Page 167 - Introduction to chemical reaction engineering and kinetics

6.6 Elementary Reactions Involving Other Than Gas-phase Neutral Species 149

6.6.2.4 General Observations
Simple theories provide useful rate expressions for reactions involving solid surfaces
(Chapter 8). In fundamental studies, there are examples of adsorption kinetics which
obey the simple Langmuir rate expressions. However, many others are more complex
and do not show first-order dependence on the number of open sites. These variations
can be appreciated, if we accept the notion that a solid can be thought of as a giant
molecule which presents a large number of locations where bonds can be made, and
that changes in the bonding at one site on this molecule can change the bonding at
other locations. As a result, the site properties can depend on whether molecules are
adsorbed on neighboring sites. Furthermore, molecules can “pre-adsorb” weakly even
on occupied sites and “hunt” for an open site. The desorption rate constant can vary
with the amount of adsorbed material, if, for instance, the surface bond strength de-
pends on the amount of adsorbed material. For these reasons, and because of the dif-
ficulty in obtaining reliable information on the structure of surface-adsorbed reaction
intermediates, quantitative theories of surface reactions are not generally available.

6.6.3 Photochemical Elementary Reactions

Light energy interacts with matter in quantum units called photons which contain en-
ergy E = hv (Section 6.2.1.2). The frequency v is related to the wavelength A by

A = CIV (6.6-7)

where c is the speed of light (3 x lo8 m s-l). The energy of photons can be expressed
in units, such as J mol-l, to compare with chemical energies:

EIJ mol-i = N,,hv = N,,hclh = 0.1196Zh (6.6-8)

where h is in m. Low-energy photons (infrared wavelengths and longer, A > = 0.8 pm,
Ephoton < 150 kJ mol-i) are generally only capable of exciting vibrational levels in the
molecules. In photochemistry, we are usually concerned with photons with enough en-
ergy to produce changes in electronic states (visible wavelengths and shorter, A <=
> 150 kJ mol-l), and therefore to disrupt chemical bonds.
o.8 E.Lm, Ephoron

6.6.3.1 Light Absorption
Although light behaves like both waves and particles, photons can be thought of as
particles which participate in elementary reactions analogous to those for neutral
molecules. Furthermore, the language of collision theories is often used to describe
the rates of these reactions. For example, the absorption of light can be treated in a
collision theory as a “bimolecular” process in which light particles (photons) collide
with the molecules, and are absorbed to produce a higher-energy “excited” state in the
molecule:

hv+A + A* (6.6-9)

There is a cross-section for absorption, U, which characterizes the size of the “target”
a photon has to hit to be absorbed. The rate of absorption is given a little differently,
since the photons travel much faster than the A molecules (which can be treated as
stationary). If the flux of photons (number traversing a given area per unit time) is I,
then the rate of absorption per unit volume is

r/events mP3 s-l = (Zl(photons m -2 s-r) X (cX/molecules mP3) X (a/m2) (6.6-10)