11.4 Inclusion of a Reverse Reaction. Chemical Equilibrium
509
E X A M P L E 11.11
For a hypothetical isomerization that is first order in both directions with k f 17.7 min −1
and k r 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
k f
k r
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 − 0.528x
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)
k f + k r
ln(2)
17.7 min −1 + 32.2 min −1 0.0139 min
τ
1
k f + k r
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 time t 0.100 min.
P R O B L E M S
Section 11.4: Inclusion of a Reverse Reaction. Chemical
Equilibrium
11.28 Assume 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 that k f 10.0 s −1 and k r 1.00 s −1 .
b. Repeat part a for k f k r 10.0 s −1 .
c. Calculate the half-life of the reaction for both part a
and part b.
11.29 Calculate the concentration of each substance after a
reaction time of 0.35 s for the reaction of part a of the
previous problem.
11.30 Assume that the reaction
A B
is first order in both directions.