Kinetics in Homogeneous Catalysis

Hydrogenation of cis-1,4-polybutadiene RuCl(CO)(OCOPh)(PPh )2 (Section 2.2) r = CpPh3 110] 

Oxidation of ethylene (Wacker) PdCf/CuCf (Section 2.4.1) kCKCpiCf- = 2 [13] 

Oligomerization of ethylene (SHOP) Ni(C6Hs)2PCH2COOH (Section 2.3.1.3) kJCc c gx 1 + Kca [15] 

Ca = concentration of the organic reactant Cb = concentration of hydrogen Ccat = concentration of the catalyst. 

To derive the overall kinetics of a gas/liquid-phase reaction it is required to consider a volume element at the gas/liquid interface and to set up mass balances including the mass transport processes and the catalytic reaction. These balances are either differential in time (batch reactor) or in location (continuous operation). By making suitable assumptions on the hydrodynamics and, hence, the interfacial mass transfer rates, in both phases the concentration of the reactants and products can be calculated by integration of the respective differential equations either as a function of reaction time (batch reactor) or of location (continuously operated reactor). In continuous operation, certain simplifications in setting up the balances are possible if one or all of the phases are well mixed, as in continuously stirred tank reactor, hereby the mathematical treatment is significantly simplified. 

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According to Eq. (2.110) we find that the rate of product formation is proportional to the number of sites, N. In heterogeneous catalysis, reactions described by Eq. (2.110) are said to behave according to Langmuir adsorption kinetics. In homogeneous catalysis, it is called Michaelis-Menten kinetics. 

As explained in Chapter 1, catalytic reactions occur when the reacting species are associated with the catalyst. In heterogeneous catalysis this happens at a surface, in homogeneous catalysis in a complex formed with the catalyst molecule. In terms of kinetics, the catalyst must be included as a participating species that leaves the reaction unaltered, as indicated schematically in Fig. 2.7, which shows the simplest conceivable catalytic cycle. We will investigate the kinetics of this simple two-step mech-... 

In homogeneous catalysis, the quantification of catalyst activities is commonly carried out by way of TOF or half-life. From a kinetic point of view, the comparison of different catalyst systems is only reasonable if, by giving a TOF, the reaction is zero order or, by giving a half-time, it is a first-order reaction. Only in those cases is the quantification of activity independent of the substrate concentration utilized ... 

Following the course of a reaction by NMR remains one of the most popular applications of this technique in homogeneous catalysis. The resulting kinetic information and/or the detection and identification of intermediates are important sources of mechanistic information. Often, isotopic labeling with [5-12] or [13-15] facilitates the acquisition and interpretation of the resulting NMR spectra. 

In situ spectroscopic measurements of a catalytic system provide a considerable opportunity to determine the chemical species present under reactive conditions. FTIR and NMR have been the two most frequently used in situ spectroscopic methods (see Chapters 2 and 3). They have been successfully used to identify labile, non-isolatable transient species believed to be involved in the catalytic product formation. Furthermore, efforts have been made to use this information in order to obtain more detailed kinetics, by decoupling induction, product formation, and deactivation. Thus, in situ spectroscopic techniques have the potential for considerably advancing mechanistic studies in homogeneous catalysis. 

Figure 4.1S Representation of the three primary steps for the generic inverse problem in chemical kinetics including homogeneous catalysis. In situ spectroscopic data is represented by 4kexv Tbe inverse spectroscopic problem (Eq. (2)), which is the focus of this chapter, is represented by S [,s, Ojxv The inverse problem associated with stoichiometries and reaction topology is represented by r rxs moles, reactions, extents of reaction and reaction stoi-...

Platinum alkene complexes have been known since 1830 when Zeise s salt was discovered. Alkene complexes of platinum(II) are kinetically more stable than their palladium counterparts, but this feature makes them less attractive for applications in homogeneous catalysis. A number of reviews have been written on alkene complexes.620-623... 

Mechanistic studies are of great importance in homogeneous catalysis. The active catalyst, often prepared in situ, is not easily isolated and, even when it is, can prove misleading (17). The comprehension of the catalytic process is therefore not an easy matter. In addition to producing kinetic measurements,... 

This result, caused by the proximity effect between peripheral catalytic sites, can translate into higher or lower catalytic activity of the metallodendrimer in homogeneous catalysis, and is commonly termed the dendritic effect. In the above case, a negative dendritic effect is observed. An interesting example of a positive dendritic effect on catalyst activity was reported by Jacobsen et al. in the hydrolytic kinetic resolution of terminal epoxides by peripherally Co(salen)-substituted PAMAM dendrimers [39]. 

In heterogeneous catalysis these models are generally referred to as the Langmuir-Hinshelwood-Hougen-Watson (LHHW) models. The term Michaelis-Menten kinetics is often used in homogeneous catalysis, enzyme reactions and reactions of microbial systems. 

In heterogeneous catalysis reactants have to be transported to the catalyst and (if the catalyst is a porous, solid particle) also through the pores of the particle to the active material. In this case all kinds of transport resistance s may play a role, which prevent the catalyst from being fully effective in its industrial application. Furthermore, because appreciable heat effects accompany most reactions, heat has to be removed from the particle or supplied to it in order to keep it in the appropriate temperature range (where the catalyst is really fully effective). Furthermore, heterogeneous catalysis is one of the most complex branches of chemical kinetics. Rarely do we know the compositions, properties or concentrations of the reaction intermediates that exist on the surfaces covered with the catalytically effective material. TTie chemical factors that govern reaction rates under these conditions are less well known than in homogeneous catalysis. Yet solid catalysts display specificities for particular reactions, and selectivity s for desired products, that in most practical cases cannot be equaled in other ways. Thus use of solid catalysts and the proper (mathematical) tools to describe their performance are essential. 

Adsorption on a solid catalyst surface, complex formation in homogeneous catalysis with metallo-organic complexes and in biocatalysis with enzymes share the same principle, i.e. the total number of sites is constant. Therefore, the rate expressions for reactions on heterogeneous, homogeneous and biocatalysts have a similar form. The constant number of active sites results in rate expressions that differ from homogeneous gas phase kinetics. Partial pressures are usually used in rate expressions for gas-phase reactions, while concentrations are used when the reactions take place in the liquid phase. It appears that definitions and nomenclature of particular kinetics constants in the different sub-communities differ sometimes. In the following sections the expressions used by the different subdisciplines will be compared and their conceptual basis outlined. 

In homogeneous catalysis, enzyme reactions, and reactions of microbial systems the same types of equations are used as in the LHHW models. In the latter disciplines, however, they are often referred to as Michaelis-Menten kinetics. 

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