Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 401

and the total coverage is

X

n T

q A n s ¼

1 q Ai n si

(9.19)

i¼

where n si is the number of adsorption sites belonging to group i and can be represented by an
appropriate distribution function. It is reasonable to write this distribution function in terms
of the heat of chemisorption, H ad , as the interaction between the adsorbate and adsorbent

molecules is expected to vary. With different distribution functions, one would expect
different adsorption isotherms and deviating differently from the Langmuir adsorption
isotherm.

D

9.1.2.1. ExLan Isotherm
One simplistic distribution function for a nonideal surface the available adsorption sites
are exponentially distributed with the excess interaction energy,

E s
RT d E s

d n si ¼ f s0 e

(9.20)

where E s ¼ DH ad DH ad , f s 0 is a scaling constant and dn

i the fraction of sites with heats of s

DH ad þ E s and DH ad þ E s þ

chemisorption between d E s . If we further assume, as indi-

cated by the form of Eqn (9.20) , that the groups of sites do not differ greatly in energy level
as one goes from one level to the next, the summation may be replaced by integration with
respect to the distribution function.

Z

n s E max

Z

E max
RT

f s0 e

Es
RT d E s ¼ RTf s0 ð

e n s ¼ d n si ¼ 1 Þ (9.21)

0 0

DH ad þ E max
are the maximum adsorption heats required for the adsorbate molecule to be adsorbed on the
adsorbent surface, where the minimum merely corresponds to a phase change to the more
orderly state on the adsorbent surface. It is expected that the minimum adsorption heat is
at least higher than the condensation (from gas to liquid) while could be lower than the solid-
ification (from gas to solid) for gas adsorbate molecules. For liquid adsorbate molecules, this
minimum adsorption heat could be lower than the solidification (from liquid to solid) heat.
Eqn (9.21) is reduced to

DH ad and where n is the total number of active (adsorption) sites available,

s

n s

f s0 ¼ (9.22)

E max
RT

e

RTð 1 Þ

The fraction of active sites that are occupied by the adsorbate molecules is

Z

n s E max

Z

K A e D H ad þ Es

1
n s

f s 0
n s

RT C A

E s
RT

e q A ¼ q Ai d n si ¼ d E s (9.23)

þ K A e D H ad þ E s

1

RT C A

0 0