An activity coefficient model using molecular solvation based on the COSMO-RS method is proposed. In this model, quantum mechanical COSMO calculations are performed to obtain the screening charges for molecules in a perfect conductor. A statistical mechanical model that considers molecules to be a collection of surface segments is developed for the calculation of segment activity coefficients using these screening charges. Activity coefficients for molecules are then obtained by summing the contributions of the segments. This model requires only a single radius for each atom in the COSMO solvation calculations, one universal parameter to discern hydrogen-bond acceptors and donors, and two universal parameters to determine segment interactions. This is a significantly fewer number of parameters for phase equilibrium calculations than group contribution methods such as the UNIFAC (168 parameters) and modified UNIFAC (612 parameters) models. The resulting completely a priori prediction method results in absolute average deviations of 0.03 in vapor-phase mole fractions and 9% in total pressure for vapor-liquid equilibrium predictions of 243 binary mixtures and root-mean-square deviations of the octanol/water partition coefficient log K-OW, infinite dilution activity coefficients In gamma(infinity) in water, and in hexane for 64 compounds of 0.48, 1.65, and 0.50, respectively. This model is general and applicable for the a priori prediction of the phase behavior of most compounds, though admittedly it is less accurate than group contribution and other methods with many more parameters whose values have been obtained by regressing large amounts of data.