A thermodynamic approach to analyzing relative permittivity and solvent mole fraction models, and application to SN1 reactions.

The standard methods for analyzing solvent effects on chemical reactions largely include linear free energy relations that relate kinetic and spectroscopic terms to solvent interactive parameters. The number of these parameters has grown over the years in order to make linear free energy techniques more accurate and cover a wider range of reaction systems. However, even with the myriad of parameters, the details of specific reaction systems make the application of these techniques sometimes unreliable. On the other hand, a thermodynamic approach provides a more precise analysis, and has proven particularly useful for reactions in multi-component solvent systems. In this article we present the mathematical formalism for relating the activation free energy to the bulk thermodynamic properties for a binary (cosolvent) system. We then use this thermodynamic approach, coupled with selected solvent models, to analyze the hydrolysis rates of tert-butyl chloride in the acetonitrile/water solvent system under iso-mole fraction, isodielectric, and isothermal conditions. These analyses allow us to differentiate and quantify bulk electrostatic effects and the effects of close-range solute-solvent interactions.

Configuration-specific kinetic theory applied to an ideal binary gas mixture.

This paper is the second in a two-part series dealing with the configuration-specific analyses for molecular collision events of hard, spherical molecules at thermal equilibrium. The first paper analyzed a single-component system, and the reader is referred to it for the fundamental concepts. In this paper, the expressions for the configuration-specific collision frequencies and the average line-of-centers collision angles and speeds are derived for an ideal binary gas mixture. The analyses show that the average line-of-centers quantities are all dependent upon the ratio of the masses of the two components, but not upon molecular size. Of course, the configuration-specific collision frequencies do depend on molecular size. The expression for the overall binary collision frequency is a simple sum of the configuration-specific collision frequencies and is identical to the conventional expression.

Configuration-specific kinetic theory applied to the elastic collisions of hard spherical molecules.

Classical trajectory simulations can be used to glean a wealth of information on the geometric details of gas-phase molecular collision events for which the standard theoretical treatment lacks the ability to predict. For instance, the standard treatment gives no information on configuration-specific collision parameters. A configuration-specific parameter is defined here as the average value for a collision parameter that is exclusive to either an ensemble of front-end or an ensemble of rear-end molecular collisions. This paper presents statistical results of simulation "measurements" on several configuration-specific parameters, including the configuration-specific collision frequencies. The simulations use single-component systems of hard spherical molecules confined within a spherical boundary. To complement the simulation effort, a systematic mathematical analysis for the configuration-specific parameters is presented. This analysis uses the Maxwell-Boltzmann distribution of molecular speeds as usual, but exploits the distinction between front-end and rear-end collision space, and uses the line-of-centers speed rather than the relative speed. The configuration-specific expressions derived from this analysis are in very good agreement with the simulation measurements for every molecular collision parameter studied in this work.