Kinetic factors rate limiting step

As with the decompositions of single solids, rate data for reactions between solids may be tested for obedience to the predictions of appropriate kinetic expressions. From the identification of a satisfactory representation for the reaction, the rate-limiting step or process may be identified and this observation usually contributes to the formulation of a reaction mechanism. It was pointed out in Sect. 1, however, that the number of parameters which must be measured to define completely all contributory reactions rises with the number of participating phases. The difficulties of kinetic analyses are thereby also markedly increased and the factors which have to be considered in the interpretation of rate data include the following. 

The factors that influence elimination v. substitution are discussed subsequently (p. 260). Evidence for the involvement of C—H bond fission in the rate-limiting step—as a concerted pathway requires— is provided by the observation of a primary kinetic isotope effect (cf. p. 46) when H is replaced by D on the ft-carbon. 

Kinetic Term The designation kinetic term is something of a misnomer in that it contains both rate constants and adsorption equilibrium constants. For thfe cases where surface reaction controls the overall conversion rate it is the product of the surface reaction rate constant for the forward reaction and the adsorption equilibrium constants for the reactant surface species participating in the reaction. When adsorption or desorption of a reactant or product species is the rate limiting step, it will involve other factors. 

The interpretation of the stress dependent intensities is that the stress raises the energy of those B—H configurations with their axis along the direction of stress. The H has sufficient thermal energy at 100 K to reorient (Fig. 20b) the different orientations are populated according to their (stress-dependent) Boltzmann factors. Because the H can move at the measurement temperature (100 K) on the time scale of a Raman measurement (a few minutes) Herrero and Stutzmann (1988b) were able to estimate an upper limit for the barrier for H-motion. These authors assumed that the rate limiting step for H motion obeys first order kinetics and obtained Eb < 0.3 eV. 

It has been believed that P-450 reduction by NADPH cytochrome P-450 reductase is a biphasic process, but it was recently shown [7] that some P-450 cytochromes are reduced with single-exponential kinetics and that the presence of substrate is not an obligatory condition for the reduction of all P-450 forms. Thus, the kinetics of reduction of various ferric P-450 cytochromes possibly depends on many factors such as substrate, rate-limiting step, etc. 

Figures 7-9 show the fractional conversion of methanol in the pulse as a function of temperature for the three catalysts and the three methanol feeds. Evidently the kinetic isotope effect is present on all three catalysts and over the complete temperature range, indicating that the rate limiting step is the breaking of a carbon-hydrogen bond under all conditions. From these experiments, the effect cannot be determined quantitatively as in the case of the continuous flow experiments, but to obtain the same conversion of CD,0D, the temperature needs to be 50-60° higher. This corresponds to a factor of about three in reaction rate. The difference in activity between PfoCL and Fe.(MoO.), is larger in the pulse experiments compared to tHe steady stateJ results.

The enzyme kinetics has been studied in considerable detail by the Klinman group [31-37] and others [38]. These analyses indicate that the rate-limiting step is either the proton abstraction step or the re-oxidation of reduced co-factor which depends on the species and substrate. 

FIGURE 2.1 9. Homogeneous catalysis electrochemical reactions with the homogeneous electron transfer as a rate-limiting step. Variation of the current ratio ip/yfp with the kinetic parameter, A, far a series of values of the excess factor, y. From left to right, logy = 0, 0.3, 0.5, 1,1.5, 2. 

If the overall reaction rate is controlled by step three (k3) (i.e. if that is the rate limiting step), then the observed isotope effect is close to the intrinsic value. On the other hand, if the rate of chemical conversion (step three) is about the same or faster than processes described by ks and k2, partitioning factors will be large, and the observed isotope effects will be smaller or much smaller than the intrinsic isotope effect. The usual goal of isotope studies on enzymatic reactions is to unravel the kinetic scheme and deduce the intrinsic kinetic isotope effect in order to elucidate the nature of the transition state corresponding to the chemical conversion at the active site of an enzyme. Methods of achieving this goal will be discussed later in this chapter. 

We here review the factors that control the kinetics of product formation through reaction at an active surface. This includes consideration of the availability of those adsorbed intermediates which participate in the rate-limiting step (this term is analogous to concentration in a homogeneous reaction) and the mobility of the same species, which may determine, or at least influence, the frequency of occurrence of the reaction situation. The discussion is given under three broadly interpreted general headings, between which there is considerable overlap. 

According to the Equation (30) the experimental isotope effect depends not only on the intrinsic isotope effects a,-, but also on the rate constants k2 and k. The intrinsic isotope effects describe the structure of the transition states and the commitment reflects the relative heights of energetic barriers of competitive reactions. If k2i. k -[li(x l), the formation of intermediate B is the rate-limiting step and experimental isotope effect is equal to ai(aexp = i). When intermediate B returns to substrate much faster than forms the product k2, k it (x 1), the experimental isotope effect is aexp = (a1a2)/a 1. For more complex multistep reactions the analysis of isotope effects is analogous, however the commitment factor become a complex collection of kinetic terms.54... 

Both studies show that at relatively low temperatures, i.e., during ignition of the catalyst, the rate-limiting step shifts from chemical kinetics to diffusion in the washcoat. This is clear from Fig. 7, computed using a one-dimensional model by Nakhjavan et al. [54]. Figure 7A shows the Thiele modulus and Fig. 7B an external diffusion limiting factor F versus dimensionless axial position in the reactor at various times on-stream for the catalytic combustion of propene in monolith reactors. The time is defined as the time after injection of the fuel in a preheated air flow. 

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