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Rate laws catalytic reactions

The use of power law kinetics to describe the rates of catalytic reactions. This is an empirically oriented approach which considerably limits the generdity of the rate equations obtained and makes it valid only in the region of parameters in which the empirical power law kinetics was obtained. [Pg.31]

The rate law describing reaction initiation is more complicated than the law for the "steady state" region. Several of the reaction mechanisms discussed in Part 1 involve steps in which the catalyst is somehow activated. Sorokin and Shode found that the catalyst eventually reacts completely to form the active catafytic species. A"steady state" is reached when the TPP has completely reacted to form the active catalytic species. [Pg.146]

Sequences such as the above allow the formulation of rate laws but do not reveal molecular details such as the nature of the transition states involved. Molecular orbital analyses can help, as in Ref. 270 it is expected, for example, that increased strength of the metal—CO bond means decreased C=0 bond strength, which should facilitate process XVIII-55. The complexity of the situation is indicated in Fig. XVIII-24, however, which shows catalytic activity to go through a maximum with increasing heat of chemisorption of CO. Temperature-programmed reaction studies show the presence of more than one kind of site [99,1(K),283], and ESDIAD data show both the location and the orientation of adsorbed CO (on Pt) to vary with coverage [284]. [Pg.732]

When a relatively slow catalytic reaction takes place in a stirred solution, the reactants are suppHed to the catalyst from the immediately neighboring solution so readily that virtually no concentration gradients exist. The intrinsic chemical kinetics determines the rate of the reaction. However, when the intrinsic rate of the reaction is very high and/or the transport of the reactant slow, as in a viscous polymer solution, the concentration gradients become significant, and the transport of reactants to the catalyst cannot keep the catalyst suppHed sufficientiy for the rate of the reaction to be that corresponding to the intrinsic chemical kinetics. Assume that the transport of the reactant in solution is described by Fick s law of diffusion with a diffusion coefficient D, and the intrinsic chemical kinetics is of the foUowing form... [Pg.161]

It is clear that in case (a) the rate, r, of the catalytic reaction (e.g. CO oxidation) will not be affected while in case (b) the rate increase, Ar, will at most equal I/nF (e.g. direct reaction of O2 with CO). In case (c), however, the new species introduced electrochemically onto the catalyst surface will interact with coadsorbed reactants and will change the catalytic properties of the catalyst surface in an a priori unpredictable manner, which is nevertheless not subject to Faraday s law. Thus in cases (a) and (b) there will be no NEMCA but in case (c) it is entirely logical to anticipate it. Even in case (b) one may anticipate NEMCA, if the product remains on the surface and has some catalytic or promotional properties. [Pg.5]

Overall, catalytic processes in industry are more commonly described by simple power rate law kinetics, as discussed in Chapter 2. However, power rate laws are simply a parameterization of experimental data and provide little insight into the underlying processes. A micro-kinetic model may be less accurate as a description, but it enables the researcher to focus on those steps in the reaction that are critical for process optimization. [Pg.299]

How appropriate is the power rate law for describing the kinetics of a catalytic reaction ... [Pg.402]

This simple example of a non-catalytic reaction demonstrates how a reaction rate law may be comprehensively defined in two substrates by just two reaction progress experiments employing two different values of excess [e]. A classical kinetics approach using initial rate measurements would require perhaps a dozen separate initial rate or pseudo-zero-order experiments to obtain the same information. [Pg.450]

The values of x = 0.5 and = 1 for the kinetic orders in acetone [1] and aldehyde [2] are not trae kinetic orders for this reaction. Rather, these values represent the power-law compromise for a catalytic reaction with a more complex catalytic rate law that corresponds to the proposed steady-state catalytic cycle shown in Scheme 50.3. In the generally accepted mechanism for the intermolecular direct aldol reaction, proline reacts with the ketone substrate to form an enamine, which then attacks the aldehyde substrate." A reaction exhibiting saturation kinetics in [1] and rate-limiting addition of [2] can show apparent power law kinetics with both x and y exhibiting orders between zero and one. [Pg.451]

Although not all facets of the reactions in which complexes function as catalysts are fully understood, some of the processes are formulated in terms of a sequence of steps that represent well-known reactions. The actual process may not be identical with the collection of proposed steps, but the steps represent chemistry that is well understood. It is interesting to note that developing kinetic models for reactions of substances that are adsorbed on the surface of a solid catalyst leads to rate laws that have exactly the same form as those that describe reactions of substrates bound to enzymes. In a very general way, some of the catalytic processes involving coordination compounds require the reactant(s) to be bound to the metal by coordinate bonds, so there is some similarity in kinetic behavior of all of these processes. Before the catalytic processes are considered, we will describe some of the types of reactions that constitute the individual steps of the reaction sequences. [Pg.780]

A more robust way to write a rate law for a catalytically promoted reaction is to include the concentrations of one or more surface complexes, in place of the surface area As. In this case, the simulation can account not only for the catalyzing surface area, since the mass of a surface complex varies with the area of the sorbing surface, but the effects of pH, competing ions, and so on. [Pg.249]

The oxidation rate should, in principle, be described by a law using a rate constant independent of pH, as long as a single reaction mechanism is involved. The rate law (28.4) is unusual in that the rate varies with the concentration of the Mn11 component, rather than an individual species. If we hypothesize that the catalytic activity is promoted by a surface complex >MnOMnOH, a slightly different form of the rate law may be appropriate. Since the surface complex would... [Pg.421]

Kinetic investigations of catalytic processes under transient conditions have to take into account this problem (see e.g. (4 ), where the macrorelaxation of the redox type reaction has been suppressed by means of a specific periodic operation). Kinetic expressions obtained by dynamic methods in general would give a better understanding of the rate law than those obtained from steady state measurements. [Pg.278]

Central to catalysis is the notion of the catalytic site. It is defined as the catalytic center involved in the reaction steps, and, in Figure 8.1, is the molybdenum atom where the reactions take place. Since all catalytic centers are the same for molecular catalysts, the elementary steps are bimolecular or unimolecular steps with the same rate laws which characterize the homogeneous reactions in Chapter 7. However, if the reaction takes place in solution, the individual rate constants may depend on the nonreactive ligands and the solution composition in addition to temperature. [Pg.179]

Here, L is a mobile ligand which can leave the metal site (M) open briefly for reaction with A in the initial step of the catalytic cycle. The transformation of the M A complex into products completes the cycle. The equilibrium in step (1) lies far to the left in most cases, because the ligands protect the metal centers from agglomeration. Thus, the concentration of M is very small, and the total concentration of catalyst is cMr = cm a + cm l- The rate law which arises from this mechanism is... [Pg.187]

Autocatalysis is a special type of molecular catalysis in which one of the products of reaction acts as a catalyst for the reaction. As a consequence, the concentration of this product appears in the observed rate law with a positive exponent if a catalyst in the usual sense, or with a negative exponent if an inhibitor. A characteristic of an autocat-alytic reaction is that the rate increases initially as the concentration of catalytic product increases, but eventually goes through a maximum and decreases as reactant is used up. The initial behavior may be described as abnormal kinetics, and has important consequences for reactor selection for such reactions. [Pg.187]

Surface catalysis is involved in a large majority of industrial catalytic reactions. The rate laws developed in this section are based on the following assumptions ... [Pg.191]

The mechanisms, and hence theoretically derived rate laws, for noncatalytic heterogeneous reactions involving solids are even less well understood than those for surface-catalyzed reactions. This arises because the solid surface changes as the reaction proceeds, unlike catalytic surfaces which usually reach a steady-state behavior. The examples discussed here are illustrative. [Pg.255]

In Section 5.3 for reversible reactions, it is shown that the rate of an exothermic, reversible reaction goes through a maximum with respect to T at constant fractional conversion /, but decreases with respect to increasing / at constant T. (These canchisians apply whether the reaction is catalytic or noncatalytic.) Both features are illustrated graphically in Figure 21.4 for the oxidation of SO, based on the rate law of Eklund (1956) ... [Pg.521]

Equilibrium studies under anaerobic conditions confirmed that [Cu(HA)]+ is the major species in the Cu(II)-ascorbic acid system. However, the existence of minor polymeric, presumably dimeric, species could also be proven. This lends support to the above kinetic model. Provided that the catalytically active complex is the dimer produced in reaction (26), the chain reaction is initiated by the formation and subsequent decomposition of [Cu2(HA)2(02)]2+ into [CuA(02H)] and A -. The chain carrier is the semi-quinone radical which is consumed and regenerated in the propagation steps, Eqs. (29) and (30). The chain is terminated in Eq. (31). Applying the steady-state approximation to the concentrations of the radicals, yields a rate law which is fully consistent with the experimental observations ... [Pg.404]

Reports by Li and Zuberbuhler were in support of the formation of Cu(I) as an intermediate (16). It was confirmed that Cu(I) and Cu(II) show the same catalytic activity and the reaction is first-order in [Cu(I) or (II)] and [02] in the presence of 0.6-1.5M acetonitrile and above pH 2.2. The oxygen consumption deviated from the strictly first-order pattern at lower pH and the corresponding kinetic traces were excluded from the evaluation of the data. The rate law was found to be identical with the one obtained for the autoxidation of Cu(I) in the absence of Cu(II) under similar conditions (17). Thus, the proposed kinetic model is centered around the reduction of Cu(II) by ascorbic acid and reoxidation of Cu(I) to Cu(II) by dioxygen ... [Pg.406]

The reaction features a complex pH dependence which was not resolved. Nevertheless, it was suggested that the variation of the reaction rate as a function of pH was consistent with an additional term in the rate law which was proportional to [HA-]. The kinetic role of [HA-] was interpreted in terms of its reaction with Cu02, which is presumably formed as an intermediate during the autoxidation of Cu(I). In the presence of acetonitrile, Cu(I) can be stabilized as [Cu(MeCN)2]+ and [Cu(MeCN)3]+. As a consequence, the oxidation of Cu(I) becomes rate determining and the overall rate of the catalytic reaction becomes independent of [HA-]. [Pg.407]

Linn and Halpern later found that the active catalyst in the ketone and anthracene hydrogenation reactions of Pez was likely to be Ru( 2-H2)(H)2(PPh3)3 (Fig. 3.6) [67]. For example, cyclohexanone is converted to cyclohexanol under mild conditions in toluene (see Table 3.3). The TOF depends on the substrate concentration, and the rate law for the catalytic reaction was determined to be given by Eq. (2), with k= 1.3x 10 M-1 s-1 at 20°C. [Pg.59]

The combination of Eqs. (13-16) implies that both reactions are catalytic under aerobic conditions, which, indeed, they are. The kinetics of catalytic product formation established that two different mechanisms operate. For aldehyde or ketone formation a rate law as in Eq. (18) has been established, whereas the 1,2-diol formation follows the rate law Eq. (19). [Pg.201]

The similarity in the rate laws does not allow a clear choice to be made between mechanisms, but Mechanism A is required in H20 by the observation of general base catalysis. However, the relative stability of the (red) T° intermediate in Me2SO (this is dependent on the nature of the AA side chain, cf. Section III,C) in the absence of proton-ated amine makes us prefer Mechanism B for reaction in this solvent, since the solvent is unable to assist the departure of MeOH. The similar catalytic rate constants found for B = imidazole, Af-methylimidazole (26) suggest that transfer of the proton from T+ to the alcohol function remains stepwise (i.e., via T°) since N-methylimidazole cannot carry out a concerted transfer. Such general acid-catalyzed loss of MeOH from T° supports a suggestion made many years ago by Burnett and Davies relating to purely organic esters (62). [Pg.358]

In the biochemical network, the processing elements do not learn from task examples, but the knowledge is already built in. For example, an enzyme recognizes a specific substrate and applies a specific rate for the catalytic reaction, as a function of the particular conditions, pH, temperature, and so on. Therefore, in such systems, adaptation is implemented by adjusting the catalytic characteristics according to environmental conditions and following laws already built in by evolution. [Pg.131]

We see that in this simplest possible rate expression we could have for a unimolecular catalytic reaction there is no simple power-law dependence on partial pressures (Figure 7-25). [Pg.304]

Rate expressions obtained in one set of pressures and temperatures might not describe a reactor in another situation because rate expressions of catalytic reactions do not obey the power law ... [Pg.310]


See other pages where Rate laws catalytic reactions is mentioned: [Pg.249]    [Pg.324]    [Pg.66]    [Pg.79]    [Pg.209]    [Pg.219]    [Pg.220]    [Pg.450]    [Pg.221]    [Pg.95]    [Pg.78]    [Pg.176]    [Pg.192]    [Pg.443]    [Pg.50]    [Pg.132]    [Pg.392]    [Pg.144]    [Pg.568]    [Pg.349]    [Pg.664]    [Pg.140]    [Pg.73]   
See also in sourсe #XX -- [ Pg.671 , Pg.672 , Pg.673 ]

See also in sourсe #XX -- [ Pg.431 , Pg.432 , Pg.433 ]




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