Catalytic constant meaning

Another way of evaluating enzymatic activity is by comparing k2 values. This first-order rate constant reflects the capacity of the enzyme-substrate complex ES to form the product P. Confusingly, k2 is also known as the catalytic constant and is sometimes written as kcal. It is in fact the equivalent of the enzyme s TOF, since it defines the number of catalytic cycles the enzyme can undergo in one time unit. The k2 (or kcat) value is obtained from the initial reaction rate, and thus pertains to the rate at high substrate concentrations. Some enzymes are so fast and so selective that their k2/Km ratio approaches molecular diffusion rates (108—109 m s-1). This means that every substrate/enzyme collision is fruitful, and the reaction rate is limited only by how fast the substrate molecules diffuse to the enzyme. Such enzymes are called kinetically perfect enzymes [26],... 

This expression gives another meaning to the Michaelis constant. When = [S] then V = V J2. Using these parameters, it is also useful to define the catalytic constant of an enzyme as... 

Km for an enzymatic reaction are of significant interest in the study of cellular chemistry. From equation 13.19 we see that Vmax provides a means for determining the rate constant 2- For enzymes that follow the mechanism shown in reaction 13.15, 2 is equivalent to the enzyme s turnover number, kcat- The turnover number is the maximum number of substrate molecules converted to product by a single active site on the enzyme, per unit time. Thus, the turnover number provides a direct indication of the catalytic efficiency of an enzyme s active site. The Michaelis constant, Km, is significant because it provides an estimate of the substrate s intracellular concentration. 

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. 

The rate constant /ct, determined by means of Eq. (6-47) or (6-48), may describe either general base or nucleophilic catalysis. To distinguish between these possibilities requires additional information. For example, in Section 3.3, we described a kinetic model for the N-methylimidazole-catalyzed acetylation of alcohols and experimental designs for the measurement of catalytic rate constants. These are summarized in Scheme XVIIl of Section 3.3, which we present here in slightly different form. 

The simultaneous determination of a great number of constants is a serious disadvantage of this procedure, since it considerably reduces the reliability of the solution. Experimental results can in some, not too complex cases be described well by means of several different sets of equations or of constants. An example would be the study of Wajc et al. (14) who worked up the data of Germain and Blanchard (15) on the isomerization of cyclohexene to methylcyclopentenes under the assumption of a very simple mechanism, or the simulation of the course of the simplest consecutive catalytic reaction A — B —> C, performed by Thomas et al. (16) (Fig. 1). If one studies the kinetics of the coupled system as a whole, one cannot, as a rule, follow and express quantitatively mutually influencing single reactions. Furthermore, a reaction path which at first sight is less probable and has not been therefore considered in the original reaction network can be easily overlooked. 

As shown on Figure 9.1 when the circuit is opened (I = 0) the catalyst potential starts increasing but the reaction rate stays constant. This is different from the behaviour observed with O2 conducting solid electrolytes and is due to the fact that the spillover oxygen anions can react with the fuel (e.g. C2H4, CO), albeit at a slow rate, whereas Na(Pt) can be scavenged from the surface only by electrochemical means.1 Thus, as shown on Fig. 9.1, when the potentiostat is used to impose the initial catalyst potential, U r =-430 mV, then the catalytic rate is restored within 100-150 s to its initial value, since Na(Pt) is now pumped electrochemically as Na+ back into the P"-A1203 lattice. 

MPC dynamics follows the motions of all of the reacting species and their interactions with the catalytic spheres therefore collective effects are naturally incorporated in the dynamics. The results of MPC dynamics simulations of the volume fraction dependence of the rate constant are shown in Fig. 19 [17]. The MPC simulation results confirm the existence of a 4> 2 dependence on the volume fraction for small volume fractions. For larger volume fractions the results deviate from the predictions of Eq. (92) and the rate constant depends strongly on the volume fraction. An expression for rate constant that includes higher-order corrections has been derived [95], The dashed line in Fig. 19 is the value of /. / ( < )j given by this higher-order approximation and this formula describes the departure from the cf)1/2 behavior that is seen in Fig. 19. The deviation from the <[)11/2 form occurs at smaller values than indicated by the simulation results and is not quantitatively accurate. The MPC results are difficult to obtain by other means. 

With due regard to the lateral variations in composition which can arise as a consequence of source geometry and positioning (discussed in Section II), it is vise to analyze the alloy film at a number of representative points. For example, if a catalytic reaction was carried out over an alloy film deposited inside a spherical vessel maintained at a constant temperature over its entire area, then the mean alloy composition (and the uniformity of composition) is required. A convenient procedure is to cut glass reaction vessels carefully into pieces at the end of the experiment and to determine the composition by X-ray fluorescence analysis of a number of representative pieces. Compositions of Pd-Ag alloy films (40) determined at 12 representative parts of a spherical vessel from the intensities of the AgK 12 and PdKau fluorescent X-ray emissions are shown in Table V mean compositions are listed in the first column. (The Pd and Ag sources were separate short concentric spirals.) In other applications of evaporated alloy films to adsorption and catalytic studies, as good or better uniformity of composition was achieved. Analyses of five sections of a cylindrical... 

If a reaction that must be investigated follows a reaction sequence as in Scheme 10.1, and if the reaction order for the substrate equals unity, it means that (with reference to Eq. (4 b)), the observed rate constant (k0bs) is a complex term. Without further information, a conclusion about the single constants k2 and fCM is not possible. Conversely, from the limiting case of a zero-order reaction, the Michaelis constant cannot be determined for the substrate. For particular questions such as the reliable comparison of activity of various catalytic systems, however, both parameters are necessary. If they are not known, the comparison of catalyst activities for given experimental conditions can produce totally false results. This problem is described in more detail for an example of asymmetric hydrogenation (see below). 

No general discussion of the multitude of behaviour patterns, especially as regards dependence on concentration of catalyst, or of components of a syncatalyst, can be profitable at this stage. As for the termination reactions - our special concern here - this kinetic pattern implies that Vt is of first order, Vt of zero order, with respect to monomer. This means that k3 or k4 contain a term k iplky, they may also contain one or more equilibrium constants - depending on the nature of the catalytic system. 

SnCl4 or TiCl4 [11, 13, 20, 21]. On the contrary, the experiments show that in the system styrene-TiCl4-(CH2Cl)2 there is no termination at all, since successive portions of styrene added to the same solution of TiCl4 in (CH2C1)2 polymerized at the same rate [11]. This means that the concentration of the catalytic species remained constant. There is evidence to show that in this system polymerization is initiated by C1 CH2.CH2+ ions. 

Hence the dimension ("the order") of the reaction is different, even in the simplest case, and hence a comparison of the two rate constants has little meaning. Comparisons of rates are meaningful only if the catalysts follow the same mechanism and if the product formation can be expressed by the same rate equation. In this instance we can talk about rate enhancements of catalysts relative to another. If an uncatalysed reaction and a catalysed one occur simultaneously in a system we may determine what part of the product is made via the catalytic route and what part isn t. In enzyme catalysis and enzyme mimics one often compares the k, of the uncatalysed reaction with k2 of the catalysed reaction if the mechanisms of the two reactions are the same this may be a useful comparison. A practical yardstick of catalyst performance in industry is the space-time-yield mentioned above, that is to say the yield of kg of product per reactor volume per unit of time (e.g. kg product/m3.h), assuming that other factors such as catalyst costs, including recycling, and work-up costs remain the same. 

For the catalytic electrode mechanism, the total surface concentration of R plus O is conserved throughout the voltammetric experiment. As a consequence, the position and width of the net response are constant over entire range of values of the parameter e. Figure 2.35 shows that the net peak current increases without limit with e. This means that the maximal catalytic effect in particular experiment is obtained at lowest frequencies. Figure 2.36 illustrates the effect of the chemical reaction on the shape of the response. For log(e) < -3, the response is identical as for the simple reversible reaction (curves 1 in Fig. 2.36). Due to the effect of the chemical reaction which consumes the O species and produces the R form, the reverse component decreases and the forward component enhances correspondingly (curves 2 in Fig. 2.36). When the response is controlled exclusively by the rate of the chemical reaction, both components of the response are sigmoidal curves separated by 2i sw on the potential axes. As shown by the inset of Fig. 2.36, it is important to note that the net currents are bell-shaped curves for any observed kinetics of the chemical reaction, with readily measurable peak current and potentials, which is of practical importance in electroanalytical methods based on this electrode mecharusm. 

Although Ymax/ m is traditionally treated as a first-order rate constant for enzyme reactions at low substrate concentration, Northrop recently pointed out that V JK actually provides a measure of the rate of capture of substrate by free enzyme into a productive complex or the complexes destined to go on to form products and complete a turnover at some later time. His analysis serves to underscore the concepts (a) that any catalytic cycle must be characterized by the efficiency of reactant capture and product release, and (b) the Michaelis constant takes on meaning beyond that typically associated with affinity for substrate. Consider the case of an enzyme and substrate operating by the following sequence of reactions ... 

Complex Mean formation constant Relative catalytic activity Refs. 

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