CHAP. 9: CHEMICAL KINETICS [CONTENTS] 310
whereKis the equilibrium constant of formation of the intermediate. This relation is a math-
ematical expression of the assumption of pre-equilibrium. Combining equations (9.146) and
(9.147) yields
dcC
dτ
=k 3 KcAcB. (9.148)9.5.8 Mechanism of some third-order reactions
If the third-order reaction (second-order with respect to A and first-order with respect to B)
2 A + B → 2 C (9.149)were trimolecular [see9.5.1], there would have to be two molecules of substance A and one
molecule of substance B coming into contact. However, a collision of three molecules is a rare
event. Consequently, a mechanism has been suggested explaining some reactions of the type
(9.149) as a sequence of bimolecular reactions
2 A
k 1
→ A 2 , A 2
k 2
→ 2 A, A 2 + B
k 3
→ 2 C. (9.150)The rate of formation of the product is
dcC
dτ=k 3 cA 2 cB. (9.151)Provided that the pre-equilibrium principle (see the preceding subsection) applies for the in-
termediate A 2 , its concentration is given by the relation
cA 2
c^2 A=
k 1
k 2=K. (9.152)
Substituting into relation (9.151) forcA 2 from (9.152) leads us to
dcC
dτ=k 3 Kc^2 AcB. (9.153)