A family of new mixing rules for the cubic equation of state through a synthesis between the classical van der Waals mixing rule and the local composition concept is proposed. The binary interaction parameter in the van der Waals mixing rule, which is devoid of physical meaning, is thus replaced with a more physically meaningful parameter. The new mixing rules were used to correlate the dependence on pressure of the solubilities of a number of solid substances, including penicillins, in supercritical fluids. Because the new mixing rules contain physically meaningful parameters, dependent on the energies of the binary intermolecular interactions, the calculations of those energies can allow one to predict the solubilities of solids in supercritical fluids. Such predictions were made for the solubility of solid CCl4 in the supercritical CF4. The required binary intermolecular energies were computed with the help of quantum mechanical ah initio calculations, and a good agreement between the predicted and experimental solubilities was obtained.