We have developed a new method, called the reaction Gibbs ensemble Monte Carlo (RGEMC) method, for the computer simulation of the phase equilibria for multicomponent mixtures, given an intermolecular potential model for the constituent molecular species. The approach treats the phase equilibrium conditions as a special type of chemical reaction and incorporates knowledge of the pure-substance vapor pressure data into the simulations. Unlike macroscopic thermodynamic-based approaches like the Wilson and the universal quasichemical functional group activity coefficients (UNIFAC) approximations, no experimental information concerning the mixtures is required. In addition to the PTxy phase equilibrium data, the volumetric properties of the mixture are calculated. We developed intermolecular potential models based on the optimized potentials for liquid simulations (OPLS) of Jorgrensen and used the RGEMC method to predict phase equilibrium data for the binary systems isobutene + methyl tert-butyl ether (MTBE) and the binaries formed by methanol with isobutene, MTBE, and n-butane. The predictions are excellent, and of comparable accuracy to those obtained using the Wilson and the UNIFAC thermodynamic-based approaches, even though such approaches use experimental mixture information.