The Gibbs–Duhem condition and the relations between mixing coefficients of binary mixed electrolytes

Abstract

It is shown that Ialenti and Caramazza have incorrectly equated the terms on the two sides of the Gibbs–Duhem cross-differential equation and hence have arrived at a false conclusion. In this paper the Harned equations are developed by a correct application of the cross-differentiation condition required by the Gibbs–Duhem equation so as to obtain inter-relations among the Harned coefficients, including one general relation which is required. A necessary condition for the general Gibbs–Duhem equation to hold is also derived and the methods of Scatchard, Pitzer and the higher-order limiting law are all shown to satisfy this condition. For a special case in which a further inter-relation also applies, it is shown that A_k and B_k must be constants for k 2. Relations between the Harned coefficients and the mixing coefficients in Δ_mG^ex and their derivatives are also obtained.