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Excess thermodynamic properties are widely used quantitatively for fluids. It was found that at constant temperature and pressure a molar excess quantity of a mutually miscible binary mixture at the extreme points equals the excess partial molar quantities of the two components, i.e.F_(1)~E = F_(2)~E = F_(m)~E , forming a triple cross point. The relationship is hold for properties such as en-thalpy, entropy, Gibbs free energy, and volume, and is applicable for excess functions with multi extreme points. Solutions at extreme points can be referred to as special mixtures. Particularly fora special mixture of Gibbs free energy, activity coefficients of the two components are identical.
Excess thermodynamic properties are widely used for quantitatively for fluids. It was found that at constant temperature and pressure a molar quantity of a mutually miscible binary mixture at the extreme points equals the excess partial molar quantities of the two components, ieF_ (1) ~ E = F_ (2) ~ E = F_ (m) ~ E, forming a triple cross point. The relationship is hold for properties such as en-thalpy, entropy, Gibbs free energy, and volume, and is applicable for excess functions with Many extreme points. Solutions at extreme points can be referred to as special mixtures. Particularly fora special mixture of Gibbs free energy, activity coefficients of the two components are identical.