A multi-phase, multi-component critical equation of state

Realistic equations of state valid in the whole state space of a multi-component mixture should satisfy at least three important constraints: (i) The Gibbs phase rule holds. (ii) At low densities, one can deduce a virial equation of state with the correct multi-component structure. (iii) Close to critical points, plait points, and consolute points, the correct universality and scaling behavior is guaranteed. This paper discusses semiempirical equations of state for mixtures that express the pressure as an explicit function of temperature and the chemical potentials. In the first part, expressions are derived for the most important thermodynamic quantities. The main result of the second part is the construction of a large family of equations of state with the properties (i)--(iii).