Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems

Abstract

To obtain a semi‐theoretical equation for the excess Gibbs energy of a liquid mixture, Guggenheim's quasi‐chemical analysis is generalized through introduction of the local area fraction as the primary concentration variable. The resulting universal quasi‐chemical (UNIQUAC) equation uses only two adjustable parameters per binary. Extension to multicomponent systems requires no ternary (or higher) parameters. The UNIQUAC equation gives good representation of both vapor‐liquid and liquid‐liquid equilibria for binary and multicomponent mixtures containing a variety of nonelectrolyte components such as hydrocarbons, ketones, esters, amines, alcohols, nitriles, etc., and water. When well‐defined simplifying assumptions are introduced into the generalized quasi‐chemical treatment, the UNIQUAC equation reduces to any one of several well‐known equations for the excess Gibbs energy, including the Wilson, Margules, van Laar, and NRTL equations. The effects of molecular size and shape are introduced through structural parameters obtained from pure‐component data and through use of Staverman's combinatorial entropy as a boundary condition for athermal mixtures. The UNIQUAC equation, therefore, is applicable also to polymer solutions.