Bimorphic lattice theory of electrolyte solutions

Abstract

It is shown that lattice concepts can account for the functional behaviour of electrolyte solutions at all concentrations. A layered lattice structure leads to log ƒ_± against C^1/2 behaviour in agreement with Debye–Hückel theory. By analogy with Evjen's stability theory of ionic crystals, transition to a “three-dimensional” lattice form could occur at a higher concentration. The C^1/2 dependence can be connected with continuity of log ƒ_± and ∂ log ƒ_±/∂C^1/2 to a high-concentration relation including a C^1/3 term derived from lattice theory. This requires introduction of a constant leading term (depending only on valence type) into the log ƒ_± relation, which is interpreted as due to the energy difference between standard states of the two lattice forms. A third term BC is needed to deal with high-concentration behaviour, where B is an adjustable constant. This term was previously derived by Bahe and by Ruff as a field-dielectric-gradient lattice-stabilizing repulsion term. The three-term equation provides an accurate representation of activity-coefficient data for HCl, NaCl and KCl up to 4 mol dm^–3 with the NaCl lattice constant. A similar fit is obtained for CaCl₂ only if the crystal lattice constant is replaced by a value 25% higher. The success achieved with these examples suggests that the three-term log ƒ_± equation and others derived therefrom can be employed for the accurate representation of thermodynamic properties in general with a minimum of adjustable parameters.