Physical Chemistry

L. L. Makarov and Yu. G. Vlasov

Thermodynamics of Solid Solutions CsCl—RbCl at 25°

(Presented by Academician A. N. Terenin, 27 XII 1957)

X-ray structural studies \((^1)\) and crystallographic characteristics (lattice type, ion sizes) make it possible to expect limited miscibility of CsCl with RbCl at low temperatures. In the present work, in order to determine the limits of existence of the CsCl—RbCl solid solution and to study its thermodynamic properties, the system CsCl—RbCl—H\(_2\)O at 25° was investigated. The experimental data and the results of thermodynamic calculations carried out in accordance with the relations of A. V. Storonkin—M. M. Shul’ts \((^2)\) are presented in Table 1, where \(m\) denotes the concentration in moles per 1000 g of water; \(x\) is the mole fraction; \(P_{\mathrm{H_2O}}\) is the vapor pressure of water over the solution, in mm Hg; \(f\) is the rational activity coefficient in the solid phase, \(\lim_{x\to 1} f \to 1\); \(\gamma_{\pm}\) is the mean ionic activity coefficient in the aqueous solution at the indicated concentrations \(m_{\mathrm{CsCl}}\) and \(m_{\mathrm{RbCl}}\); \(D_{2,1}\) is the crystallization coefficient, determined from the relation: \(D_{2,1}\frac{x_2}{1-x_2} : \frac{m_1}{m_2}\), where the subscripts 1 and 2 refer, respectively, to the solvent substance and the dissolved substance in the solid phase (the solvent in the solid solution will be called the substance present in the larger amount).

To attain the state of equilibrium between the liquid and solid phases, the method of isothermal

Table 1

of removing supersaturation, followed by prolonged (10 h) stirring. The solid phase was analyzed by the Schreinemakers method. Radioactive isotopes \( \mathrm{Rb}^{86} \) and \( \mathrm{Cs}^{134} \) were used for the purposes of the analysis. The vapor pressure of water over the solutions was determined by an isopiestic method. The experimental results (Table 1) show that CsCl and RbCl form solid solutions with a miscibility gap from 10.7 to 93.3 mol. % CsCl (these limits of existence of the CsCl—RbCl solid solutions are calculated from the value \(D_{2,1}\) and the composition of the liquid phase at the ternary point).

Fig. 1. Free energy of formation of CsCl—RbCl solid solutions at \(25^\circ\). \(a\)—\(x\Delta\mu_{\mathrm{CsCl}}\), \(b\)—\((1-x)\Delta\mu_{\mathrm{RbCl}}\), \(v\)—\(\Delta\Phi\)

As is seen from Table 1, the activity coefficients in saturated aqueous solutions, within the limits of experimental error, remain constant over the entire length of the solubility isotherm. In the case of limiting dilution with respect to one of the components, the following relations hold:

\[ \gamma_{\pm \mathrm{CsCl}(\mathrm{RbCl}\ m=7.78)}=\gamma_{\pm \mathrm{CsCl}\ m=7.78}, \]

\[ \gamma_{\pm \mathrm{RbCl}(\mathrm{CsCl}\ m=11.4)}=\gamma_{\pm \mathrm{RbCl}\ m=7.78}. \]

In the solid phase, the activity coefficients of the solvent component determining the crystal structure of the solid solution are, with high accuracy, equal to unity. The activity coefficients of the dissolved substance retain a constant value, different from unity, but with large deviations from the mean, which is a peculiarity of the calculation method employed.

The results of the final calculations of the changes in chemical potentials \(\Delta\mu_{\mathrm{CsCl}}\) and \(\Delta\mu_{\mathrm{RbCl}}\) and of the change in free energy upon formation of the CsCl—RbCl solid solution are presented in Table 2* and in Fig. 1.

The form of the obtained curve for the dependence of \(\Delta\Phi\) on composition (Fig. 1) shows that formation of the solid solution occurs under the condition

\[ \frac{\partial \Delta \Phi}{\partial x_2}<0, \]

where \(x_2\) is the mole fraction of the dissolved substance.

Table 2

Near the stability boundary of the solid solution the following relations hold:

\[ \left(\frac{\partial \Delta\Phi}{\partial x}\right)_{\simeq x^{\mathrm{sat}}}=0, \]

\[ \text{* In calculating } \Delta\Phi \text{, the values of the activity coefficients of the dissolved substances at the ternary point were used: } f_{\mathrm{CsCl}}=8.6 \text{ and } f_{\mathrm{RbCl}}=13.3. \]

or

\[ \Delta \mu_1 \cong \Delta \mu_2, \]

whence

\[ x_1^{\mathrm{sat}} = \frac{f_2}{f_1 + f_2} \]

\[ x_2^{\mathrm{sat}} = \frac{f_1}{f_1 + f_2} \]

Consequently, the composition of saturated solid solutions \(x^{\mathrm{sat}}\) is determined through the activity coefficients of both components.

Leningrad State University
named after A. A. Zhdanov

Received
24 XII 1957

References Cited

1. R. J. Havighurst, E. Mack, Jr., F. C. Blake, J. Am. Chem. Soc., 47, 1 (1925).
2. A. A. Storonkin, M. M. Shults, Vestn. LGU, No. 11 (1954).
3. V. G. Khlopin, Tr. gos. radiev. inst., 4 (1938).