The expected time to attain chemical equilibrium from a thermodynamic probabilistic analysis

Abstract

Employing a stochastic model, both Planck and Fokker proposed almost a century ago that stoichiometric chemical reactions proceed by a chain mechanism involving discrete reaction steps. To determine whether such a chain mechanism was in fact a valid mechanism for chemical reactions was the subject of a recent study (Garfinkle, M. 2002. J. Phys. Chem. 106A: 490). Using a thermodynamic–probabilistic algorithm the stochastic reaction paths were found to be in excellent agreement with the observed reaction paths plotted from experimental data. This study was then extended to test the conclusions of Ehrenfest and Prigogine that a chain mechanism dictates that the number of discrete reaction steps required for a chemical reaction to attain equilibrium must be finite. The stochastic and empirical reaction paths were compared using experimental data for first-, second-, and third-order reactions as well as fractional order reactions. The empirical verification was excellent.