Kinetic Theory and Reaction Kinetics - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 267

To simplify the collision theory outlined above, we devise a more illustrative simplistic
elementary kinetic description for the steps taken as

AB

A þ B # (6.30)

AB / C (6.31)

To illustrate the reaction kinetics for a bimolecular reaction

(6.32)
In the reaction kinetic steps, AB* is regarded as the active reaction complex, which can be
regarded as a transitional state (to achieve required active energy) or as the collision occur-
rence. Therefore, we regard the transitional state theory, active complex theory, and the more
fundamental collision theory to be compatible. It is thus expected that the transitional state
theory, active complex theory, and the collision theory would all produce similar rate expres-
sions. No effort will be made to distinguish these three “theories.” This discussion will also
lead to us to treat the kinetics in simplistic form like Eqns (6.30) and (6.31) , whereby no direct
reference to the more fundamental representation with collision theory is needed.
It is interesting to note from the collision theory that an elementary reaction should not
have more than three reactant molecules involved as the collision of three or more molecules
at one location is increasingly rare.

A þ B / C

6.3 . REACTION RATE ANALYSIS/APPROXIMATIO N

Collision theory provides a vivid conceptual description of chemicals: contacting of react-
ing species, activating the reaction, and spontaneous reaction. It offers the form of reaction
rates for elementary reactions: frequency of collision depends on the product of reacting
species concentrations. In most practical reactions, the process does occur in such a simple
fashion. It naturally leads to more steps to complete the reaction path. To illustrate how to
deal with reaction rates from multiple-reaction steps or pathways, we use a simplistic
example as given by reactions (6.30) and (6.31) :

AB A þ B # (6.30)

AB / C (6.31)

where the overall reaction is given by (6.32)

(6.32)
There are two steps in this reaction. One can treat the reactions as multiple reactions and
thus deal with each reaction equally. At this stage, we have learned how to do so (Chapter 3).
The reaction rate for any given species in a multiple reaction can be computed by Eqn (3.66)
or

A þ B / C

X

N R

r j ¼ n ij r i (6.33)

i ¼ 1