quantitative claim is made for the derived values of the activities of gallium and indium which are shown graphically in Fig. 10. Activities.-Reference to Fig. 1 shows that the zinc-indium system, the zinc-gallium system, and all of the ternary systems exhibit positive deviations from Raoult's law for zinc over the entire concentration range with the largest deviation being exhibited by the zinc-indium binary system. Raoult's law is approached in each case as the solution composition approaches pure zinc. Furthermore, the zinc activity in the ternary system shows more positive deviation as N I , becomes greater in proportion to N G in ~ the pseudobinary systems.
Vol. 66
Isothermal Surfaces.-The excess molal free energy surface (Fig. 7) and the molal heat of solution surface (Fig. S) show positive values at all compositions. The excess molal entropy of solution surface (Fig. 9) shows mostly positive values. Other Comments.-Reference to Fig. 5 shows that in the two different binary systems
