Reaction rate determined by a single step

When the overall rate of a multistep reaction is determined solely by a single elementary step whose rate is extremely small compared with the rates of the other elementary steps, the multistep reaction is called the reaction of a single rate-determining step. In such a multistep reaction, as shown in Fig. 7-11 (a), all the elementary steps except for the rate-determining step are cmisidered to be in quasi-equilibrium. Note that the multistep reaction of a sin le rate-determining step is rather uncommon in practice. 

With a single rate-determining step, the affinity of elementary steps other than the rate-determining step is negligible, and the overall reaction affinity — AG approximately equals the affinity - 4gr multiplied by the stoichiometric number of the rate-determining step in Eqn. 7-44 as has been shown in Eqn. 

We then obtain from Eqn. 7-45 the overall reaction rate vr = v -vj as expressed in Eqn. 7-46  

In the regime of affinity close to the equilibrium (-AG - 0), Eqn. 7-46 gives the approximate equation in Eqn. 7-47  

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