Page 206 - Introduction to chemical reaction engineering and kinetics

188 Chapter 8: Catalysis and Catalytic Reactions

The rate of decomposition of gaseous ethylene iodide (C,H,I,) into ethylene (C2H4) and
molecular iodine is proportional to the concentration of C,H,I, and to the square root of
the concentration of molecular iodine. Show how this can be accounted for if the reaction
is catalyzed by iodine atoms, and if there is equilibrium between molecular iodine and
iodine atoms at all times.

SOLUTION

The decomposition of C2H41, is represented overall by

VLJ,(A) + C,H, + I,
and the observed rate law is
II2
C-r*) = k*C‘&*
A possible mechanism to account for this involves the rapid establishment of dissociation-
association equilibrium of molecules and atoms, followed by a slow bimolecular reaction
between C2H4I2 and I atoms:
K-?
12+M=21+M Vast)
k2
CzH4I2 + I + C2H4 + I* + I (slow)
where M is a “third body” and the catalyst is atomic I. The rate law, based on the second
step as the rds, is
(-rA) = /t2cAcI = kAcAc;;

as above, where kA = k,KLf
To illustrate quantitatively the kinetics characteristics of autocatalysis in more detail,
we use the model reaction
A + . . . +B+... (8.3-1)

with the observed rate law

(8.3-2)
(-rA) = kACACB
That is, the reaction is autocatalytic with respect to product B. If the initial concentra-
tions are CA0 and cnO (which may be zero), and, since

CB = c&, + CA0 - CA = M, - CA (8.3-3)

where
(8.3-3a)
M. = cAo + cBo
the rate law may be written in terms of CA only:

(8.3-4)
(-IA) = kACA(Mo - cA)