Page 215 - Introduction to chemical reaction engineering and kinetics

8.4 Surface Catalysis: Intrinsic Kinetics 197

SOLUTION
(a) From equation 8.4-26, with KAcA << 1 >> Kncn,

(-r*) = k’CACB (8.4-28)

which is a second-order reaction, with k’ = kKAKB.
(b) From equation 8.4-26, with KAcA << 1,

(-rA) = kc,c,l(l + KBcB)2 (8.4-29)

and the reaction is first-order with respect to A, but not with respect to B. As cn increases,
B occupies more of the surface, and its presence inhibits the rate of reaction.

8.4.4 Beyond Langmuir-Hinshelwood Kinetics

The two rate laws given by equations 8.4-24 and -26 (Types I and II) are used extensively
to correlate experimental data on surface-catalyzed reactions. Nevertheless, there are
many surface-catalyzed reaction mechanisms which have features not covered by LH
kinetics.
Multiple surface steps: The basic LH mechanisms involve a single surface reaction,
while many surface-catalyzed reactions, like the methanol synthesis mechanism in
Figure 8.3, involve a series of surface steps. The surface sites are shared by the in-
termediates and the adsorbed reactants and products; thus, the coverages are altered
from those predicted by adsorption of gas-phase species alone. The steady-state cov-
erages are obtained from analyses identical to those used for gas-phase mechanisms
involving reactive intermediates (Chapter 7). Although it is possible to obtain analyt-
ical rate laws from some such mechanisms, it often becomes impossible for complex
mechanisms. In any case, the rate laws are modified from those of the standard LH ex-
pressions. For example, the following mechanistic sequence, involving the intermediate
species I

exhibits zero-order kinetics, if the irreversible unimolecular step I l s + P l s is rate-
determining. In this case, the surface is filled with I (0, = l), and the competition among
A, B, and C for the remaining sites becomes unimportant. In a similar manner, if a series
of initial steps which are in equilibrium is followed by a slow step, extra factors appear
in the rate law.
Irreversible adsorption: The LH mechanisms assume that the adsorption of all gas-
phase species is in equilibrium. Some mechanisms, however, occur by irreversible steps.
In these cases, the intermediates are again treated in the same manner as reactive inter-
mediates in homogeneous mechanisms. An example is the Mars-van Krevelen (1954)
mechanism for oxidation, illustrated by the following two steps:

0, +2s + 200s
o.s+co~co2+s

Eley-Rideal mechanisms: If the mechanism involves a direct reaction between a
gas-phase species and an adsorbed intermediate (Eley-Rideal step, reaction 8.4-5) the
competition between the reactants for surface sites does not occur. From equations
8.4-6 and -21, since one reactant does not have to adsorb on a site in order to react,