Concepts from Chemical Reaction Kinetics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 216

amides and diphthalate esters obey the Taft LFER. The rates of photooxidation of
substituted phenols by single oxygen ( 1 O 2 ) have also been shown to obey an LFER.
Although several hundred LFERs exist in the organic chemistry literature, few have
direct applicability in environmental engineering since (a) the compounds are not
of relevance to environmental engineers, (b) the solvents used to develop these are
not representative of environmental matrices, or (c) considerable uncertainty exists
in these predictions because they are based on limited data. More work is certainly
warranted in this area. Nonetheless, at least order of magnitude estimates of reaction
rates are possible using these relationships as starting points.

5.5 REACTION MECHANISMS
Reactions in the environment are complex in nature, consisting of several steps.
Empirical rate laws determined through experiments can give us ideas about the
underlying mechanisms of these complex reactions (Moore and Pearson, 1981). It
is best illustrated using a reaction which admittedly has only limited significance in
environmental engineering. The reaction is the formation of hydrogen halides from
its elements. The hydrogen halides do play a central role in the destruction of ozone
in the stratosphere through their involvement in the reaction of ozone with CFCs.
Several introductory physical chemistry textbooks use this reaction as an illustration
of complex reactions. Hence, only a cursory look at the essential concept is intended,
namely that of the deduction of reaction mechanism from a knowledge of the rate law
for the formation of a hydrogen halide.

5.5.1 C HAIN R EACTIONS
In the early part of the twentieth century Bodenstein and Lind (1907) studied in great
detail the reaction

H 2 + Br 2 2HBr. (5.89)

It was observed that the rate expression at the initial stages of the reaction where
[ HBr ][ H 2 ] and [Br 2 ]was

d [ HBr ]

= k [

1 / 2 .

r = H 2 ][ Br 2 ] (5.90)

d t

At later times the rate was

k [

1 / 2

d [ HBr ] H 2 ][ Br 2 ]

r = =

) .

(5.91)

(k [

d t 1 + HBr ][ Br 2 ]

Thus as time progressed the rate was inhibited by HBr formed during the reaction.The
fractional orders in the rate expression invariably indicate a chain reaction involving
free radicals . A chain reaction is one in which an intermediate compound is gener-
ated and consumed, which initiates a series of several other reactions leading to the
final product. A chain reaction involves an initiation step, a propagation step, and a
termination step.