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

Abstract

P txpression for the Excess Gibbs Energy of Partly or Completely Miscible SystemsTo 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 vaporliquid and liquid-liquid equilibria for binary and multicomponent mixtures containing a variety of nonelectrolyte components such as hydrocarbons, ketones, esters, amines, alcohols, nitiles, 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 wellknown 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. SCOPEA significant fraction of chemical process design is concerned with separation of fluid mixtures by diffusional operations. All design methods for such separations require quantitative estimates of fluid-phase equilibria; this work provides a contribution toward making such estimates for liquid-phase mixtures of nonelectrolytes, including polymers, and including those mixtures where nonideality is sufficiently strong to produce two liquid phases.Activity coefficients in liquid mixtures can be calculated from a model which expresses the excess Gibbs energy of the mixture as a function of the composition. A new model, called UNIQUAC, is presented here. This model is derived from a statistical-mechanical basis extending that used by Guggenheim in his quasi-chemical theory. Unlike Guggenheim's theory, however, UNIQUAC is applicable to mixtures wh0.e molecules differ appreciably in size and shape and, unlike previous attempts to gener-alize Guggenheim's method, UNIQUAC contains no more than two adjustable parameters per binary.UNIQUAC is applicable to multicomponent mixtures of nonpolar and polar liquids (including those that participate in hydrogen bonding) as encountered in typical chemical and petrochemical processes. No ternary (or higher) constants are required. Attention is given to vapor-liquid and liquid-liquid equilibria.When well-defined simplifying assumptions are made, the UNIQUAC model can yield any one of several wellknown expressions for the excess Gibbs energy, including the van Law, Wilson, and NRTL equations. Relative to these well-known equations, the advantage of UNIQUAC is that, for a large variety of multicomponent systems and using only two adjustable parameters per binary, reliable estimates can b...

Flash-point prediction for binary partially miscible mixtures of flammable solvents

“…The original Wilson thermodynamic model [17] is not applicable for evaluating the liquid-phase activity coefficients for mixtures that exhibit a miscibility gap [18]. Unlike Wilson's equation, the NRTL [19] and UNIQUAC thermodynamic models [20] are applicable to both vapor-liquid and liquid-liquid equilibria [18]. The Wilson thermodynamic model was modified as T-K-Wilson thermodynamic model by Tsuboka and Katayama (1975) to be applicable to liquid-liquid equilibria [21].…”

An empirical method to correlate and predict solute distribution in ternary liquid-liquid systems

“…Using a model f or the activity coefficients calculations can be carried out to obtain liquid-liquid compositions (Sørensen et al, 1979b). Two models were used in our calculations: UNIQUAC (Abrams and Prausnitz, 1975) and UNIFAC (Fredenslund et al, 1975). The data, equations, parameters and programs were taken from Sørensen and Arlt (1980) and Magnussen et al (1981).…”

A Survey of Equations of State for Polymers

“…The most widely used activity coefficient models are based on this formalism, e.g. [12], [69]- [71]. For compressible lattices, equations of state based on lattice models result.…”