PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 298

9.4.5.2 Kinetic equations.

dcA

dτ

=

dcB

dτ

= −(k 1 +k 2 )cAcB =⇒

dx

dτ

= (k 1 +k 2 )(cA0−x)(cB0−x), (9.104)

dcC

dτ

= k 1 cAcB=k 1 (cA0−x)(cB0−x), (9.105)

dcD

dτ

= k 2 cAcB=k 2 (cA0−x)(cB0−x). (9.106)

9.4.5.3 Integrated forms of the kinetic equations.

cA = cA0−x , (9.107)

cB = cB0−x , (9.108)

cC = cC0+

k 1

k 1 +k 2

x , (9.109)

cD = cD0+

k 2

k 1 +k 2

x , (9.110)

where

x=cA0cB0

z− 1

zcA0−cB0

and z= exp [(k 1 +k 2 )(cA0−cB0)τ]. (9.111)

We may explicitly express time from equation (9.111) as

τ=

1

(cA0−cB0)(k 1 +k 2 )

ln

cB0cA

cA0cB

=

1

(cA0−cB0)(k 1 +k 2 )

ln

cB0(cA0−x)

cA0(cB0−x)

. (9.112)

If the concentrations of products C and D are zero at the start of the reaction, the ratio
of their concentrations at an arbitrary time is given by equation (9.103) and Wegscheider’s
principle applies.

9.4.6 First- and second-order parallel reactions

9.4.6.1 Type of reaction

A →k^1 C,