Mechanisms with a Slow Initial Step

We can most easily see the relationship between the slow step in a mechanism and the rate law for the overall reaction by considering an example in which the first step in a multistep mechanism is the rate-determining step. Consider the reaction of NO2 and CO to produce NO and CO2 (Equation 14.23). Below 225 °C, it is found experimentally that the rate law for this reaction is second order in NO2 and zero order in CO Rate = /c[N02]. Can we propose a reaction mechanism consistent with this rate law Consider the two-step mechanism  

Step 2 is much faster than step 1 that is, /c2 /cj, telling us that the intermediate NOs( ) is slowly produced in step 1 and immediately consumed in step 2. 

Because step 1 is slow and step 2 is fast, step 1 is the rate-determining step. Thus, the rate of the overall reaction depends on the rate of step 1, and the rate law of the 

the rate law predicted by this mechanism agrees with the one observed experimentally. The reactant CO is absent from the rate law because it reacts in a step that follows the rate-determining step. 

A scientist would not, at this point, say that we have proved that this mechanism is correct. All we can say is that the rate law predicted by the mechanism is consistent with experiment. We can often envision a different sequence of steps that leads to the same rate law. If, however, the predicted rate law of the proposed mechanism disagrees with experiment, we know for certain that the mechanism cannot be correct. 

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Mechanisms with a Slow Initial Step We ve already seen one mechanism with a rate-determining first step—that for the reaction of NO2 and CO. Another example is the reaction between nitrogen dioxide and fluorine gas ... 

Mechanisms with a Slow Initial Step The reaction between NO2 and CO that we considered earlier has a mechanism with a slow initial step that is, the first step is rate-determining. The reaction between nitrogen dioxide and fluorine is another... 

For mechanisms with a slow initial step, we derive the rate law from the slow step. 

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. 

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. 

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. 

The polymerization occurs by the activated monomer mechanism, which supposes a two-step mechanism involving the acylation of the lactam anion (NaL) by the AT-acyllactam end-group followed by a fast proton-exchange with the monomer. In bulk polymerization, the preformed AT-acyllactams or their precursors (so-called CIs) are introduced into the system in order to avoid the slow initiation step due to the absence of AT-acyllactam groups at the beginning of polymerization ... 

The reported data are in agreement with the mechanism of H.M.A. formation reported in the literature (15,15,19) and can be understood on the basis of a slow initial growth step and a rate of growth favoured by the increase of the CO partial pressure. 

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 slow initiation step can be rationalized by a mechanism involving [2+2] cycloaddition of the olefin at the Ru=C bond of the vinylidene ligand, with generation of a new Ru carbene species able to propagate faster polymerization (Scheme 14). This mechanism has been documented by Ozawa" for ROMP of norbomene with [RuCl2(PPh3)2(=C=CHFc)] (Fc = ferrocenyl) and by Kirchner in a stoichiometric reaction using a Tp-coordi-nated Ru complex (Tp = tris(pyrazolyl)borohydride)." ... 

Figure 6.2 Effect of preincubation time with inhibitor on the steady state velocity of an enzymatic reaction for a very slow binding inhibitor. (A) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the single-step binding mechanism of scheme B of Figure 6.3. (B) Preincubation time dependence of velocity in the presence of a slow binding inhibitor that conforms to the two-step binding mechanism of scheme C of Figure 6.3. Note that in panel B both the initial velocity (y-intercept values) and steady state velocity are affected by the presence of inhibitor in a concentration-dependent fashion.

Bond energy considerations indicate that the initiation reaction (4.2.2) should be quite slow because its activation energy must be quite high (at least equal to the bond dissociation energy). If one were dealing with an open sequence reaction mechanism, such a step would imply that the overall reaction rate would also be low because in these cases the overall reaction becomes approximately equal to that of the rate limiting step. In the case of a chain reaction, on the other hand, the overall reaction rate is usually much faster because the propagation steps occur many times for each time that an initiation step occurs. 

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