Some new expressions concerning individual ionic activities and their physical significance

Abstract

According to local thermodynamic arguments, at constant temperature (T) and zero field strength (E), individual ionic chemical potentials µ_i are functions of the local number densities and vice versa. In this paper it is shown that the quantities L_ki defined by (δ_ki+L_ki)=kT(∂ ln n_k//_∂µi)_{T, µi}, where δ_ki= 0; i≠k, δ_ki= 1; i=k are given by L_ki=n_i∫^∞_o[g_ki(r)–g^″_ki(r)]4πr² dr in homogeneous solutions, where n_i is the number density of i, g_ki(r) is the pair distribution function and g^″_ki(r) is the limiting form of g_ki(r) as r→∞. Expressions are derived in terms of physically significant quantities for the liquid-junction potential and Donnan potential differences between two solutions. It is also shown that as n_k→ 0, L_ki=n_i–n′_i//_nk where n′_i refers to a solute-free solution with the same µ_i at the mid-plane between identical overlapping double layers. These results show that the L_ki have a similar significance to the Kirkwood–Buff integrals in solutions of non-electrolytes.

By considering a hypothetical solution in which the valency of solute → 0 a simple method is developed for treating solution non-ideality in double-layer theory at the Debye—Hückel level. The work is compared with the statistical mechanical treatment of Stell and Lebowitz (J. Chem. Phys., 1968, 48, 3706).