Nonelementary reaction

Chapter 1 treated single, elementary reactions in ideal reactors. Chapter 2 broadens the kinetics to include multiple and nonelementary reactions. Attention is restricted to batch reactors, but the method for formulating the kinetics of complex reactions will also be used for the flow reactors of Chapters 3 and 4 and for the nonisothermal reactors of Chapter 5. 

Note that the Roman numeral subscripts refer to numbered reactions and have nothing to do with iodine. All these examples have involved elementary reactions. Multiple reactions and apparently single but nonelementary reactions are called complex. Complex reactions, even when apparently single, consist of a number of elementary steps. These steps, some of which may be quite fast, constitute the mechanism of the observed, complex reaction. As an example, suppose that... 

Reactions for which the rate equations follow the stoichiometry as given in Equations 5.23 to 5.26 are known as elementary reactions. If there is no direct correspondence between the reaction stoichiometry and the reaction rate, these are known as nonelementary reactions and are often of the form ... 

When there is no direct correspondence between stoichiometry and rate, then we have nonelementary reactions. The classical example of a nonelementary reaction is that between hydrogen and bromine. 

Nonelementary reactions are explained by assuming that what we observe as a single reaction is in reality the overall effect of a sequence of elementary reactions. The reason for observing only a single reaction rather than two or more elementary reactions is that the amount of intermediates formed is negligibly small and, therefore, escapes detection. We take up these explanations later. 

A nonelementary reaction is one whose stoichiometry does not match its kinetics. For example. 

To explain the kinetics of nonelementary reactions we assume that a sequence of elementary reactions is actually occurring but that we cannot measure or observe the intermediates formed because they are only present in very minute quantities. Thus, we observe only the initial reactants and final products, or what appears to be a single reaction. For example, if the kinetics of the reaction... 

A large difference in the order of magnitude between the experimentally found frequency factor of a reaction and that calculated from collision theory or transition-state theory may suggest a nonelementary reaction however, this is not necessarily true. For example, certain isomerizations have very low frequency factors and are still elementary. 

Thus we search for the approximate solution for the single nonelementary reaction A —> C, which proceeds through the reaction intermediate B in the two preceding reactions. We of course know the exact solution in batch, PFTR, and CSTR This will allow us to test... 

Following these guidelines, it is often possible to distinguish between elementary and nonelementary reactions. However, there are classes of elementary reactions that do involve breakage of and/or formation of more than one chemical bond. For this reason it can be a difficult task to determine whether a reaction is an elementary step or a multi-step reaction. 

In nonelementary reactions, the reaction order and stoichiometric coefficients are different. A single reaction is observed, but in reality a sequence of elementary reactions occurs. The amount of intermediates formed is negligible and, therefore, not detectable. One famous example is the reaction between hydrogen and bromine. The overall reaction can be described as ... 

However, the following chain of reactions occur, which explains the nonelementary reaction ... 

As an example, consider the reaction A + B —> C, and let us assume that this is a nonelementary reaction. The rate equation in this case is Eq. (2.53), and we must find the values of a, p, and k. We do this by designing experiments in a way that isolates the contribution of each reactant to the initial rate, as shown in Table 2.1. 

One more comment seems necessary. The Arrhenius expression [Eq. (32)] is commonly used to describe the rates of nonelementary reactions including several steps. In this case, the measured value of A is the apparent (global) activation energy, which is the resultant of sums and differences (with some coefficients) of activation energies of elementary steps whose rates contribute to the global rate (108). In our model approach, we calculate A for elementary steps only. Thus, there is no direct and simple way to compare our calculated barriers with the apparent barriers of nonelementary processes. This is particularly true for energy estimates made from the thermal-stability thresholds of chemisorbed species. 

When the rate equation does not correspond stoichiometrically, the reaction is called a nonelementary reaction. Consider the thermal decomposition of nitrous oxide to nitrogen and oxygen as follows ... 

Nonelementary reactions, such as Equation (5.4), are expressed as a single reaction [i.e., Equation (5.3)] because the overall reaction is the result of sequential elementary reactions and the intermediates are very small, unnoticeable, and difficult to isolate. Therefore, some of these intermediates do not appear in the stochiometric equation of the reaction. In this chapter (and generally in pharmaceutical sciences), nonelementary reactions will be ignored. 

It is interesting to note that although the reaction orders correspond to the stoichiometric coefficients for the reaction between hydrogen and iodine, the rate expression for the reaction between hydrogen and another halogen, bromine, is quite complex. This nonelementary reaction... 

Nonelementary reaction is seen as a sequence of elementary reactions... 

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