CHAP. 9: CHEMICAL KINETICS [CONTENTS] 308
i.e. the rate of formation of these species is almost equal to their rate of consumption. If we
assume that the concentration of these components does not change with time, we obtain
dcA∗
dτ= 0. (9.139)
This assumption is called Bodenstein’s principle or the steady-state principle. It does not apply
absolutely accurately but it is often used as a good approximation.
9.5.6 Lindemann mechanism of first-order reactions
Some reactions of the type A→B proceed neither as unimolecular nor as bimolecular (i.e.
those in which a molecule reacts on colliding with another molecule). Lindemann suggested
the following mechanism for these reactions:
A + A →k^1 A + A∗, (9.140)
A∗+ A
k 2
→ A + A, (9.141)
A∗
k 3
→ B, (9.142)where A∗is theactivated molecule, a molecule endowed with a substantially higher energy
than its fellow-molecules.
The rate of formation of the product according to (9.142) is
dcB
dτ=k 3 cA∗. (9.143)The concentrations of activated molecules are determined using Bodenstein’s principle:
dcA∗
dτ=k 1 c^2 A−k 2 cA∗cA−k 3 cA∗= 0 =⇒ cA∗=k 1 c^2 A
k 3 +k 2 cA. (9.144)
By substituting the concentrations of activated molecules from (9.144) into (9.143) we obtain
the resulting kinetic equation
dcB
dτ
=
k 1 k 3 c^2 A
k 3 +k 2 cA