The Mathematics of General Catalysis

26 shows a scenario in which the first step involves an acid that facilitates a reaction of water witli the substrate. This is the rate-determining step. An intermediate is formed that results from the addition of water to the reactant [HRCHaO) ] the structural details are unimportant here. The intermediate then loses a proton in a second fast step to regenerate the acid HA and give the product. General catalysis does not require that water be one of the reactants. This just simplifies our current analysis because we assume that its concentration is constant and is incorporated into the rate constant k. The kinetic expression for this reaction is given in Eq. 9.27, which reflects only the first step of Eq. 9.26 because it is rate-determining. Alternatively, one can substitute the relationship [HA] = [HjO llA I/K, to achieve Eq. 

Since the acid or base is always regenerated after the reaction, its concentration never changes over the course of the reaction. Hence, the reaction is pseudo-first order, as in Eq. 

The concentration of either HA or A is now in the rate expression, in contrast to that found for specific catalysis. This means that the concentration of the acid (or its conjugate base) that results from addition of an acid to the reaction vessel does affect the rate of the reaction. We should expect this because the acid is actually in the rate-determining step. Any acid in the solution will act as a catalyst. 

An example of a pnjssible mechanism involving the general-acid-catalyzed hydration of acetone. B. Anexampleof a possible mechanism involving a general-ba.se-catalyzed hydration. Do not take these scenarios as the correct mechanisms for these addition reactions, but consider them, instead, as simply possibilities highlighting our discussion. 

---