Detailed thermodynamic analysis of the activation parameters for the simple hydrolysis of acetic anhydride in the acetonitrile/water cosolvent system

Abstract

A detailed thermodynamic analysis of the activation parameters for the simple hydrolysis of acetic anhydride in an acetonitrile/water cosolvent system is presented. The activation parameters are obtained using regression analyses of the Eyring rate equation under iso-mole fraction and isodielectric conditions. The iso-mole fraction Eyring plots are linear, indicating the activation enthalpy and entropy are both temperature independent under these conditions. However, the isodielectric Eyring plots are non-linear, and the analysis shows both the activation entropy and activation enthalpy are strongly temperature dependent under isodielectric conditions. The thermodynamic analysis is complemented by linear solvent energy analysis and computational studies of possible transition structures, the latter showing that a concerted six-member ring structure with a single water molecule is the likely transition state.

Analyses of reaction rate data for the simple hydrolysis of acetic anhydride in the acetonitrile/water and acetone/water cosolvent systems using recently developed thermodynamic rate equations

“…Orders were generally determined to be between 3 and 4 . However, the authors’ work here and in a previous article indicates that k generally varies with X , so that n cannot be determined simply by varying X . Figure , which shows plots of k obs versus [H 2 O] for the two cosolvent systems studied in this work, aptly illustrates this point.…”

“…Whether this step involves one or two water molecules is uncertain. However, computational results in vacuo and with the SM8 solvent model strongly favor a single‐step mechanism involving a cyclic six‐membered, one water‐molecule transition state . The calculations further show that adding more water molecules in the transition state greatly increases the entropic demand with nominal decreases in the energy demand.…”

“…The general differential expression for the molar activation free energy in a cosolvent system is in which P is the pressure, T is the temperature, X is the mole fraction of the reference solvent, and ε is the isotropic relative permittivity. The first two right‐hand‐side terms are standard thermodynamic terms applicable to any system.…”

“…It can be shown that for systems in which the isomole fraction Eyring plots are precisely linear . Hence, this term is negligible (though not necessarily zero) for systems that exhibit linear isomole fraction plots.…”

“…These expressions are applied with the following considerations. First, detailed analysis shows that and are (essentially) independent of ε for systems that have linear isomole fraction plots . Hence, , , and .…”