# A thermodynamic study of multiple reaction systems at and near equilibrium

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## Abstract

The near-equilibrium dynamic behavior of a homogeneous batch chemical reactor in which only one reaction occurs has been studied. The system has been analyzed thermodynamically and kinetically near equilibrium. The equations obtained have been linearized and then solved by means of Laplace transform techniques. The derivation for isobaric case has been presented in detail. The solutions for other cases, which include isothermal, isochoric, and adiabatic, have also been given. One numerical application indicates that the linearized equations can be useful even for protracted time intervals providing the forcing function is sufficiently small. A general expression for the displacement of extent of reactions and mole fractions for multiple reaction systems near equilibrium has been derived. The displacement of extent of reactions for a two-reaction system which obeys ideal solution laws under isobaric condition has also been given. A numerical example has been worked out. The result agrees with the one obtained by brute force approach. The condition for a multiple reaction system to obey LeChatelier's theorem is derived. It is shown that for the system to obey the theorem the matrix composed of Onsager phenomenological coefficients must be positive definite. Expressions for the initial distribution of reactants required to maximize a desired product or to suppress an undesired product of a system of chemical reactions proceeding toward equilibrium have been derived. The system consists of R independent reactions and behaves as an ideal solution. It is assumed that the initial feed contains only the reactants and no inerts are present. Three different cases have been considered. They are isothermal-isobaric, isothermal-isochoric and adiabatic-isobaric. The expressions are implicit and complex so that no direct conclusion can be deduced. However, a numerical example (methane-steam system) shows that the effect of initial feed on the distribution of the final product is significant and deserves attention.

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