Modeling of ionic liquid + polar solvent mixture molar volumes using a generalized volume translation on the Peng–Robinson equation of state

In this study, a volume-translated version of the Peng–Robinson equation of state (PR EoS) is developed for ionic liquid + polar solvent mixtures to estimate molar volumes within a range of compositions and temperatures. The ionic liquids investigated consisted of various combinations of either the 2-hydroxyethylammonium or the alkyl-methylimidazolium cation with various alkyl chain lengths, with the anions methyl-sulfate, ethyl-sulfate, hydrogen-sulfate, dicyanamide, acetate, bis(trifluoromethylsulfonyl)imide, and tetrafluoroborate. The polar solvents consisted of water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, acetone, nitromethane and dichloromethane. The volume shift parameter, c, was first optimized for all of the systems investigated at each composition and temperature. Based on the values obtained, it was observed that temperature-dependency is negligible. Therefore, a generalized equation was presented for the c parameter as a function of the molar composition of the polar solvent and the molecular weight of the ionic liquid. This relation, which contains a combination of exponential, logarithmic and polynomial terms, was able to improve the predictions of the PR EoS and reduce the errors with respect to experimental data. The average errors of the conventional PR EoS and the volume-translated PR EoS (both without using any binary interaction parameters) were equal to 14.92% and 5.91%, respectively. The added advantage of using this correlation is that it omits the need to optimize any binary interaction coefficients in such highly nonideal systems, making it a very simple and practical engineering tool for the industries, while at the same time increasing predictive accuracy.