Page 203 - Introduction to chemical reaction engineering and kinetics

8.2 Molecular Catalysis 185

A mechanism for a pseudo-first-order reaction involving the hydrolysis of substrate
S catalyzed by acid HA that is consistent with the observed rate law rs = kobscS, is as
follows:

S + HA&H+ + A- (fast)
SH+ + H,O 3 products (slow)

This gives

(-3) = k2CsH+‘kzo

= k24 CHzO % cHAicA-
(8.2-7)
= (k2KliKa)cH20cH+cS
if, in addition, the acid HA is at dissociation equilibrium, characterized by K,, the acid
dissociation constant. According to this, the observed catalytic rate constant is

k obs = @2fh~KakH20CH+ + h-x+%+ (8.243)

which, with cHZo virtually constant (H,O in great excess), has the characteristics of
specific hydrogen-ion catalysis (type B above), with the second term on the right of
equation 8.2-5 predominating.

8.2.2.2 General Acid-Base Catalysis
In general acid-base catalysis, the observed rate constant depends on the concentrations
of all acids and bases present. That is, in aqueous systems,

k obs = k, + kH+ CH+ + kOH- COH- + 2 kHAcHA + 1 kA- CA- (8.2-9)

The systematic variation of cH+, CoH-, etc. allows the experimental determination of
each rate constant. If the terms in the first summation on the right of equation 8.2-9
predominate, we have general acid catalysis; if those in the second summation do so, we
have general base catalysis; otherwise, the terminology for specific acid-base catalysis
applies, as in the previous section.
The mechanism in the previous section with a single acid can be used to show the
features of, say, general acid catalysis, if the second step is not rate-determining but
fast, and the first step is not a rapidly established equilibrium but involves a slow (rate-
determining) step in the forward direction characterized by the rate constant kHA.
Then,

(8.2-10)
(-rS) = kHACHACS = kobsCS
which would result in

k obs = 2 kHACHA (8.2-11)

if more than one acid were present as catalyst, corresponding to the first summation on
the right in equation 8.2-9.
Acid-base catalysis is important for reactions of hydrocarbons in the petrochemical
industry. Acids, either as solids or in solution, react with hydrocarbons to form reactive