No Rate-Controlling Step

The diacyl peroxide-amine system, especially BPO-DMT or BPO-DMA, has been used and studied for a long time but still no sound initiation mechanism was proposed. Some controversy existed in the first step, i.e., whether there is formation of a charge-transfer complex of a rate-controlling step of nucleophilic displacement as Walling 1] suggested ... 

Also, the rates of the propagation steps are equal to one another (see Problem 8-4). This observation is no surprise The rates of all the steps are the same in any ordinary reaction sequence to which the steady-state approximation applies, since each is governed by the same rate-controlling step. The form of the rate law for chain reactions is greatly influenced by the initiation and termination reactions. But the chemistry that converts reactant to product, and is presumably the matter of greatest importance, resides in the propagation reactions. Sensitivity to trace impurities, deliberate or adventitious, is one signal that a chain mechanism is operative. 

Case (b) Reaction E(b) is sufficiently fast then a chemical reaction subsequent to the electrode reaction, C(b), is either an equilibrium or rate-controlling step. If E(b) is sufficiently slow, then C(b) has no effects whatever its rate. 

In the above series of reactions, the slow reaction involving N2O2 is the rate-controlling step. The reaction involving NO is fast enough to maintain equilibrium with the N2O2. Consequently, it can be seen that the rate of production of Nj and H2O is third order with respect to NO and H2. The overall sum of these reaction steps is indeed third order, while the elementary reactions are all bimolecular, i. e., second order. 

Radical chain processes break down whenever the velocity of a termination reaction is comparable to the velocity of the rate-controlling step in a chain reaction. This situation would occur, for example, if one attempted to use EtsSiH as the hydrogen atom donor in the alkyl halide reduction sequence in Figure 4.6 and employed typical tin-hydride reaction conditions because the rate constant for reaction of the silane with an alkyl radical is 4 orders of magnitude smaller than that for reaction of Bu3SnH. Such a slow reaction would not lead to a synthetically useful nonchain sequence, however, because no radical is persistent in this case. In fact, a silane-based radical chain reduction of an alkyl halide could be accomplished successfully if the velocity of the initiation reaction was reduced enough such that it (and, hence, also the velocity of alkyl radical termination... 

The hydrolysis rate of all three enamines (1-3) undergoes a sharp decline as the pH drops below 1 (for 2 and 3) or 0 (for 1). This result signifies that equation 23 (or 23a) is no longer the rate law and that another change in rate-controlling step has occurred. The last stage of Scheme 1 is the breakdown of the carbinolamine, equations 17-19. At the acidities in question (pH < 1), equations 14-17 are in equilibrium, that is, the enamine is fully protonated ([EH+] = [NH+] + [CH+], see Table 2) as is the hydration product, the carbinolamine72. Equation 24 describes the situation. The observed inverse... 

The overall reaction involves five reactant molecules, but it is by no means necessarily of fifth order. Indeed the rate-controlling step in this proposed mechanism is bimolecular, and the overall reaction order predicted by the mechanism is It is also important to note that this mechanism is not the only one that would predict the above - -order rate law for the given overall reaction thus experimental verification of the predicted rate law would by no means constitute proof of the validity of the above proposed mechanism. 

Contrary to what is true for pathways with no reversible steps, fast reversible steps preceding the rate-controlling step do affect the rate of product formation. The rate depends on the equilibrium constants of such steps and thus on the ratios of their forward and reverse rate coefficients. Specifically, equilibria favoring the reverse reaction reduce the rate. 

Example 4.4. Nitration of aromatics of intermediate reactivity. In Example 4.1 the concept of a rate-controlling step was used to obtain simple rate equations for nitration of aromatics of either low or high reactivity. For aromatics of intermediate reactivity, no single step is rate-controlling. However, if the concentrations of H2N03+, NOz+, and ArN02+ in the pathway 4.6 remain at trace level—this is a judgment call—the Bodenstein approximation can be applied repeatedly to obtain an explicit, closed-form rate equation. 

In acid-base catalysis, both an acid (or base) and its conjugate base (or acid) take part in different reaction steps and are eventually restored. Such reactions are first order in acid (or base) if the link-up with that species controls the rate, or first order in H+ (or OH") if a subsequent step involving the conjugate base (or acid) does so. Traditionally, the first alternative is called "general" acid or base catalysis the second, "specific" acid or base catalysis. However, this distinction is not always applicable as there may be no clear-cut rate-controlling step, and reversibility of later steps may produce a more complex behavior. 

Kaufman and Decker [303] considered the rate controlling step in the reaction to be the reduction of NO to N2O, after which the more rapid steps associated with the propagation mechanism in the H2 + N2O system could take place. The mechanism has been further investigated by Wilde [299] using computer modelling techniques. The principal elementary steps contributing to the first stage, i.e. the removal of NO, are probably reactions (—xxix), (xxviii), (xlvii) and (i), with contributions also from reaction (xlvi) and the forward reaction (xxix), viz. 

Additional studies [212,218,219,242,243] to quantitate the role of the adenine nucleotide translocator in the control of mitochondrial respiration have been performed utilizing inhibitor titrations with carboxyatractyloside. The results indicated that in State 4 (no ADP), no control was exerted by the translocator. However, as the rate of respiration was increased up to State 3 (excess ADP), the control strength of the carrier increased to a maximum value of 30%, at 80% of State 3 respiration. These studies indicate that the adenine nucleotide translocator cannot be considered to be the only rate-controlling step in oxidative phosphorylation. However, they do provide experimental support for a controlling role for the carrier at intermediate to maximal levels of respiration. An important corollary of these studies is that the reaction rate may be altered by a change in substrate concentration (elasticity). It is also clear that to confirm these studies quantitatively, they must be extended to intact cells. Although such studies have been more difficult, the results are compatible with the conclusion reached by Tager et al. [212]. 

Ingold , however, argued in favour of a rate-controlling step involving halogen heterolysis, but no hydrogen loosening of any kind . 

Figure 11 2. Nitration. Formation of carbonium ion is rate-controlling step occurs equally rapidly whether protium (H) or deuterium (D) at point of attack. All carbonium ions go on to product. There is no isotope effect, and nitration is irreversible.

The first elementary reaction is the rate-controlling step, because it is the slow step. The second elementary reaction is fast and does not affect the overall reaction order, which is second order as a result of the fact that the rate-controlling step is bimolecular. rate = [NO][Br2]... 

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