Catalysis Steady-state approximation

Kinetics is one of the key issues of catalysis together with selectivity and catalyst stability. Chemical kinetics has been discussed in several dedicated works [1] and the readers will be aware of its basics [2], In the following sections several commonly used concepts are mentioned such as steady state approximation, rate-determining step, determination of selectivity, and a few points of particular interest to catalysis will be high-lighted such as incubation. 

CHAPTEB 4 Thfi Steady-State Approximation Catalysis ... 

Even from the very beginning it became clear that kinetic methods generally accepted in heterogeneous catalysis, which are based on the analysis of adsorption-desorption equilibria and surface reactions in the steady-state approximation, cannot be applied to the studies of heterogeneous-homogeneous processes. However, on the eve of 1980s no developed methodology applicable... 

The application of the steady-state approximation to heterogeneous catalysis does not require that the surface concentrations are low, but implies that they do not change with time. 

The Bodenstein steady state approximation is widely applied in catalysis. At the same time this approximation is often not valid and the dynamics should be taken into accout. Transient kinetic modelling as well as oscillation reactions will be considered in Chapter 8. 

In the following derivation we will apply the concept of steady state approximation, which was introduced to enzymatic catalysis by Briggs and Haldane (1925), who had proposed that the rate of formation of ES = ki [E][S] balances the rate of breakdown of the complex ES = (k i + k2)[ES], or in other words (Figure 6.2) d(ES)/dt = 0... 

Rapid equilibrium conditions need not be assumed for the derivation of an enzyme catalysis model. A steady-state approximation can also be used to obtain the rate equation for an enzyme-catalyzed reaction. 

Specific detail on Michaelis-Menten kinetics, quasi steady-state approximations, competitive and non-competitive inhibitions, substrate inhibition, rate expressions for enzyme catalysis and deactivations, Monod growth kinetics, etc. are not presented in an extensive manner although additional information is available in the work of Vasudevan for the interested leader. " Also note that the notation adopted by Vasudevan is employed throughout this chapter. 

First application of the steady-state approximation Quantitative theory of adsorption description of catalysis in terms of a layer of gas molecules held on a surface, by the same forces that held atoms of a solid together Mechanism of unimolecular reactions... 

In the context of catalysis, steady state (also called the Bodenstein approximation) [2, 22, 27] means that all the concentrations of intermediates and the elementary rates are fixed, as long as the experimental conditions are fixed (temperature, reactant, and product concentrations, etc.), while a change in those conditions generate an instantaneous adaptation of the catalytic cycle this includes... 

The mechanism of each of the four possible combinations may involve an Arrhenius or a van t Hoff intermediate. This leads to eight possible mechanisms, schematically presented in Table 13.2. Each of these mechanisms can be developed using either the preequilibrium or the steady-state approximation to arrive at the corresponding rate law. The lessons that can be learnt from the treatment of these mechanisms are also indicated in Table 13.2 some mechanisms lead exclusively to specific acid or base catalysis, while others lead to general acid or base catalysis. Furthermore, the specific catalysis is associated with the existence of a limiting rate, that is the rate that will not increase indefinitely with the H+, or OH , concentration, but attain a limiting valne eqnal to 2[S]o-... 

It may be worthwhile to summarize our discussion of the kinetic step in gas-solid reactions by stating that on the basis of the analogy with heterogeneous catalysis, the overall reaction process may be broken down into individual steps, namely, adsorption, the formation of a surface complex, and desorption. Each of these steps can be regarded as reversible and assigned both a forward and a reverse rate constant. The resultant overall rate expressions may then be simplified with the aid of the steady state approximation and a knowledge of the overall reaction equilibrium. This then results in characteristic rate expressions containing certain constants and the partial... 

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