🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning ## Chapter 14 ## Chemical Kinetics ## Educators ES   + 2 more educators ### Problem 1 Explain why lizards become sluggish in cold weather. How is this phenomenon related to chemistry? Allison K. Numerade Educator ### Problem 2 Why are reaction rates important (both practically and theoretically)? ES Eugene S. University of Minnesota - Twin Cities ### Problem 3 Using the idea that reactions occur as a result of collisions between particles, explain why reaction rates depend on the concentration of the reactants. Allison K. Numerade Educator ### Problem 4 Using the idea that reactions occur as a result of collisions between particles, explain why reaction rates depend on the temperature of the reaction mixture. ES Eugene S. University of Minnesota - Twin Cities ### Problem 5 What units are typically used to express the rate of a reaction? Allison K. Numerade Educator ### Problem 6 Why is the reaction rate for reactants defined as the negative of the change in reactant concentration with respect to time, whereas for products it is defined as the change in reactant concentration with respect to time (with a positive sign)? ES Eugene S. University of Minnesota - Twin Cities ### Problem 7 Explain the difference between the average rate of reaction and the instantaneous rate of reaction. Allison K. Numerade Educator ### Problem 8 Consider a simple reaction in which a reactant A forms products: What is the rate law if the reaction is zero order with respect to A? First order? Second order? For each case, explain how a doubling of the concentration of A would affect the rate of reaction. ES Eugene S. University of Minnesota - Twin Cities ### Problem 9 How is the order of a reaction generally determined? Allison K. Numerade Educator ### Problem 10 For a reaction with multiple reactants, how is the overall order of the reaction defined? ES Eugene S. University of Minnesota - Twin Cities ### Problem 11 Explain the difference between the rate law for a reaction and the integrated rate law for a reaction. What relationship does each kind of rate law express? Ricajoy M. Numerade Educator ### Problem 12 Write integrated rate laws for zero-order, first-order, and second-order reactions of the form A products. ES Eugene S. University of Minnesota - Twin Cities ### Problem 13 What does the term half-life mean? Write the expressions for the half-lives of zero-order, first-order, and second-order reactions. Ricajoy M. Numerade Educator ### Problem 14 How do reaction rates typically depend on temperature? What part of the rate law is temperature dependent? ES Eugene S. University of Minnesota - Twin Cities ### Problem 15 Explain the meaning of each term within the Arrhenius equation: activation energy, frequency factor, and exponential factor. Use these terms and the Arrhenius equation to explain why small changes in temperature can result in large changes in reaction rates. Ricajoy M. Numerade Educator ### Problem 16 What is an Arrhenius plot? Explain the significance of the slope and intercept of an Arrhenius plot. ES Eugene S. University of Minnesota - Twin Cities ### Problem 17 Explain the meaning of the orientation factor in the collision model. Ricajoy M. Numerade Educator ### Problem 18 Explain the difference between a normal chemical equation for a chemical reaction and the mechanism of that reaction. ES Eugene S. University of Minnesota - Twin Cities ### Problem 19 In a reaction mechanism, what is an elementary step? Write down the three most common elementary steps and the corresponding rate law for each one. Ricajoy M. Numerade Educator ### Problem 20 What are the two requirements for a proposed mechanism to be valid for a given reaction? ES Eugene S. University of Minnesota - Twin Cities ### Problem 21 What is an intermediate within a reaction mechanism? Ricajoy M. Numerade Educator ### Problem 22 What is a catalyst? How does a catalyst increase the rate of a chemical reaction? ES Eugene S. University of Minnesota - Twin Cities ### Problem 23 Explain the difference between homogeneous catalysis and heterogeneous catalysis. Ricajoy M. Numerade Educator ### Problem 24 What are the four basic steps involved in heterogeneous catalysis? ES Eugene S. University of Minnesota - Twin Cities ### Problem 25 What are enzymes? What is the active site of an enzyme? What is a substrate? Ricajoy M. Numerade Educator ### Problem 26 What is the general two-step mechanism by which most enzymes work? ES Eugene S. University of Minnesota - Twin Cities ### Problem 27 Consider the reaction. a. Express the rate of the reaction in terms of the change in concentration of each of the reactants and products. b. In the first 25.0 s of this reaction, the concentration of HBr drops from 0.600 M to 0.512 M. Calculate the average rate of the reaction during this time interval. c. If the volume of the reaction vessel in part b is 1.50 L, what amount of Br2 (in moles) forms during the first 15.0 s of the reaction? Allison K. Numerade Educator ### Problem 28 Consider the reaction. a. Express the rate of the reaction in terms of the change in concentration of each of the reactants and products. b. In the first 15.0 s of the reaction, 0.015 mol of O2 is produced in a reaction vessel with a volume of 0.500 L. What is the average rate of the reaction during this time interval? c. Predict the rate of change in the concentration of N2O during this time interval. In other words, what is [N2O]> t? ES Eugene S. University of Minnesota - Twin Cities ### Problem 29 For the reaction 2 A(g) + B(g)->3 C(g), a. determine the expression for the rate of the reaction in terms of the change in concentration of each of the reactants and products. b. when A is decreasing at a rate of 0.100 M>s, how fast is B decreasing? How fast is C increasing? Allison K. Numerade Educator ### Problem 30 For the reaction A(g) + 12 B(g)->2 C(g), a. determine the expression for the rate of the reaction in terms of the change in concentration of each of the reactants and products. b. when C is increasing at a rate of 0.0025 M>s, how fast is B decreasing? How fast is A decreasing? ES Eugene S. University of Minnesota - Twin Cities ### Problem 31 Consider the reaction. Complete the table. Allison K. Numerade Educator ### Problem 32 Consider the reaction. Complete the table. ES Eugene S. University of Minnesota - Twin Cities ### Problem 33 Consider the reaction: The tabulated data were collected for the concentration of C4H8 as a function of time. a. What is the average rate of the reaction between 0 and 10 s? Between 40 and 50 s? b. What is the rate of formation of C2H4 between 20 and 30 s? Allison K. Numerade Educator ### Problem 34 Consider the reaction. The tabulated data were collected for the concentration of NO2 as a function of time. a. What is the average rate of the reaction between 10 and 20 s? Between 50 and 60 s? b. What is the rate of formation of O2 between 50 and 60 s? ES Eugene S. University of Minnesota - Twin Cities ### Problem 35 Consider the reaction. The graph shows the concentration of Br2 as a function of time. a. Use the graph to calculate each quantity. (i) the average rate of the reaction between 0 and 25 s (ii) the instantaneous rate of the reaction at 25 s (iii) the instantaneous rate of formation of HBr at 50 s b. Make a rough sketch of a curve representing the concentration of HBr as a function of time. Assume that the initial concentration of HBr is zero. Allison K. Numerade Educator ### Problem 36 Consider the reaction. The graph shows the concentration of H2O2 as a function of time. a. Use the graph to calculate each quantity. (i) the average rate of the reaction between 10 and 20 s (ii) the instantaneous rate of the reaction at 30 s (iii) the instantaneous rate of formation of O2 at 50 s b. If the initial volume of the H2O2 is 1.5 L, what total amount of O2 (in moles) is formed in the first 50 s of reaction? ES Eugene S. University of Minnesota - Twin Cities ### Problem 37 This graph shows a plot of the rate of a reaction versus the concentration of the reactant A for the reaction A->products. a. What is the order of the reaction with respect to A? b. Make a rough sketch of a plot of [A] versus time. c. Write a rate law for the reaction including an estimate for the value of k. Allison K. Numerade Educator ### Problem 38 This graph shows a plot of the rate of a reaction versus the concentration of the reactant. a. What is the order of the reaction with respect to A? b. Make a rough sketch of a plot of [A] versus time. c. Write a rate law for the reaction including the value of k. ES Eugene S. University of Minnesota - Twin Cities ### Problem 39 What are the units of k for each type of reaction? a. first-order reaction b. second-order reaction c. zero-order reaction Allison K. Numerade Educator ### Problem 40 This reaction is first order in N2O5: The rate constant for the reaction at a certain temperature is 0.053>s. a. Calculate the rate of the reaction when [N2O5] = 0.055 M. b. What is the rate of the reaction at the concentration indicated in part a if the reaction is second order? Zero order? (Assume the same numerical value for the rate constant with the appropriate units.) ES Eugene S. University of Minnesota - Twin Cities ### Problem 41 A reaction in which A, B, and C react to form products is first order in A, second order in B, and zero order in C. a. Write a rate law for the reaction. b. What is the overall order of the reaction? c. By what factor does the reaction rate change if [A] is doubled (and the other reactant concentrations are held constant)? d. By what factor does the reaction rate change if [B] is doubled (and the other reactant concentrations are held constant)? e. By what factor does the reaction rate change if [C] is doubled (and the other reactant concentrations are held constant)? f. By what factor does the reaction rate change if the concentrations of all three reactants are doubled? Allison K. Numerade Educator ### Problem 42 A reaction in which A, B, and C react to form products is zero order in A, one-half order in B, and second order in C. a. Write a rate law for the reaction. b. What is the overall order of the reaction? c. By what factor does the reaction rate change if [A] is doubled (and the other reactant concentrations are held constant)? d. By what factor does the reaction rate change if [B] is doubled (and the other reactant concentrations are held constant)? e. By what factor does the reaction rate change if [C] is doubled (and the other reactant concentrations are held constant)? f. By what factor does the reaction rate change if the concentrations of all three reactants are doubled? ES Eugene S. University of Minnesota - Twin Cities ### Problem 43 Consider the tabulated data showing the initial rate of a reaction (A->products) at several different concentrations of A. What is the order of the reaction? Write a rate law for the reaction including the value of the rate constant, k. Allison K. Numerade Educator ### Problem 44 Consider the tabulated data showing the initial rate of a reaction (A->products) at several different concentrations of A. What is the order of the reaction? Write a rate law for the reaction including the value of the rate constant, k. ES Eugene S. University of Minnesota - Twin Cities ### Problem 45 The tabulated data were collected for this reaction: Write an expression for the reaction rate law and calculate the value of the rate constant, k. What is the overall order of the reaction? Allison K. Numerade Educator ### Problem 46 The tabulated data were collected for this reaction: Write an expression for the reaction rate law and calculate the value of the rate constant, k. What is the overall order of the reaction? ES Eugene S. University of Minnesota - Twin Cities ### Problem 47 Indicate the order of reaction consistent with each observation. a. A plot of the concentration of the reactant versus time yields a straight line. b. The reaction has a half-life that is independent of initial concentration. c. A plot of the inverse of the concentration versus time yields a straight line. Ricajoy M. Numerade Educator ### Problem 48 Indicate the order of reaction consistent with each observation. a. The half-life of the reaction gets shorter as the initial concentration is increased. b. A plot of the natural log of the concentration of the reactant versus time yields a straight line. c. The half-life of the reaction gets longer as the initial concentration is increased. ES Eugene S. University of Minnesota - Twin Cities ### Problem 49 The tabulated data show the concentration of AB versus time for this reaction: Determine the order of the reaction and the value of the rate constant. Predict the concentration of AB at 25 s. David C. Numerade Educator ### Problem 50 The tabulated data show the concentration of N2O5 versus time for this reaction: Determine the order of the reaction and the value of the rate constant. Predict the concentration of N2O5 at 250 s. ES Eugene S. University of Minnesota - Twin Cities ### Problem 51 The tabulated data show the concentration of cyclobutane (C4H8) versus time for this reaction: Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [C4H8] = 0.25 M? David C. Numerade Educator ### Problem 52 A reaction in which A->products is monitored as a function of time. The results are tabulated here. Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [A] = 0.10 M? ES Eugene S. University of Minnesota - Twin Cities ### Problem 53 This reaction was monitored as a function of time: A plot of ln[A] versus time yields a straight line with slope -0.0045>s. a. What is the value of the rate constant (k) for this reaction at this temperature? b. Write the rate law for the reaction. c. What is the half-life? d. If the initial concentration of A is 0.250 M, what is the concentration after 225 s? Ricajoy M. Numerade Educator ### Problem 54 This reaction was monitored as a function of time: A plot of 1>[AB] versus time yields a straight line with slope -0.055>M # s. a. What is the value of the rate constant (k) for this reaction at this temperature? b. Write the rate law for the reaction. c. What is the half-life when the initial concentration is 0.55 M? d. If the initial concentration of AB is 0.250 M, and the reaction mixture initially contains no products, what are the concentrations of A and B after 75 s? ES Eugene S. University of Minnesota - Twin Cities ### Problem 55 The decomposition of$\mathrm{SO}_{2} \mathrm{Cl}_{2}$is first order in$\mathrm{SO}_{2} \mathrm{Cl}_{2}$and has a rate constant of$1.42 \times 10^{-4} \mathrm{~s}^{-1}$at a certain temperature. a. What is the half-life for this reaction? b. How long will it take for the concentration of$\$O_{2} C l_{2}$ to decrease to $25 \%$ of its initial concentration?
c. If the initial concentration of $\$ O_{2} C l_{2}$is$1.00 \mathrm{M}$, how long will it take for the concentration to decrease to$0.78 \mathrm{M} ?$d. If the initial concentration of$\mathrm{SO}_{2} \mathrm{Cl}_{2}$is$0.150 \mathrm{M}$, what is the concentration of$\$\mathrm{SO}_{2} \mathrm{Cl}_{2}$ after $2.00 \times 10^{2} \mathrm{~s}$ ? After $5.00 \times 10^{2} \mathrm{~s}$ ? David C.

### Problem 56

The decomposition of XY is second order in XY and has a rate
constant of 7.02 * 10-3 M-1 # s-1 at a certain temperature.
a. What is the half-life for this reaction at an initial concentration
of 0.100 M?
b. How long will it take for the concentration of XY to decrease
to 12.5% of its initial concentration when the initial concentration
is 0.100 M? When the initial concentration is 0.200 M?
c. If the initial concentration of XY is 0.150 M, how long will it
take for the concentration to decrease to 0.062 M?
d. If the initial concentration of XY is 0.050 M, what is the concentration
of XY after 5.0 * 101 s? After 5.50 * 102 s?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 57

The half-life for the radioactive decay of U-238 is 4.5 billion years
and is independent of initial concentration. How long will it take
for 10% of the U-238 atoms in a sample of U-238 to decay? If a
sample of U-238 initially contained 1.5 * 1018 atoms when the
universe was formed 13.8 billion years ago, how many U-238
atoms does it contain today? Ronald P.

### Problem 58

The half-life for the radioactive decay of C-14 is 5730 years and is
independent of the initial concentration. How long does it take
for 25% of the C-14 atoms in a sample of C-14 to decay? If a
sample of C-14 initially contains 1.5 mmol of C-14, how many
millimoles are left after 2255 years?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 59

The diagram shows the energy of a reaction as the reaction
progresses. Label each blank box in the diagram.
a. reactants b. products
c. activation energy (Ea) d. enthalpy of reaction (Hrxn) Ricajoy M.

### Problem 60

A chemical reaction is endothermic and has an activation energy
that is twice the value of the enthalpy change of the reaction.
Draw a diagram depicting the energy of the reaction as it
progresses. Label the position of the reactants and products and
indicate the activation energy and enthalpy of reaction.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 61

The activation energy of a reaction is 56.8 kJ>mol and the
frequency factor is 1.5 * 1011>s. Calculate the rate constant of
the reaction at 25 C. Ricajoy M.

### Problem 62

The rate constant of a reaction at 32 C is 0.055>s. If the
frequency factor is 1.2 * 1013>s, what is the activation barrier?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 63

The rate constant (k) for a reaction is measured as a function of
temperature. A plot of ln k versus 1>T (in K) is linear and has a
slope of -7445 K. Calculate the activation energy for the reaction. Ricajoy M.

### Problem 64

The rate constant (k) for a reaction is measured as a function of
temperature. A plot of ln k versus 1>T (in K) is linear and has a slope of -1.01 * 104 K. Calculate the activation energy for the
reaction.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 65

The tabulated data shown here were collected for the first-order
reaction:
Use an Arrhenius plot to determine the activation barrier and
frequency factor for the reaction. David C.

### Problem 66

The tabulated data show the rate constant of a reaction measured at several different temperatures. Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 67

The tabulated data were collected for the second-order reaction:
Use an Arrhenius plot to determine the activation barrier and
frequency factor for the reaction. David C.

### Problem 68

The tabulated data show the rate constant of a reaction measured
at several different temperatures. Use an Arrhenius plot to determine
the activation barrier and frequency factor for the reaction.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 69

A reaction has a rate constant of 0.0117>s at 400.0 K and 0.689>s
at 450.0 K.
a. Determine the activation barrier for the reaction.
b. What is the value of the rate constant at 425 K? Ricajoy M.

### Problem 70

A reaction has a rate constant of 0.000122>s at 27 C and 0.228>s
at 77 C.
a. Determine the activation barrier for the reaction.
b. What is the value of the rate constant at 17 C?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 71

If a temperature increase from 10.0 C to 20.0 C doubles the rate
constant for a reaction, what is the value of the activation barrier
for the reaction? Ricajoy M.

### Problem 72

If a temperature increase from 20.0 C to 35.0 C triples the rate
constant for a reaction, what is the value of the activation barrier
for the reaction?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 73

Consider these two gas-phase reactions:
a. AA(g) + BB(g)->2 AB(g)
b. AB(g) + CD(g)->AC(g) + BD(g)
If the reactions have identical activation barriers and are carried
out under the same conditions, which one would you expect to
have the faster rate? Ricajoy M.

### Problem 74

Which of these two reactions would you expect to have the
smaller orientation factor? Explain.
a. O(g) + N2(g)->NO(g) + N(g)
b. NO(g) + Cl2(g)->NOCl(g) + Cl(g)

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 75

Consider this overall reaction, which is experimentally observed
to be second order in AB and zero order in C:

Is the following mechanism valid for this reaction? Ricajoy M.

### Problem 76

Consider this overall reaction, which is experimentally observed
to be second order in X and first order in Y:
a. Does the reaction occur in a single step in which X and Y
collide?
b. Is this two-step mechanism valid?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 77

Consider this three-step mechanism for a reaction:
a. What is the overall reaction?
b. Identify the intermediates in the mechanism.
c. What is the predicted rate law? Ricajoy M.

### Problem 78

Consider this two-step mechanism for a reaction:
a. What is the overall reaction?
b. Identify the intermediates in the mechanism.
c. What is the predicted rate law?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 79

Many heterogeneous catalysts are deposited on high surface-area
supports. Why? Ricajoy M.

### Problem 80

Suppose that the reaction A->products is exothermic and
has an activation barrier of 75 kJ>mol. Sketch an energy diagram
showing the energy of the reaction as a function of the progress
of the reaction. Draw a second energy curve showing the effect of
a catalyst.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 81

Suppose that a catalyst lowers the activation barrier of a reaction
from 125 kJ >mol to 55 kJ >mol. By what factor would you
expect the reaction rate to increase at 25 C? (Assume that the
frequency factors for the catalyzed and uncatalyzed reactions
are identical.) Ricajoy M.

### Problem 82

The activation barrier for the hydrolysis of sucrose into glucose
and fructose is 108 kJ>mol. If an enzyme increases the rate of the
hydrolysis reaction by a factor of 1 million, how much lower
must the activation barrier be when sucrose is in the active site of
the enzyme? (Assume that the frequency factors for the catalyzed
and uncatalyzed reactions are identical and a temperature of
25 C.)

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 83

The tabulated data were collected for this reaction at 500 C:
a. Determine the order of the reaction and the value of the rate
constant at this temperature.
b. What is the half-life for this reaction (at the initial
concentration)?
c. How long will it take for 90% of the CH3CN to convert to
CH3NC? David C.

### Problem 84

The tabulated data were collected for this reaction at a certain
temperature:
a. Determine the order of the reaction and the value of the rate
constant at this temperature.
b. What is the half-life for this reaction (at the initial
concentration)?
c. What is the concentration of X after 10.0 hours?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 85

Consider the reaction:
The rate law for this reaction is:
Suppose the rate of the reaction at certain initial concentrations
of A, B, and C is 0.0115 M>s. What is the rate of the reaction if
the concentrations of A and C are doubled and the concentration
of B is tripled? Ricajoy M.

### Problem 86

Consider the reaction:
The rate law for this reaction is:
Suppose that a 1.0 L reaction vessel initially contains 1.0 mol of
O3 and 1.0 mol of O2. What fraction of the O3 has reacted when
the rate falls to one-half of its initial value?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 87

At 700 K acetaldehyde decomposes in the gas phase to methane
and carbon monoxide. The reaction is:
A sample of CH3CHO is heated to 700 K, and the pressure is
measured as 0.22 atm before any reaction takes place. The
kinetics of the reaction are followed by measurements of total
pressure, and these data are obtained:
Determine the rate law, the rate constant, and the total pressure
after 2.00 * 104 s. David C.

### Problem 88

At 400 K oxalic acid decomposes according to the reaction:
In three separate experiments, the initial pressure of oxalic acid
and the final total pressure after 20,000 s are measured.
Find the rate law of the reaction and its specific rate constant.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 89

Dinitrogen pentoxide decomposes in the gas phase to form
nitrogen dioxide and oxygen gas. The reaction is first order in dinitrogen
pentoxide and has a half-life of 2.81 h at 25 C. If a 1.5 L
reaction vessel initially contains 745 torr of N2O5 at 25 C, what
partial pressure of O2 is present in the vessel after 215 minutes? David C.

### Problem 90

Cyclopropane (C3H6) reacts to form propene (C3H6) in the gas
phase. The reaction is first order in cyclopropane and has a rate
constant of 5.87 * 10-4>s at 485 C. If a 2.5 L reaction vessel
initially contains 722 torr of cyclopropane at 485 C, how long will
it take for the partial pressure of cyclopropane to drop to below
1.00 * 102 torr?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 91

Iodine atoms combine to form I2 in liquid hexane solvent with a
rate constant of 1.5 * 1010 L>mol # s. The reaction is second
order in I. Since the reaction occurs so quickly, the only way to
study the reaction is to create iodine atoms almost instantaneously,
usually by photochemical decomposition of I2. Suppose
a flash of light creates an initial [I] concentration of 0.0100 M.
How long will it take for 95% of the newly created iodine atoms
to recombine to form I2? David C.

### Problem 92

The hydrolysis of sucrose (C12H22O11) into glucose and fructose
in acidic water has a rate constant of 1.8 * 10-4 s-1 at 25 C.
Assuming the reaction is first order in sucrose, determine the
mass of sucrose that is hydrolyzed when 2.55 L of a 0.150 M
sucrose solution is allowed to react for 195 minutes.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 93

The reaction AB(aq)->A(g) + B(g) is second order in AB and
has a rate constant of 0.0118 M-1 # s-1 at 25.0 C. A reaction vessel
initially contains 250.0 mL of 0.100 M AB that is allowed to react
to form the gaseous product. The product is collected over water
at 25.0 C. How much time is required to produce 200.0 mL of
the products at a barometric pressure of 755.1 mmHg? (The vapor
pressure of water at this temperature is 23.8 mmHg.) David C.

### Problem 94

The reaction 2 H2O2(aq)->2 H2O(l) + O2(g) is first order
in H2O2 and under certain conditions has a rate constant of
0.00752 s-1 at 20.0 C. A reaction vessel initially contains
150.0mL of 30.0% H2O2 by mass solution (the density of the
solution is 1.11 g >mL). The gaseous oxygen is collected over
water at 20.0 C as it forms. What volume of O2 forms in
85.0 seconds at a barometric pressure of 742.5 mmHg? (The
vapor pressure of water at this temperature is 17.5 mmHg.)

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 95

Consider this energy diagram:
a. How many elementary steps are involved in this reaction?
b. Label the reactants, products, and intermediates.
c. Which step is rate limiting?
d. Is the overall reaction endothermic or exothermic? Ricajoy M.

### Problem 96

Consider the reaction in which HCl adds across the double bond
of ethene:
The following mechanism, with the accompanying energy
diagram, has been suggested for this reaction:
a. Based on the energy diagram, determine which step is rate
limiting.
b. What is the expected order of the reaction based on the
proposed mechanism?
c. Is the overall reaction exothermic or endothermic?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 97

The desorption of a single molecular layer of n-butane from a
single crystal of aluminum oxide is found to be first order with a
rate constant of 0.128>s at 150 K.
a. What is the half-life of the desorption reaction?
b. If the surface is initially completely covered with n-butane at
150 K, how long will it take for 25% of the molecules to
desorb? For 50% to desorb?
c. If the surface is initially completely covered, what fraction
will remain covered after 10 s? After 20 s? David C.

### Problem 98

The evaporation of a 120-nm film of n-pentane from a single
crystal of aluminum oxide is zero order with a rate constant of
1.92 * 1013 molecules>cm2 # s at 120 K.
a. If the initial surface coverage is 8.9 * 1016 molecules>cm2,
how long will it take for one-half of the film to evaporate?
b. What fraction of the film is left after 10 s? Assume the same
initial coverage as in part a.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 99

The kinetics of this reaction were studied as a function of temperature.
(The reaction is first order in each reactant and second
order overall.)
a. Determine the activation energy and frequency factor for the
reaction.
b. Determine the rate constant at 15 C.
c. If a reaction mixture is 0.155 M in C2H5Br and 0.250 M in
OH-, what is the initial rate of the reaction at 75 C? David C.

### Problem 100

The reaction 2 N2O5->2 N2O4 + O2 takes place at around
room temperature in solvents such as CCl4. The rate constant at
293 K is 2.35 * 10-4 s-1, and at 303 K the rate constant is
9.15 * 10-4 s-1. Calculate the frequency factor for the reaction.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 101

This reaction has an activation energy of zero in the gas phase:
a. Would you expect the rate of this reaction to change very
much with temperature?
b. Why might the activation energy be zero?
c. What other types of reactions would you expect to have little
or no activation energy? Ricajoy M.

### Problem 102

Consider the two reactions:
a. Why is the activation barrier for the first reaction so much
higher than that for the second?
b. The frequency factors for these two reactions are very close
to each other in value. Assuming that they are the same,
calculate the ratio of the reaction rate constants for these two
reactions at 25 C.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 103

Anthropologists can estimate the age of a bone or other sample of
organic matter by its carbon-14 content. The carbon-14 in a living
organism is constant until the organism dies, after which carbon-14
decays with first-order kinetics and a half-life of 5730 years.
Suppose a bone from an ancient human contains 19.5% of the C-14
found in living organisms. How old is the bone? Ricajoy M.

### Problem 104

Geologists can estimate the age of rocks by their uranium-238
content. The uranium is incorporated in the rock as it hardens
and then decays with first-order kinetics and a half-life of
4.5 billion years. A rock contains 83.2% of the amount of
uranium-238 that it contained when it was formed. (The amount
that the rock contained when it was formed can be deduced from
the presence of the decay products of U-238.) How old is the rock?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 105

Consider the gas-phase reaction:
The reaction was experimentally determined to be first order in
H2 and first order in I2. Consider the proposed mechanisms.
Proposed mechanism I:
Proposed mechanism II:
a. Show that both of the proposed mechanisms are valid.
b. What kind of experimental evidence might lead you to favor
mechanism II over mechanism I? Ricajoy M.

### Problem 106

Consider the reaction:
This three-step mechanism is proposed:
a. Show that the mechanism sums to the overall reaction.
b. What is the rate law predicted by this mechanism?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 107

The proposed mechanism for the formation of hydrogen bromide
can be written in a simplified form as:
What rate law corresponds to this mechanism? Ricajoy M.

### Problem 108

A proposed mechanism for the formation of hydrogen iodide can
be written in simplified form as:
What rate law corresponds to this mechanism?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 109

A certain substance X decomposes. Fifty percent of X remains
after 100 minutes. How much X remains after 200 minutes if the
reaction order with respect to X is (a) zero order, (b) first order,
(c) second order? Prashant B.

### Problem 110

The half-life for radioactive decay (a first-order process) of
plutonium-239 is 24,000 years. How many years does it take for
one mole of this radioactive material to decay until just one atom
remains?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 111

The energy of activation for the decomposition of 2 mol of HI to
H2 and I2 in the gas phase is 185 kJ. The heat of formation of
HI(g) from H2(g) and I2(g) is -5.68 kJ>mol. Find the energy of
activation for the reaction of 1 mol of H2 and 1 mol of I2 to form
2mol of HI in the gas phase. Ricajoy M.

### Problem 112

Ethyl chloride vapor decomposes by the first-order reaction:
The activation energy is 249 kJ>mol, and the frequency factor is
1.6 * 1014 s-1. Find the value of the specific rate constant at
710K. What fraction of the ethyl chloride decomposes in
15minutes at this temperature? Find the temperature at which
the rate of the reaction would be twice as fast.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 113

In this chapter we have seen a number of reactions in which a
single reactant forms products. For example, consider the following
first-order reaction:
However, we also learned that gas-phase reactions occur through
collisions.
a. One possible explanation is that two molecules of CH3NC
collide with each other and form two molecules of the product
in a single elementary step. If that is the case, what reaction
order would you expect?
b. Another possibility is that the reaction occurs through more
than one step. For example, a possible mechanism involves
one step in which the two CH3NC molecules collide, resulting
in the 'activation' of one of them. In a second step, the activated
molecule goes on to form the product. Write down this
mechanism and determine which step must be rate determining
in order for the kinetics of the reaction to be first order.
Show explicitly how the mechanism predicts first-order
kinetics. David C.

### Problem 114

The first-order integrated rate law for a reaction A->products
is derived from the rate law using calculus:
The equation just given is a first-order, separable differential
equation that can be solved by separating the variables and
integrating:
In the integral just given, [A]0 is the initial concentration of A.
We then evaluate the integral:
a. Use a procedure similar to the one just shown to derive an
integrated rate law for a reaction A->products, which is
one-half-order in the concentration of A (that is,
Rate = k[A]1>2).
b. Use the result from part a to derive an expression for the halflife
of a one-half-order reaction.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 115

The previous exercise shows how the first-order integrated rate
law is derived from the first-order differential rate law. Begin
with the second-order differential rate law and derive the
second-order integrated rate law. Ricajoy M.

### Problem 116

The rate constant for the first-order decomposition of N2O5(g) to
NO2(g) and O2(g) is 7.48 * 10-3 s-1 at a given temperature.
a. Find the length of time required for the total pressure in a
system containing N2O5 at an initial pressure of 0.100 atm to
rise to 0.145 atm.
b. Find the length of time required for the total pressure in a
system containing N2O5 at an initial pressure of 0.100 atm to
rise to 0.200 atm.
c. Find the total pressure after 100 s of reaction.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 117

Phosgene (Cl2CO), a poison gas used in World War I, is formed
by the reaction of Cl2 and CO. The proposed mechanism for the
reaction is:
What rate law is consistent with this mechanism? Ricajoy M.

### Problem 118

The rate of decomposition of N2O3(g) to NO2(g) and NO(g) is
monitored by measuring [NO2] at different times. The following
tabulated data are obtained.
The reaction follows a first-order rate law. Calculate the rate
constant. Assume that after 50,000 s all the N2O3(g) had
decomposed.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 119

At 473 K, for the elementary reaction 2 NOCl(g) k1
k-1
2 NO(g) + Cl2(g)
A sample of NOCl is placed in a container and heated to 473 K.
When the system comes to equilibrium, [NOCl] is found to be
0.12 mol>L. What are the concentrations of NO and Cl2? David C.

### Problem 120

Consider the reaction:
The reaction is first order in CHCl3 and one-half order in Cl2. Which
reaction mixture would you expect to have the fastest initial rate?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 121

The accompanying graph shows the concentration of a reactant as
a function of time for two different reactions. One of the reactions
is first order and the other is second order. Which of the two
reactions is first order? Second order? How would you change
each plot to make it linear? Ricajoy M.

### Problem 122

A particular reaction, A->products, has a rate that slows down
as the reaction proceeds. The half-life of the reaction is found to
depend on the initial concentration of A. Determine whether each
statement is likely to be true or false for this reaction.
a. A doubling of the concentration of A doubles the rate of the
reaction.
b. A plot of 1>[A] versus time is linear.
c. The half-life of the reaction gets longer as the initial
concentration of A increases.
d. A plot of the concentration of A versus time has a constant
slope.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 123

A student says, 'The initial concentration of a reactant was doubled,
and the rate doubled. Therefore, the reaction is second
order in that reactant.'Why might the student say that? What is
wrong with the statement? What is the actual order with respect
to the reactant? Explain your reasoning clearly. Prashant B.

### Problem 124

A certain compound, A, reacts to form products according to the
reaction A->P. The amount of A is measured as a function of
time under a variety of different conditions and the tabulated
results are shown here:
Have one group member make a graph of [A] versus t, one group
member make a graph of ln[A] versus t, and one group member
make a graph of 1>[A] versus t using the data for 25 C.
Additional group members can make similar graphs for the other
temperatures. What is the order of the reaction with respect to
a. Use the data to determine the rate constant at each
temperature.
b. What is the activation energy for this reaction?
c. The same reaction is conducted in the presence of a catalyst,
and the following data are obtained:
What effect does a catalyst have on the rate of the reaction? What
is the activation energy for this reaction in the presence of the
catalyst? How does it compare with the activation energy for the
reaction when the catalyst isn"t present?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 125

Methane (CH4) is a greenhouse gas emitted by industry, agriculture,
and waste systems. It is the second most prevalent greenhouse
gas (after carbon dioxide). Methane plays an important
role in climate change because it absorbs infrared radiation more
efficiently than carbon dioxide. Methane is broken down in the
atmosphere by ozone (O3), making its atmospheric lifetime
shorter than that of carbon dioxide.
A research group studied the rate of the reaction by which
methane reacts with ozone and gets the data shown in the tables
shown here. Study the data and answer the questions that follow.
a. Use the data in the first table to determine the order of the
reaction with respect to each reactant.
b. Use the data in the second table to determine the activation
barrier and pre-exponential factor for the reaction.
c. Atmospheric concentrations of methane and ozone can vary
depending on the location and altitude. Calculate the rate of
the reaction at 273 K for a methane concentration of 1.8 ppm
(by volume) and an ozone concentration of 5.0 ppm (by
volume). Note that 1 ppm of CH4 by volume means 1 L
CH4>106 L air. Assume STP (standard temperature and
pressure) so that 1 mol gas occupies 22.4 L.
d. What is the half-life of methane in the atmosphere in years at
323 K? (Assume that [CH4] = [O3] = [A]0 = 5.0 * 10-7 M.) David C.