CHEMISTRY

Corresponding Member of the Academy of Sciences of the USSR Ya. I. Gerasimov, I. A. Vasil’eva, T. P. Chusova, V. A. Geiderikh, and M. A. Timofeeva

STUDY OF THE THERMODYNAMICS OF LOWER TUNGSTEN OXIDES BY THE E.M.F. METHOD AT HIGH TEMPERATURES

The equilibrium of the reduction of tungsten oxides by hydrogen, studied earlier \((^{1,2})\), made it possible to calculate the thermodynamic functions of formation of tungsten trioxide from the elements.

The insufficient accuracy of measurement of high equilibrium constants and the dependence of the accuracy of the calculated data on the values for water vapor make it desirable to determine the thermodynamic functions of formation of tungsten oxides from the elements by another, independent route. For this purpose we chose the electromotive-force method, which, as applied to oxide electrodes, is described in \((^{3-6})\). The procedure of these works was somewhat modified. Our experiments were carried out in vacuum in a specially constructed metal cell insulated with fused quartz. The furnace temperature was measured with a platinum–platinum-rhodium thermocouple and a potentiometer. As the electrolyte, a solid solution \(0.85\,\mathrm{ZrO_2} + 0.15\,\mathrm{CaO}\), possessing anionic conductivity, was used.

In the temperature interval \(900\text{—}1230^\circ\mathrm{K}\), the e.m.f. of cells of the type
\(\mathrm{WO}_x \mid \mathrm{ZrO_2CaO} \mid \mathrm{Fe}_{0.95}\mathrm{O}, \mathrm{Fe}\) were measured, where \(x = 2.719\) (1); 2.66 (2); 2.39 (3); 1.90 (4); 1.69 (5) and 1.45 (6). Oxides of the indicated composition were obtained by reduction with hydrogen of the low-temperature modification \(\mathrm{WO_3}\)-\(\alpha\) \((^2)\). The first three compositions correspond to a mixture of the phases \(\mathrm{WO}_{2.72}\) and \(\mathrm{WO_2}\), the last to mixtures of \(\mathrm{WO_2}\) and W. The mixture \(\mathrm{Fe}_{0.95}\mathrm{O} + \mathrm{Fe}\) served as the reference electrode.

The experimental e.m.f. values of cells 1—3 and 4—6 are described by equations (1) and (2), respectively:

\[ E_1 = 76.8 - 0.06T\ \text{(mV)} \tag{1} \]

with an accuracy of representation of the mean experimental values by the equation of \(\pm 1.5\) mV;

\[ E_2 = -6.68 + 0.045T\ \text{(mV)} \tag{2} \]

with an accuracy of representation of the mean experimental values by the equation of \(\pm 0.5\) mV.

Combining \(\Delta G\) of cells (1, 2), calculated from the known equation \(G_{\text{cell}} = -zFE_{\text{cell}}\), and \(\Delta G\) of formation of \(\mathrm{Fe}_{0.95}\mathrm{O}\) from the elements (Lange’s data \((^7)\)), gives, for the reaction

\[ {}^{1}/_{2}\mathrm{W} + {}^{1}/_{2}\mathrm{O_2} = {}^{1}/_{2}\mathrm{WO_2} \tag{I} \]

the equation

\[ \Delta G_1 = -68542 - 7.21T\lg T + 1.26\cdot 10^{-3}T^2 - 0.47\cdot 10^5T^{-1} + 40.62T \]
\[ (943\text{—}1230^\circ\mathrm{K}). \]

The values of \(\Delta G_1\) calculated from this equation in the temperature interval \(973\text{—}1273^\circ\mathrm{K}\), and the values of \(\Delta G'_1\) for reaction (I) at these temperatures, obtained by us earlier \((^2)\) from equilibrium data, are presented in Table 1.

For the reaction

\[ {}^{100}/_{72}\,\mathrm{WO}_2 + {}^{1}/_{2}\mathrm{O}_2 = {}^{100}/_{72}\,\mathrm{WO}_{2,72} \tag{II} \]

the equation is

\[ \Delta G_2 = -65308 - 7,21\,T\lg T + 1,26\cdot 10^{-3}T^2 - 0,47\cdot 10^5T^{-1} + 39,93\,T \]

\[ (900—1173^\circ \mathrm{K}). \]

The values of \(\Delta G_2\) calculated from this equation in the interval 923—1173°K and the values of \(\Delta G'_2\) for reaction (II) at these temperatures, obtained by us earlier \((^2)\) from equilibrium data, are presented in Table 2.

Table 1

Table 2

Combining reactions (I) and (II), respectively, gives for the reaction

\[ \mathrm{W} + 1,36\,\mathrm{O}_2 = \mathrm{WO}_{2,72} \tag{III} \]

the equation

\[ \Delta G_3 = -184106 + 9,23\,T\lg T + 3,43\cdot 10^{-3}T^2 - 1,28\cdot 10^5T^{-1} + 109,9\,T. \]

For calculating the standard thermodynamic quantities we used the heat capacities of \(\mathrm{O}_2\) and W, data in \((^8)\), and for \(\mathrm{WO}_2\) the equation

\[ c_p = 17,83 + 1,89\cdot 10^{-3}T - 3,342\cdot 10^5T^{-2} \]

(accuracy ±3%), derived by us on the basis of the value \(c_{p\,298}\) for \(\mathrm{WO}_2\) \((^9)\), values of \(c_p\) for

Table 3

solids at the transformation temperature and averaged equations for the oxides \(\mathrm{UO}_2\) \((^{10})\), \(\mathrm{VO}_2\) \((^{11})\), and \(\mathrm{ThO}_2\) \((^{11})\), with values of \(c_{p\,298}\) close to those of \(\mathrm{WO}_2\).

Using these values, we obtain for the reaction

\[ \mathrm{W} + \mathrm{O}_2 = \mathrm{WO}_2 \tag{IV} \]

the equation

\[ \Delta G_T = -136,6 - T(4,66M_0 + 0,21M_1 - 2,44M_{-2}) + 41,7T \]

(\(M_0,\ M_1,\ M_{-2}\) are the coefficients of the Temkin–Schwarzman equation \({}^{(12)}\)), whence

\[ \Delta H^0_{298} = -136.6 \pm 2\ \text{kcal}; \]

\[ \Delta S^0_{298} = -41.7 \pm 1.5\ \text{e.u.}; \]

\[ \Delta G^0_{298} = -124 \pm 2\ \text{kcal}. \]

Using the values of \(S^0_{298}\) for W \({}^{(13)}\) and O\(_2\) \({}^{(14)}\), we obtain for WO\(_2\)

\[ S^0_{298} = 15.0 \pm 1.5\ \text{e.u.} \]

For comparison, Table 3 gives some literature data for the thermodynamic functions of formation of WO\(_2\) from the elements under standard conditions.

Moscow State University
named after M. V. Lomonosov

Received
3 VI 1960

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