Catalytic rate constant

Boltzmann universal constant first-order inactivation rate constant Planck universal constant catalytic rate constant catalytic rate constant at infinite dilution reaction rate constants according to reaction scheme molar concentration of product molar concentration of competitive inhibitor product molar concentration of non-competitive inhibitor product... 

Figure C2.7.4. Catalytic cycle for hydrogenation of methyl-(Z)-a-acetamidocinnamate tire rate constants were measured at 298 K S is solvent [8],...

A different kind of shape selectivity is restricted transition state shape selectivity. It is related not to transport restrictions but instead to size restrictions of the catalyst pores, which hinder the fonnation of transition states that are too large to fit thus reactions proceeding tiirough smaller transition states are favoured. The catalytic activities for the cracking of hexanes to give smaller hydrocarbons, measured as first-order rate constants at 811 K and atmospheric pressure, were found to be the following for the reactions catalysed by crystallites of HZSM-5 14 n-... 

The rate constants for the catalysed Diels-Alder reaction of 2.4g with 2.5 (Table 2.3) demonstrate that the presence of the ionic group in the dienophile does not diminish the accelerating effect of water on the catalysed reaction. Comparison of these rate constants with those for the nonionic dienophiles even seems to indicate a modest extra aqueous rate enhancement of the reaction of 2.4g. It is important to note here that no detailed information has been obtained about the exact structure of the catalytically active species in the oiganic solvents. For example, ion pairing is likely to occur in the organic solvents. 

In the kinetic runs always a large excess of catalyst was used. Under these conditions IQ does not influence the apparent rate of the Diels-Alder reaction. Kinetic studies by UV-vis spectroscopy require a low concentration of the dienophile( 10" M). The use of only a catalytic amount of Lewis-acid will seriously hamper complexation of the dienophile because of the very low concentrations of both reaction partners under these conditions. The contributions of and to the observed apparent rate constant have been determined by measuring k pp and Ka separately. ... 

In determining the values of Ka use is made of the pronounced shift of the UV-vis absorption spectrum of 2.4 upon coordination to the catalytically active ions as is illustrated in Figure 2.4 ". The occurrence of an isosbestic point can be regarded as an indication that there are only two species in solution that contribute to the absorption spectrum free and coordinated dienophile. The exact method of determination of the equilibrium constants is described extensively in reference 75 and is summarised in the experimental section. Since equilibrium constants and rate constants depend on the ionic strength, from this point onward, all measurements have been performed at constant ionic strength of 2.00 M usir potassium nitrate as background electrolyte . 

The kinetic data are essentially always treated using the pseudophase model, regarding the micellar solution as consisting of two separate phases. The simplest case of micellar catalysis applies to unimolecTilar reactions where the catalytic effect depends on the efficiency of bindirg of the reactant to the micelle (quantified by the partition coefficient, P) and the rate constant of the reaction in the micellar pseudophase (k ) and in the aqueous phase (k ). Menger and Portnoy have developed a model, treating micelles as enzyme-like particles, that allows the evaluation of all three parameters from the dependence of the observed rate constant on the concentration of surfactant". ... 

The catalytic effect on unimolecular reactions can be attributed exclusively to the local medium effect. For more complicated bimolecular or higher-order reactions, the rate of the reaction is affected by an additional parameter the local concentration of the reacting species in or at the micelle. Also for higher-order reactions the pseudophase model is usually adopted (Figure 5.2). However, in these systems the dependence of the rate on the concentration of surfactant does not allow direct estimation of all of the rate constants and partition coefficients involved. Generally independent assessment of at least one of the partition coefficients is required before the other relevant parameters can be accessed. 

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. 

Decomposition of diphenoylperoxide [6109-04-2] (40) in the presence of a fluorescer such as perylene in methylene chloride at 24°C produces chemiluminescence matching the fluorescence spectmm of the fluorescer with perylene was reported to be 10 5% (135). The reaction follows pseudo-first-order kinetics with the observed rate constant increasing with fluorescer concentration according to = k [flr]. Thus the fluorescer acts as a catalyst for peroxide decomposition, with catalytic decomposition competing with spontaneous thermal decomposition. An electron-transfer mechanism has been proposed (135). 

Complexes of Ir(III) are kineticaHy inert and undergo octahedral substitution reactions slowly. The rate constant for aquation of prBr(NH3)3] " [35884-02-7] at 298 K has been measured at 2 x 10 ° (168). In many cases, addition of a catalytic reducing agent such as hypophosphorous acid... 

Condensation occurs most readily at a pH value equal to the piC of the participating silanol group. This representation becomes less vaUd at pH values above 10, where the rate constant of the depolymerization reaction k 2 ) becomes significant and at very low pH values where acids exert a catalytic influence on polymerization. The piC of monosilicic acid is 9.91 0.04 (51). The piC value of Si—OH decreases to 6.5 in higher order sihcate polymers (52), which is consistent with piC values of 6.8 0.2 reported for the surface silanol groups of sihca gel (53). Thus, the acidity of silanol functionahties increases as the degree of polymerization of the anion increases. However, the exact relationship between the connectivity of the silanol sihcon and SiOH acidity is not known. 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

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. 

In the presence of 6-iodo-l-phenyl-l-hexyne, the current increases in the cathodic (negative potential going) direction because the hexyne catalyticaHy regenerates the nickel(II) complex. The absence of the nickel(I) complex precludes an anodic wave upon reversal of the sweep direction there is nothing to reduce. If the catalytic process were slow enough it would be possible to recover the anodic wave by increasing the sweep rate to a value so fast that the reduced species (the nickel(I) complex) would be reoxidized before it could react with the hexyne. A quantitative treatment of the data, collected at several sweep rates, could then be used to calculate the rate constant for the catalytic reaction at the electrode surface. Such rate constants may be substantially different from those measured in the bulk of the solution. The chemical and electrochemical reactions involved are... 

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. 

Throughout this section attention is restricted to rate equations that include concentrations of only the substrate, H, and OH. The observed first-order rate constant, therefore, contains concentrations of only H and OH (the quantity [OH ] is often replaced by A",v/[H j). The substrate (reactant) may be ionizable. Rate equations containing the concentration of additional solutes (especially catalytic additives) can be developed as shown in Section 6.3. 

These are rate constants for the hydrolysis of cinnamic anhydride in bicarbonate-carbonate buffers. The pK of bicarbonate is 10.22. Find the rate constant for hydrolysis, at each pH, at zero buffer concentration. Analyze the data to determine if the acid or base component of the buffer, or both, are responsible for catalysis, and give the catalytic rate constant(s). 

These rate constants are for the hydrolysis of cinnamic anhydride in carbonate buffer, pH 8.45, total buffer concentration 0.024 M, in the presence of the catalysts pyridine, A -methylimidazole (NMIM), or 4-dimethylaminopyridine (DMAP). In the absence of added catalyst, but the presence of buffer, the rate constant was 0.005 24 s . You may assume that only the conjugate base form of each catalyst is catalytically effective. Calculate the catalytic rate constant for the three catalysts. What is the catalytic power of NMIM and of DMAP relative to pyridine ... 

These data are for the nucleophilic catalysis of the hydrolysis of p-nitrophenyl acetate by imidazoles and benzimidazoles at pH 8.0. Tbe apparent second-order catalytic rate constants are defined by... 

That is, k t/K,n is an apparent second-order rate constant ior the reaction of E and S to form product. Because A , is inversely proportional to the affinity of the enzyme for its substrate and is directly proportional to the kinetic efficiency of the enzyme, A , provides an index of the catalytic efficiency of an enzyme operating at substrate concentrations substantially below saturation amounts. 

But k must always be greater than or equal to k h / (A i + kf). That is, the reaction can go no faster than the rate at which E and S come together. Thus, k sets the upper limit for A ,. In other words, the catalytic effieiency of an enzyme cannot exceed the diffusion-eontroUed rate of combination of E and S to form ES. In HgO, the rate constant for such diffusion is approximately (P/M - sec. Those enzymes that are most efficient in their catalysis have A , ratios approaching this value. Their catalytic velocity is limited only by the rate at which they encounter S enzymes this efficient have achieved so-called catalytic perfection. All E and S encounters lead to reaction because such catalytically perfect enzymes can channel S to the active site, regardless of where S hits E. Table 14.5 lists the kinetic parameters of several enzymes in this category. Note that and A , both show a substantial range of variation in this table, even though their ratio falls around 10 /M sec. 

Interpretations may be ephemeral, but experimental data are permanent. To conserve space, the collection of kinetic data presented here is confined to studies which include the determination of at least one activation parameter. For kinetic studies reporting rate constants at a single temperature the following references should be consulted 21, 23, 27, 29(b), 30, 31, 33-39, 44, 46, 48, 52, 81, 86, 92, 96, 99, 141, and 142, as well as some of the tables in this review. Among the excluded studies, those involving catalytic phenomena are especially worthy of mention. 

There is a complication in choosing a catalyst for selective reductions of bifunctional molecules, For a function to be reduced, it must undergo an activated adsorption on a catalytic site, and to be reduced selectively it must occupy preferentially most of the active catalyst sites. The rate at which a function is reduced is a product of the rate constant and the fraction of active sites occupied by the adsorbed function. Regardless of how easily a function can be reduced, no reduction of that function will occur if all of the sites are occupied by something else (a poison, solvent, or other function). 

A few examples have been reported in which no steric parameter is involved in the correlation analysis of cyclodextrin catalysis. Straub and Bender 108) showed that the maximal catalytic rate constant, k2, for the (5-cyclodextrin-catalyzed decarboxylation of substituted phenylcyanoacetic acid anions (J) is correlated simply by the Hammett a parameter. 

Figure 5a indicates the effect of the CTAB concentration on the rate constants of the complexes of 38b and 38c. In the case of the water soluble 38b ligand, the rate increases with increasing CTAB concentration up to a saturation level. This type of saturation kinetics is usually interpreted to show the incorporation of a ligand-metal ion complex into a micellar phase from a bulk aqueous phase, and the catalytic activity of the complex is higher in the micellar phase than in the aqueous phase. In the case of lipophilic 38c, a very similar curve as in Fig. 4 is obtained. At a first glance, there appears to be a big difference between these two curves. However, they are rather common in micellar reactions and obey the same reaction mechanism 27). 

Table 9. Catalytic rate constants of PVIin A A and imidazole with ANTI108 ...

The example of consecutive, irreversible heterogeneous catalytic reaction of the type A —> B — C has been solved in a more general way by Thomas et al. (16). The authors considered scheme (III) with the listed values of the rate constants of surface reactions along with the constants of adsorption and desorption of the reactant A and of the product C. 

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