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where i is the sum of the stoichiometric coefficients for the reaction, andT is the isothermal compressibility. The reaction volume is defined as the sum of the products of the stoichiometric coefficient and the partial molar volume Vi for each species in the reaction. The reaction volume is Vrxn (V V ...)(aVA VB ...) (4.3) The difficulty in using (4.2) and (4.3) with experimental data is that experimental measurements of partial molar volumes are challenging (Guo and Akgerman, 1998). Measuring partial molar volumes is very difficult because of the problems associated with observing the supercritical phase the low concentrations and short lifetimes of highly reactive species. An alternative approach to experimental measurements of partial molar volumes or equilibrium constants is theoretical determination of these quantities. 4.5.2 Effect of density on Kinetic Constant In conventional transition state theory, the pressure dependence of a rate constant is related to the activation volume as it described by Equation (2.5) lnkC V# P RT (1...) (4.4) T,C where T is the isothermal compressibility of the solvent. The activation volume is calculated as the difference in the partial molar volumes of the transition state (“TS”) and the reactants. V# VTS aVA VB (4.5) The partial molar volumes can be calculated like the equilibrium constant case from the pair correlation functions for infinitely dilute mixtures. 62PDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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