Physical Chemistry

F. A. KUZNETSOV, V. I. BELYI, T. N. REZUKHINA
and Corresponding Member of the Academy of Sciences of the USSR Ya. I. GERASIMOV

THERMODYNAMIC PROPERTIES OF CERIUM OXIDES

The thermodynamic properties of compounds of the rare-earth elements have as yet been studied very little. This also applies to cerium.

The aim of our work was to obtain thermodynamic data which, together with those already available in the literature, would make it possible to give a sufficiently complete thermodynamic characterization of the cerium—oxygen system. The literature contains the following information on the thermodynamic properties of cerium oxides and metallic cerium. Parkinson, Simon, and Spedding (¹) measured the low-temperature heat capacity of metallic cerium and obtained the value of its standard entropy \((S^0_{298} = 16.64\ \text{e.u.})\). Spedding, McKeown, and Daane measured the heat capacity of metallic cerium at high temperatures (²). Westrum and Beall * measured the heat capacity of CeO₂ at low temperatures and gave \(S^0_{298} = 14.89\ \text{e.u.}\). Huber and Holley (³), by combustion of metallic cerium in a calorimetric bomb for the reaction \(\mathrm{Ce} + \mathrm{O}_2 \to \mathrm{CeO}_2\), found \(\Delta H^0_{298} = -260.18\ \text{kcal}\).

Earlier, we measured by the mixing method in a massive calorimeter the high-temperature heat capacity of CeO₂ (⁴) and Ce₂O₃ (⁵), and with the aid of a calorimetric bomb for the reaction \(\mathrm{Ce}_2\mathrm{O}_3 + {}^{1}/_{2}\mathrm{O}_2 \to 2\mathrm{CeO}_2\) obtained \(\Delta H^0_{298} = -85.43\ \text{kcal}\) (⁶).

In the present work the thermodynamic properties of cerium oxides were studied in the composition interval CeO₂—CeO₁.₅. For this purpose we used the method of e.m.f. with a solid electrolyte, recently proposed by Kiukkola and Wagner (⁷), and also measured the equilibrium constants of cerium oxides with hydrogen. In (⁸) a new, more convenient apparatus implementation of the Kiukkola–Wagner method is described, which we used in the present work in measuring the e.m.f. of a cell of the form:

\[ \begin{array}{c|c|c} \mathrm{CeO}_x & \text{Solid} & \mathrm{Fe} + \text{wüstite} \\ (2 > x > 1.5) & \text{electrolyte} & \end{array} \tag{1} \]

Mixed crystals in the ThO₂—La₂O₃ system, possessing purely ionic conductivity, were used as the electrolyte. The electrolyte was checked for the absence of electronic conductivity, and the Fe + wüstite electrodes were prepared in the same way as in (⁷).

The CeOₓ electrodes were pressed at a pressure of 10 t/cm² from a mixture of corresponding amounts of CeO₂ and Ce₂O₃. Preliminary annealing of the pellets was not required, since the 5–7 hr needed to heat the cell to the required temperature proved sufficient for the formation of the oxide CeOₓ from the mixture. The oxygen content in the specimen was determined after the e.m.f. measurement by the “active oxygen” method (⁹).

In view of the extreme pyrophoricity of CeOₓ, all manipulations with it during removal of the pellet from the apparatus and transfer of it to the flask for analysis of the oxygen content were carried out in an argon atmosphere.

* E. F. Westrum, A. F. Beall, private communication—will be published in J. Chem. Phys., 1961.

The values of the equilibrium emf of cell (1) correspond to the change in the isobaric potential \((\Delta \bar G_I^0 = -2FE)\)* of the current-producing reaction:

\[ \frac{1}{\delta}\mathrm{CeO}_x+\mathrm{Fe}_{0.947}\mathrm O \to \frac{1}{\delta}\mathrm{CeO}_{x+\delta}+0.947\,\mathrm{Fe}. \tag{I} \]

Combining \(\Delta \bar G_I^0\) with \(\Delta \bar G_{II}^0\) for the reaction of formation of wüstite from the elements

\[ 0.947\,\mathrm{Fe}+\frac{1}{2}\mathrm O_2 \to \mathrm{Fe}_{0.947}\mathrm O, \tag{II} \]

for which, according to the data of Darken and Gurry \((^{10})\) and Peters and Möbius \((^{11})\),

\[ \Delta G_{II}=-63570+16.06\,T \quad (1073-1270^\circ \mathrm K), \]

makes it possible to calculate the differential \((\Delta \bar G_{III}^0)\) of the reaction

\[ \frac{1}{\delta}\mathrm{CeO}_x+\frac{1}{2}\mathrm O_2 \to \frac{1}{\delta}\mathrm{CeO}_{x+\delta}. \tag{III} \]

Table 1

Table 1 gives the results of measurement of the emf of cell (1) at various temperatures. For each of the studied compositions \(\mathrm{CeO}_x\), over the entire temperature interval in which the measurements were made, \(E\) varies linearly with temperature according to the equation \(E=a+bT\).

Table 2

Table 2 gives the coefficients \(a_1, b_1\) of this equation for \(\mathrm{CeO}_x\) preparations with \(x\) from 1,581 to 1,96. The same table gives the coefficients

* A bar over the top denotes differential thermodynamic quantities referred to the oxide of the given composition \(\mathrm{CeO}_x\).

$a_1$ and $b_1$ of the equation $\Delta \overline{G}^{0}_{\mathrm{III}} = a_1 + b_1T$ for reaction (III), and the coefficients $A$ and $B$ of the equation $\lg P_{\mathrm{O}_2(\mathrm{atm})} = \dfrac{A}{T} + B$, which relates the dissociation pressure of cerium oxide of a given composition $\mathrm{CeO}_x$ to temperature.

Measurement of the equilibrium constants $K_p = \dfrac{p_{\mathrm{H}_2\mathrm{O}}}{p_{\mathrm{H}_2}}$ for the reduction reaction of cerium oxides $\mathrm{CeO}_x$ by hydrogen

\[ \frac{1}{\delta}\mathrm{CeO}_{x+\delta} + \mathrm{H}_2 \to \frac{1}{\delta}\mathrm{CeO}_x + \mathrm{H}_2\mathrm{O} \tag{IV} \]

was carried out by the circulation method in an apparatus described in (12).

Because of the pyrophoric nature of the intermediate cerium oxides, either $\mathrm{CeO}_2$ or $\mathrm{Ce}_2\mathrm{O}_3$ was taken for measurement of the equilibrium constants; the composition of the equilibrium oxide was then determined by subsequent oxidation to $\mathrm{CeO}_2$. All operations were carried out in a chamber with purified nitrogen.

Combining the found values

\[ \Delta \overline{G}^{0}_{\mathrm{IV}} = -RT \ln K_p \]

with $\Delta G^{0}_{\mathrm{V}}$ of the reaction of formation of water vapor

\[ \mathrm{H}_2 + \frac{1}{2}\mathrm{O}_2 \to \mathrm{H}_2\mathrm{O} \]

\[ (\Delta G^{0}_{\mathrm{V}} = -59000 + 13.38\,T \text{ according to } (13)) \tag{V} \]

also makes it possible to calculate $\Delta \overline{G}^{0}_{\mathrm{III}}$. The results of measurements of the equilibrium constants of reaction (IV) and the values of $\Delta G^{0}_{\mathrm{III}}$ and $\lg P_{\mathrm{O}_2}$ calculated from them are given in Table 3.

Table 3

Fig. 1. Curves of the dependence of the dissociation pressure of cerium oxides on composition. Recorded by different methods: $a$ — e.m.f., $b$ — equilibrium, $c$ — Bauer’s data.

By the time our work was completed, Brauer (14) had published data on the dissociation pressure of cerium oxides obtained by the dynamic method. A comparison of Brauer’s data with ours is shown in Fig. 1. As follows from Fig. 1, the form of the isotherms characterizing the dependence of the dissociation pressure of the oxides on composition over the entire temperature range studied is the same for us as for Brauer. Consequently, our data confirm the phase relationships established by Brauer in this system. The discrepancy between the values of $\lg P_{\mathrm{O}_2}$ from our data and from Brauer’s data does not exceed 1.5–2%. Taking into account the difference in methods, such agreement of the data should be considered good.

The thermodynamic quantities characterizing the reaction

\[ \mathrm{Ce}_2\mathrm{O}_3 + \frac{1}{2}\mathrm{O}_2 \to 2\mathrm{CeO}_2, \tag{VI} \]

were found by graphical integration of the isotherms $\Delta \overline{G}^{0}_{\mathrm{III}}$—composition $\mathrm{CeO}_x$ at $1.5 \leq x \leq 2$ for temperatures of 973, 1073, 1173, and 1273°K. The values of $\Delta G^{0}_{\mathrm{VI}}$ found are given in Table 4. On the basis of these data and the value $(\Delta H_{298})_{\mathrm{VI}} = -85.43$ kcal (6), taking into account the dependence of the heat capacity of $\mathrm{CeO}_2$

and Ce₂O₃ on temperature (⁴,⁵), an equation was obtained for \(\Delta G^0_{\mathrm{VI}}\) in the temperature interval 298–1273° K.

\[ \Delta G^0_{\mathrm{VI}}=-85500-4.007\lg T+1.495\cdot10^{-3}T^2-\frac{0.47\cdot10^5}{T}+35.8T . \]

Table 4

Table 4 gives the values of \(\Delta G^0_{\mathrm{VI}}\) and \(\Delta S^0_{\mathrm{VI}}\), calculated on the basis of this equation.

Having obtained \((\Delta S^0_{298})_{\mathrm{VI}}\) and taking, according to (¹), for cerium \(S^0_{298}=16.64\) e.u. and for CeO₂ \(S^0_{298}=14.89\) e.u. (²), we find \((S^0_{298})_{\mathrm{Ce_2O_3}}=30.8\) e.u.

Having this value and the other data given earlier in the article, it is not difficult to calculate all the thermodynamic quantities characterizing the reaction

\[ 2\mathrm{Ce}+\frac{3}{2}\mathrm{O}_2\to \mathrm{Ce}_2\mathrm{O}_3. \tag{VII} \]

Table 5

Table 5 compiles the thermodynamic properties of CeO₂ and Ce₂O₃ obtained in the present work and previously known from the literature.

Moscow State University
named after M. V. Lomonosov

Received
5 V 1961

CITED LITERATURE

¹ D. H. Parkinson, F. E. Simon, F. H. Spedding, Proc. Roy. Soc., 207, 137 (1951).
² F. H. Spedding, J. McKlown, A. H. Daane, cited in the collection Properties and Applications of Rare-Earth Elements, Foreign Literature Publishing House, 1960.
³ E. Huber, Ch. Holley, J. Am. Chem. Soc., 75, 5645 (1953).
⁴ F. A. Kuznetsov; T. N. Rezukhina, ZhFKh, 34, 2467 (1960).
⁵ F. A. Kuznetsov, T. N. Rezukhina, ZhFKh, 35, No. 5 (1961).
⁶ F. A. Kuznetsov, T. N. Rezukhina, A. N. Golubenko, ZhFKh, 34, No. 9 (1960).
⁷ K. Kiukkola, C. Wagner, J. Elektrochem. Soc., 104, 379 (1957).
⁸ T. N. Rezukhina, V. I. Lavrent’ev, F. A. Kuznetsov, V. A. Levitskii, ZhFKh, 35, No. 6 (1961).
⁹ G. L. Banthauen, D. W. Pearce, Ind. and Eng. Chem., 18, 479 (1946).
¹⁰ L. S. Darken, R. W. Garry, J. Am. Chem. Soc., 61, 1398 (1945).
¹¹ H. Peters, H. H. Möbius, Zs. phys. Chem., 209, 298 (1958).
¹² T. N. Rezukhina, Ya. I. Gerasimov, V. I. Morozova, ZhFKh, 25, 93 (1951).
¹³ F. D. Richardson, J. H. Jeffes, J. Iron and Steel Inst., 160, 261 (1948).
¹⁴ G. Brauer, K. A. Gingerich, U. Holtschmidt, J. Inorg. and Nucl. Chem., 16, 77 (1960).