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.