We present a novel way of obtaining the interactions parameters in the Peng-Robinson equation of state (PR EOS) such that it is applicable for all types of fluid phase equilibrium calculations without the need of input of any experimental data. This is made possible by determining the temperature and composition dependence of the energy parameter a(T, x) and volume parameter b(x) in PR EOS from first-principles solvation calculations. This method requires only element specific parameters (three parameters for each element, including one atomic radius and two parameters for describing dispersion interactions), and 15 nonspecies dependent, universal parameters for electrostatic and hydrogen-bonding interactions. We validate this method using (1) vapor pressure, liquid density, and critical properties of 1296 pure substances, (2) 116 binary vapor-liquid equilibrium mixtures (including about 3000 data points with temperatures ranging from 255.37 to 623.15 K and pressures from 0.03 KPa to 18.97 MPa), (3) 68 binary and 39 ternary liquid-liquid equilibrium systems at atmospheric pressure, and (4) the solubility of 52 pharmaceuticals in 37 different pure solvents and their mixtures at the temperatures ranged from 273.15 to 323.15 K (including about 2900 data points). All the calculations are done with the same set of 33 parameters. We believe that this approach is a useful tool for providing thermodynamic properties of fluids prior to experimental measurements.