Generalized Peng–Robinson equation of state with pair potential parameters for liquid n-alkanes

Abstract

Peng–Robinson EOS is generalized with pair potential parameters for the PVT relation of liquid n-alkanes C 1 to C 30, C 32, 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 ɛ and the characteristic length d, which is determined with the pair potential parameters ɛ and σ. Two reduced parameters in the EOS, a ˆ = a / ( N A 2 ε d 3 ) and b ˆ = b / ( N A d 3 ) , where N A is Avogadro number, are in the corresponding states with reduced temperature, T ˆ = k T / ε . The pair potential parameters ɛ and σ 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 ɛ and σ are expressed by generalized functions of acentric factor ω, 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.