There has recently been extensive interest in the nature of the melting/freezing transition for a two-dimensional system of molecules interacting with Lennard-Jones 6:12 potentials, which is a prototype for physisorbed systems. We have therefore made a detailed study of the thermodynamics of the phase diagram for this system. We first made calculations using liquid-state perturbation theory for the fluid state and a self-consistent cell theory for the solid state to determine thermodynamic functions; these results led to ordinary first-order phase transitions between solid/fluid and liquid/gas phases, in agreement with the constant-pressure Monte Carlo results of Abraham. We refined the calculations by using constant-pressure and constant-density Monte Carlo results to improve the accuracy of the calculated free energies, and we determined the two-phase equilibria by making direct Monte Carlo calculations for two-phase systems. The results are internally consistent and lead to a phase diagram qualitatively similar to the three-dimensional Lennard-Jones system. © 1981.