General catalysis kinetic plots

The data for the reactions of potassium cyanide with benzyl halides at 85 C and 25 C are summarized in Tables I-III and graphical representations of these data are shown in Figures 1-3. The reactions carried out at 85 C were followed to 70% completion, while those at 25 C were followed to 50% completion. In general, excellent first-order kinetic plots were obtained. Each point on the graphs represents an average of at least three kinetic determinations. It is interesting to note that in the absence of added water (solid-liquid phase transfer catalysis), the rates of benzyl halide disappearance were more accurately described by zero-order kinetics. 

The distinctive kinetic plots for general-acid and general-base catalysis. A. The dependence of Jtobs for a general-acid-catalyzed reaction on the concentration of an added acid HA at constant pH. B. The dependence of for a general-base-catalyzed reaction on the concentration of an added base B at constant... 

A number of studies of the acid-catalyzed mechanism of enolization have been done. The case of cyclohexanone is illustrative. The reaction is catalyzed by various carboxylic acids and substituted ammonium ions. The effectiveness of these proton donors as catalysts correlates with their pK values. When plotted according to the Bronsted catalysis law (Section 4.8), the value of the slope a is 0.74. When deuterium or tritium is introduced in the a position, there is a marked decrease in the rate of acid-catalyzed enolization h/ d 5. This kinetic isotope effect indicates that the C—H bond cleavage is part of the rate-determining step. The generally accepted mechanism for acid-catalyzed enolization pictures the rate-determining step as deprotonation of the protonated ketone ... 

Belke et al. (1971) reported general base and general acid catalysis in cyclization of 2-hydroxymethylbenzamide [equation (18)]. However, with 2-hydroxymethyl-6-aminobenzamide strict general base catalysis by buffer bases is observed with a Bronsted coefficient of O 39 (Fife and Benjamin, unpublished data). In contrast with the unsubstituted amide, the Bronsted plot is nicely linear. An amino-group in the 6-position might assist decomposition of a tetrahedral intermediate as in [37a, b] or a kinetic equivalent. The pH-rate constant profile for spontaneous cyclization at zero buffer concentra-... 

Mandelate racemase, another pertinent example, catalyzes the kinetically and thermodynamically unfavorable a-carbon proton abstraction. Bearne and Wolfenden measured deuterium incorporation rates into the a-posi-tion of mandelate and the rate of (i )-mandelate racemi-zation upon incubation at elevated temperatures. From an Arrhenius plot, they obtained a for racemization and deuterium exchange rate was estimated to be around 35 kcal/mol at 25°C under neutral conditions. The magnitude of the latter indicated mandelate racemase achieves the remarkable rate enhancement of 1.7 X 10, and a level of transition state affinity (K x = 2 X 10 M). These investigators also estimated the effective concentrations of the catalytic side chains in the native protein for Lys-166, the effective concentration was 622 M for His-297, they obtained a value 3 X 10 M and for Glu-317, the value was 3 X 10 M. The authors state that their observations are consistent with the idea that general acid-general base catalysis is efficient mode of catalysis when enzyme s structure is optimally complementary with their substrates in the transition-state. See Reference Reaction Catalytic Enhancement... 

The kinetic law is generally of the type rate = A 2 [acetylene] [H+]. In concentrated acid solutions, the plot of log koha vs H0 in the case of compounds 2 is linear with essentially unit slope (Noyce et al., 1965, 1967 Noyce and De Bruin, 1968). The study of the reaction in a series of buffers showed that it is subject to general acid catalysis (Noyce and Schiavelli, 1968a Stamhuis and Drenth, 1961) and the application of the Bunnett, Grunwald and similar treatments in the case of thio-alkoxyacetylene derivatives (Hogeveen and Drenth, 1963b) clearly indicate that the addition of a water molecule does not take place in the slow step of the reaction. 

A number of other proton transfer reactions from carbon which have been studied using this approach are shown in Table 8. The results should be treated with reserve as it has not yet been established fully that the derived Bronsted exponents correspond exactly with those determined in the conventional way. One problem concerns the assumption that the activity coefficient ratios cancel, but doubts have also been raised by one of the originators of the method that, unless solvent effects on the transition state are intermediate between those on the reactants and products, anomalous Bronsted exponents will be obtained [172(c)]. The Bronsted exponents determined for menthone and the other ketones in Table 8 are roughly those expected by comparison with the values obtained for ketones using the conventional procedure (Table 2). For nitroethane the two values j3 = 0.72 and 0.65 which are shown in Table 8 result from the use of different H functions determined with amine and carbon acid indicators, respectively. Both values are roughly similar to the values (0.50 [103], 0.65 [104]), obtained by varying the base catalyst in aqueous solution. The result for 2-methyl-3-phenylpropionitrile fits in well with the exponents determined for malononitriles by general base catalysis but differs from the value j3 0.71 shown for l,4-dicyano-2-butene in Table 8. This latter result is also different from the values j3 = 0.94 and 0.98 determined for l,4-dicyano-2-butene in aqueous solution with phenolate ions and amines, respectively. However, the different results for l,4-dicyano-2-butene are to be expected, since hydroxide ion is the base catalyst used in the acidity function procedure and this does not fit the Bronsted plot observed for phenolate ions and amines. The primary kinetic isotope effects [114] also show that there are differences between the hydroxide ion catalysed reaction (feH/feD = 3.5) and the reaction catalysed by phenolate ions (kH /kP = 1.4). The result for chloroform, (3 = 0.98 shown in Table 8, fits in satisfactorily with the most recent results for amine catalysed detritiation [171(a)] from which a value 3 = 1.15 0.07 was obtained. 

Figure 3 Idealized pH dependence of a ribozyme reaction. Ideal pH-species plots and pH-/cobs profiles according to a kinetic model for general acid/base catalysis. The solid lines depict a mechanism in which the species with the lower pKa (pKa,1) acts as the general base (shown by blue lines), and the species with the higher pKa (pKa,2) acts as the general acid (shown by red lines). The black line indicates the observed pH dependence of the reaction rate. The dotted lines simulate a mechanism in which the catalytic roles of the species with pKa,1 and pKa,2 have been switched. Adapted from References 34 and 35.

There are several types of pH-dependent kinetic behavior that can be interpreted in terms of one or more of the various forms of the specific acid-base catalysis relation [equation (7.3.2)]. Skrabal (33) classified the various possibilities that may arise in reactions of this type, and Figure 7.3 is based on this classification. The various forms of the plots of log k versus pH reflect the relative importance of each of the various terms in equation (73.2) as the pH shifts. Curve a represents the most general type of behavior. This curve consists of a region where add catalysis is superimposed on the noncatalytic reaction, a region where neither acid nor base catalysis is significant. 

The results indicate that the use of Eq. (3.3.33), which is exact for first-order kinetics, for other reaction orders may introduce a serious error. This is in contrast to the result for the heterogeneous catalysis in a porous pellet or on a solid surface, in which the difference between the effectiveness factors for different reaction orders is much smaller, when plotted against the Thiele modulus generalized for different reaction order [25, 26]. 

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