Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 448

treatment for the case where the rates of reactions are the same for the adsorption and the
surface reaction with k A ¼

10 k S . This is a case where we did not show any solu-
tions from the equilibrium step assumptions. One can observe that the agreement between
the full solutions and the PSSH solutions is rather good for the bulk phase concentrations
( k S t

k S and k B ¼

0.1) despite the fact that two steps together are rate-controlling steps.
Therefore, the PSSH approximations are better suited as kinetic models than the equilib-
rium step assumptions when true kinetic constants are employed. However, the rate expres-
sions are quite similar to those of LHHWor equilibrium step assumptions. When utilized to
correlate experimental data, one would not be able to distinguish the two treatments.

>

9.3. CHEMICAL REACTIONS ON NONIDEAL SURFACES BASED
ON DISTRIBUTION OF INTERACTION ENERGY

The development presented for rates of surface reactions has thus far involved only the
theory for ideal surfaces, quite directly in the treatment of surface reaction rate-determining
steps and a little more implicitly using the chain reaction analysis. Yet, we have made a special
effort in the discussion of adsorption and desorption to point out that ideal surfaces are
rare; in fact, when one is concerned with the applications of catalysis in reaction engineering
it is probably fair to say that ideal surfaces are never involved. Nonetheless, LHHW rate
forms or modifications of it are widely used and accepted, particularly in chemical engi-
neering practice, for the correlation of rates of catalytic reactions. This is so even though it
has been shown in many instances that the adsorption equilibrium constants appearing in
the denominator of the kinetic expressions do not agree with adsorption constants obtained
in adsorption experiments. There are many reasons for this, but the voluminous illustrations
of Table 9.3 show that such equations are of a very flexible mathematical form, with separate
product and summation terms in numerator and denominator and are richly endowed with
constants that become adjustable parameters when correlating rate data.
The empirical Freundlich isotherm is a favorable isotherm for kinetic studies although there
is no rigorous theoretical basis behind it. Although Freundlich isotherm is not as good as
Langmuir and other isotherms that have a theoretical basis, it is accurate enough in low
coverage regions as it is an approximation to a variety of isotherms. The success of the
Freundlich isotherm suggests immediately that simple, power-law forms might be applied
successfully to surface reaction kinetics. However, this is just empirical. One other isotherm
of interest is the Temkin isotherm. Temkin isotherm was derived above based on the fact that
available active centers are linearly distributed with adsorption heat, Eqn (9.37)

n s

d n si ¼

E max d E s

(9.37)

and

DH ad ¼ DH ad;0 E s (9.32)

We know that the adsorption occurs first on highly energetic sites (sites of higher D H ad

values). Therefore, Eqn (9.37) is equivalent to