A new method for estimation of parameters in cubic equations of state from ab initio solvation calculations is presented. In this method, the temperature-dependent interaction parameter a(T) is determined from the attractive component of solvation free energy, whereas the volume parameter b is assumed to be that of solvation cavity. This method requires only element-specific parameters, i.e., atomic radius and dispersion coefficient, and nine universal parameters for electrostatic and hydrogen-bonding interactions. The equations of state (EOS) parameters so determined allow the description of the complete fluid phase diagram, including the critical point. We have examined this method using the Peng-Robinson EOS for 392 compounds and achieved an accuracy of 43% in vapor pressure, 17% in liquid density, 5.4% in critical temperature, 11% in critical pressure, and 4% in critical volume. This method is, in principle, applicable to any chemical species and is especially useful for those whose experimental data are not available.