Quasi-Lattice Model of Reciprocal Salt Systems. A Generalized Calculation

Abstract

A generalized statistical-mechanical calculation of the solution thermodynamics of the reciprocal molten salt system A+, B+, C−, and D− dilute in A+ ions has been made. The calculation is based on the quasi-lattice model of reciprocal salt systems and treats the problem as an order-disorder problem. Associations of the A+ and C− ions as A++C−⇌ACAC+C−⇌AC2−AC2−+C−⇌AC3=are taken into account. In terms of the conventional equilibrium constants K1, K2, and K3 for (A), (B), and (C), respectively, K1=Z(β1−1)K1K2=Z(Z−1)2!(β1β2−2β1+1)K1K2K3=Z(Z−1)(Z−2)3!(β1β2β3−3β1β2+3β1−1),where Z is the quasi-lattice coordination number, βj=exp(—ΔAj/kT) and ΔAj may be termed a specific bond free energy of the jth C− ion and is the specific Helmholtz free energy change for the formation of the jth bond. Equations (1), (2), and (3) demonstrate the surprising fact that the higher order association constants are dependent on the magnitude of the lower order association constants not only through the factor containing Z but also through the values of the βi for the lower association constants. If β1=β2=β3=··· etc., the equations reduce to the statistical ratios of Bjerrum. The higher association constants can be shown to be smaller for a case in which the bonding is directional (e.g., linear AC2−), than if they are nondirectional, as in Eqs. (2) and (3), even if the bond free energies are equal in the two cases.