A Simple Model to Access Equilibrium Constants of Reactions Type A ⇋ B Using Monte Carlo Simulation

Abstract

A simple theoretical model to describe equilibrium properties of homogeneous reversible chemical reactions is proposed and applied to an A ⇋ B type reaction. For this purpose the equilibrium properties are analyzed by usual Monte Carlo simulation. It is shown that the equilibrium constant (Ke) for this kind of reaction exhibits distinct characteristics for Eba < 1, Eba = 1 and Eba > 1, where Eba is the ratio between the reverse and forward activation energies. For Eba < 1 (Eba > 1) and increase (decrease) the temperature our results recover the principle of Le Chˆatelier applied to temperature effects. The special and interesting case is obtained for Eba = 1 since Ke = 1 for all range of temperature. Another important parameter in our analysis is θA, defined as temperature measured with relation the activation energy of the forward reaction. For fixed values of Eba and for θA ≫ 1 the equilibrium constant approaches 1, showing that all transitions are equally likely, no matter the difference in the energy barriers. The data obtained in our simulations show the well known relationship between Ke, Eb, Ea and kBT. Finally we argue that this theoretical model can be applied to a family of homogeneous chemical reactions characterized by the same Eba and θA showing the broad application of this stochastic model to study chemical reactions. Some of these results will be discussed in terms of collision theory.