Physical Chemistry Third Edition

11.4 Inclusion of a Reverse Reaction. Chemical Equilibrium 507

11.4 Inclusion of a Reverse Reaction. Chemical

Equilibrium

If the reverse reaction cannot be neglected we must extend our previous discussion. We

consider the simplest case, an isomerization reaction that is first order in both directions:

A

kf




kr

B (11.4-1)

We denote the rate constant for the forward reaction bykfand the rate constant for the

reverse reaction bykr. The observable rate of the reaction is anet rategiven by the

difference between the forward rate and the reverse rate:

rnet−

d[A]

dt

kf[A]−kr[B] (11.4-2)

At equilibrium,

rnet,eqkf[A]eq−kr[B]eq 0 (11.4-3)

If we can ignore activity coefficients, the equilibrium constant for this reaction is

K

[B]eq

[A]eq



kf

kr

(11.4-4)

A large value for the equilibrium constant means that the rate constant for the forward

reaction is large compared with the rate constant for the reverse reaction. A small value

means that the rate constant for the forward reaction is small compared with the rate

constant for the reverse reaction. Equation (11.4-4) can apply to a more general case if

orders are equal to stoichiometric coefficients, as shown in the following exercise:

Exercise 11.16

For the reaction

aA+bB

kf




kr

dD+fF (11.4-5)

assume that the order with respect to each substance is equal to its stoichiometric coefficient:

rfkf[A]a[B]b and rrkr[D]d[F]f (11.4-6)

Show that

K

kf

kr

(11.4-7)

We subtract Eq. (11.4-3) for the equilibrium case from Eq. (11.4-2) to obtain

−

d[A]

dt

kf([A]−[A]eq)−kr([B]−[B]eq) (11.4-8)