Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 433

Substituting Eqns (9.97), (9.91), and (9.93) into Eqn (9.98) , we obtain

k s n 2

s K A K B C A C B
ðK A C A þ K B C B þ K C C C þ K D C D Þ

r ¼ (9.99)

2

It is clear from Eqn (9.98) that when a surface reaction step is rate controlling, one needs only
information concerning adsorption equilibria of reactant and product species in order to write
the appropriate rate equation. Table 9.3 shows a collection of the LHHW rate expressions.
As shown in Table 9.3 , in each of these reactions, the active centers or sites form a closed
sequence in the overall reaction. According to this view, when the stoichiometry between
reactants and products is not balanced, the concentration of vacant active centers also enters
the rate equation, reaction 2 in Table 9.3 .
The bimolecular reaction involving one reactant nonadsorbed is sometimes referred to as
a Rideal or Eley-Rideal mechanism. It is encountered primarily in interpretation of catalytic
hydrogenation kinetics. In general, when a reactant or product is no adsorbed on the surface,
this particular species is not to appear in the denominator of the rate expression if the surface
reaction is the rate-limiting step.
The rate-controlling steps other than surface reaction on ideal surfaces are also shown in
Table 9.3 . If, for example, the rate of adsorption of a reactant species on the surface is slow
compared to other steps, it is no longer correct to suppose that its surface concentration is
determined by adsorption equilibrium. Rather, there must be chemical equilibrium among
all species on the surface, and the surface concentration of the species involved in the rate-
limiting step is determined by this equilibrium. The actual concentration of the rate-limiting
adsorbate consequently will not appear in the adsorption terms (denominator) of the rate
equation but is replaced by that concentration corresponding to the surface concentration
level established by the equilibrium of other steps. Again consider the isomerization example
of Eqn (9.1) , this time in which the rate of adsorption of A is controlling. From Eqn (9.2) ,we
may write the net rate of reaction as the difference between rates of adsorption and desorp-
tion of A:

r ¼ k A C A qC s k A q A C s (9.100)

in which k A (or k ad) ,and k

A (or k des ) are adsorption and desorption rate constants (i.e.

E A
RT )and q A is the fraction of surface coverage by A as determined by the equi-
librium of all other steps. Since the surface reaction (9.1b) is a rapid equilibrium step,
we have

k A ¼ k A e

0 ¼ r s ¼ k s q A C s k s q B C s (9.101)

which leads to

k s ¼ q B

k s

K s ¼ (9.102)

q A

or

q B
K s

q A ¼ (9.103)