PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 281

9.2.4.6 Kinetic equation

−

dcA

dτ

=kAc^2 AcB =⇒ 2

dx

dτ

=kA(cA0− 2 x)^2 (cB0−x). (9.57)

9.2.4.7 Integrated forms of the kinetic equation

For time as a function of the variablexit holds

kAτ=

1

2 cB0−cA0

(

1

cA0− 2 x

−

1

cA0

)

+

1

(2cB0−cA0)^2

ln

[

cB0(cA0− 2 x)

cA0(cB0−x)

]

. (9.58)

For the concentrations of the reactants we write

cA=cA0− 2 x , cB=cB0−x , (9.59)

wherexhas to be determined from equation (9.58) numerically, see basic course of mathematics.

9.2.4.8 Type.

A + B + C→products. (9.60)

9.2.4.9 Kinetic equation

−

dcA

dτ

=kcAcBcC =⇒

dx

dτ

=k(cA0−x)(cB0−x)(cC0−x). (9.61)

9.2.4.10 Integrated forms of the kinetic equation

For time as a function of the variablexwe write

kτ =

1

(cA0−cB0)(cA0−cC0)

ln

cA0

cA0−x

+

1

(cB0−cA0)(cB0−cC0)

ln

cB0

cB0−x

+

1

(cC0−cA0)(cC0−cB0)

ln

cC0

cC0−x

. (9.62)