Thermochemical excess properties of multicomponent systems: Representation and estimation from binary mixing data

A general equation for the estimation of thermodynamic excess properties of multicomponent systems from observed excess properties of the various binary combinations of the components has been developed, based on a simple model of the multicomponent system. This estimation takes the form $$\Delta \bar Z_{12...N}^{ex} = \sum\limits_{i = 1}^N {\sum\limits_{j > i}^N {(X_i + X_j )(f_i + f_j )(\Delta \bar Z_{ij}^{ex} )^* } } $$ in which \((\Delta \bar Z_{ij}^{ex} )^* \) is the molar excess property (enthalpy, entropy, volume, free energy, etc.), of the binary system with components at the same molar ratio as in the multicomponent system, and f_i, f_j are weighted mole fractions using weighting factors based on the excess properties of the binary systems. The important features of this equation are: it is applicable to a broad range of thermodynamic properties, its application to both integral and differential mixing properties is independent of the manner in which the binary mixing data is represented (Redlich-Kister equation, Wilson equation, etc.), and it provides reasonably accurate predictions ranging from quite good for simple systems of nonspecific interactions to only fair for associated solutions. This equation is recommended as a point-of-departure for mathematical representation of experimental data for multicomponent systems.