  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).
