Characteristics of Chain Reactions

There are two classes of chain reactions. In one, the rate law leads directly to the elemental composition and charge of the transition state, just as for nonchain reactions. In 

Two examples are (1) the thermal, gas-phase decomposition of acetaldehyde at high temperatures and (2) the reaction of the hydrated 2-propylchromium ion with molecular oxygen in aqueous solution. The reactions and their rate laws are as follows  

Clearly, neither rate expression yields to the ordinary interpretation. Transition states with a nonintegral number of atoms or a fractional ionic charge cannot exist (not that the one represented by Eq. (8-4) is fractional, but others we shall see would be). These reactions are believed to proceed by chain mechanisms. 

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One characteristic of chain reactions is that frequentiy some initiating process is required. In hydrocarbon oxidations radicals must be introduced and to be self-sustained, some source of radicals must be produced in a chain-branching step. Moreover, new radicals must be suppHed at a rate sufficient to replace those lost by chain termination. In hydrocarbon oxidation, this usually involves the hydroperoxide cycle (eqs. 1—5). 

The degree of polymerization is controlled by the rate of addition of the initiator. Reaction in the presence of an initiator proceeds in two steps. First, the rate-determining decomposition of initiator to free radicals. Secondly, the addition of a monomer unit to form a chain radical, the propagation step (Fig. 2) (9). Such regeneration of the radical is characteristic of chain reactions. Some of the mote common initiators and their half-life values are Hsted in Table 3 (10). 

Another characteristic of chain reactions is that they generate minorproducts (C2H6 and CHO ) as well as the major products (CO and CH4). The major products are made by the propagation steps and the minor products by the initiation and termination steps. In fact, the ratio of CH4 to C2H gives the ratio of rp to r, ... 

The subject of this chapter has been the peculiar characteristics of chain reactions. This is a very common type of chemical reaction, which chemical engineers need to be able to handle and to be aware of how different a chain reaction can be than an ordinary reaction, A —> products, r = kCA, its variants. Chain reactions are involved in autooxidation and in combustion, the subjects of this chapter, and also in polymerization, the subject of the next chapter. 

A substance that slows down or stops a reaction even though present in small amount is called an inhibitor. The period of time during which inhibition lasts, and after which the reaction proceeds normally, is called the inhibition period. Inhibition by a relatively small amount of an added material is quite characteristic of chain reactions of any type, and is often one of the clues that first leads us to suspect that we are dealing with a chain reaction. It is hard to see how else a few molecules could prevent the reaction of so many. (We shall frequently encounter the use of oxygen to inhibit free-radical reactions.)... 

Nonlinear mechanisms are very common in heterogeneous catalytic reactions. They are also characteristic of chain reactions and, perhaps, of homogeneous catalysis involving metal complexes. Because of this, the classification of these mechanisms is of considerable interest. 

The complexity of the actual mechanisms of homogeneous catalytic reactions is seen also from the different activities of catalysts at the initial and subsequent reaction times (see Section XI.38). This specific feature of the activity of homogeneous catalysts is characteristic of chain reactions (see Chapter XI) with their complicated chemical mechanisms. It will also be noted that in many reactions the part played by a homogeneous catalyst usually is initiation of the reaction, i.e. generation of active intermediates. Sometimes, the catalyst not only accelerates the reaction but also alters its path, i.e. causes preferential generation of some species. 

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