PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 283

9.2.4.14 Integrated forms of the kinetic equation

For time as a function ofxwe write

k′τ =

1

(c′A0−c′B0)(c′A0−c′C0)

ln

c′A0

c′A0−x

+

1

(c′B0−c′A0)(c′B0−c′C0)

ln

c′B0

c′B0−x

+

1

(c′C0−c′A0)(c′C0−c′B0)

ln

c′C0

c′C0−x

. (9.68)

For the concentrations of the reactants we have

cA=cA0−ax , cB=cB0−bx , cC=cC0−cx , (9.69)

wherexis determined by the numerical solution of equation (9.68).

9.2.5 nth-order reactions with one reactant

9.2.5.1 Type of reaction

A→products. (9.70)

9.2.5.2 Kinetic equation

−

dcA

dτ

=kcnA. (9.71)

9.2.5.3 Integrated forms of the kinetic equation

For time as a function of the reactant concentration we have

kτ=

1

n− 1

(

1

cnA−^1

−

1

cnA0−^1

)

. (9.72)

For the concentration of substance A as a function of time we have

cA=cA0

[

1 + (n−1)cnA0−^1 kτ

] 1 −^1 n

. (9.73)