Page 213 - Introduction to chemical reaction engineering and kinetics

8.4 Surface Catalysis: Intrinsic Kinetics 195

8.4.3 Langmuir-Hinshelwood (LH) Kinetics

By combining surface-reaction rate laws with the Langmuir expressions for surface cov-
erages, we can obtain Langmuir-Hinshelwood (LH) rate laws for surface-catalyzed re-
actions. Although we focus on the intrinsic kinetics of the surface-catalyzed reaction,
the LH model should be set in the context of a broader kinetics scheme to appreciate
the significance of this.
A kinetics scheme for an overall reaction expressed as

where A is a gas-phase reactant and B a gas-phase product, is as follows:

A(g) 2 A (surface vicinity); mass transfer (fast) (1)
kJ.4
A(surface vicinity) + s c A 0 s; adsorption-desorption (fast) (2)
A 0 s A B(surface vicinity) + s; surface reaction (slow, rds) (3)
B(surface vicinity) 2 B(g); mass transfer (fast) (4)

Here A(g) and B(g) denote reactant and product in the bulk gas at concentrations CA
and cn, respectively; k& and kng are mass-transfer coefficients, s is an adsorption Site,
and A l s is a surface-reaction intermediate. In this scheme, it is assumed that B is not
adsorbed. In focusing on step (3) as the rate-determining step, we assume kAs and k,,
are relatively large, and step (2) represents adsorption-desorption equilibrium.

8.4.3.1 Unimolecular Surface Reaction (Type I)

For the overall reaction A -+ B, if the rds is the unimolecular surface reaction given by
equation 8.4-1, the rate of reaction is obtained by using equation 8.4-21 for OA in 8.4-2
to result in:

kKACA (8.4-24)l
(-IA) = 1 + KAcA + KBcB

‘The equations of the LH model can be expressed in terms of partial pressure pi (replacing cl). For example,
equation 8.4-23 for fractional coverage of species i may be written as (with ni = nj = 1)

0; = 1 +~~~j,,j;i, j = l,L...,N

where 4, is the ratio of adsorption and desorption rate constants in terms of (gas-phase) partial pressure,
4, = k,,Jkdi. Similarly the rate law in equation 8.4-24 may be written as

I
k&pPA
(-TA) = (8.4-24a)
1 + KAPPA + KB~TPB

Some of the problems at the end of the chapter are posed in terms of partial pressure.
Appropriate differences in units for the various quantities must be taken into account. If (-r~) is in mol me2
,
s-l and pi is in kE’a, the units of kapl are mol m-z s- 1 kF’a-’ and of Kip are kF%’ ; the units of kdi are the same
as before.