PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 284

9.2.5.4 Reaction half-life

τ 1 / 2 =c^1 A0−n

2 n−^1 − 1

(n−1)k

. (9.74)

9.2.6 nth-order reactions with two and more reactants

The general case of annth-order reaction with two reactants is

aA +bB→products. (9.75)

9.2.6.1 Kinetic equation

−

dcA

dτ

=kcαAcβB =⇒ a

dx

dτ

=k(cA0−a x)α(cB0−b x)β, (9.76)

whereαandβare the partial orders of reaction; the overall order isn=α+β. For individual
specific cases when we know the partial orders of reaction and the stoichiometric coefficients of
the equation, we obtain the integrated forms of kinetic equations using the method of separation
of variables [see9.1.6].
The general case of annth-order reaction with three reactants is

aA +bB +cC→products. (9.77)

The partial orders of reaction with respect to components A, B, C areα,β,γ(α+β+γ=
n), and the initial concentrations of the components arecA0,cB0,cC0.
The kinetic equation of the reaction is

−

dcA

dτ

=kcαAcβBcγC. (9.78)

Using material balance we rewrite the equation to

a

dx

dτ

=k(cA0−ax)α(cB0−bx)β(cC0−cx)γ (9.79)

and separate variables
∫x

0

a

(cA0−ax)α(cB0−bx)β(cC0−cx)γ

dx=

∫τ

0

kdτ=kτ. (9.80)