Alternative formalism for the evaluation of the activity coefficients on ternary electrolyte solutions from osmotic coefficient data

Abstract

An alternative method is presented, which is independent of any physicochemical model of the electrolyte solution, for the evaluation of the mean ionic activity coefficient in molal scale, γ±i (i: 2,3), of the solutes of a ternary solution (1–2–3), starting from experimental data of the osmotic coefficient on composition ϕexp(m,xi). It is based on the dependence of ln γ±i on ϕ originally derived by H.A.C. McKay and confirmed by S.G. Canagaratna and M. Maheswaran as a particular solution of Gibbs-Duhem equation for multicomponent systems. Its application involves the integration of both ϕ and its derivative ∂ϕ/∂mi, so that it requires a very precise correlation of the dependence ϕexp(m,xi). Therefore, in order to achieve the required precision, the theoretical expression ϕ(m,xi) is developed as the sum of three contributions, (i) ϕDH: the limiting behaviour given by the Debye-Hückel equation for multicomponent systems, (ii) ΔϕDDH: the sum of the deviations to the Debye-Hückel behaviour of the corresponding binary solutions (1–2 and 1–3) and (iii) ΔϕM: a contribution of mixing effect. Finally, introducing the resulting ϕ(m,xi) into the Gibbs-Duhem equation and operating, the corresponding expression of ln γ±i (m,xi) is derived. The capacity of the ϕ(m,xi) equation to correlate the dependence ϕexp(m,xi), the methodology employed to obtain the parameters values, as well as the ln γ±i (m,xi) resulting dependence are illustrated through its application to the analysis of two ternary systems.