The Stationary-state Hypothesis Chain Reactions

Let us consider the simplest possible case of a system of consecutive reactions involving two intermediates, namely 

Such reactions are not important unless E, which has the same composition as A, is a distinguishable isomer. In such cases B is, in effect, a catalyst for the isomerization of A (e.g., Walden inversions and ortho- to para-H conversion). 

Equations (III.9.6) imply that there is no time lag, or there is at least a negligible time lag, between the destruction of the individual reactants A and C and the appearance of the product P. By combining this condition with Eqs. (III.9.2) and (III.9.4) it leads to the further condition that dM. /dt and dM-t/di are also negligibly small and effectively zero. 

If we make use of this result by setting these rates equal to zero in the chain equations (III.9.3), we can solve the equations as a amultaneous set of algebraic equations for the concentrations of Mi and M2. From the second of the two equations we find 

Equation (III.9.11) can be integrated directly by means of the substitution (Ao — x) = if, and we finally obtain 

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