A principle to correlate extreme values of excess thermodynamic functions with partial molar quantities

Excess thermodynamic properties are widely used quantitatively for fluids. It was found that at constant temperature and pressure a molar excess quant ity 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 prope rties such as enthalpy, entropy, Gibbs free energy, and volume, and is appl icable for excess functions with multi extreme points. Solutions at extreme points can be referred to as special mixtures, Particularly for a special mixture of Gibbs free energy, activity coefficients of the two components a re identical.