Solid Solutions of the Alkali Halides. II. The Theoretical Calculation of Lattice Constants, Heats of Mixing, and Distributions between Solid and Aqueous Phases

In all previous attempts to calculate interionic distances and heats of mixing for alkali-halide solid solutions, uniform anion-cation distances throughout a given solution have been postulated. In the present paper, the more logical assumption is made that the ions are not at a constant nearest-neighbor distance, but take up positions of minimum potential energy relative to one another. A method making use of the Born-Mayer-Huggins equation for the lattice energies of the alkali halides is developed for the determination of these positions in a simplified model and for the calculation of the potential energy associated with the resultant lattice. From these values, the average lattice constant, the heat of mixing, and the activity-coefficient ratio in the solid solution are calculated; from the latter is obtained the theoretical distribution ratio between solid and aqueous solutions. Values of the listed properties have been calculated at various mole fractions for the solid solutions KBr–KCl, RbBr–RbCl, RbCl–KCl, RbBr–KBr at 25° and have been found to be in good agreement with the experimental data available.