A new method for estimating the cubic of equation of state parameters for both pure and mixture fluids without using critical properties is proposed. In this method, the solvation charging free energy and the solvation cavity are used to determine the temperature-dependent energy parameter a(T) and volume parameter b. This method requires only element specific parameters (3 parameters for each element, including one atomic radius and two parameters for describing dispersion interactions), and 10 universal parameters for electrostatic and hydrogen-bonding interactions. The equation of state (EOS) parameters so determined allow for the description of the complete phase diagram, including the critical point, for pure and mixture fluids. We have examined this method using the Peng-Robinson (PR) EOS1 for 1295 compounds and 141 binary mixture systems. For pure compounds, this model achieved an accuracy of 48% in vapor pressure at normal boiling point, 21.4% in liquid density, 4.1% in critical temperature, 10% in critical pressure, and 5.3% in critical volume. For binary mixture systems, the overall average deviation in total pressure and vapor phase composition are 28.5% and 5.5%, respectively. The errors can be reduced significantly (to 6.8% and 2.5%) if the critical properties and acentric factor of the pure components are used. This method is, in principle, applicable to any chemical species and is especially useful for those whose experimental data are not available.