Relaxation in catalytic reactions

Let us consider the catalytic isomerization reaction whose steady-state kinetic model has already been considered in the previous section. Its detailed mechanism is of the form (1) A + Z AZ (2) AZ = BZ (3) BZ B + Z. Under the assumption of constant concentrations of substances in the gas phase, it will be written as 

The set of equations (102) can be represented as a matrix. Elements of the whole of its columns have co-factors a, b and c, respectively. Dividing the columns by these 

It is just the characteristic eqn. (80) for a given case. Let us write the determinant of matrix (103) as a sum of the products for the elements of the first row with their algebraic complement 

It is interesting that the product of the characteristic roots is the sum of the whole of the trees in the graph for this reaction mechanism [see eqns. (60) and (64)]. 

One must remember one important thing. The values of X determining relaxation are not rate constants as such. In general, the characteristic roots X are rather complex functions of these constants. 

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