Mechanisms with a Fast Initial Step

When the proposed mechanism for a reaction has a slow initial step— Uke the one shown previously for the reaction between NO2 and CO—the rate law predicted by the mechanism normally contains only reactants involved in the overall reaction. However, when a mechanism begins with a fast initial step, some other subsequent step in the mechanism is the rate-limiting step. In these cases, the rate law predicted by the rate-limiting step may contain reaction intermediates. Since reaction intermediates do not appear in the overall reaction equation, a rate law containing intermediates cannot generally correspond to the experimental rate law. Fortunately, however, we can often express the concentration of intermediates in terms of the concentrations of the reactants of the overall reaction. 

In a multistep mechanism where the first step is fast, the products of the first step may build up, because the rate at which they are consumed is limited by some slower step further down the line. As those products build up, they can begin to react with one another to re-form the reactants. As long as the first step is fast enough compared to the rate-limiting step, the first-step reaction will reach equilibrium. We indicate equilibrium as follows  

The double arrows indicate that both the forward reaction and the reverse reaction occur. If equilibrium is reached, then the rate of the forward reaction equals the rate of the reverse reaction. 

As an example, consider the reaction by which hydrogen reacts with nitrogen monoxide to form water and nitrogen gas  

The experimentally observed rate law is Rate = fc[H2][NO]. The reaction is first order in hydrogen and second order in nitrogen monoxide. The proposed mechanism has a slow second step  

It is possible, but not particularly straightforward, to derive the rate law for a mechanism in which an intermediate is a reactant in the rate-determining step. This situation arises in multistep mechanisms when the first step is fast and therefore not the ratedetermining step. Let s consider one example the gas-phase reaction of nitric oxide (NO) with bromine (Br2)  

The experimentally determined rate law for this reaction is second order in NO and first order in Br2  

We seek a reaction mechanism that is consistent with this rate law. One possibility is that the reaction occurs in a single termolecular step  

As noted in Practice Exercise 2 of Exercise 14.13, this does not seem likely because termolecular processes are so rare. 

Why are termolecular elementary steps rare In gas-phase reactions  

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Mechanisms with a Fast Initial Step If the rate-determining step in a mechanism is not the initial step, it acts as a bottleneck later in the reaction sequence. As a result, the product of a fast initial step builds up and starts reverting to reactant, while waiting for the slow step to remove it. With time, the product of the initial step is changing back to reactant as fast as it is forming. In other words, fast initial step reaches equilibrium. As you ll see, this situation allows us to fit the mechanism to the overall rate law. 

Deriving the Rate Law for a Mechanism with a Fast Initial Step... 

Analyze We are given a mechanism with a fast initial step and asked to write the rate law for the overall reaction. 

For mechanisms with a fast initial step, we first write the rate law based on the slow step bnt then assume that the fast steps reach equilibrium, so we can write concentrations of intermediates in terms of the reactants. 

Thus, to test the validity of a mechanism with a fast initial, reversible step ... 

Understand elementary steps and molecularity, and be able to construct a valid reaction mechanism with either a slow or a fast initial step ( 16.7) (SP 16.8) (EPs 16.53-16.64)... 

The above classification of polymers according to polymerization mechanism, as shown by the variation of molecular weight with conversion [Figs. 1.2(a) and 1.2(b)], is not without its ambiguities. Certain polymerizations show a linear increase of molecular weight with conversion [Fig. 1.2(c)] when the polymerization mechanism deviates from the normal chain or step pathway. This is observed in certain ionic chain polymerizations, which involve a fast initiation process coupled with the absence of reactions that terminate the propagating reactive centers. Biological syntheses of proteins also show the behavior described by Fig. 1.2(c) because the various... 

Based on the preceding NMR spectra, a pre-equilibrium exists between the borane initiator and ylide that strongly favors formation of the zwitterionic complex 7. The preequilibrium is established immediately and complex 7 is stable at — IS C. These results are consistent with the proposed mechanism of a fast pre-equilibrium followed by a rate-limiting 1,2-migration step since homologation was observed only after warming above 0°C (Busch et al, 2002). 

The transition states of the E2 and ElcB mechanisms are represented in Fig. 37.3 together with the KIEs that should be observed in each case. Just by comparing the three transition states, it becomes clear that no primary D KIE should be observed in the (E1cB)r mechanism, as the proton has been already removed. As the experimental fact is a clear primary D KIE at C3, the EIcBr mechanism must be discarded. Additionally it is an experimental fact that no H/D exchange with the solvent has been observed in the elimination of substrates 1. Solvent H/D exchange is indicative for an EIcBr mechanism where the carbanion is reprotonated by the solvent in the fast initial step (see equation C in Scheme 37.2). 

On the basis of these correlations, Gold and Satchell463 argued that the A-l mechanism must apply (see p. 4). However, a difficulty arises for the hydrogen exchange reaction because of the symmetrical reaction path which would mean that the slow step of the forward reaction [equilibrium (2) with E and X = H] would have to be a fast step [equivalent to equilibrium (1) with E and X = H] for the reverse reaction, and hence an impossible contradiction. Consequently, additional steps in the mechanism were proposed such that the initial fast equilibrium formed a 7t-complex, and that the hydrogen and deuterium atoms exchange positions in this jr-complex in two slow steps via the formation of a a-complex finally, in another fast equilibrium the deuterium atom is lost, viz. 

In the first step an S03 molecule is inserted into the ester binding and a mixed anhydride of the sulfuric acid (I) is formed. The anhydride is in a very fast equilibrium with its cyclic enol form (II), whose double bonding is attacked by a second molecule of sulfur trioxide in a fast electrophilic addition (III and IV). In the second slower step, the a-sulfonated anhydride is rearranged into the ester sulfonate and releases one molecule of S03, which in turn sulfonates a new molecule of the fatty acid ester. The real sulfonation agent of the acid ester is not the sulfur trioxide but the initially formed sulfonated anhydride. In their detailed analysis of the different steps and intermediates of the sulfonation reaction, Schmid et al. showed that the mechanism presented by Smith and Stirton [31] is the correct one. 

The kinetics of the coupling mechanism include a number of sometimes very fast and competitive side reactions. The following steps, for instance, proceed simultaneously as a separately prepared diazonium salt solution is combined with an initially dissolved coupling component ... 

A very interesting and complex protonation mechanism has been snggested for the hydride cluster [W3S4H3(dmpe)3]PF6 in CH2CI2 solutions. In the presence of an excess of HCl, a careful kinetic study of the process in eq. (10.4) by the stopped-flow technique [9] has revealed three kinetically distinguishable steps very fast, fast, and slow, with rate constants A 1, ki, and k3. The kinetic order in the initial hydride cluster in the slow step has been measured as 1. At the same time, rate constants k and A 2 have corresponded to a second-order dependence on acid concentration, while the third step has shown a zero kinetic order on HCl. The rate constants have been determined as A i =2.41 x 10 M-2/s, k2 = 1.03 X 10 M /s, A 3 = 4 X 10 s . Note that the protonation process becomes simple at lower concentrations of HCl. Under these conditions it shows a single step with a first kinetic order on the acid. 

Free radical polymerization A process with a complex mechanism of initiation, propagation, and termination, of which the propagation and termination steps are typically very fast. 

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