A new three-parameter generalized equation of state for application to mixtures and multicomponent equilibrium systems has been developed. The equation of state is developed from isothermal and isochoric behavior of pure fluids. This equation of state is based on the hard sphere equation of state and is made to favor vapor-liquid equilibrium computations, and also gives satisfactory prediction of other properties. It models the second order perturbation theory expansion in powers of 1/KT for which there is a theoretical base for the mixing rules. This is much more effective than a completely empirically derived set of mixing rules. Methane, Ethane, and Propane were selected for testing this approach. Satisfactory results in the calculation of densities, compressibility factors, vapor pressure and fugacity over a wide range of temperature and pressure demonstrates the applicability of this equation of state. The possibility of a completely analytical expression of the methods previously developed, such as the van der Waals' one-fluid theory and the original Hard Sphere Expansion theory on vapor-liquid equilibrium is in sight.