Reduction of Chemical and Rate Equations to an Independent Set

Definition of the Stoichiometric Matrix and Submatrices 1. The Complete Matrix 

It is not unusual to encounter a reacting system in which a given set of products may be obtained by more than one reaction path. In a simple 

The quantities involved in such a scheme are derived from the stoichiometric coefficients that appear in the chemical equations, the equations being written in such a form that the coefficients tell the number of moles of the substance in question produced by one mole of the reaction. 

A familiar example of multiple reaction paths is the catalytic oxidation of ethylene to ethylene oxide, where the by-products water and carbon dioxide are produced both by direct oxidation of ethylene and by further oxidation of ethylene oxide. For this example, the equations may be written in the form 

The array of coefficients on the right-hand side of the equations is manipulated as a matrix, which may be denoted as S, the matrix of stoichiometric coefficients. In the example, 

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