# A technique for analyzing the variability of activation thermodynamic and solvent model parameters

## TL;DR

This paper introduces a three-step technique to analyze how activation and solvent model parameters vary in chemical reactions.

## Contribution

A novel three-step method is developed to evaluate the functional dependencies of activation and solvent model parameters.

## Key findings

- The intrinsic activation entropy and Kirkwood–Onsager parameter depend on the solvent's electrostatic environment and solvation shell interactions.
- Mathematical expressions for intrinsic parameters cannot be evaluated, as shown through analysis.
- An empirical expression correlates the solvent mole fraction with the solvation shell's effect.

## Abstract

The fundamental thermodynamic equation of chemical kinetics has recently been used to analyze rate data from the hydrolysis reaction of tert-butyl chloride in the acetonitrile/water solvent system. Although this study showcased the deeper level of insight afforded from the fundamental equation, at the time of the publication no technique had been developed for analyzing the functional dependencies of the activation thermodynamic and solvent model parameters. We have since developed a three-step technique briefly described as follows. The first step includes conducting a linear regression analysis using a linearized form of the fundamental equation to determine if the parameters are constant. The second step includes a technique for evaluating the functional forms of the parameters if they are not constant, and the third step includes a technique for constructing parameter grid equations. The three-step analysis has been applied to some of the rate data from our studies on the tert-butyl chloride hydrolysis reaction. The results show the intrinsic activation entropy and Kirkwood–Onsager parameter depend on the electrostatic environment of the bulk solvent and the close-range interactions associated with the solvation shell. Auxiliary topics also presented in this article include an analysis showing mathematical expressions for intrinsic parameters cannot be evaluated, a discussion on the modeling benefits of the fundamental equation, and presentation of an empirical expression that correlates the solvent mole fraction term with the effect of the solvation shell.

The fundamental thermodynamic equation of chemical kinetics has recently been used to analyze rate data from the hydrolysis reaction of tert-butyl chloride in the acetonitrile/water solvent system.