Catalytic rates

FIG. 7-2 Linear analysis of catalytic rate equations, a), (h) Sucrose hydrolysis with an enzyme, r = 1curve-fitted with a fourth-degree polynomial and differentiated for r — (—dC/dt). Integrated equation,... 

In gradientless reactors the catalytic rate is measured under highly, even if not completely uniform conditions of temperature and concentration. The reason is that, if achieved, the subsequent mathematical analysis and kinetic interpretation will be simpler to perform and the results can be used more reliably. The many ways of approximating gradientless operating conditions in laboratory reactors will be discussed next. 

Figure 6.3.2 shows the feed-forward design, in which acrolein and water were included, since previous studies had indicated some inhibition of the catalytic rates by these two substances. Inert gas pressure was kept as a variable to check for pore diffusion limitations. Since no large diffusional limitation was shown, the inert gas pressure was dropped as an independent variable in the second study of feed-back design, and replaced by total pressure. For smaller difftisional effects later tests were recommended, due to the extreme urgency of this project. 

The check for homogeneous reactions should be done by repeating some experiments with different quantities of catalyst charge. For example, make measurements over 20, 40 and 80 cm of catalyst charges with proportionally increased makeup feed rates. Change the RPM to keep the recycle ratio constant (if possible) or the linear rate u constant. The measured catalytic rate should remain the same if nothing happens in the empty space. 

The catalytic triad consists of the side chains of Asp, His, and Ser close to each other. The Ser residue is reactive and forms a covalent bond with the substrate, thereby providing a specific pathway for the reaction. His has a dual role first, it accepts a proton from Ser to facilitate formation of the covalent bond and, second, it stabilizes the negatively charged transition state. The proton is subsequently transferred to the N atom of the leaving group. Mutations of either of these two residues decrease the catalytic rate by a factor of 10 because they abolish the specific reaction pathway. Asp, by stabilizing the positive charge of His, contributes a rate enhancement of 10. ... 

Mutations in the specificity pocket of trypsin, designed to change the substrate preference of the enzyme, also have drastic effects on the catalytic rate. These mutants demonstrate that the substrate specificity of an enzyme and its catalytic rate enhancement are tightly linked to each other because both are affected by the difference in binding strength between the transition state of the substrate and its normal state. 

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. 

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... 

Several features of these RNA enzymes, or ribozymes, lead to the realization that their biological efficiency does not challenge that achieved by proteins. First, RNA enzymes often do not fulfill the criterion of catalysis in vivo because they act only once in intramolecular events such as self-splicing. Second, the catalytic rates achieved by RNA enzymes in vivo and in vitro are... 

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. 

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

The overall catalytic rate constant of SNase is (see, for example, Ref. 3) kcat — 95s 1 at T = 297K, corresponding to a total free energy barrier of Ag at = 14.9 kcal/mol. This should be compared to the pseudo-first-order rate constant for nonenzymatic hydrolysis of a phosphodiester bond (with a water molecule as the attacking nucleophile) which is 2 x 10 14 s corresponding to Ag = 36 kcal/mol. The rate increase accomplished by the enzyme is thus 101S-1016, which is quite impressive. 

Figure 1.3. Rate and catalyst potential response to step changes in applied current during C2H4 oxidation on Pt deposited on YSZ, an O2 conductor. T = 370°C, p02=4.6 kPa, Pc2H4=0.36 kPa. The catalytic rate increase, Ar, is 25 times larger than the rate before current application, r0, and 74000 times larger than the rate I/2F,16 of 02 supply to the catalyst. N0 is the Pt catalyst surface area, in mol Pt, and TOF is the catalytic turnover frequency (mol O reacting per surface Pt mol per s). Reprinted with permission from Academic Press.

C.G. Vayenas, S. Bebelis, and S. Ladas, Dependence of Catalytic Rates on Catalyst Work Function, Nature 343, 625-627 (1990). 

Figure 2.3. Catalysis (0), classical promotion ( ), electrochemical promotion ( , ) and electrochemical promotion of a classically promoted (sodium doped) ( , ) Rh catalyst deposited on YSZ during NO reduction by CO in presence of gaseous 02.14 The Figure shows the temperature dependence of the catalytic rates and turnover frequencies of C02 (a) and N2 (b) formation under open-circuit (o.c.) conditions and upon application (via a potentiostat) of catalyst potential values, UWr, of+1 and -IV. Reprinted with permission from Elsevier Science.

Electrochemical promotion of the unpromoted Rh/YSZ film, via application of 1 or -1 V, leads to significant rate enhancement (tenfold increase in rCo2> four fold increase in rN2 (filled circles and diamonds in Fig. 2.3). This is a catalytic system which as we will see in Chapters 4 and 8 exhibits inverted volcano behaviour, i.e. the catalytic rate is enhanced both with positive and with negative potential. 

In the single-chamber type reactor (Fig. 4.1b) all three electrodes (catalyst-working (W), counter (C) and reference (R)), electrode are all in the same chamber and are all exposed to the reactants and products.1 3 In this case the counter and reference electrodes must be made from a catalytically inert (e.g. Au) material for otherwise the catalytic rate on them will obscure the measured (via gas-chromatography or mass-spectrometry, Fig. 4.2) rate on the catalyst-working electrode. 

Since electrochemical promotion (NEMCA) studies involve the use of porous metal films which act simultaneously both as a normal catalyst and as a working electrode, it is important to characterize these catalyst-electrodes both from a catalytic and from an electrocatalytic viewpoint. In the former case one would like to know the gas-exposed catalyst surface area A0 (in m2 or in metal mols, for which we use the symbol NG throughout this book) and the value, r0, of the catalytic rate, r, under open-circuit conditions. 

Figure 4.14 shows a similar galvanostatic transient obtained during C2H4 oxidation on Rh deposited on YSZ.50 Upon application of a positive current 1=400 pA with a concomitant rate of O2 supply to the catalyst I/2F=2.M0 9 mol O/s the catalytic rate increases from its open-circuit value r0=1.8 10 8 mol O/s to a new value r= 1.62-1 O 6 mol O/s which is 88 times larger than the initial unpromoted rate value. The rate increase Ar is 770 times larger than the rate of supply of O2 ions to the Rh catalyst surface. 

As shown in Fig. 4.15, increasing 0wa up to 0.02 causes a linear decrease in Uwr and a concomitant 230% increase in catalytic rate. The rate increase Ar 5,5T0 7 mol O/s is 2600 times larger than -I/F. Upon further increasing 0Na in the interval O.O2<0Nadecreases sharply and reaches values below the initial unpromoted value ro. When 0Na exceeds 0.06, UWr starts decreasing sharply while r decreases more slowly. The system cannot reach steady state since 0Na is constantly increasing with time due to the applied constant current. 

The common feature of galvanostatic electrochemical promotion experiments is that, both in the case of O2 and Na+-conductors, one obtains pronounced changes in catalytic rate which are orders of magnitude larger than the rate of supply of ions onto the catalyst surface. 

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