We calculate the free energy of solvation for two binary mixtures: hexane/nitrobenzene and carbon disulfide/acetone, examples of regular and azeotropic mixtures, respectively. Using the coupling parameter approach and thermodynamic integration, we obtain Henry's and Raoult's laws at the opposite ends of the composition range, with coefficients that compare reasonably with experiment. For the regular mixture, we compare with regular solution theory. The free energy data can be described by a single Flory-Huggins interaction parameter, close to the theoretical value at the critical point. For the azeotropic mixture, we calculate the boiling and dew point curves, and estimate the azeotropic composition at room temperature.