Page 166 - Introduction to chemical reaction engineering and kinetics

148 Chapter 6: Fundamentals of Reaction Rates

where ii is the average velocity (8kJ’l~mA) u2. If the reaction requires a direct impinge-
ment on an open surface site (one with no molecules bonded to it), then the rate of
adsorption per unit area on the surface should be proportional to the number of open
sites on the surface:
r /mol mP2sP1 = Z,N+JN,, = (2.5 X 10-4~iiN)80~A = kaBncA (6.6-3)
a

where N is the number of sites mm2 of surface, 8, is the fraction of sites which are open,
and cA is the gas-phase concentration in mol L-l. This “bimolecular” type of adsorption
kinetics, where the cross-section does not depend on the amount of adsorbed material,
is said to obey Langmuir adsorption kinetics. The factor in parentheses is the SCT ex-
pression for the adsorption rate constant k,. Like bimolecular combination reactions,
no activation energy is expected, unless bond-breaking must take place in the solid or
in the adsorbing molecule.

6.6.2.2 Desorption

Desorption, the reverse of reaction 6.6-1, that is,

A.&A+s (6.6-4)

is a unimolecular process, which, like gas-phase analogues, requires enough energy
to break the bond to the surface. Similar to reactions in liquids, energy is transferred
through the solid, making collisions unnecessary to supply energy to the adsorbed
molecule. If the sites are independent, the rate is proportional to the amount of ad-
sorbed material:

r,lmol mP2sW1 = k&IA

where kd is the unimolecular desorption rate constant, which is expected to have an
activation energy similar to the adsorption bond strength, and eA is the fraction of
the sites which have A adsorbed on them, often called the “coverage” of the surface
by A.

6.6.2.3 Surface Reactions

The simplest theories of reactions on surfaces also predict surface rate laws in which
the rate is proportional to the amount of each adsorbed reactant raised to the power of
its stoichiometric coefficient, just like elementary gas-phase reactions. For example, the
rate of reaction of adsorbed carbon monoxide and hydrogen atoms on a metal surface
to produce a formyl species and an open site,

CO.s+H.s-+HCO.s+s (6.6-5)

is assumed to exhibit the following rate law:

r/m01 mP2 s-l = ke,,e, (6.6-6)

This behavior arises, as in the gas phase, from assuming statistical encounter rates of
the reactants on the surface. Because the motion of adsorbed species on surfaces is not
well understood, however, quantitative prediction of this encounter rate is not generally
possible.