Physical Chemistry Third Edition

11.4 Inclusion of a Reverse Reaction. Chemical Equilibrium 509

EXAMPLE11.11

For a hypothetical isomerization that is first order in both directions withkf 17 .7 min−^1

andkr 32 .2 min−^1 , find the equilibrium composition if the initial concentration of A is

equal to 0.175 mol L−^1 and the initial concentration of B is equal to zero. Find the half-life

and the relaxation time.

Solution

K

kf

kr



17 .7 min−^1

32 .2 min−^1

 0. 528

We let

x

[B]eq

1 mol L−^1



[A] 0 −[A]eq

1 mol L−^1

0. 528 

x

0. 150 −x

x(0.528)(0. 150 −x) 0. 0792 − 0. 528 x

x

0. 0792

1. 528

 0. 0518

[B]eq 0 .0518 mol L−^1

[A]eq 0 .0982 mol L−^1

t 1 / 2 

ln(2)

kf+kr



ln(2)

17 .7 min−^1 + 32 .2 min−^1

 0 .0139 min

τ

1

kf+kr



1

17 .7 min−^1 + 32 .2 min−^1

 0 .0200 min

Exercise 11.19

Find the composition for the reaction of the previous example at timet 0 .100 min.

PROBLEMS

Section 11.4: Inclusion of a Reverse Reaction. Chemical

Equilibrium

11.28Assume that the reaction

A
B

is first order in both directions. The initial concentration

of A is 1.000 mol L−^1 and that of B is 0.

a. Construct a graph of[A]and[B]as a function of time

for the case thatkf 10 .0s−^1 andkr 1 .00 s−^1.

b. Repeat part a forkfkr 10 .0s−^1.

c.Calculate the half-life of the reaction for both part a

and part b.

11.29Calculate the concentration of each substance after a

reaction time of 0.35 s for the reaction of part a of the

previous problem.

11.30Assume that the reaction

A
B

is first order in both directions.