Catalytic coefficients

Find the catalytic coefficient for the hydrogen ions and the specific rate of the uncatalyzed reaction. 

A catalytic process (often involving proton transfer) in which both functional groups of a bifunctional chemical species participate in the rate-controlling step. In such systems, the catalytic coefficient is larger than would be expected were only one functional group present. Bifunctional catalysis is not the same as two different catalysts acting in concert. 

The catalysis of mutarotation of glucosamine hydrochloride involves an intramolecular mechanism, and so the catalytic coefficient of glucosamine. fcc,iNH2> must have the dimension, min.-1, instead of liters/mole min. The total rate is then... 

It seems much more likely that the transfer of the proton is actually involved in the rate-limiting step for the hydrolysis of carboxylic orthoesters. This is consistent with the observed catalytic constants. If Bunton and Dewolfe s estimate of Ka = 107 is accepted for the dissociation constant of the conjugate acid of an orthoester, and if the rate coefficient for the loss of the proton, k2, is of the order of 10" sec-1, then k, will be about 104 l mole-l sec-1, close to the value observed, for example, for the catalytic coefficient for the acid-catalyzed hydrolysis of ethyl orthoacetate at 20°C103. 

As the concentration of BH increases, the observed catalytic coefficient will decrease until, when 2[BH] > k, the catalytic coefficient equals ,[OH ] and the rate-determining step is the addition of hydroxide ion to the substrate. Choice may be made between a number of unsymmetrical mechanisms depending upon the rate dependence upon hydrogen ion, hydroxide ion or water concentrations at high buffer concentrations or [B] or [BH] at low buffer concentrations. Johnson has tabulated the 18 kinetic possibilities and the 13 different types of kinetic behaviour of general acid-base-catalysed reaction, pointing out that this tabulation uses only one ionic form for the tetrahedral intermediate. 

Bunton and Fendler297 have shown that fluoride ion will catalyse the hydrolysis of acetic and succinic anhydrides in water and aqueous dioxan. In water, the rate of loss of acetic anhydride is greater than the rate of formation of acetic acid, showing the build up of acetyl fluoride. The hydrolysis of succinic anhydride is also catalysed by fluoride ion but no build up of succinyl fluoride is seen. The catalysis of anhydride hydrolysis by pyridine has been discussed in the previous section, and it is perhaps sufficient to mention here that the catalytic coefficient for pyridine is about 30,000 times greater than that for acetate ion in 50% aqueous acetone at 25°C. 

The chemical properties of the crystalline enzyme obtained from beef kidney cortex, have been studied extensively (72, 88). Based upon a molecular weight of 37,000, and a specific activity of 26,500 units/mg, the catalytic coefficient for glucose is calculated to be 0.98 X 106 (72). Because of this high efficiency, the nature of the active site is of considerable interest. 

Hydronium ion catalytic coefficients for enolization and ketonization of simple aldehydes and ketones correlate with the enolization equilibrium constants pAE.48 The slopes of the two correlations are of opposite sign (-0.17 and 0.83, respectively), ketonization being considerably more sensitive to a change in the driving force. 

According to transition-state theory it is possible to consider reaction velocities in terms of a hypothetical equilibrium between reactants and transition state. It follows that the influence of the isotopic composition of the medium on reaction velocity can be considered to be the same as its influence on the concentration of transition states. The kinetic formulation of the problem can thus be replaced by one couched in equilibrium terms, and the equilibrium theory of the preceding section can be applied with a minimum of modification (Kresge, 1964). The rate constant, or catalytic coefficient, (k) for a catalysed reaction can be written as the product of three factors, viz. the equilibrium constant (K ) for the process forming the transition state from the reactants, the transmission coefficient, and the specific rate of transition state decomposition (kT/h). We recognize that the third factor is independent of the isotopic nature of the reaction and assume that there is no isotope effect on the transmission coefficient. It follows that... 

It is an empirical fact that the fractionation factor < LA for acetic acid has a value close to unity (Gold and Lowe, 1968), whence it follows that kn should be a linear function of n, as has been observed (Gold and Waterman, 1968a, b). The profoundly contrasting behaviour of the catalytic coefficients for the hydrogen ion and for a monobasic acid, in the predicted maimer, powerfully supports the analysis in terms of exchange effects as against an interpretation in terms of transfer effects (see IVCI). 

Accordingly, the catalytic coefficients of hydrogen ion in the isotopically pure media (ka and kD) are related to the coefficients of HsO+ and D80+ in isotopically mixed media by the equations ... 

The Brensted a s were determined by carboxylic acids unless otherwise noted. 6 The catalytic coefficients for this reaction are actually composite quantities. c Anilinium ions were used. 

If a proton-transfer reaction is visualized as a three-body process (Bell, 1959b), a linear free energy relationship is predicted between the acid dissociation constant, Aha, and the catalytic coefficient for the proton-transfer reaction, HA. Figure I shows the relationships between ground-state energies and transition-state energies. This is a particular case of the Bronsted Catalysis Law (Bronsted and Pedersen, 1924) shown in equation (9). The quantities p and q are, respectively, the number of... 

There have now been a number of tests of equation (9) for A-SE2 reactions (see Table 1), and some of the results are shown in Figs. 2a-c. It is accurately obeyed by catalytic coefficients for carboxylic acids, but other classes of acids give rise to systematic deviations. Phosphoric acid and bisulfate ion seem always to be above the line generated by carboxylic acids, and H+, if its conjugate base, H20, is considered to be present in 55m concentration, is always below this line. Other homogeneous classes of acids, such as anilinium ions, may give rise to separate Bronsted lines (Thomas and Long, 1964). These deviations would seem to imply that the three-center model is at least oversimplified. 

It may be noted that kha/kda values are only a little different from cH//cd values, at least when the acids are fairly strong. For monobasic acids values of catalytic coefficient ratios, HA/fcDA, are also similar to kmaIkj>a> thus, for semi-quantitative mechanistic purposes these three quantities may be used interchangeably as a first approximation. 

The anomalous catalytic coefficient of HSOj" becomes reasonable if the solvation of the acid fragment of the transition state is characteristic of the acid itself (Kreevoy et al., 1967). The solvation of the SO 4 fragment... 

Kresge et al. (1967) have recently chosen to emphasize those features of AS and zlH for aromatic proton exchange which behave as would be predicted from equilibrium theory. However these systems show the quantitative anomalies referred to in a fairly typical way. The AS values for H+ are more negative by 5-10 cal mole""1 deg-1 than can be readily accommodated and the catalytic coefficient for HSOj" is as large or larger than that for H+ (Kresge et al., 1965a). 

Catalytic Coefficients, Br nsted Coefficients and Acidities for the Halogenation of Various Carbonyl Compounds"... 

R is the catalytic coefficient obtained using the anion of a hypothetical acid of pKa — 4 and indicates the reactivity of the substrate. 

Br nsted Coefficients and Catalytic Coefficients for Various Vinyl Ethers"... 

R is the catalytic coefficient using a hypothetical acid catalyst of pAfa = 4 and indicates substrate reactivity. 

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