Fast Initial Step

It is less straightforward to derive the rate law for a mechanism in which an intermediate is a reactant in the rate-deterrnining step. This situation arises in multistep mechanisms when the first step is fast and therefore not the rate-determining 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 14.13, this does not seem likely because termolecular processes are so rare. 

Why are termolecular elementary steps rare in gas-phase reactions  

---

The reaction rate is the rate of the elementary slow step Reaction rate = ksi0VI [AlB,] But B2 is a reaction intermediate whose concentration is difficult to determine. We can determine that concentration by assuming that the fast initial step goes equally rapidly in the forward and reverse directions. MB1-MB>1 [b.H aHb] ... 

Now we consider some very positive examples of this type of reaction sequence. Some organic molecules have weak C-H bonds that are easily broken. This fact has been exploited for some key industrial reactions. Some of these weak chemical bonds are hsted in Table 10-1. We will refer to these molecules and bonds throughout this chapter because weak bonds cause fast initiation steps in chain reactions. 

For example, the formation of living polymers allows the preparation of block polymers by sequential addition of monomers. It also permits the introduction of functional groups on the ends of each chain. From kinetic considerations of live polymer systems, it follows that, in a batch reaction, a fast initiation step relative to the propagation step will result in a very narrow molecular-weight distribution. It also follows that the molecular weight will be directly proportional to the mole ratio of initiator to monomer. 

A possible mechanism that includes a fast initial step is ... 

The fast initiation step is followed by an equally fast propagation reaction. While the rate constant of the former has been measured by Kunitake and Takarabe the dimerisation kinetics have not been measured for this particular system. The following slow reactions consist of the proton transfer between the dimeric cation and the monomer to gjve alternatively the unsaturated dimer or the indanylic one. Finally, the protonated dimer can isomerise to a more stable configuration due to the direct interaction of the two phenyl groups through space polarisation effects Thus ... 

Figure 6 schematically depicts the proton-promoted dissolution of hydrous oxides (e.g., A1203). In fast initial steps, the protons become bound to the surface hydroxyl groups or to the oxide ions closest to the metal center at the surface of the lattice. Subsequent to surface protonation, the detachment of the metal ion from the surface is the slowest of the consecutive steps. Therefore, the rate of the proton-promoted dissolution, RH, is proportional to the concentration (activity) of the surface species D(Fig. 6). 

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. 

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)... 

Figure 3 shows the kinetics of Ni sorption on pyrophyllite, kaolinite, gibbsite, and montmorillonite from a 3 mMNi solution at pH = 7.5 (16). For kaolinite and pyrophyllite relative Ni removal from solution follows a similar sorption trend with -90% Ni sorbed within the first 24 hours. At the end of the experiments, relative Ni removal from solution was almost complete (Ni/kaolinite system, 97% sorbed after 70 hours Ni/pyrophyllite system, 98% sorbed after 200 hours). Nickel sorption on gibbsite and montmorillonite exhibited a fast initial step. Thereafter, relative Ni removal from solution distinctively slowed down. Relative Ni sorption increased from 42-58% for the Ni/montmorillonite system (time range 0.5-7Q hours) and from 15-41% for the Ni/gibbsite system (time range... 

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. 

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. 

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. 

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). 

---