Page 205 - Introduction to chemical reaction engineering and kinetics

8.3 Autocatalysis 187

Reaction kinetics involving such catalysts can be demonstrated by the following
mechanism:

L.M&L+M (1)
M+A>MeA (2)
M.A-%M+B (3)

Here, L is a mobile ligand which can leave the metal site (M) open briefly for reac-
tion with A in the initial step of the catalytic cycle. The transformation of the M l A
complex into products completes the cycle. The equilibrium in step (1) lies far to the
left in most cases, because the ligands protect the metal centers from agglomeration.
Thus, the concentration of M is very small, and the total concentration of catalyst is
cMr = cILIeA + cILIeL. The rate law which arises from this mechanism is

(--A) = k2 k3 KCACMlt (8.2-12)
k3cL + kIKCA

This rate expression has a common feature of catalysis-that of rate saturation. The
(nonseparable) rate is proportional to the amount of catalyst. If reaction step (2) is
slow (b is small and the first term in the denominator of 8.2-12 is dominant), the rate
reduces to

(8.2-13)
terA) = (k&Mtk)CA

In this limit, the reaction is first order with respect to A, and most of the catalyst is in
the form of M l L. Notice the inhibition by the ligand. If reaction step (3) is slow (k3
small), the rate simplifies to

(8.2-14)
(-rA) = k3CMt
In this case, most of the catalyst is in the form of M 0 A and the reaction is zero order
with respect to A. Thus, the kinetics move from first order at low CA toward zero order
as CA increases. This featUre Of the rate “SatUrating” or reaching a phteaU iS common t0
many catalytic reactions, including surface catalysis (Section 8.4) and enzyme catalysis
(Chapter 10).

8.3 AUTOCATALYSIS
Autocatalysis is a special type of molecular catalysis in which one of the products of
reaction acts as a catalyst for the reaction. As a consequence, the concentration of this
product appears in the observed rate law with a positive exponent if a catalyst in the
usual sense, or with a negative exponent if an inhibitor. A characteristic of an autocat-
alytic reaction is that the rate increases initially as the concentration of catalytic product
increases, but eventually goes through a maximum and decreases as reactant is used up.
The initial behavior may be described as “abnormal” kinetics, and has important con-
sequences for reactor selection for such reactions.
Examples of autocatalytic reactions include the decomposition of C2H,12 either in
the gas phase or in solution in CCI, (Arnold and Kistiakowsky, 1933) hydrolysis of
an ester, and some microbial fermentation reactions, The first of these may be used to
illustrate some observed and mechanistic features.