Kinetics of complex reactions

The irreversible and reversible complex or multiple reactions have a different behavior and as such cannot be solved by simple integral methods. In most cases, numerical methods are employed. These reactions can occnr in series, parallel, or a combination of both. The goal is to determine the rate constants for reactions of any order. Although the order of these reactions is not integer, we can assnme that it is entire in the different steps. In such cases, an analytical solution can be obtained. The most complex solutions of generic order will not be studied in this chapter. Consider the three cases as follows. 

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From a theoretical point of view the study of the kinetics of coupled catalytic reactions makes it possible to investigate mutual influencing of single reactions and the occurrence of some phenomena unknown in the kinetics of complex reactions in the homogeneous phase. This approach can yield additional information about interactions between the reactants and the surface of the solid catalyst. 

The studies mentioned in this brief account did not concern the kinetics of complex reactions taking place on the so-called polyfunctional catalysts, which were treated by Weisz (56) the theory of the use of these catalysts has been further worked out for some consecutive or parallel reactions carried out in the reactors with a varying ratio of catalyst components along the catalyst bed [e.g. (90, 91, 91a) ]. Although the description of these reactions, not coupled in the sense defined in Section III, is beyond the scope of this treatment, we mention here at least an experimental... 

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. 

The order of reaction is an empirical factor widely used in chemical kinetics which may give an insight into the events at the molecular level for kinetics of complex reactions. It relates the reaction rate to the activity of the participating species in the kinetic equation. 

It is surprising that complicated dynamic behaviour proved to be characteristic of the simplest and quite ordinary kinetic models of catalytic reactions, namely of the Langmuir Hinshelwood adsorption mechanism. We are possibly at the initial stage of interpreting the kinetics of complex reactions and the "Sturm und Drang period has not yet been completed. 

The Soviet school of chemical kinetics has accumulated a unique experience in interpreting concrete catalytic reactions in terms of the stepwise mechanism concept. In the present book we have made an attempt to interpret this experience on the basis of modern formal kinetics of complex reactions. Since the authors have addressed the book to chemists and mathematicians, it is desirable that they both read the whole of the book. 

As far as the chemical kinetics of complex reactions is concerned, an important milestone was the chain reaction theory developed by Bodenstein, Semenov and Hinshelwood. It is almost the first theory of complex chemical reactions. A great achievement is that the role of free atoms and radicals has been interpreted on the basis of the analysis of kinetic relationships. Kinetic chemists began to operate with structural "mechanistic units, i.e. "chains and "cycles . 

The most general description for the kinetics of complex reactions in terms of the ideal adsorbed layer model was given in the Horiuti-Temkin steady-state reaction theory [43-47] (see Chap. 1). 

Thus, the determinant equation was found useful for the analysis of the kinetics of complex reactions in that it made simpler the kinetic calculations at determination of the kinetic model of interrelated and synchronized reactions proceeding in the reaction mixture and also the qualitative and quantitative assessment of chemical interference itself. 

Mauser developed a method for the mathematical analysis of the kinetics of complex reaction systems, " which can apply here because the reactions at different sites are kinetically independent. As simple graphic instruments, the Mauser diagrams are useful for determining how many kinetically independent reactions (s) occur in the reaction system (the three elementary reactions in Scheme I are not independent). 

In distinction from the more refined, and thus much more complicated lattice-gas model, the form of the model of the surface electronic gas provides possibilities for its application to chemisorption of gas mixtures and thus to modelling of kinetics of complex reactions. Derivation of multicomponent chemisorption isotherms based on thermodynamic approach was presented in the previous chapter. Within the framework of this model the following generalized elementary reaction A+ZI+Z=>S is considered. This reaction is written as a three-body collision, which is highly improbable, but is presented here only for illustrative purposes of how to express the reaction rate... 

Another option in analysis kinetics of complex reactions is to separate activity from selectivity and to eliminate time as a parameter in the system of differential equations. 

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