Reactivity of the rate-determining step

In what follows, ( )y will denote the reactivity of a step y in a system determined by step i. 

As previously, we will reason on the same linear chain. 

According to the previous theorem, the reactivity of each step has an indeterminate form 0.°o except that of the determining step i, which is written as follows  

By referring to the concentration expressions [8.12] and [8.15], and by taking into account relations of definitions of multiplying coefficients  

As all other reactivities are at equilibrium, for the reactivity of step / we obtain  

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Reactivity of the rate-determining step in pure mode... 

We see on this expression that, if the intensive variables of the reaction (temperature, partial pressures of gases, concentrations of the main reactants and products) are maintained constant, the various rate factors are independent of time and thus the reactivity remains constant. We can conclude that in pure mode, the reactivity of the rate-determining step can depend on the time only if the intensive variables vary with time. 

It is checked that the reactivity of the rate-determining step calculated by this method always has the stmeture of relation [7.42] ... 

Remark.- The product of the first two terms, in fact, expresses the reactivity of the rate-determining step considered as occurring only from left to right, that is, far from equilibrium. 

Theorem.- In a pure mode, the rate of the reaction is the product, balanced by the reverse of the multiplying coefficient, of the reactivity of the rate-determining step (other steps being at equihbrium) and the space function relating to the zone where the rate-determining step proceeds. 

Remark.- We can also check that, if the two space functions are constantly equal to each other, the reactivities of the rate-determining steps are independent of time. For example, applying relation [7.59], for the reactivity of step i for the pseudo-steady state mixed mode i, j we obtain ... 

In this case the rate is the product of the reactivity of the rate-determining step by its space function, divided by its multiplying coefficient the rate has the form [7.43] ... 

Within the fiamewoik of the formation of a sohd MG starting from gas G2, the multiplying coefficients of the steps of adsorption, external interface, and internal interface are I/2, 1, and 1, respectively, from which the reactivities in pure modes according to the reactivities of the rate determining step are ... 

To establish the reactivity in each pme mode, we calculate the fraction of free site 9 and the defect concentration in carbonate by using the law of mass action applied at the two non-rate-determining steps and substitute these expressions into the reactivity of the rate-determining step. The used equations are gathered in Table 19.18 and we obtain the expressions in Table 19.19. 

For alkyl-substituted alkynes, there is a difference in stereochemistry between mono-and disubstituted derivatives. The former give syn addition whereas the latter react by anti addition. The disubstituted (internal) compounds are considerably ( 100 times) more reactive than the monosubstituted (terminal) ones. This result suggests that the transition state of the rate-determining step is stabilized by both of the alkyl substituents and points to a bridged intermediate. This would be consistent with the overall stereochemistry of the reaction for internal alkynes. 

The question of the rate-determining step in the Chichibabin reaction is still open. Clearly, it is difficult to expect that such a complex process can be controlled by any single parameter. On the basis of the rate of hydrogen gas evolution, the following sequence of the reactivity of aza-heterocyclic compounds has been established 1-R-benzimidazoles > isoquinoline > 1-R-perimidines > benzo[/]quinoline > pyridine acridine. Evidently, this raw indicates that sodamide amination depends on number of factors, involving electron deficiency of the substrate C(a)-atom, ease of the adduct aromatization, substrate basicity, etc. Evidently, acridine s position in this raw reflects the difficulty of the y-amination. 

Since organic reactivity in water depends crucially on the hydration of reactants and the activated complex of the rate-determining step, some important aspects will be discussed in more detail below. 

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