Statistical-mechanical equation of state for nonpolar fluids: Prediction of phase boundaries

Abstract

A perturbation correction term for the effect of attraction forces on the equation of state is calculated and combined with previous statistical-mechanical analytical equations of state proposed by Song and Mason and by Ihm, Song, and Mason. The major effect of the correction on the p–v isotherms occurs in the metastable and unstable regions (the ‘‘van der Waals loops’’), with the result that the vapor pressures and orthobaric densities predicted from the Maxwell equal-area construction are greatly improved in accuracy. Comparison is made with experimental data for 13 selected nonpolar fluids (Ar, Kr, Xe, N2, O2, CO2, CH4, C2H6, C3H8, n-C4H10, i-C4H10, C2H4, and benzene) and one slightly polar fluid (toluene). Densities in the stable region of the p–v–T surface are accurate to about 1%–2% in the dense fluid region, and to better than 1% in the low-density gas region; the accuracy is slightly better than that achieved without the perturbation correction. Vapor pressures are predicted with an accuracy of about 2%, with orthobaric densities that are accurate to about 2% for the saturated vapor and to better than 1% for the saturated liquid. As usual for analytical equations of state, the critical region is described less accurately. In principle, the entire fluid equation of state and its vapor–liquid phase boundaries can be calculated from the intermolecular potential plus a few liquid densities. If the potential is not known, measurements of the second virial coefficient as a function of temperature can be used instead; in the absence of any such measurements, the calculation can use as input only the critical temperature, the critical pressure, and the Pitzer acentric factor, with only slight loss of accuracy. Comparison is also made with several widely used empirical equations of state. The present equation of state can be extended to include mixtures, but numerical computations on mixtures are postponed for future work.