The development of van der Waals cubic equations of state and their application to the correlation and prediction of phase equilibrium properties is presented and analyzed. The discussion starts with a brief account of the contributions to equation of state development during the years before van der Waals. Then, the original equation proposed in the celebrated thesis of van der Waals in 1873 and its tremendous importance in describing fluid behavior are analyzed. A chronological critical walk through the most important contributions during the first part of the 1900s is made, to arrive at the proposal that I consider to be the most outstanding since van der Waals:  the equation proposed by Redlich and Kwong in 1949. The contributions after Redlich and Kwong to the modern development of equations of state and the most recent equations proposed in the literature are analyzed. The application of cubic equations of state to mixtures and the development of mixing rules is put in a proper perspective, and the main applications of cubic equations of state to binary and multicomponent mixtures, to high-pressure phase equilibria, to supercritical fluids, to reservoir fluids, and to polymer mixtures are summarized. Finally, recommendations on which equations of state and which mixing rules to use for given applications are presented.

The critical properties, the normal boiling temperatures, and the acentric factors of ionic liquids have been determined using an extended group contribution method based on the well-known concepts of Lydersen and of Joback and Reid. The critical properties of ionic liquids cannot be experimentally determined in many cases since most of these compounds start to decompose as the temperature approaches the normal boiling point. However, for the development of thermodynamic models either for pure components or for mixtures containing ionic liquids, the critical properties and other physical parameters are required. The so-called group contribution methods have been commonly used to estimate the critical properties of many substances for which these properties are not available, but no attempt has been made to estimate the critical properties of ionic liquids, as presented in this study. The method does not require any additional data besides the knowledge of the structure of the molecule and its molecular weight. Since experimental critical properties of ionic liquids are not available, the accuracy of the method is checked by calculating the liquid densities of the ionic liquids considered in the study. The results show that the values determined for the critical properties, for the normal boiling temperatures, and for the acentric factors are accurate enough for engineering calculations, for generalized correlations, and for equation of state methods, among other applications.

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The group contribution method proposed by Valderrama and Robles in 2007 and extended by to estimate the critical properties of ionic liquids is revised and new groups have been included. The method originally proposed has been used by several authors in applications such as high pressure phase equilibrium, density correlations, heat capacity estimations, and consistency tests for mixture data. Therefore, it is important to have a consistent and reliable method so all applications consider the same assumptions and values for the critical properties. The values previously reported by the authors are recalculated, unifying criteria for the names of the ionic liquids, for the assignment of the groups forming the molecules, and for the equivalence of groups. Also, a spreadsheet file that allows any reader to calculate the critical properties of any ionic liquid containing the 44 groups defined by the method is provided as Supporting Information.

The critical properties, the normal boiling temperature, and the acentric factor of 200 ionic liquids have been determined using an extended group contribution method, which is based on the well-known concepts of Lydersen and Joback and Reid, that was developed by the authors. The method does not require any additional data besides knowledge of the structure of the molecule and its molecular mass. Because experimental critical properties of ionic liquids are not available, the accuracy of the method is checked by calculating the liquid density of the ionic liquids considered in the study for which experimental data are available in the literature. The results show that the values determined for the critical properties, the normal boiling temperature, and the acentric factor are sufficiently accurate for engineering calculations, generalized correlations, and equation of state methods, among other applications.

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The group contribution method proposed by Valderrama and Robles in 2007 and extended by Valderrama and Rojas in 2009 to estimate the critical properties of ionic liquids is revised and an additional test for determining the consistency of the estimated properties is proposed. The new testing method includes the calculation of the saturation pressure at the normal boiling temperature using an equation of state and an accurate model to represent the temperature function of the attractive term in the equation of state. In determining the vapor pressure, the critical temperature, the critical pressure, the critical volume, and the acentric factor determined by group contribution are included. The proposed method complements the previous density test of the authors that tested the critical temperature, the critical volume, and the normal boiling temperature only. A total of 1130 ionic liquids are considered in this work, and double checking, using the density and the normal vapor pressure, is applied. Also, a spreadsheet file that allows any reader to calculate and check the critical properties of other ionic liquids containing any of the 44 groups defined by the method is provided.

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