Page 156 - Introduction to chemical reaction engineering and kinetics

138 Chapter 6: Fundamentals of Reaction Rates

(2) Unimolecular dissociation of P* (reverse of (A)):

P*5A+B OV

(3) Stabilization of P” by collision with M (any other molecule):

P*+MaP+M w

Treatment of steps (A), (B), and (C) similar to that for the steps in a unimolecular
reaction, including application of the SSH to P*, results in

(6.4-24)

= kbicAcB (6.4-25)

where kbi is an effective second-order rate constant that depends on cIvI. Just as for a
unimolecular reaction, there are two limiting cases for equation 6.4-24, corresponding
to relatively high and low cM:

rp = klcAcB (“high-pressure” limit) (6.4-26)
rp = (k, kZIk-JcMcAcB (“low-pressure” limit) (6.4-27)

Thus, according to this three-step mechanism, a bimolecular recombination reaction is
second-order at relatively high concentration (cM), and third-order at low concentra-
tion. There is a transition from second- to third-order kinetics as chl decreases, resulting
in a “fall-off” regime for kbi.
The low-pressure third-order result can also be written as a termolecular process:

A+B+M+P+M

which implies that all three species must collide with one another at the same time. In
the scheme above, this is pictured as taking place in two sequential bimolecular events,
the second of which must happen within a very short time of the first. In the end, the
distinction is a semantic one which depends on how collision is defined. There are few
termolecular elementary reactions of the type

A+B+C+P+Q

and the kinetics of these can also be thought of as sequences of bimolecular events.
The “fall-off” effects in unimolecular and recombination reactions are important in
modern low-pressure processes such as chemical vapor deposition (CVD) and plasma-
etching of semiconductor chips, and also for reactions in the upper atmosphere.
The importance of an “energized” reaction complex in bimolecular reactions is illus-
trated by considering in more detail the termination step in the ethane dehydrogenation
mechanism of Section 6.1.2:

Ho + C,H; + C,H,