Rate-controlling step, chain reaction sequence

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. 

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 PTOC carbamate method for efficient and controlled generation of aminyl radicals allows kinetic studies that previously were not possible with tetrazene precursors. As is the case with carbon radicals, optimum synthetic utility of chain reaction sequences is found when absolute rate constants or ratios of rate constants for competing reactions are known, i.e., Scheme 8, step D vs step E. If an absolute rate constant is known for one reaction, then other absolute rate constants can be determined for other reactions from the product distributions in competitions of the reactions of interest with the reaction with a known rate constant. 

At the beginning of this chapter it was stated that reaction sequences involving surface steps [such as (XXV)], could be visualized as a type of chain reaction. This is indeed so, and we shall have more to say concerning the analysis of surface reactions via the pssh a little later on. However, also associated with the development of the theory of surface reaction kinetics has been the concept of the rate-limiting or rate-controlling step. This presents a rather different view of sequential steps than does pure chain reaction theory, since if a single step controls the rate of reaction then all other steps must be at equilibrium. This is a result that is not a consequence of the general pssh. 

A biochemical pathway can be compared to an assembly line in which a skeletal structure is progressively adorned with new conveniences. In passing from one step of a metabolic pathway to the next, the product of the first reaction becomes the substrate of the second. Normally, the skeleton (first substrate in the chain of reactions) is converted to the finished product (last product in the sequence of reactions) at a steady pace. When the conditions of the environment change in such a way that the requirements for the finished product are either greater or smaller, then the pace of the entire pathway changes. A control mechanism could hardly accelerate or decelerate simultaneously all the steps of the pathway and maintain them in synchrony therefore, the control of a metabolic pathway often acts at one step. The rate of a single reaction of the sequence is expressed by the amount of product that is formed at the expense of the substrate in a unit of time. The conversion of the substrate to the product is a function of the concentrations of substrate, cofactor, activator, inhibitor, etc. 

Although reaction (3.61) is endothermic and its reverse step reaction (-3.61) is faster, the competing step reaction (3.63) can be faster still thus the isomerization [reaction (3.61)] step controls the overall rate of formation of ROO and subsequent chain branching. This sequence essentially negates the extent of reaction (-3.48). Thus the competition between ROO and olefin production becomes more severe and it is more likely that ROO would form at the higher temperatures. 

Autocatalytic reactions in closed, homogeneous systems characteristically start slowly or at imperceptible speeds, accelerate to a maximum rate and then subside until all the material has been transformed. The most deeply studied example is the explosively rapid reaction between oxygen and hydrogen for which the observed rate is the consequence of a network of elementary steps with linear chain-branching. The acceleratory phase is dominated by the sequence HO + H2 -> H2O + H H + 02-> j O+H2 HO + H. The second of these three steps is the slowest, and at low temperatures it controls the rate. The overall stoichiometry corresponds to ... 

---