Cavity functions and association in models for weak electrolytes and sticky hard spheres

Abstract

Weak electrolytes and other association reactions are modeled as sticky spheres. An analysis of the density expansion, including the bridge diagrams, of the cavity functions yAB(L) for sticky hard spheres (charged or uncharged spheres binding at a distance L) leads to an approximation which provides the degree of association α as the solution to a simple quadratic equation determined by the association constant K0 and the cavity function y0AB(L) for the reference system in which the chemical bonding between the reacting species has been turned off. Similar relations are assumed to hold when the bonding is directional and specific enough to lead only to the formation of dimers. Applications to the determination of the reference cavity functions for acetic acid and monochloro acetic acid from experimental data of the degree of association are discussed. In a discrete solvent, the approximation scheme for α remains the same, except that the reference cavity function is scaled differently. Solvent medium effects on the association constant are shown to be related to the cavity function of the undissociated dimer in a pure solvent. An exponential approximation for the reference cavity function y0AB(L) is derived when the associating species are of the same size and the bonding is spherically symmetric. Expressions for the changes in the thermodynamic functions due to association are obtained analytically in terms of the degree of association and the reference cavity functions. The magnitude of the degree of association, calculated from the exponential approximation for y0AB(L), and its effect on the thermodynamic properties are different from what was previously observed using the hypernetted chain (HNC) approximation. The thermodynamics of weak 1–1 electrolytes are discussed using the new method and a comparison is made between the new and old methods for 2–2 electrolytes.