Systems with a Simple Overall Reaction

Most systems treated in the literature exhibit a simple overall reaction, which can be uniquely represented by a conventional chemical equation. In addition, the elementary reactions are usually selected so that all of them must be combined to form the overall reaction, which means that the system is cycle free and that there is no mathematical distinction between an elementary reaction and the step which produces it. Often the combination of steps giving the overall reaction is such that each intermediate is produced by exactly one step and consumed by exactly one step. The following example illustrates such a system. 

The important commercial process of sulfur dioxide oxidation has been studied by a number of investigators. A set of steps that has been proposed for both platinum and vanadium oxide-based catalysis by Horiuti (7) for the overall reaction 2SOz + 02 2SOs is as follows  

This is the form in which steps will be listed in all our examples—a symbol 

This displays the convention, tacitly assumed later, that the positive direction of a step corresponds to the advancement from left to right of the stated chemical equation. The matrix of stoichiometric coefficients for these reactions is shown in Table II. The diagonalization of the matrix in Table II gives the matrix in Table III, from which the steady-state mechanism is S + 2s2 + 2s3 + 2s4. In Horiuti s terminology the stoichiometric numbers are 1 for Sj and 2 for s2, s3, and s4. 

even in the case of simple reactions, it is possible to encounter systems with cycles. The following is an illustration of this situation. 

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