Physical Chemistry Third Edition

520 11 The Rates of Chemical Reactions

K 1 

k 1

k′ 1



[H 2 O]^2

[

H+

][

OH−

]

(55.35 mol L−^1 )^2

1. 008 × 10 −^14 mol^2 L−^2

 3. 039 × 1017

k 1 ′

k 1

K 1



1. 4 × 1011 L mol−^1 s−^1

3. 039 × 1017

 4. 6 × 10 −^7 L mol−^1 s−^1

b.From Eq. (11.7-14):

1

τ



(1. 4 × 1011 L mol−^1 s−^1 )(2× 1. 004 × 10 −^7 mol L−^1 )

2

+2(4. 6 × 10 −^7 L mol−^1 s−^1 )(55.35 mol L−^1 )

 1. 4 × 104 s−^1

τ 7. 1 × 10 −^5 s

Similar expressions for the relaxation time can be derived for other rate laws.a

aK. J. Laidler,Chemical Kinetics, 3rd ed., Harper and Row, New York, 1987, p. 38.

Exercise 11.24

a.Verify Eq. (11.7-14).

b.For the reaction equation

A+B
X+Y

assume second order in both directions, show that the relaxation time is given by

1

τ

k 1 ([A]eq+[B]eq)+k′ 1 ([X]eq+[Y]eq) (11.7-15)

We have discussed temperature-jump experiments. Pressure-jump experiments are

analyzed in the same way, with sudden changes in pressure that produce partial pres-

sures that deviate from equilibrium partial pressures at the new total pressure.

PROBLEMS

Section 11.7: The Experimental Study of Fast Reactions

11.37Find the expression for the relaxation time for the
reaction A
C when the system is subjected to a small
perturbation from equilibrium. Assume both the forward
reaction and the reverse reaction to be second order.

11.38a.Find the expression for the relaxation time for the
reaction
A
2X

when the system is subjected to a small perturbation

from equilibrium. Assume the forward reaction to be

first order and the reverse reaction to be second order.

b.Find the expression for the relaxation time for the

reaction

2A
X

when the system is subjected to a small perturbation

from equilibrium. Assume the forward reaction to be