Kinetics in homogeneous systems

In analyzing the kinetics of surface reactions, it will be illustrated that many of these processes are rate-controlled at the surface (and not by transport). Thus, the surface structure (the surface speciation and its microtopography) determine the kinetics. Heterogeneous kinetics is often not more difficult than the kinetics in homogeneous systems as will be shown, rate laws should be written in terms of concentrations of surface species. 

Equation (13) appears to be a good approximation for describing isothermal chemiluminescence kinetics for homogeneous systems where oxidation takes place uniformly. However, as has been shown by several authors [53-58], the different sections of a polymer sample may oxidize with its autonomous kinetics determined by different rates of primary initiation. A chemiluminescence imaging technique revealed that the light emission may be spread from some sites of the polymer film and the isothermal chemiluminescence vs. time runs are then modified, particularly in the stage of an advanced oxidation reaction [59]. 

Before discussing the kinetics of reactions in biphasic systems, the basics of kinetics in homogeneous reactions will be briefly revised. In all systems, the rate of a reaction corresponds to the amount of reactant that will be converted to product over a given time. The rate usually refers to the overall or net rate of the reaction, which is a result of the contributions of the forward and reverse reaction considered together. For example, consider the isomerization of -butane to Ao-butane shown in Scheme 2.1. 

The rate form of Eq. 57 and some of its generalizations are used to represent a number of widely different kinds of reactions. For example, in homogeneous systems this form is used for enzyme-catalyzed reactions where it is suggested by mechanistic studies (see the Michaelis-Menten mechanism in Chap. 2 and in Chap. 27). It is also used to represent the kinetics of surface-catalyzed reactions. 

The rate at which a chemical reaction occurs in homogeneous systems (single-phase) depends primarily on temperature and the concentrations of reactants and products. Other variables, such as catalyst concentration, initiator concentration, inhibitor concentration, or pH, also can affect reaction rates. In heterogeneous systems (multiple phases), chemical reaction rates can become more complex because they may not be governed solely by chemical kinetics but also by the rate of mass and/or heat transfer, which often play significant roles. 

For the production of chemicals, the rate of the reaction is a key parameter for the productivity defined in Equation (5) as the number of molecules produced per time. In homogeneous systems, the reaction rate depends on temperature, pressure, and composition [1]. In the case of solarthermal cycles, a metal oxide is used for the C02-splitting reaction rendering the reaction medium a heterogeneous two-phase system consisting of a solid (metal, metal oxide) and a fluid (CO2, CO, or carrier gas with O2). Therefore, the reaction kinetics becomes much more complex. Whereas microscopic kinetics only deals with time-dependent progress of the reaction, macroscopic kinetics additionally takes the heat- and mass-transport phenomena in heterogeneous systems into account. The transfer of species from one phase to the other must be considered in the overall mass balance [1]. The reaction of a gas with a porous solid consists of seven steps ... 

Krambeck, F. J., The mathematical structure of chemical kinetics in homogeneous single-phase systems. Arch. Rati. Mech. Anal. 38,317 (1970). 

Despite research dating back to the 19th century, the combustion or oxidation of CO is less well defined both mechanistically and kinetically than that of hydrogen. This section, which reviews relevant research in this field, is divided into five sub-sections. The first three of these consider the reaction with oxygen, dealing with explosion limits and slow oxidation oxidation in flames and other high temperature systems and elementary reactions. The fourth sub-section deals with several other oxidation reactions in homogeneous systems, and the fifth will be introduced below. 

Compared to conventional heterogeneous Ziegler-Natta systems in which a variety of active centers with different structures and activities usually coexist, homogeneous metallocene-based catalysts give very uniform catalyt-ically active sites which possess controlled, well-defined ligand environments [37]. Consequently, the polymerization processes in homogeneous systems are often more simple, and kinetic and mechanistic analyses for these systems are greatly simplified [38]. 

The first kinetic model for propagation in homogeneous systems was proposed by Ewen [47], assuming that the propagation took place as shown in Fig. 9.18. This scheme, shown for Cp2Ti(IV) polymerization of propylene, is representative of the kinetics for dl of the polymerizations with Group IVB metallocenes. In the scheme, species 1 and 4 represent coordinatively unsaturated Ti(IV) complexes that are-formally 16-electron pseudo-tetrahedral species, species 2 represents the interacting catalyst/cocatalyst combination, while intermediate 3 is shown with the monomer coordinated... 

The lipases and phospholipase A2 differ from classic esterases in that their natural substrates are insoluble in water and their activity is maximal only when the enzyme is adsorbed to the oil/water interface. Therefore a special treatment of the enzyme kinetics of these enzymes is imposed. The term substrate concentration becomes different, as only the substrate present in the interface is available for the enzyme. Consequently, the interface itself becomes the substrate. While in homogeneous systems, the enzymatic work space is in three dimensions, and substrate concentrations are expressed in terms of volume, the concentration of insoluble substrates only has meaning when expressed as interface area/volume or, when dealing with two-dimensional kinetics, as moles/area. 

The kinetic laws governing the polymerization of ethylene oxide in the presence of alcoholates of alkali-earth metals are similar to those described above. However, because of the high electric field intensity of doublecharged cations, the association of ion pairs in homogeneous systems is even stronger than for alkali metals. In addition the effective rate constants are much smaller than in the previous case. 

Most FIA methods are based on the use of chemical reactions, the products of which are measurable by a detector of choice. Indeed, FIA is useful only because it can accommodate such a wide variety of chemistries. Thus, in most cases, a FIA peak is a result of two processes of the physical dispersion, discussed in previous sections, and of subsequent chemical reactions. These two kinectic processes occur simultaneously in any flow system yet, in FIA their mutual interaction is very complex, since the dispersed zones are not homogeneously mixed, but are composed from concentration gradients formed by gradual penetration of reacting species in both axial and radial directions. An exact description of chemical kinetics taking place in FIA system is therefore very difficult, and this is why so few papers dealing with the theory of chemical kinetics in FIA systems have been published [150, 151, 181, 391, 541, 554, 1064, 1065], although this problem is central to further development of FIA. 

The mechanistic and stereochemical options available to allylic carbanions are fully as complex as those available to allylic carbonium ions. Much that is known concerning the mechanisms of base-catalyzed alkene isomerizations was obtained from stereochemical, isotope exchange, and product composition studies. The present discussion is limited to alkene isomerizations whose kinetics have been studied in homogeneous systems. Isomerizations involving allylic carbanion intermediates have been reviewed by Cram . ... 

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