General Formulas for Mechanisms and Reactions

Equation (7) characterizes a steady-state mechanism algebraically, but it does not provide an explicit formula for any such mechanism. Therefore, using only the matrix (2) of elementary reaction coefficients and the knowledge of which columns in the matrix correspond to terminal species, let us derive a general formula for any steady-state mechanism. 

The basis s. ss for the mechanism space will be changed to one which contains H non-steady-state mechanisms and P steady-state mechanisms. The latter will be what Temkin (16) calls a basis for all routes. A route is what we are calling a steady-state mechanism, and a basis is a maximal linearly independent set of them. The basis is stoichiometric in Temkin s 

To construct the new basis, described above, we will change the basis st,. .., ss of the S-dimensional space of all mechanisms into a basis (9), which separates into 3 parts, 

Basic Overall Reactions, Steady-State Mechanisms, and Cycles 

An explicit basis for the space of overall reactions is characterized by rows H + 1 through Q of the diagonalized matrix of Fig. 1. If the matrix is expressed by (Pu), then the desired basis is 

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