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

Author(s): R. R. Farias, L. A. M. Cardoso, N. M. Oliveira Neto

Journal: Exatas Online
ISSN 2178-0471

Volume: 2;
Issue: 2;
Start page: 7;
Date: 2011;
Original page

Keywords: Monte Carlo | Chemical Reaction | Equilibrium | Metropolis.

A simple theoretical model to describe equilibrium properties of homogeneous re-versible chemical reactions is proposed and applied to an A ⇋ B type reaction. Forthis purpose the equilibrium properties are analyzed by usual Monte Carlo simula-tion. It is shown that the equilibrium constant (Ke ) for this kind of reaction exhibitsdistinct characteristics for Eba < 1, Eba = 1 and Eba > 1, where Eba is the ratio be-tween the reverse and forward activation energies. For Eba < 1 (Eba > 1) and increase(decrease) the temperature our results recover the principle of Le Chˆtelier applied ato temperature effects. The special and interesting case is obtained for Eba = 1 sinceKe = 1 for all range of temperature. Another important parameter in our analysisis θA , defined as temperature measured with relation the activation energy of theforward reaction. For fixed values of Eba and for θA ≫ 1 the equilibrium constantapproaches 1, showing that all transitions are equally likely, no matter the differencein the energy barriers. The data obtained in our simulations show the well knownrelationship between Ke , Eb , Ea and kB T . Finally we argue that this theoreticalmodel can be applied to a family of homogeneous chemical reactions characterizedby the same Eba and θA showing the broad application of this stochastic model tostudy chemical reactions. Some of these results will be discussed in terms of collisiontheory.

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