Page 212 - Introduction to chemical reaction engineering and kinetics

194 Chapter 8: Catalysis and Catalytic Reactions

we can “count” the number of catalytic sites. The type of adsorption considered here is
chemical in nature-chemical bonds are formed with the catalytically active surface-
and is known as chemisorption. A weaker type of adsorption due to physical forces
(like the forces which hold liquids together) can also occur. This latter type of adsorp-
tion (which can occur anywhere on the surface-not just on catalytic sites) is used to
measure the surface area of porous materials.

8.4.2.3 Adsorption of Competing Species
For a surface reaction between two adsorbed gaseous species, A and B, we need to
consider the simultaneous adsorption of the two species, competing for the available
sites. For species A, the rate of adsorption is

rllA = kaAcA(l - OA - 0,) (8.4-16)
For this expression, it is assumed that a molecule of A from the bulk gas striking a site
occupied by a B molecule is reflected, and does not displace the adsorbed B molecule.
The rate of desorption, as for a single species, is

(8.4-17)
rdA = ‘tiAeA
At adsorption equilibrium, r,A = r&,, and

(8.4-18)
kaACA(1 - eA - %> = kdAeA
Or, if KA = kaAlkdA,

KAcA(l - 8, - e,) = 8, (8.4-19)

Similarly,

KBCB(l - eA - e,) = eB (8.4-20)

where KB = kaB/kdB, the ratio of adsorption and desorption rate constants for B.
From equations 8.4-19 and 20, we obtain expressions for 8, and 8,:

OA = KAcAI(l + KAcA + KBcB) (8.4-21)
8, = K,c,l(l + KAcA + KBcB) (8.4-22)

According to these equations, each adsorbed species inhibits the adsorption of the
other, as indicated by the term KBcB in the denominator of the equation for 8, and
conversely for 8,.
In a more general form of equation 8.4-21 or -22, a Kici term appears in the denomi-
nator for each adsorbing species i in competition for the adsorption sites. Furthermore,
if the species dissociates into IZ~ fragments, the appropriate term is (Ki~i)l’ni as in equa-
tion 8.4-15 for yt = 2. Therefore, in the most general case, the expression for Langmuir
adsorption of species i from a multispecies gas mixture is:

I I
(Kici)‘lni
ei = ; i, j = 1,2, . . . , N (8.4-23)
1 + xj(Kjcj)l’nj
I