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6.4 Simple Collision Theory of Reaction Rates 135

enough energy must wait until sufficient energy is transferred by collision, as in Section
6.4.1.6. Therefore, as Lindemann (1922) recognized, three separate basic processes are
involved in this reaction:
(1) Collisions which transfer the critical amount of energy:

I, + M (any molecule in the mixture) 3 I;(energized molecule) + M (4

(2) The removal of this energy (deactivation) by subsequent collisions (reverse of
(A)):
I;+MbI,+M (B)

(3) The dissociation reaction:

I;. -Z 21’ (0

Steps (A), W, and CC> constitute a reaction mechanism from which a rate law may
be deduced for the overall reaction. Thus, if, in a generic sense, we replace I, by the
reactant A, I; by A*, and 21’ by the product P, the rate of formation of A* is

?-A. = -k2cA* + klcAcM - kelcA*cM (6.4-18)

and the rate of reaction to form product P, r,, is:

kZ(hcAcM - IA”)
rP = k2cA. = (6.4-19)
k2 + k-,c,

if we use equation 6.4-18 to eliminate cA.. Equation 6.4-19 contains the unknown rA*.
To eliminate this we use the stationary-state hypothesis (SSH): an approximation used
to simplify the derivation of a rate law from a reaction mechanism by eliminating the
concentration of a reactive intermediate (RI) on the assumption that its rate of forma-
tion and rate of disappearance are equal (i.e., net rate r,, = 0).
By considering A* as a reactive intermediate, we set rA* = 0 in equations 6.4-18 and
-19, and the latter may be rewritten as

(6.4-20)

(6*4-20a3

where kuni is an effective first-order rate constant that depends on CM. There are two
limiting cases of equation 6.4-20, corresponding to relatively high CM (“high pressure”
for a gas-phase-reaction), k-,cM >> b, and low CM (“low pressure”), k2 >> k-,c,:

rp = (klk21k-l)cA (“high-pressure” limit) (6.4-21)
T-, = klCMC/, (“low-pressure” limit) (6.4-22)

Thus, according to this (Lindemann) mechanism, a unimolecular reaction is first-order
at relatively high concentration (cM) and second-order at low concentration. There is a