Physical Chemistry Third Edition

494 11 The Rates of Chemical Reactions

Exercise 11.8

a.Verify Eq. (11.2-18).

b.Find the units of the rate constantkffor annth-order reaction.

c.For a third-order reaction with a single reactant and negligible reverse reaction, find an

expression for the time required for 80% of the reactant to react.

d.In terms oft 1 / 2 , how long will it take for 7/8 (87.5%) of the reactant of part c to react?

Zero-Order Reactions

In the rare case that a reaction of a single reactant is zero order (the rate is independent

of the concentration of the reactant), the rate law for the forward reaction is

r−

d[A]

dt

kf[A]^0 kf (11.2-19)

If there is no reverse reaction and if the temperature is constant, the solution of this

equation is

[A]t

{

[A] 0 −kft if 0<t<[A] 0 /kf

0if[A] 0 /kf<t

(11.2-20)

where the first line of the solution is obtained from Eq. (11.2-19). The second line

of the solution is obtained from the fact that the reaction stops when no reactant

remains.

EXAMPLE11.5

A hypothetical zero-order reaction has a rate constant equal to 0.0150 mol L−^1 s−^1 at a certain

temperature. If the initial concentration of the single reactant is 1.000 mol L−^1 , find the

concentration after a reaction time of 5.00 s at this temperature.

Solution

[A]t[A] 0 −kft 1 .000 mol L−^1 −(0.0150 mol L−^1 s−^1 )(5.00 s) 0 .925 mol L−^1

Exercise 11.9

a.Find the time required for all of the reactant of the previous example to react at this temper-

ature.

b.Find an expression for the half-life of a zero-order reaction and the value of the half-life of

the reaction of the previous example.

Determination of Reaction Order Using Integrated

Rate Laws

For a reaction of a single substance with a negligible reverse reaction, we can com-

pare the integrated rate law with experimental data on the concentration of the reac-

tant. Since graphs of linear functions are easy to recognize, for each order one can

plot the appropriate function of the reactant’s concentration that will give a linear