Experimental Indications of General Catalysis

General catalysis is detected by rate measurements at constant pH but different buffer concentrations. If the rate of the reaction is independent of the concentration of the buffer, specific acid catalysis is involved; the rate is dependent specifically on the concentration of hydronium ion. The components of the buffer have no effect on the rate other than to establish the pH of the solution.

On the other hand, if the rate of the reaction does increase with increasing concentration of the buffer at a constant pH, the rate of the reaction is thus shown to be dependent upon the concentration of a component of the buffer, HA in the case of acid catalysis, or A− in the case of base catalysis. Dependence of the rate of an acid- or base-catalyzed reaction on the concentration of the buffer as well as on the pH of the solution indicates general catalysis by all Brønsted acids in acid catalysis, and general catalysis by all Brønsted bases in base catalysis.

Conditions for General Catalysis

Kwan suggests that we consider a hypothetical acid-catalyzed reaction in which three paths contribute to the overall transformation. The first path involves catalysis by hydronium ion, the second path involves catalysis by the acidic component of the buffer, HA, and the third path is an “uncatalyzed” process, or “water” reaction. Kwan writes the observed pseudo first-order rate constant for the overall reaction, kobs, as

In this equation the first term on the right represents catalysis by hydronium ion, the “specific” reaction; the second term on the right represents catalysis by the acidic member of the buffer pair, the “general” reaction; and the third term on the right represents the “water” reaction.

The question is When might the “general” path, represented by the second term on the right in eq 4, be important? Kwan answers the question by expressing the contribution of the general path as a fraction, f, of the total rate. Representing the fraction as fgeneral we write Kwan’s “fractional function” as

Division of both the top and the bottom of the fraction by the rate of the general reaction converts eq 5 to

Consideration of eq 5a leads to the following conclusions:

• fgeneral will be important only when the general rate is greater than the acid rate (term 1 in the denominator is small) and when the general rate is greater than the water rate (term 3 in the denominator is small).
• As the solution becomes more acidic than the pKa of HA the numerator of term 1 of the denominator will become large as [H3O+] will continue to increase after [HA] has reached its limit; fgeneral will then be small.
• As the solution becomes more basic than the pKa of HA the denominator of term 3 becomes small as [HA] becomes small; term 3 of the denominator becomes large and fgeneral will then be small.

The overall conclusion is that if general acid catalysis is to be observed it should be sought in a range of pH that includes the pKa of the weak acid HA.

As Kwan says, general base catalysis can be approached in the same way. The overall conclusion is that if general base catalysis is to be observed it should be sought in a range of pH that includes the pKa of the weak acid HA.

Mechanistic Implications of General Catalysis

In specific acid catalysis a reactant is in equilibrium with its conjugate acid, and the proton transfer is not rate-determining. In contrast, proton transfer is part of the rate-determining step in general acid catalysis. In specific acid catalysis there is only one path when the uncatalyzed or water reaction is insignificant and that one path includes equilibrium formation of the conjugate acid of a reactant. The position of the equilibrium is determined by the pH of the solution, which is set by the ratio of the members of the conjugate pair of the buffer and the pKa of the conjugate acid of the reactant. The concentration of the buffer does not affect the position of the equilibrium.

In general catalysis the proton transfer is part of the rate-determining step, and there will be multiple paths to product. In general acid-catalyzed reactions there will be as many paths as there are proton donors. In general base-catalyzed reactions there will be as many paths as there are proton acceptors. Not all paths, of course, will carry the same amount of traffic. The Brønsted relationship indicates the relative magnitudes of the rate constants for reactions over the various paths. The actual traffic over a path is determined by the product of a rate constant and the corresponding concentration. This is why in more acidic solutions most of the traffic is over the hydronium ion path, and in more basic solutions most of the traffic is over the hydroxide ion path. Under these conditions the traffic over a general path may be too small to be detected.

The short answer is “when proton transfer might be slow”, or, more usefully, “when the reaction of the product of proton transfer might be especially fast.” Since proton transfers to and from oxygen are typically fast, equilibrium is usually established and specific catalysis is observed. If the conjugate acid of the reactant is especially reactive, however, partial transfer of the proton may be sufficient to allow the next step of the reaction to occur as the proton is transferred. When this happens one can find general catalysis. The general acid-catalyzed hydrolysis of the di-tert-butyl acetal of benzaldehyde in acetate buffers, cited by Kwan, can be seen as an example of this.

In contrast to rapid proton transfer to and from oxygen, proton transfer to or from carbon is often rate-limiting and can be the occasion for general catalysis. Examples include the general acid-catalyzed hydrolysis of the enol ether of cyclohexanone and the general acid-catalyzed interconversion of enols and enolates.

Biochemical reactions are limited to an environment with a pH of about 7. While the chemist might make the solution more acidic or more basic so as to speed the reaction, the cell does not have this option. One of the alternatives available to biochemical systems, however, is general catalysis.

The most conceptually problematic feature of general catalysis is its mechanistic ambiguity. That is, general catalysis can often be interpreted in two ways that, at first sight, appear to be contradictory. Thus the experimental observation of general acid catalysis can sometimes be interpreted either as mechanistic general catalysis by HA or as mechanistic specific acid catalysis by hydronium ion and general base catalysis by A−.

Summary

General catalysis is indicated when the rate of the reaction depends upon the concentration of the buffer as well as the pH of the solution, it is most likely to be observed when the pH of the solution is near the pKa of the buffer, and the reaction mechanism involves proton transfer in the rate-determining step.

Supplemental Material

Recommended reading on this subtle and important subject are available below.

Literature Cited

1. Kwan, E. E. J. Chem. Educ. 2005, 82, 1026-1030.

See author’s reply.