Physical Chemistry Third Edition

11.7 The Experimental Study of Fast Reactions 521

second order and the reverse reaction to be first

order.

c.Find the expression for the relaxation time for the

reaction

A
X

when the system is subjected to a small perturbation

from equilibrium. Assume both the forward reaction

and the reverse reaction to be first order.

11.39Find the expression for the relaxation time for the reaction

A+B+C
 X

when the system is subjected to a small perturbation from

equilibrium. Assume the forward reaction to be third

order overall, first order with respect to each reactant, and

the reverse reaction to be first order.

11.40For the reaction at 298 K

CH 3 CO− 2 +H+
CH 3 CO 2 H

kf 4. 5 × 1010 L mol−^1 s−^1 andkr 8. 0 × 105 s−^1.

A solution is made from 0.100 mol of acetic acid and

enough water to make 1.000 L.

a.Find the value of the equilibrium constant for the

reaction at 298 K, using the concentration description.

b.Find the equilibrium concentrations of all three solutes

at 298 K.

c.Find the relaxation time if a small perturbation is

imposed on the solution such that the final temperature

is 298 K.

11.41For the reaction at 298.15 K in aqueous solution

NH 3 +H 2 O
NH+ 4 +OH−

the equilibrium constant at 25.00◦C is equal to

1. 75 × 10 −^5 , and the reverse rate constantk′is equal to

4. 0 × 1011 L mol−^1 s−^1.

a.Find the molalities of OH−and NH+ 4 in a solution

made from 0.0100 mol of NH 3 and 1.000 kg of water.

Assume that all activity coefficients are equal to unity.

b.Find the value of the forward rate constant at this

temperature.

c.If the solution is originally at 15◦C and is suddenly

brought to a temperature of 25.00◦C, find the

relaxation time for the reaction.

Summary of the Chapter

A rate law of the form

ratek[A]α[B]β

is said to have definite orders, with orderαwith respect to A and with orderβwith

respect to B. The proportionality constantkis called the rate constant although it

depends on temperature. We solved several such differential rate laws to obtain the

integrated rate laws.

Some techniques for determination of the rate law involve comparison of the inte-

grated rate equation with experimental data on the concentration of a reactant. The

method of initial rates allows direct comparison of the differential rate law with the

experimental data. In the method of isolation, the concentration of one reactant is made

much smaller than the concentrations of the other reactants. During the reaction, the

fractional changes in the larger concentrations are negligible, and the small concentra-

tion behaves like the concentration in a reaction with one reactant.

For a reversible reaction that is first order in each direction the difference between

the concentration of the reactant and its equilibrium value relaxes exponentially, and

it was found that the relaxation time and the half-life are both inversely proportional

to the sum of the two rate constants.

A reaction mechanism consisting of two consecutive first-order reactions without

reverse reactions was considered. It was found that the concentration of the reactive

intermediate rose and then fell as the reaction proceeds.