Complex multiroute reaction

We now Ulustrate what has been said so far with an example of a complex multiroute reaction (the isomerization of butenes over C0-M0/AI2O3 (22)) with a linear mechanism ... 

The rate of an elementary step in a complex multiroute reaction is given by the following equation (29 30) ... 

Conversions of aUyl alcohol (S) in PdCU solution can he used as another example of a complex multiroute reaction (Fig. 5.33), where several forms of the metal (palladium) catalyst are taking part in different redox reactions. Besides oxidation products Pi P3 also a reduction product P4 is formed. 

In formulating hypotheses for the mechanism of a given complex reaction, and in using different procedures for the selection of one out of many hypotheses (discrimination of hypotheses), the question arises as to the hierarchy of the hypotheses. The intuitive principle of simplicity cannot play the role of a tool for the selection of hypotheses in the case of multiroute reactions because the number of vertices and cycles and the ways of linking cycles in the kinetic graph are already variables. Proceeding from linear mechanisms, we examine here possible approaches to the construction of a quantitative scale for mechanistic complexity or to the selection of a complexity index". 

We have proposed the complexity index, K, based on the fractional rational form of the rate laws for reaction routes. This index is deHned as the total number of weights (rate constants) for the elementary steps included in the numerator and denominator of the kinetic laws for all routes of a multiroute reaction. In calculating K it is convenient to use the Vorkenstein-Gordstein algorithm which is applicable to the derivation of the rate laws for the routes of all catdytic and noncatal3d ic reactions having linear mechanisms. 

Studies on the mechanisms of catalytic and non catalytic reac tions undertaken over the past 15-20 years have led to significant progress in the theory of reaction mechanisms. Most of the reactions involving homogeneous, metal-complex, and enzymatic catalyses were shown to be no less complex in terms of their mechanism compared with the mechanisms of radical chain processes. Infact, they appear to be much more complicated. Numerous examples of complicated mechanisms can be found in the literature. At present, multiroute mechanisms (with 2 to 4 reaction routes), involving as many as 8 intermediates and up to 12 elementary steps, are widely known to exist even in heterogeneous catalysis by metals and nonmetals where the simplest two-step schemes have hitherto been very popular. The existence of many routes and elementary steps is the most important general feature of the mechanisms of catalytic and also many noncatalytic reactions. 

Contemporary chemical kinetics and the theory of reaction mechanisms are characterized not only by increased complexity of the mechanisms (hypotheses of mechanisms) but also by the considerable number of hypotheses (the possible mechanisms describing each reaction). Cases are known where the mechanism of formation of a certain product in a complicated multiroute mechanism incorporates completely different sequences of elementary steps and intermediates" even in the case of reactions that have one linearly independent stoichiometric equation The greater mechanistic complexity and high number of hypotheses raise the issue of the formalization and automation of the procedure adopted for the generation of hypotheses. 

Often in heterogeneous catalysis, the reaction mechanism is rather complex and cannot be represented by a one-route multistep reaction sequence, as there are several routes leading to a variety of products. An example of the rate derivation for a multiroute mechanism of butadiene hydrogenation was presented in Chapter 4. Often for the derivation of kinetic equations in such a case, it is assumed that the adsorption/desorption steps are in quasi-equdibria. The rate of formation of a certain component in the reaction mixture is then defined as... 

---