494
11 The Rates of Chemical Reactions
Exercise 11.8
a. Verify Eq. (11.2-18).
b. Find the units of the rate constant k f for an nth-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 of t 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
k f [A]
0
k f
(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 − k f t if 0 < t < [A] 0 /k f
0
i f[A] 0 /k f < 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.
E X A M P L E 11.5
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 − k f t 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 temperature.
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 compare the integrated rate law with experimental data on the concentration of the reactant. 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
11 The Rates of Chemical Reactions
Exercise 11.8
a. Verify Eq. (11.2-18).
b. Find the units of the rate constant k f for an nth-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 of t 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
k f [A]
0
k f
(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 − k f t if 0 < t < [A] 0 /k f
0
i f[A] 0 /k f < 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.
E X A M P L E 11.5
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 − k f t 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 temperature.
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 compare the integrated rate law with experimental data on the concentration of the reactant. 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