Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 398

or

A þ 2s % s$ A $s (9.11)

and the corresponding adsorption equilibrium is

2

C 2

2

A C 2

r ¼ k ad q

s C A 2 k des q s ¼

0 (9.12)

q A
q

2

k ad
k des C A 2

¼ (9.13)

which leads to the isotherm equation

1 = 2

ðK A C A 2 Þ

q A ¼ (9.14)

1 = 2

1 þðK A C A 2 Þ

If the adsorbate molecule is immobile on the surface, the occupancy of nearest-neighbor
active sites should be accounted. This is not a large refinement, however, and Eqn (9.12)
will be employed without reference to the detailed nature of the adsorbate layer.
A second modification of practical importance is when more than one adsorbate species is
present on the surface competing for the same type of active centers (or sites). For example,
consider the adsorption equilibrium (no surface reaction)
A þ s % A $s

B $s % B þ s

where A and B are chemisorbed on the same type of surface site, s ; that is, they are compet-
itively adsorbed on the surface. In this case, Eqn (9.6) is applicable to both A and B (with
different heats of adsorption) as dictated by the net adsorption rate of zero at equilibrium,
i.e. q A
q

¼ K A C A and q B

q ¼ K B C B . The total number of active site balance is now
q A þ q B þ q ¼ 1

as the active sites are shared by three parts: active sites occupied by A, active sites occupied
by B, and free active sites available for adsorption. Therefore, the corresponding isotherm
equations for the surface coverages of A and B are

K A C A

q A ¼ (9.15a)

1 þ K A C A þ K B C B

K B C B

q B ¼ (9.15b)

1 þ K A C A þ K B C B

A major property of the Langmuir isotherm is that of saturation. In Eqn (9.9) , for example
when K A C A >> 1, and no further adsorption occurs. This is a result of the surface

model, in which each adsorption site can accommodate only one adsorbate molecule. Satu-
ration of the surface, then, corresponds to the occupancy of all sites and is called monolayer
coverage. At low concentrations, K A C A <<

1, q A /

1 and Eqn (9.9) assumes a linear form in C A cor-
responding to Henry's law of adsorption. These general features are shown in Fig. 9.4 . Exper-
imentally, one measures either the weight or volume of material adsorbed, and the ratio of