  Using the formalism of rigorous statistical mechanics, we study the phenomena
of phase separation and freezing-point depression upon freezing of solutions.
Specifically, we devise an Ising-based model of a solvent-solute system and
show that, in the ensemble with a fixed amount of solute, a macroscopic phase
separation occurs in an interval of values of the chemical potential of the
solvent. The boundaries of the phase separation domain in the phase diagram are
characterized and shown to asymptotically agree with the formulas used in
heuristic analyses of freezing point depression. The limit of infinitesimal
concentrations is described in a subsequent paper.
