Interaction between Solute Elements at Any Given Concentration in Homogeneous Multicomponent Solution

Abstract

The general relationship between activities and activity coefficients based on Raoultian and Henrian reference states at any given concentration was derived from a somewhat different point of view. It was shown that Wagner type theoretical series expansion is valid at any concentrated solution, and that Taylor series expansion using the interaction parameters at constant concentration ratio is also possible. The conversion equations between several kinds of interaction parameters valid at any given concentration in a multicomponent solution were derived by the aid of Gibbs-Duhem equation and Maxwell cross differentials. In a ternary system 1-2-3, the following relations were obtained at any given concentration : where γ (or f) is the activity coefficient in mole fraction basis (or in weight percent basis), N (or X) is the mole fraction (or weight percent), M is the atomic weight and the underscript signified the component to be kept constant. It was also shown that βᵢ⁽j⁾=βj⁽i⁾ is valid at the condition Nᵢ=Nj, and consequently it follows that ∂1nγ₁/∂N₂=∂1nγ₂/∂N₁ at N₁=N₂=0.5 in a binary solution.