Peng-Robinson EOS is generalized with pair potential parameters for the PVT relation of liquid n-alkanes C-1 to C-30, and C-36 with the saturated vapors for temperatures near the normal boiling point to the critical point. The EOS is reduced with the Lennard-Jones pair potential depth parameter epsilon and the characteristic length d, which is determined with the pair potential parameters epsilon and sigma are expressed by universal functions of temperature reduced with critical temperature, T-r = T/T-c. The values of the coefficients in the functions are specific to each alkane. The vapor pressure and the liquid molar volume calculated with the EOS agreed to the observed ones with the root mean square deviation of 2.21 % and 0.63%, respectively, better than those from the modified PR-EOS in the literature. The coefficients and the powers in the universal functions for epsilon and sigma are expressed by generalized functions of acentric factor omega, where the calculated vapor pressure and liquid molar volume agreed well to the observed ones with the root mean square deviation of 4.16% and 1.57%, respectively. (c) 2007 Elsevier B.V. All rights reserved.