Page 210 - Introduction to chemical reaction engineering and kinetics

192 Chapter 8: Catalysis and Catalytic Reactions

(2) Bimolecular surface reaction, for example,

A.s+B.s --;r Cosfs (8.4-3)
where the rate is given by

(-rA) = kO,8, (8.4-4)

The rates (and rate constants) can be expressed on the basis of catalyst mass
(e.g., mol kg-lh-l), or of catalyst surface area (e.g., pmol rnw2 s-l), or as a
turnover frequency (molecules site-l s-l), if a method to count the sites exists.
(3) Eley-Rideal reaction, wherein a gas-phase species reacts directly with an ad-
sorbed intermediate without having to be bound to the surface itself; thus,
A.s+B --f C+s (8.4-5)

Here, the rate is given by

(-rA) = kOAcB (8.4-6)

where cn is the gas-phase concentration of B.

8.4.2 Adsorption without Reaction: Langmuir Adsorption Isotherm

We require expressions for the surface coverages, 8, for use in the equations in Section
8.4.1 to obtain catalytic rate laws in terms of the concentrations of gas-phase species.
Langmuir-Hinshelwood (LH) kinetics is derived by assuming that these coverages are
given by the equilibrium coverages which exist in the absence of the surface reactions.
The required expressions were obtained by Langmuir in 1916 by considering the rate
of adsorption and desorption of each species.

8.4.2.1 Adsorption of Undissociuted Single Species
The reversible adsorption of a single species A, which remains intact (undissociated)
on adsorption, can be represented by
kI.4
AfssAes (8.4-7)
bA
The rate of adsorption of A, raA, is proportional to the rate at which molecules of A
strike the surface, which in turn is proportional to their concentration in the bulk gas,
and to the fraction of unoccupied sites, 1 - 8,:

(8.4-8)
rCZA = kaACA(l - eA)
where kaA is an adsorption rate constant which depends on temperature. (If the units
are mol rnw2 s-l and of CA are mol mP3, the units of kaA are m s-l.) A molecule
Of raA
which strikes a site already occupied may reflect without adsorption or may displace
the occupying molecule; in either case, there is no net effect.
The rate of desorption of A, r,A, is proportional to the fraction of surface covered,
8,:

(8.4-9)
I;iA = kdAeA
where kdA is a desorption rate constant which also depends on temperature. (The units
of kdA are Id In - 2 s-1 a>