A modified Lennard-Jones (LJ) equation of state is extended to the calculation of vapor-liquid equilibria and solid-fluid equilibria in systems containing n-alkanes, carbon dioxide, water, and alcohols. The predictive capabilities of the equation were examined by extrapolating data at ambient conditions to high temperatures and pressures, where the extrapolations were compared with experimental data. Excellent agreement was obtained between extrapolations and actual data in all cases. Comparisons between the predictive capabilities of the LJ equation and several cubic equations with a variety of mixing rules are shown.