The paper develops a new approach to the analysis of a solid-liquid phase diagram in terms of the chemical potentials of the single phases. The approach stems from the basic hypothesis that chemical potentials between different phases are equal at equilibrium. To make the idea operative, the mathematical dependence of the pertinent chemical potentials on the temperature and the mass fraction is determined by means of Aspen Plus; for definiteness a sodium chloride solution is examined. The phase diagram is established and the analytical properties of the curve are obtained. Moreover, the functional dependence of the mass fraction on the temperature at the freezing point is determined. The satisfactory agreement with new experimental data proves the validity of the procedure. The methodology so developed, provides an improved and rigorous mathematical overview for the analysis of phase diagrams. The approach is likely to be applicable to the investigation of solutions with several constituents or alloys.