Book Title: eTextbook: Chemistry
Chapter 12. Chemical Kinetics
Challenge Problems
Challenge Problems
132. Consider a reaction of the type
law is found to be
, in which the rate
(termolecular reactions are improbable
but possible). If the first half-life of the reaction is found to be
s,
what is the time for the second half-life? Hint: Using your calculus
knowledge, derive the integrated rate law from the differential rate law
for a termolecular reaction:
133. A study was made of the effect of the hydroxide concentration on
the rate of the reaction
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The following data were obtained:
(mol/L)
(mol/L)
(mol/L)
Initial Rate
(mol/L · s)
Determine the rate law and the value of the rate constant for this
reaction.
SHOW ANSWER
134. Two isomers (
and
) of a given compound dimerize as
follows:
Both processes are known to be second order in reactant, and
known to be
and
⋅ at
. In a particular experiment
were placed in separate containers at
and
each reaction had progressed for
the rate laws are defined as
is
, where
. It was found that after
min ,
. In this case
a. Calculate the concentration of
b. Calculate the value of
after
min .
.
c. Calculate the half-life for the experiment involving
.
135. The reaction
was studied by performing two experiments. In the first experiment
the rate of disappearance of
large excess of
was followed in the presence of a
. The results were as follows (
effectively constant at
remains
):
Time (ms)
(
了
In the second experiment
was held constant at
. The data for the disappearance of
are as
follows:
Time (ms)
a. What is the order with respect to each reactant?
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b. What is the overall rate law?
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c. What is the value of the rate constant from each set of experiments?
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d. What is the value of the rate constant for the overall rate law?
SHOW ANSWER
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136. The reaction
is expected to obey the mechanism
Write the rate law for this reaction.
137. In the gas phase, the production of phosgene from chlorine and
carbon monoxide is assumed to proceed by the following mechanism:
Overall reaction:
a. Write the rate law for this reaction.
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b. Which species are intermediates?
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138. Most reactions occur by a series of steps. The energy profile for a
certain reaction that proceeds by a two-step mechanism is
Details
On the energy profile, indicate
a. the positions of reactants and products.
b. the activation energy for the overall reaction.
c.
for the reaction.
d. Which point on the plot represents the energy of the intermediate
in the two-step reaction?
e. Which step in the mechanism for this reaction is rate determining,
the first or the second step? Explain.
139. You are studying the kinetics of the reaction
and you wish to determine a mechanism
for the reaction. You run the reaction twice by keeping one
reactant at a much higher pressure than the other reactant (this
lower-pressure reactant begins at
atm ). Unfortunately, you
neglect to record which reactant was at the higher pressure, and
you forget which it was later. Your data for the first experiment are
Pressure of HF (atm)
Time (min)
When you ran the second experiment (in which the higher-pressure
reactant was run at a much higher pressure), you determine the values
of the apparent rate constants to be the same. It also turns out that you
find data taken from another person in the lab. This individual found
that the reaction proceeds
times faster at
than at
.
You also know, from the energy-level diagram, that there are three steps
to the mechanism, and the first step has the highest activation energy.
You look up the bond energies of the species involved and they are (in
kJ/mol):
,
, and
.
a. Sketch an energy-level diagram (qualitative) that is consistent with
the one described previously. Hint: See Exercise 138.
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b. Develop a reasonable mechanism for the reaction.
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c. Which reactant was limiting in the experiments?
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140. The decomposition of
occurs by the following bimolecular
elementary reaction:
The rate constant at
energy is
K is
⋅ , and the activation
kJ/mol . How long will it take for the concentration of
to decrease from an initial partial pressure of
atm at
atm to
K ? Assume ideal gas behavior.
141. The following data were collected in two studies of the reaction
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Time (s)
Experiment 1
In Experiment 1,
.
In Experiment 2,
a. Why is
Experiment 2
.
much greater than
?
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b. Give the rate law and value for
for this reaction.
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c. Which of the following mechanisms could be correct for this
reaction? Justify your choice.
i.
ii.
iii.
SHOW ANSWER
142. Consider the following hypothetical data collected in two studies of
the reaction
Time (s)
Experiment 1 [A]
(mol/L)
?
In Experiment 1,
.
In Experiment 2,
.
Experiment 2 [A]
(mol/L)
a. Use the concentration versus time data to determine the rate law
for the reaction.
b. Solve for the value of the rate constant
for the reaction.
Include units.
c. Calculate the concentration of
in Experiment 1 at
143. Consider the hypothetical reaction
In a study of this reaction three experiments were run at the same
temperature. The rate is defined as
.
Experiment 1:
[B] (mol/L)
Time (s)
.
Experiment 2:
[A] (mol/L)
Experiment 3:
Time (s)
[C] (mol/L)
Time (s)
Write the rate law for this reaction, and calculate the value of the rate
constant.
SHOW ANSWER
144. Hydrogen peroxide and the iodide ion react in acidic solution as
follows:
The kinetics of this reaction were studied by following the decay of the
concentration of
and constructing plots of
versus time.
All the plots were linear and all solutions had
. The slopes of these straight lines depended
on the initial concentrations of
and
. The results follow:
(mol/L)
(mol/L)
The rate law for this reaction has the form
a. Specify the order of this reaction with respect to
b. Calculate the values of the rate constants,
and
and
.
.
c. What reason could there be for the two-term dependence of the rate
on
505m
?
Book Title: eTextbook: Chemistry
Chapter 12. Chemical Kinetics
Marathon Problem
Marathon Problem
This problem is designed to incorporate several concepts and
techniques into one situation.
145. Consider the following reaction:
At
, the following two experiments were run, yielding the
following data:
Experiment 1:
(mol/L)
Experiment 2:
Time (h)
(mol/L)
Time (h)
Experiments also were run at
was found to be
. The value of the rate constant at
(with the time in units of hours),
where
and
.
a. Determine the rate law and the value of
for this reaction at
.
b. Determine the half-life at
c. Determine
d. Given that the
.
for the reaction.
bond energy is known to be about
kJ/mol , suggest a mechanism that explains the results in parts a
and c.
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