Physical Chemistry Third Edition

12.4 Reaction Mechanisms and Rate Laws 545

Exercise 12.10

Apply the steady-state approximation to the reaction of Exercise 12.9.

a.Find the rate law if the steady-state approximation is used without the reverse of step 1.

b.Find the rate law if the steady-state approximation is used with inclusion of the reverse of

step 1.

c.Under what circumstances would the rate laws of parts a and b of Exercise 12.9 be obtained?

The Lindemann Mechanism

There is a problem with unimolecular gas-phase reactions that was recognized in the

late 1800s. It is unreasonable to assume that a single molecule could undergo any

process that breaks or forms chemical bonds without transferring energy to it or from

it. For a time there was a theory called theradiation theory, which asserted that the

necessary energy to break a bond in a unimolecular process came from the absorption

of radiation. However, unimolecular reactions can occur in the absence of ultraviolet

radiation, and visible and infrared radiation do not have enough energy to break chemi-

cal bonds. Around 1920 Lindemann^11 proposed that unimolecular processes are neither

strictly unimolecular nor strictly elementary. Consider a class of gas-phase reactions

represented by

A−→B+C (12.4-11)

An example of a reaction in this class is the thermal decomposition of cyclopentene to

form cyclopentadiene and hydrogen:

C 5 H 8 −→C 5 H 6 +H 2

The forward reaction for this class of reactions is found experimentally to be described

by the following rate law:

rate

d[B]

dt



k[A]^2

k′+k′′[A]

(12.4-12)

wherek,k′, andk′′are temperature-dependent parameters.

Lindemann proposed the following mechanism, which was also advanced by

Christiansen:^12

(1) A+A
A∗+A (12.4-13a)

(2) A∗−→B+C (12.4-13b)

The symbol A* stands for a molecule of A that is in an excited state due to energy

gained through the inelastic collision of step 1. If another substance, M, is present,

Eq. (12.4-13a) can be replaced by

(1) A+M
A∗+M (12.4-13c)

(^11) F. A. Lindemann,Trans. Faraday Soc., 17 , 598 (1922).
(^12) J. S. Christiansen, Ph.D. Dissertation, University of Copenhagen, 1921.