The generalized van Laar approximation for free energy

The van Laar equation for the uniform substance phase is analyzed. Based on this, an expression for free energy is found. The structure of the expression allowed us to create a method for determining the free energy in an arbitrary order of the perturbation theory. A generalized equation for free energy is derived based on the using thermodynamic perturbation theory and the accelerated method of convergence of the series of the perturbation theory. This expression agrees well with the asymptotic behavior of the free energy and with the known experimental data. It can be successfully used to describe the behavior of the substance in a super-critical region, as well as to investigate the metastable phase. It is shown that the expression for free energy can be used for a broad class of substances.