Excess thermodynamic functions of n-alkane mixtures. Prediction and interpretation through the corresponding states principle

Abstract

Using published reduction parameters for pure normal alkanes, the Prigogine corresponding states principle is extended to excess thermodynamic functions of n-alkane mixtures. All alkane segments have identical interactions (no end-effects), an assumption justified by the success of the treatment. The TC^E_p data of Trejo Rodriguez and Patterson (J. Chem. Soc., Faraday Trans. 2, 1982, 78, 491), for n-alkane mixtures through the composition range at 20, 40, 55 °C are given by a single reduced TC^E_p against T curve. Similarly, single curves against T of H^E, G^E_R and TS^E_R represent literature H^E, residual G^E and residual TS^E data through the composition ranges and at various temperatures for n-C₆+ n-C₁₆. The Flory and the Guggenheim–Huggins–Miller–Orr combinatorial S^E approximations lead to equally successful corresponding states representations for TS^E_R and G^E_R. Maximum deviations from the corresponding states curves correspond to ca. 10 J mol^–1 for H^E, G^E and TS^E, and ca. 0.2 J K^–1 mol^–1 in C^E_p, indicating conformity of the excess functions with the corresponding states principle. The TC^E_p, H^E, TS^E_R and G^E_R may be represented by a single C_p(T) curve for pure and mixed n-alkanes. The curve first decreases with increasing T corresponding to decreasing short-range orientational order in the liquid, then passes through a wide minimum and increases with T corresponding to an increase of free volume. The C_p function predicts all the complex temperature and composition dependences of C^E_p, H^E, TS^E_R and G^E_R for a typical system, n-C₆+ n-C₁₆, as effects of orientational order and free volume. Experimental data available for numerous n-alkane systems at different temperatures are used to test the calculations of the following quantities: equimolar H^E, finite concentration and infinite dilution activity coefficients (including polyethylene systems) and lower critical solution temperatures for polyethylene systems. Agreement with experiment is almost always within experimental error and is considerably better than with other predictive methods. Experimental data for the pure n-alkanes from n-C₅ to polyethylene follow the corresponding states principle imperfectly, but give a C_p(T) curve which is of the same shape as that obtained from excess quantities, i.e.C_p indicates both orientational order and free volume effects. However, the magnitude of C_p is considerably greater and reasons for this difference are discussed.