Page 182 - Introduction to chemical reaction engineering and kinetics

164 Chapter 7: Homogeneous Reaction Mechanisms and Rate Laws

Re-emission of a photon in the reversal of the excitation step photodissociation is unim-
portant.
If the reactive species in the chemical activation step initiates a radical chain with
a chain length CL, then the overall quantum yield based on the ultimate product is
Q, X CL, and can be greater than 1. Photons are rather expensive reagents, and are
only used when the product is of substantial value or when the overall quantum yield
is large. Examples are the use of photoinitiators for the curing of coatings (a radical-
polymerization process (Section 7.3.1)), and the transformation of complex molecules
as medications.
Sources of radiation other than ultraviolet or visible light, such as high-energy ions,
electrons, and much higher-energy photons, can also generate reactive species. Such
processes are usually much less selective, however, since reactive fragments can be
generated from all types of molecules. The individual absorption characteristics of
molecules subjected to radiation in the ultraviolet and visible range lead to greater
specificity.

7.2 COMPLEX REACTIONS

7.2.1 Derivation of Rate Laws

A complex reaction requires more than one chemical equation and rate law for its sto-
ichiometric and kinetics description, respectively. It can be thought of as yielding more
than one set of products. The mechanisms for their production may involve some of
the same intermediate species. In these cases, their rates of formation are coupled, as
reflected in the predicted rate laws.
For illustration, we consider a simplified treatment of methane oxidative coupling in
which ethane (desired product) and CO, (undesired) are produced (Mims et al., 1995).
This is an example of the effort (so far not commercially feasible) to convert CH, to
products for use in chemical syntheses (so-called “Ci chemistry” ). In this illustration,
both C,H, and CO, are stable primary products (Section 5.6.2). Both arise from a com-
mon intermediate, CH!, which is produced from CH, by reaction with an oxidative
agent, MO. Here, MO is treated as another gas-phase molecule, although in practice it
is a solid. The reaction may be represented by parallel steps as in Figure 7.l(a), but a
mechanism for it is better represented as in Figure 7.l(b).
A mechanism corresponding to Figure 7.l(b) is:

CH4 + MO 3 CH;( +reduced MO)
2CH; -% GH,
CH; + MO 2 P % C02( +reduced MO)

Application of the SSH to CHF results in the two rate laws (see problem 7-12):

-IKk3cMo)2 + f%~2C,,C,~11’2 - ~3CMO12
rG& = k2ciH; = 16k2 (7.2-1)

(a) (b)
Figure 7.1 Representations of CH4 oxidative-coupling reaction to
produce CzHe and CO2