Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 395

This would give us the maximum possible rate of adsorption (the forward reaction in Eqn
(9.1a) ) in any system if every molecule striking the surface was adsorbed. This is independent
of whether the adsorption is chemisorptions or physisorption, which we will define later.
Thus, it is not difficult to imagine the net adsorption e desorption rate is given by

(9.2)
where k ad is the adsorption rate constant, C A is the concentration of the adsorbate in the bulk
fluid phase, q is the fraction of the total possible available positions where A can be adsorbed
that are not occupied by any adsorbate molecules, C s is the surface concentration of the total
possible available positions or sites where A can be adsorbed, q A is the fraction of the total
possible available positions that are occupied by A. Eqn (9.2) is analogous to the (elementary)
reaction rate for a stoichiometry shown in Eqn (9.1a) . This is the basis of our discussion on
the adsorption and desorption. We still need to figure out what are C s and the two rate
constants. Before we move further, we shall need to define the surface and type of
interactions.

r ¼ k ad C A qC s k des q A C s

9.1.1. Ideal Surfaces
Molecules we already know something about, so in the present instance we need more
detail on the nature of the surface. The simplest model of a surface, the ideal surface is one
in which each adsorption site,

, has the same energy of interaction with the adsorbate mole-
cules, which is not affected by the presence or absence of adsorbate molecules on adjacent
adsorbent sites and in which each site can accommodate only one adsorbate molecule or
atom. We might represent the energy contours of each a surface qualitatively as shown in
Fig. 9.2 . Adsorption would occur when a molecule or atom of adsorbate with the required
energy strikes an unoccupied site, and the energy contours (or energy variation when
approaching the adsorbent surface) would be unaffected by the extent of adsorption, as
depicted by Fig. 9.3 for ideal enthalpy change.
These requirements for reaction (adsorption) to occur look very similar to those we
imposed on the bimolecular collision number in order to derive the reactive collision

s

G

Distance from a point along a given direction on the surface

FIGURE 9.2 A schematic of atomic force (interaction energy) on an energetically homogeneous surface.