PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 297

dcB

dτ

= k 1 cA, (9.97)

dcC

dτ

= k 2 cA. (9.98)

9.4.4.3 Integrated forms of the kinetic equations.

cA = cA0exp[−(k 1 +k 2 )τ], (9.99)

cB = cB0+cA0

k 1

k 1 +k 2

{ 1 −exp[−(k 1 +k 2 )τ]}, (9.100)

cC = cC0+cA0

k 2

k 1 +k 2

{ 1 −exp[−(k 1 +k 2 )τ]}. (9.101)

From equations (9.100) and (9.101) it follows that

cB−cB0

cC−cC0

=

k 1

k 2

. (9.102)

The concentrations of products B and C are usually zero at the start of the reaction,cB0=
cC0= 0, and the equation simplifies to

cB

cC

=

k 1

k 2

. (9.103)

9.4.4.4 Wegscheider’s principle.

The ratio of the concentrations of side reactions products does not depend on time. This
principle applies if the side reactions are of the same order and if the initial concentrations of
their products are zero.

9.4.5 Second-order parallel reactions.

9.4.5.1 Type of reaction

A + B

k 1

→ C,

A + B →k^2 D.