The grand partition function of dilute biregular solutions

It has been demonstrated that the grand partition function (GPF) of biregular solutions contains in one single equation such thermodynamic principles as Henry's law, Raoult's law, the Gibbs-Duhem relation, Raoultian activity coefficients and their finite power series, Wagner's rec-iprocity, Schenck-Frohberg-Steinmetz's interchange, Lupis-Elliott's additivity, Mori-Morooka's disparity, and Darken's quadratic formalism. The logarithm of the Raoultian activity coefficient of species i, In γ_i should not be expressed by the Taylor series expansion, lest its truncation infringe the Gibbs-Duhem equation. The GPF methodology establishes that In γ_i, is not a vector but a scalar point function, free from any path dependence. While Darken's quadratic formalism employs three parameters to describe a ternary solution, the present biregularity approximation offers an alternative using seven empirical parameters, in case better accuracy is needed.