PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 278

9.2.3.9 Type.

aA +bB→products. (9.43)

9.2.3.10 Kinetic equation

−

dcA

dτ

=kcAcB =⇒ a

dx

dτ

=k(cA0−a x)(cB0−b x). (9.44)

This equation can be rearranged to

dx

dτ

=k′(c′A0−x)(c′B0−x). (9.45)

wherek′=b k,c′A0=cA0/aandc′B0=cB0/b. Comparison of (9.45) with (9.37) shows that the
equations are formally identical. Hence in this case we can use equations (9.38) through (9.40)
in such a way that we substitutek′, c′A0, c′B0in place of k,cA0andcB0, respectively. Equation
(9.38), e.g., will thus rearrange to

k′τ=

1

(c′A0−c′B0)

ln

c′B0c′A

c′A0c′B

=

1

(c′A0−c′B0)

ln

c′B0(c′A0−x)

c′A0(c′B0−x)

. (9.46)

9.2.3.11 Pseudofirst-order reactions.

It often happens that one of the reactants, e.g. B, is in large excess at the beginning of the
reaction,cB0≈cA0. In the course of the reaction, its concentration changes very little and it
may be considered constant. The kinetic equation (9.37) then rearranges to

−

dcA

dτ

=k′cA, where k′=kcB.

The equation is formally identical with the first-order kinetic equation (9.23), and conse-
quently we speak about a pseudofirst-order reaction.

Note:In literature we sometimes encounter the less correct term “pseudo-unimolecular”

reaction.