GeneralIn order to obtain the standard molar free energy of formation of CoO, NiO, and Cu2O, cells of type
A, A(O) | electrolyte | B, B(O) (I)involving oxides A(O) and B(O) of metals A and B have been investigated. The electrolyte was a solid solution of ZrO2 and CaO involving oxygen ion vacancies according to Hund (9). Electrical conduction due to migration of oxygen ions via vacancies has been ascertained by tests described below. Analogous solid oxide solutions were tested but found to be less satisfactory.
where and , respectively, are the partial molar free energies of oxygen on the left-hand and the right-hand side of cell (I), Fo2° is the standard molar free energy of oxygen, and F is the Faraday constant.
Preparation of the ElectrolytesThe following solid solutions were prepared according to Hund (9, 12),
A: 0.85 ThO2 + 0.15 LaO1.5
B: 0.75 ThO2 + 0.25 LaO1.5
C: 0.85 ThO2 + 0.15 CaO
D: 0.85 ZrO2 + 0.15 CaO
E: 0.60 ZrO2 + 0.40 CaOTo prepare electrolytes A and B, a solution of Th(NO3)4 and La2O3 in dilute nitric acid was precipitated with ammonia. The coprecipitated hydroxides were converted into oxides as is described below for ZrO2-CaO. Electrolyte C was prepared by evaporating a solution of Th(NO2)4 and CaCO, in dilute nitric acid. Similarly, to prepare electrolytes D and E, zirconyl nitrate was dissolved in boiling concentrated nitric acid and calcium carbonate was dissolved in dilute nitric acid. A mixture of these solutions was evaporated in a porcelain dish to dryness on a water bath. The remaining solid material was dried overnight at 120°C, ground in an agate mortar, decomposed at about 500°C, and fired 12 hr at 1000°C and 12 hr at 1250°C in a Pt boat with grinding after each firing. The powder was pressed into tablets 0.5 cm in diameter and about 0.2 cm thick at a pressure of about 10 tons/cm2. The tablets were finally sintered overnight in a Pt boat under air at 1400°-1450°C.
Arrangement of the CellA cell of type (I) consists of a tablet of a mixture of metal A and its oxide, a tablet of the electrolyte, and a tablet of a mixture of metal B and its oxide between Pt disks connected with Pt leads. The cell assembly is shown in Fig. 1. Since one lead goes to the top and the other lead to the bottom of the furnace, the external resistance between the leads in parallel to the cell is determined by the resistivity of the structural components of the cell assembly which are at room temperature with a negligible leakage current. The small distance between the electrodes minimizes local temperature differences within the cell and therefrom eventually resulting thermoelectric forces. The temperature of the cell can be measured with the help of a thermocouple next to the top electrode of the cell.
Conductivity MeasurementsAt elevated temperatures, concentrations of excess electrons and electron holes in the solid oxide electrolytes are presumably determined by the oxygen partial pressure of the surrounding atmosphere by virtue of the reactions
02(g) + 4 excess electrons + 2 anion vacancies = 2 02- 
02(g) + 4 valence electrons + 2 anion vacancies = 2 02- + 4 electron holes 
c- = K1(po2)-1/4 
c+ = K2(po2)1/4 where c_ and c+, respectively, are the concentrations of excess electrons and electron holes, and K1 and K2 are constants.
The following atmospheres were used.
1. Oxygen of atmospheric pressure, po2 = 1 atm,
2. Air of atmospheric pressure, po2 = 0.21 atm,
3. Nitrogen of atmospheric pressure, po2 ~ 10-5 to 10-3 atm,
4. Argon saturated with water vapor at room temperature with an addition of electrolytic hydrogen corresponding to a H2O/H2 ratio of the order of unity, po2 ~ 10-17 atm,
5. Hydrogen of atmospheric pressure saturated with water vapor at 25°C, po2 ~ 10-20 atm,
6. Hydrogen of atmospheric pressure saturated with water vapor at 0°C, po2 ~ 4 x 10-22 atm.
Fe, wüstite | (ZrO2 + CaO) | Au (II)confirmed that electronic conduction yields only a minor contribution to the total conductivity. These measurements, however, were not carried sufficiently far in order to make possible a comprehensive quantitative evaluation.
Measurements on Cells Involving Iron OxidesTo verify the presupposition of predominant ionic conduction in ZrO2-CaO solid solutions, there was investigated the cell
Fe, FexO | (ZrO2 + CaO) | FeyO, Fe3O4 (III)where FexO and FeyO denote wüstite coexisting with metallic iron and with magnetite, respectively.
where the subscripts I and II, respectively, refer to the left-hand and the
right-hand electrode of cell (I). Numerical values of these ratios according to
Darken and Gurry (10) are listed in Table I. Emf values calculated from Eq. ,
which are listed in the last column of Table II, agree very satisfactorily with
observed emf values.
Standard Molar Free Energy of Formation of Cobalt OxideResults for the cell Fe, FexO | (0.85 ZrO2+0.15 CaO) | Co, CoO (IV) and the standard molar free energy of formation DF° of cobalt oxide are shown in Table III. Reliable values were obtained only above 900°C. The reproducibility of the emf values is ±0.002 v or better corresponding to an uncertainty in DF° of ±0.1 kcal.
CoO(s) + CO(g) = Co(s) + CO2(g) have been calculated. Fig. 2 shows these values together with values deduced from gas equilibrium measurements by Emmett and Shultz (15), Watanabe (16), and Schenck and Wesselkock (17) as a function of temperature. Both sets of data supplement each other and may be represented by a smooth curve.
CoO(s) + H2(g) = Co(s) + H20(g) has been calculated. Fig 3 shows that these data agree with values calculated from determinations of the H20/H2 ratio over cobalt and cobalt oxide according to Emmett and Shultz (18) and Kleppa (19) but differ from those reported by Shibata and Mori (20), possibly because of their neglect of thermal diffusion.
Standard Molar Free Energy of Formation of Nickel OxideResults of the cell Fe, FexO | 0.85 ZrO2 + 0.15 CaO) | Ni, NiO (V) are shown in Table IV. The reproducibility of the emf values is 0.002 v or better, corresponding to an uncertainty in DF° of ±0.1 kcal. Results were compared with results of gas equilibrium measurements in the same way as for cobalt, see Fig. 4 and 5. DF° values deduced from emf values for the reduction of NiO by means of CO lie between values calculated from CO2/CO ratios according to Schenck and Wesselkock (17), Watanabe (21), and Fricke and Weitbrecht (22). Since the CO2/CO ratios over nickel and nickel oxide are fairly large (63 to 454), errors are probably greater than for the analogous equilibria in the systems Fe-O and Co-O. DF° values for the reduction of NiO by means of H2 according to Pease and Cook (23) are in accord with DF° values calculated from emf values at higher temperatures as is shown in Fig. 5.
Standard Molar Free Energy of Formation of Cuprous OxideEmf values of the cells
Fe, FexO | electrolyte | Cu, Cu2O (VI)
FeyO, Fe3O4 | electrolyte | Cu, CuO (VII)with the electrolytes (0.85 ZrO2 + 0.15 CaO) and (0.6 ZrO2 + 0.4 CaO) are shown in Table V. Values for the standard molar free energy of formation of cuprous oxide are listed in Table VI. These values agree fairly well with results deduced from emf measurements made by Treadwell (24) with a correction for thermoelectric effects (25). Treadwell investigated the cell
Cu(s) | Cu2O(s), borate melt | porcelain | Ag(l), O2(g) (VIII)which involves the reaction 2Cu + 1/2 O2 = Cu2O on passing two faradays if oxygen ions alone carry the current in porcelain as an intermediate solid electrolyte.
Fe, FexO | electrolyte | Cu, CuO2 (VI)
FeyO, Fe3O4 | electrolyte | Cu, Cu20 (VI)
Standard Molar Free Energy of Formation of Silver SulfideReinhold (4) has already determined the emf of the cell
Ag(s) | AgI(s) | Ag2S(s), S(l), C (IX)involving the virtual cell reaction
2Ag(s) + S(l) = Ag2S(s) Additional measurements were made in order to obtain a higher accuracy. The setup of the cell is shown in Fig. 6. To assemble the cell, silver iodide was melted in the Pyrex tube, and the graphite electrode B, the glass tube A, and the thermocouple shield were immersed. Then the cell was transferred to another furnace whose temperature was below the melting point of AgI but above its transformation point at 146°C. After the AgI had solidified, sulfur was introduced into glass tube A, and the graphite electrode C was brought in contact with the AgI. To start a run, silver sulfide was formed electrolytically at graphite rod C by passing a current of 5 to 20 ma for about half an hour with graphite rod B as anode. In some runs, more silver sulfide was formed after the first emf measurements had been made. In other runs, graphite rod C was wrapped with silver wire which transformed to silver sulfide. The emf values were found to be independent of the procedure of preparation of silver sulfide and its amount.
DF° = -2EF The reproducibility of the emf values is ±0.001 v, corresponding to an uncertainty in DF° of ±0.05 kcal. The equilibrium of the reaction
Ag2S(s) + H2(g) = 2Ag(s) + H2S(g) has been investigated by various authors, most recently by Rosenqvist (27) between 490° and 900°C. DF° values for reaction  extrapolated to 200°-400°C from Rosenqvist's data agree within ±0.2 kcal with values calculated from standard molar free energies of formation of AgS according to Table VII and values for H2S recommended by Rossini, et al. (28) and Kelley (29).
Standard Molar Free Energy of Formation of Silver SelenideSimilarly, the emf of the cell
Ag(s) | AgI(s) | Ag2Se(s), Se(s, l), C (X)has been determined. Results are shown in Table VIII.
2 Ag(s) + Se(l) = Ag2Se(s)
DF° = -13.46 - 0.0074 X (T - 500) kcal;
DF° = -9.76 kcal; AS° = 7.4 e.u. at T > 500°K Upon using enthalpy and entropy increments of Ag, Se, and Ag2Se between 298° and 500°K as compiled by Kelley (29), the values of AH° and AS0 at 298°K are obtained. Therefrom DF° = DH °- TDS° at 298°K may be calculated. Thus,
2 Ag(s) + Se(s) = Ag2Se(s)
DF° = -11.94 kcal; DH° = -11.38 kcal;
DF° = S° = 5.24 e.u. at 298°K The value DH° = -11.38 kcal seems to be more consistent than the value of -2.9 kcal, which was obtained by Fabre (33) on combining the values for several reactions which were investigated calorimetrically.
S°Ag2se = DS° + 2S°Ag + S°Se
= 5.24 + 2 X 10.206 + 10.0 = 35.65 e.u. at 298°K with standard entropy values for Ag and Se recommended by Rossini, et al. (28).
Standard Molar Free Energy of Formation of Lead SulfideSolid lead chloride, pure or doped with KCl, is known to be an anionic conductor (34-36). Thus, the standard free energy of formation of lead sulfide should be obtainable from a cell analogous to cell (IX),
Pb(s) | PbCl2(s) | PbS(s), S(1), C (XI)The emf of cell (XI) was found to be not well reproducible, presumably for the following reason. In view of the shrinkage during the solidification of PbCl2 and lack of plasticity, no tight seal of lead chloride between the two electrodes was obtained and, therefore, sulfur vapor could diffuse to the lead electrode so that a mixed potential rather than an equilibrium potential prevailed.
Pb(s, l) | PbCl2(+KCl) | I PbS(s), Ag2S(s), Ag(s) (XII)with the virtual cell reaction
Pb(s,l) + Ag2S(s) = PbS(s) + 2 Ag(s) Preliminary investigations have shown that the solubility of Ag2S in PbS is less than 1 mole % below 400°C. Similarly, a low solubility of PbS in Ag2S is assumed. Ag2S and PbS are, therefore, considered to be present virtually in their standard states.
PbS(s) + H2(g) = Pb(l) + H2S(g) has been investigated by Jellinek and Zakowski (38), Jellinek and Deubel (39), and Sudo (40). DF° values for reaction  calculated from standard free energies of formation of PbS listed in Table IX and values for HS recommended by Rossini, et al. (28) and Kelley (29) are consistent with Sudo's measurements (40) but diverge from earlier measurements by Jellinek and his associates (38, 39).
The System Silver-TelluriumThe phase diagram of the system silver-tellurium has been investigated by Pelabon (41), Pellini and Quercigh (42), Chikashige and Saito (43), Koern (44), and Kracek and Ksanda (45). In addition to the compound Ag2Te, which has a congruent melting point at about 958oC, there is at least one other intermediate phase involving a smaller Ag/Te ratio with an incongruent melting point, for which the formulas
AgTe (42), Ag7Te4 = Ag1.75Te (43), Ag12Te7 = Ag1.71Te( 44), and Agl.50Te (45)have been suggested.
Ag(s) | AgI(s) | (Ag,Te) (XIII)
E = -(RT/F) ln aAg = -FMAg where FMAg is the partial molar free energy of mixing of silver for pure solid silver as reference state.
Dg = it / nTeF where i is the current applied during time t, nTe is the number of moles of tellurium, and F is the Faraday constant.
g = 2 - Dg At 300°C, the Ag/Te ratio ranges from 1.99 to 2.00 for the a phase, from 1.88 to 1.91 for the g phase, and from 1.63 to 1.66 for the e phase.
Ag | AgNO3(aq) | (Ag,Te) (XIV)has been determined at room temperature by Puschin (47). A plot of emf vs. the Ag/Te ratio does not indicate another compound in addition to Ag2Te. It is possible, however, that the scatter in Puschin's plot of E vs. composition obscures small steps corresponding to different compounds. Moreover, complete electrochemical equilibrium may not have been reached at room temperature as has been found, e.g., for the system Cu-Zn by Sauerwald (48).
1. F. Haber and S. Tolloczko, Z. anorg. Chem., 41, 407 (1904).
2. M. Katayama, Z. physik. Chem., 61, 566 (1908).
3. H. Reinhold, Z. anorg. u. allgem. Chem., 171, 181 (1928).
4. H. Reinhold, Z. Elektrochem., 40, 361 (1934).
5. W. D. Treadwell, H. Ammann, and Th. Zürrer, Helv. Chim. Acta, 19, 1255 (1936).
6. U. Croatto and C. Bruno, Ricerca Sci., 17, 1998 (1947).
7. B. A. Rose, G. J. Davis, and H. J. T. Ellingham, Disc. Faraday Soc., 4, 154 (1948).
8. A. Sator, Compt. rend., 234, 2283 (1952).
9. F. Hund, Z. physik. Chem., 199, 142 (1952).
10. L. S. Darken and R. W. Gurry, J. Am. Chem. Soc., 67, 1398 (1945).
11. J. P. Coughlin, U. S. Bur. Mines Bull. 542 (1954).
12. F. Hund and W. Dürrwächter, Z. anorg. u. allgem. Chem., 265, 67 (1951).
13. F. Meyer and G. Ronge, Angew. Chem., 52, 637 (1939).
14. C. Wagner, Z. Elektrochem., 60, 4 (1956); Proc. C.I.T.C.E., in press. J. B. Wagner and C. Wagner, J. Chem. Phys., June 1957.
15. P. H. Emmett and J. F. Shultz, J. Am. Chem. Soc., 52, 1782 (1930).
16. M. Watanabe, Sci. Repts. Tohoku Imp. Univ. I, 22, 892 (1933).
17. R. Schenck and H. Wesselkock, Z. anorg. u. allgem. Chem., 184, 39 (1929).
18. P. H. Emmett and J. F. Shultz, J. Am. Chem. Soc., 51, 3249 (1929).
19. 0. J. Kleppa, Svensk Kern. Tidskr., 55, 18 (1943).
20. Z. Shibata and I. Mori, Z. anorg. u. allgem. Chem., 212, 305 (1933).
21. M. Watanabe, Sci. Repts. Imp. Tohoku Univ. I, 22, 436 (1933).
22. R. Fricke and G. Weitbrecht, Z. Elektrochem., 48, 87 (1942).
23. R. N. Pease and R. S. Cook, J. Am. Chem. Soc., 48, 1199 (1926).
24. W. D. Treadwell, Z. Elektrochem., 22, 414 (1916).
25. J. Gundermann, K. Hauffe, and C. Wagner, Z. physik. Chem. B., 37, 148 (1937).
26. F. H. Smyth and H. S. Roberts, J. Am. Chem. Soc., 43, 1061 (1921).
27. T. Rosenqvist, Trans. Am. Inst. Mining Met. Engrs., 185, 451 (1949).
28. F. D. Rossini, D. D. Wagman, W. H. Evans, S. Le vine, and I. Jaffe, Nat. Bur. Standards Circ. 500, U. S. Government Printing Office, Washington (1952).
29. K. K. Kelley, Bureau of Mines Bull. 476, U. S. Government Printing Office, Washington (1949).
30. C. Tubandt, H. Reinhold, and A. Neumann, Z. Elektrochem., 39, 227 (1933).
31. M. Hansen, "Der Aufbau der Zweistofflegierungen," p. 59, Springer, Berlin (1936).
32. C. Wagner, J. Chem. Phys., 21, 1819 (1953).
33. C. Fabre, Ann. chim. phys., 14, 110 (1888).
34. C. Tubandt and S. Eggert, Z. anorg. u. allgem. Chem., 110, 196 (1920); C. Tubandt, ibid., 115, 105 (1921).
35. C. Tubandt and H. Reinhold, Z. Elektrochem., 29, 313 (1923).
36. J. B. Wagner and C. Wagner, This Journal, To be published.
37. E. Koch and C. Wagner, Z. physik. Chem. B, 38, 295 (1937).
38. K. Jellinek and K. Zakowski, Z. anorg. u. allgem. Chem., 142,1 (1925).
39. K. Jellinek and A. Deubel, Z. Elektrochem., 35, 451 (1929).
40. K. Sudo, Sci. Repts. Res. Inst. Tohoku Univ. A, 2, 325 (1950).
41. H. Pélabon, Compt. rend., 143, 295 (1906).
42. G. Pellini and E. Quercigh, Atti R. Accad. dei Lincei Roma, (5) 19, II, 415 (1910).
43. M. Chikashige and I. Saito, Mem. Coll. Sci. Kyoto Imp. Univ., 1, 361 (1916).
44. V. Koern, Naturwissenschaften, 27, 432 (1939).
45. F. C. Kracek and C. J. Ksanda, Tran. Am. Geophys. Union, 21, 363 (1940).
46. C. Wagner, "Thermodynamics of Alloys," p. 14, Addison-Wesley Press, Cambridge, Mass. (1952).
47. N. Puschin, Z. anorg. u. allgem. Chem., 56,1 (1908).
48. F. Sauerwald, ibid., 111, 243 (1920).
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