Catalytic reaction definition

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

These definitions are valid only when the concentration of the enzyme is very small compared with that of the substrate. Moreover, they apply only to the initial rate of formation of products in other words, the rate of formation of the first few percent of the product, before the substrate has been depleted and products that can interfere with the catalytic reaction have accumulated. 

Thus denoting by 0P the coverage of the promoter on the catalyst surface and by pj the partial pressures of reactants, j, of the catalytic reaction we can formulate mathematically the above definition as ... 

It thus appears safer, rather than trying to introduce such an ambiguous and sometimes impossible definition of an electrode , simply to replace the or in other circumstances in the above expression of the 1st law of Faraday by provided no catalytic reaction is taking place on the electrode or electrolyte surface . This is not necessary for processes with positive AG. 

In many cases, however, the interfacial area is not known, particularly when one is dealing with a heterogeneous catalytic reaction involving a liquid phase and a solid catalyst. Consequently, the following definitions of the reaction rate are sometimes useful. 

In the treatment of rate expressions for heterogeneous catalytic reactions the definition of local reaction rates in terms of interfacial areas (3.0.10) is appropriate. 

Sidney Altman discovered this property of RNA in the course of studies on precursor transfer RNA. It was realized that the catalytic properties of RNA are not exactly the same as those of protein enzymes, since the ribozyme is itself active and thus undergoes change during the catalytic reaction. This does not correspond to the generally accepted definition of an enzyme. Later studies, however, showed that some ribozymes are capable of acting catalytically at other RNA molecules. The ribozymes remain completely unchanged in this process, and thus fulfil the definition of a real enzyme. 

A metal cluster can be considered as a polynuclear compound which contains at least one metal-metal bond. A better definition of cluster catalysis is a reaction in which at least one site of the cluster molecule is mechanistically necessary. Theoretically, homogeneous clusters should be capable of multiple-site catalysis. Many heterogeneous catalytic reactions require multiple-site catalysis and for these reasons discrete molecular metal clusters are often proposed as models of metal surfaces in the processes of chemisorption and catalysis. The use of carbonyl clusters as catalysts for hydrogenation reactions has been the subject of a number of papers, an important question actually being whether the cluster itself is the species responsible for the hydrogenation. Often the cluster is recovered from the catalytic reaction, or is the only species spectroscopically observed under catalytic conditions. These data have been taken as evidence for cluster catalysis. 

The model shown in Scheme 2 indicates that a change in the formal oxidation state of the metal is not necessarily required during the catalytic reaction. This raises a fundamental question. Does the metal ion have to possess specific redox properties in order to be an efficient catalyst A definite answer to this question cannot be given. Nevertheless, catalytic autoxidation reactions have been reported almost exclusively with metal ions which are susceptible to redox reactions under ambient conditions. This is a strong indication that intramolecular electron transfer occurs within the MS"+ and/or MS-O2 precursor complexes. Partial oxidation or reduction of the metal center obviously alters the electronic structure of the substrate and/or dioxygen. In a few cases, direct spectroscopic or other evidence was reported to prove such an internal charge transfer process. This electronic distortion is most likely necessary to activate the substrate and/or dioxygen before the actual electron transfer takes place. For a few systems where deviations from this pattern were found, the presence of trace amounts of catalytically active impurities are suspected to be the cause. In other words, the catalytic effect is due to the impurity and not to the bulk metal ion in these cases. 

So far, catalytic systems in which the mediator plays the role of both catalyst and electron carrier have been considered. Figure 4.21 shows an example where these two roles are dissociated.21 The catalyst, in the sense of a chemical catalyst, is the Co(II) porphyrin embedded in the Nafion (a trademark of Dupont) film, while the electron are shuttled by the ruthenium hexamine 3 + /2+ couple attached electrostatically to the Nafion backbone. The catalytic reaction now involves two successive steps, as expected for a chemical catalysis process (see Sections 4.2.1 and 4.3.1), calling for the definition of two characteristic currents. One has the same... 

Asymmetric diarylmethanes, hydrogenolytic behaviors, 29 229-270, 247-252 catalytic hydrogenolysis, 29 243-258 kinetics and scheme, 29 252-258 M0O3-AI2O3 catalyst, 29 259-269 relative reactivity, 29 255-257 schematic model, 29 254 Asymmetric hydrogenations, 42 490-491 Asymmetric synthesis, 25 82, 83 examples of, 25 82 Asymmetry factor, 42 123-124 Atom-by-species matrix, 32 302-303, 318-319 Atomic absorption, 27 317 Atomic catalytic activities of sites, 34 183 Atomic displacements, induced by adsorption, 21 212, 213 Atomic rate or reaction definition, 36 72-73 structure sensitivity and, 36 86-87 Atomic species, see also specific elements adsorbed... 

In order to gain an insight into the mechanism on the basis of the slope of a Type A correlation requires a more complicated procedure. Consider the Hammett equation. The usual statement that electrophilic reactions exhibit negative slopes and nucleophilic ones positive slopes may not be true, especially when the values of the slopes are low. The correct interpretation has to take the reference process into account, for example, the dissociation equilibrium of substituted benzoic acids at 25°C in water for which the slope was taken, by definition, as unity (p = 1). The precise characterization of the process under study is therefore that it is more or less nucleophilic than the reference process. However, one also must consider the possible influence of temperature on the value of the slope when the catalytic reaction has been studied under elevated temperatures there is disagreement in the literature over the extent of this influence (cf. 20,39). The sign and value of the slope also depend on the solvent. The situation is similar or a little more complex with the Taft equation, in which the separation of the molecule into the substituent, link, and reaction center may be arbitrary and may strongly influence the values of the slopes obtained. This problem has been discussed by Criado (33) with respect to catalytic reactions. 

The catalytically active species 31 was isolated and its structure definitively determined using X-ray analysis. The complex 31 was seen to be quite stable below 70 °C under an argon atmosphere at pH 2.0-6.0 and in the absence of any reducible carbonyl compounds [50]. When the reducing ability of isolated 31 in acidic media was examined, the catalytic reactions using cyclohexanone and acetophenone (31 ketones HCOOH = 1 200 1000) yielded the corresponding alcohols quantitatively in 2h at pH2.0 at 70°C (Scheme 5.17). 

The homogeneous catalytic reaction occurs in the multi-component liquid phase P. The chemical constituents of the liquid phase include H, e", atoms, ions, and molecules etc. which are dissolved/solvated in one or more molecular or ionic solvents. Primary examples of the ions and molecules present are the dissolved organic and organometallic reagents, intermediates and products. By definition, all the molecular and ionic species involved directly in the homogeneous catalysis are soluble in this liquid phase P. The set of all dissolved species in the phase will be denoted by Eq. (3). 

In the relevant literature, many definitions of reaction rates can be found, especially in the case of catalytic systems. Depending on the approach followed, a catalytic reaction rate can be based on catalyst volume, surface, or mass. Moreover, in practical applications, rates are often expressed per volume of reactor. Each definition leads to different manipulations and special attention is required when switching from one expression to another, hi the following, the various forms of catalytic reaction rates and their connection is going to be presented. Stalling from the fundamental rate defined per active site, the reader is taken step -by step to the rate based on the volume of the reactor and the concept of the overall rate in two- and three-phase systems. 

As the gas flow rate increases beyond that at minimum fluidization, the bed may continue to expand and remain homogeneous for a time. At a fairly definite velocity, however, bubbles begin to form. Further increases in flow rate distribute themselves between the dense and bubble phases in some ways that are not well correlated. Extensive bubbling is undesirable when intimate contading between phases is desired, as in drying processes or solid catalytic reactions. In order to permit bubble formation, the... 

The phenomenon of catalysis is a subject of chemical kinetics, as follows from Ostwald s definition of catalysis. Therefore, the accumulation of data on the kinetics of concrete catalytic reactions favors the progress of the theory of catalysis. 

Frequently, particularly from the viewpoint of the technological application of a heterogeneous catalytic reaction, the conditions of experiments in a flow reactor are characterized by space velocity or contact time values. Space velocity, V, is the ratio to the volume of the catalyst bed of the volume of a gas mixture, reduced to the normal conditions (0°C, 760 Torr), passed through the reactor per hour. If the reaction involves a volume change, inlet and outlet space velocities should be distinguished. The reciprocal of V is of the dimension of time. Contact time ( conventional contact time), rc, is a value proportional to V l. It is defined as the ratio of the catalyst volume to the volume of the gas mixture passed per unit time, the gas volume being not under normal conditions but at temperature and pressure in the reactor. Usually, tc is expressed in seconds. It follows from the definitions given that... 

A heterogeneous catalytic reaction, by definition, necessitates the participation of at least one chemisorbed intermediate (54) and involves a sequence of interlinked and interdependent (55,56) steps, which include the adsorption of reactant(s), one or more surface rearrangements, and the desorption of product(s). More than one area of the solid may be active in promoting reaction the activity of such regions may vary from one crystallographic... 

In conclusion, it must be noted that the equations to describe the transient behaviour of heterogeneous catalytic reactions, usually have a small parameter e = Altsot/Alt t. Here Atsot = bsS = the number of active sites (mole) in the system and Nfot = bg V = gas quantity (mole). Of most importance is the solution asymptotes for kinetic equations at A/,tsot/7Vtflt - 0, 6S, bg and vin/S being constant. Here we deal with the parameter SjV which is readily controlled in experiments. The case is different for the majority of the asymptotes examined. The parameters with respect to which we examine the asymptotes are difficult for control. For example, we cannot, even in principle, provide an infinite increase (or decrease) of such a parameter as the density of active sites, bs. Moreover, this parameter cannot be varied essentially without radical changes in the physico-chemical properties of the catalyst. Quasi-stationarity can be claimed when these parameters lie in a definite range which does not depend on the experimental conditions. 

Thus the presence of steps for the interaction between various intermediates in the detailed mechanisms is only a necessary condition for the multiplicity of steady states in catalytic reactions. A qualitative analysis of the dynamic system (5) for mechanism (4) showed that the existence of several stable steady states with a non-zero reaction rate needs the following additional conditions (a) the stoichiometric coefficients of intermediates must fit definite relationships ensuring the kinetic competition of these substances [violation of conditions (6)] (b) the system parameters must satisfy definite inequalities. 

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