Deck 16: Kinetics: Rates and Mechanisms of Chemical Reactions

Question 1

A reaction has the following rate law:
Rate = k[A][B]²
In experiment 1,the concentrations of A and B are both 0.10 mol L^-1;in experiment 2,the concentrations are both 0.30 mol L^-1.If the temperature stays constant,what is the value of the ratio,Rate(2)/Rate(1)?

A)3.0
B)6.0
C)9.0
D)18
E)27

Answer 1

27

Question 2

The reaction A $\to$ B is first-order overall and first-order with respect to the reactant A.The result of doubling the initial concentration of A will be to

A)shorten the half-life of the reaction.
B)increase the rate constant of the reaction.
C)decrease the rate constant of the reaction.
D)shorten the time taken to reach equilibrium.
E)double the initial rate.

Answer 2

double the initial rate.

Question 3

Consider the reaction
2NH₃(g) $\to$ N₂(g)+ 3H₂(g)
If the rate $\Delta$ [H₂]/ $\Delta$ t is 0.030 mol L^-1 s^-1,then $\Delta$ [NH₃]/ $\Delta$ t is

A)-0.045 mol L^-1 s^-1
B)-0.030 mol L^-1 s^-1
C)-0.020 mol L^-1 s^-1
D)-0.010 mol L^-1 s^-1
E)None of these choices is correct.

Answer 3

-0.020 mol L^-1 s^-1

Question 4

A study of the decomposition reaction 3RS₂ $\to$ 3R + 6S yields the following initial rate data

What is the rate constant for the reaction?

A)0.0103 L mol^-1s^-1
B)0.263 L mol^-1s^-1
C)0.571 L mol^-1s^-1
D)1.17 L mol^-1s^-1
E)1.75 L mol^-1s^-1

Question 5

When the reaction A $\to$ B + C is studied,a plot of ln[A]_t vs.time gives a straight line with a negative slope.What is the order of the reaction?

A)zero
B)first
C)second
D)third
E)More information is needed to determine the order.

Question 6

Sulfuryl chloride,SO₂Cl₂(g),decomposes at high temperature to form SO₂(g)and Cl₂(g).The rate constant at a certain temperature is 4.68 $\times$ 10^-5s^-1.What is the order of the reaction?

A)zero
B)first
C)second
D)third
E)More information is needed to determine the order.

Question 7

Which of the following sets of units could be appropriate for a zero-order rate constant?

A)s^-1
B)L mol^-1 s^-1
C)L² mol^-2 s^-1
D)L³ mol^-3 s^-1
E)mol L^-1 s^-1

Question 8

Ammonium cyanate (NH₄CNO)reacts to form urea (NH₂CONH₂).At 65°C the rate constant,k,is 3.60 L mol^-1s^-1.What is the rate law for this reaction?

A)Rate = 3.60 L mol^-1s^-1[NH₄CNO]
B)Rate = 3.60 L mol^-1s^-1[NH₄CNO]²
C)Rate = 0.28 mol L^-1 s^-1[NH₄CNO]
D)Rate = 0.28 mol L^-1 s^-1[NH₄CNO]²
E)Rate = 3.60 L mol^-1s^-1[NH₂CONH₂]^-1

Question 9

The compound RX₃ decomposes according to the equation
3RX₃ \(\to\0 R + R₂X₃ + 3X₂
In an experiment the following data were collected for the decomposition at 100°C.What is the average rate of reaction over the entire experiment?

A)0.011 mol L^-1s^-1
B)0.019 mol L^-1s^-1
C)0.044 mol L^-1s^-1
D)0.049 mol L^-1s^-1
E)0.069 mol L^-1s^-1

Question 10

Sucrose decomposes to fructose and glucose in acid solution.When ln [sucrose] is plotted vs.time,a straight line with slope of -0.208 hr^-1 results.What is the rate law for the reaction?

A)Rate = 0.208 hr^-1 [sucrose]²
B)Rate = 0.208 hr^-1 [sucrose]
C)Rate = 0.0433 hr [sucrose]²
D)Rate = 0.0433 hr [sucrose]
E)Rate = 0.208 mol L^-1hr^-1 [sucrose]⁰

Question 11

Consider the general reaction
5Br^-(aq)+ BrO₃^-(aq)+ 6H⁺(aq) $\to$ 3Br₂(aq)+ 3H₂O(aq)
For this reaction,the rate when expressed as $\Delta$ [Br₂]/ $\Delta$ t is the same as

A)- $\Delta$ [H₂O]/ $\Delta$ t
B)3 $\Delta$ [BrO₃^-]/ $\Delta$ t
C)-5 $\Delta$ [Br^-]/ $\Delta$ t
D)-0.6 $\Delta$ [Br^-]/ $\Delta$ t
E)None of these choices is correct.

Question 12

For the reaction
A(g)+ 2B(g) $\to$ 2C(g)+ 2D(g)
The following data was collected at constant temperature.Determine the correct rate law for this reaction.

A)Rate = k[A] [B]
B)Rate = k[A]² [B]
C)Rate = k[A] [B]²
D)Rate = k[A]
E)Rate = k[A]³

Question 13

Which one of the following sets of units is appropriate for a second-order rate constant?

A)s^-1
B)mol L^-1 s^-1
C)L mol^-1 s^-1
D)mol² L^-2 s^-1
E)L² mol^-2 s^-1

Question 14

The rate constant for a reaction is 4.65 L mol^-1s^-1.What is the overall order of the reaction?

A)zero
B)first
C)second
D)third
E)More information is needed to determine the overall order.

Question 15

Consider the following reaction
8A(g)+ 5B(g) $\to$ 8C(g)+ 6D(g)
If [C] is increasing at the rate of 4.0 mol L^-1s^-1,at what rate is [B] changing?

A)-0.40 mol L^-1s^-1
B)-2.5 mol L^-1s^-1
C)-4.0 mol L^-1s^-1
D)-6.4 mol L^-1s^-1
E)None of these choices is correct,since its rate of change must be positive.

Question 16

For the reaction
2A + B + 2C $\to$ D + E
The following initial rate data was collected at constant temperature.Determine the correct rate law for this reaction.All units are arbitrary.

A)Rate = k [A][B][C]
B)Rate = k [A]²[B][C]
C)Rate = k [A]²[B][C]^-1
D)Rate = k [A][B]²[C] ^-1
E)None of these choices is correct.

Question 17

Which one of the following sets of units is appropriate for a third-order rate constant?

A)s^-1
B)mol L^-1 s^-1
C)L mol^-1 s^-1
D)L² mol^-2 s^-1
E)L³ mol^-3 s^-1

Question 18

When the reaction A $\to$ B + C is studied,a plot 1/[A]_t vs.time gives a straight line with a positive slope.What is the order of the reaction?

A)zero
B)first
C)second
D)third
E)More information is needed to determine the order.

Question 19

Tetrafluoroethylene,C₂F₄,can be converted to octafluorocyclobutane which can be used as a refrigerant or an aerosol propellant.A plot of 1/[C₂F₄] vs.time gives a straight line with a slope of 0.0448 L mol^-1s^-1.What is the rate law for this reaction?

A)Rate = 0.0448 (L mol^-1s^-1)[C₂F₄]
B)Rate = 22.3 (mol L^-1s)[C₂F₄]
C)Rate = 0.0448 (L mol^-1s^-1)[C₂F₄]²
D)Rate = 22.3 (mol L^-1s)[C₂F₄]²
E)Rate = 0.0448 s^-1 [C₂F₄]

Question 20

For the reaction
3A(g)+ 2B(g) $\to$ 2C(g)+ 2D(g)
The following data was collected at constant temperature.Determine the correct rate law for this reaction.

A)Rate = k[A][B]
B)Rate = k[A][B]²
C)Rate = k[A]³[B]²
D)Rate = k[A]^1.5[B]
E)Rate = k[A]²[B]

Question 21

A reaction has an activation energy of 195.0 kJ/mol.When the temperature is increased from 200.°C to 220.°C,the rate constant will increase by a factor of

A)1.1
B)4.3 $\times$ 10⁴
C)3.2
D)7.5
E)None of these choices is correct.

Question 22

The radioactive isotope tritium decays with a first-order rate constant k of 0.056 year^-1.What fraction of the tritium initially in a sample is still present 30 years later?

A)0.19
B)0.60
C)0.15
D)2.8 $\times$ 10^-38
E)None of these choices is correct.

Question 23

The rate constant for the reaction 3A $\to$ 4B is 6.00 $\times$ 10^-3 L mol^-1min^-1.How long will it take the concentration of A to drop from 0.75 M to 0.25 M?

A)2.2 $\times$ 10^-3 min
B)5.5 $\times$ 10^-3 min
C)180 min
D)440 min
E)5.0 $\times$ 10² min

Question 24

Carbon-14 is a radioactive isotope which decays with a half-life of 5730 years.What is the first-order rate constant for its decay,in units of years^-1?

A)5.25 $\times$ 10^-5 years^-1
B)1.21 $\times$ 10^-4 years^-1
C)1.75 $\times$ 10^-4 years^-1
D)3.49 $\times$ 10^-4 years^-1
E)3.97 $\times$ 10³ years^-1

Question 25

If the activation energy of a reaction decreases by 10.0 kJ/mol,from 100.0 to 90.0 kJ/mol,what effect will this have on the rate of reaction at 298K?

A)The rate will increase,by a factor of more than 50.
B)The rate will decrease,by a factor of more than 50.
C)The rate will increase,by a factor of less than 50.
D)The rate will decrease,by a factor of less than 50.
E)The rate will not change unless temperature changes.

Question 26

The reaction CH₃NC(g) $\to$ CH₃CN(g)is first-order with respect to methyl isocyanide,CH₃NC.If it takes 10.3 minutes for exactly one quarter of the initial amount of methyl isocyanide to react,what is the rate constant in units of min^-1?

A)-0.135 min^-1
B)0.0279 min^-1
C)0.089 min^-1
D)0.135 min^-1
E)35.8 min^-1

Question 27

The rate law for the reaction 3A $\to$ 2B is rate = k[A] with a rate constant of 0.0447 hr^-1.What is the half-life of the reaction?

A)0.0224 hr
B)0.0645 hr
C)15.5 hr
D)22.4 hr
E)44.7 hr

Question 28

Cyclopropane is converted to propene in a first-order process.The rate constant is 5.4 $\times$ 10^-2 hr^-1.If the initial concentration of cyclopropane is 0.150 M,what will its concentration be after 22.0 hours?

A)0.0457 M
B)0.105 M
C)0.127 M
D)0.492 M
E)None of these choices is correct.

Question 29

A first-order reaction has a half-life of 20.0 minutes.Starting with 1.00 $\times$ 10²⁰ molecules of reactant at time t = 0,how many molecules remain unreacted after 100.0 minutes?

A)1.00 $\times$ 10⁴ molecules
B)2.00 $\times$ 10¹⁹ molecules
C)3.20 $\times$ 10¹⁶ molecules
D)5.00 $\times$ 10²⁰ molecules
E)None of these choices is correct.

Question 30

The rate law for the rearrangement of CH₃NC to CH₃CN at 800 K is rate = (1300 s^-1)[CH₃NC].What is the half-life for this reaction?

A)7.69 $\times$ 10^-4 s
B)5.3 $\times$ 10^-4 s
C)1.9 $\times$ 10^-3 s
D)520 s
E)1920 s

Question 31

The decomposition of hydrogen peroxide is a first-order process with a rate constant of 1.06 $\times$ 10^-3 min^-1.How long will it take for the concentration of H₂O₂ to drop from 0.0200 M to 0.0120 M?

A)< 1 min
B)7.55 min
C)481 min
D)4550 min
E)31,400 min

Question 32

A reactant R is being consumed in a first-order reaction.What fraction of the initial R is consumed in 4.0 half-lives?

A)0.94
B)0.87
C)0.75
D)0.13
E)0.063

Question 33

The decomposition of SOCl₂ is first-order in SOCl₂.If the half-life for the reaction is 4.1 hr,how long would it take for the concentration of SOCl₂ to drop from 0.36 M to 0.045 M?

A)0.52 hr
B)1.4 hr
C)12 hr
D)33 hr
E)> 40 hr

Question 34

Butadiene,C₄H₆ (used to make synthetic rubber and latex paints)dimerizes to C₈H₁₂ with a rate law of rate = 0.014 L/(mol·s)[C₄H₆]².What will be the concentration of C₄H₆ after 3.0 hours if the initial concentration is 0.025 M?

A)0.0052 M
B)0.024 M
C)43 M
D)190 M
E)0.0000 M

Question 35

Ammonia will react with oxygen in the presence of a copper catalyst to form nitrogen and water.From 164.5°C to 179.0°C,the rate constant increases by a factor of 4.27.What is the activation energy of this oxidation reaction?

A)24.5 kJ/mol
B)165 kJ/mol
C)242 kJ/mol
D)1630 kJ/mol
E)> 10⁴ kJ/mol

Question 36

A rate constant obeys the Arrhenius equation,the factor A being 2.2 $\times$ 10¹³ s^-1 and the activation energy being 150.kJ mol^-1.What is the value of the rate constant at 227°C,in s^-1?

A)2.1 $\times$ 10¹³ s^-1
B)6.7 $\times$ 10^-22 s^-1
C)1.5 $\times$ 10¹¹ s^-1
D)4.7 $\times$ 10^-3 s^-1
E)None of these choices is correct.

Question 37

The decomposition of dinitrogen pentaoxide has an activation energy of 102 kJ/mol and $\Delta$ H°_rxn = + 55 kJ/mol.What is the activation energy for the reverse reaction?

A)27 kJ/mol
B)47 kJ/mol
C)55 kJ/mol
D)102 kJ/mol
E)More information is needed,since this is a Hess' Law calculation.

Question 38

The rate law for the reaction 3A $\to$ C is
Rate = 4.36 $\times$ 10^-2 L mol^-1 hr^-1[A]²
What is the half-life for the reaction if the initial concentration of A is 0.250 M?

A)0.0109 hr
B)0.0629 hr
C)15.9 hr
D)23.9 hr
E)91.7 hr

Question 39

Dinitrogen tetraoxide,N₂O₄,decomposes to nitrogen dioxide,NO₂,in a first-order process.If k = 2.5 $\times$ 10³ s^-1 at -5°C and k = 3.5 $\times$ 10⁴ s^-1 at 25°C,what is the activation energy for the decomposition?

A)0.73 kJ/mol
B)58 kJ/mol
C)140 kJ/mol
D)580 kJ/mol
E)> 1000 kJ/mol

Question 40

The decomposition of dinitrogen pentaoxide to nitrogen dioxide and oxygen follows first-order kinetics and has an activation energy of 102 kJ/mol.By what factor will the fraction of collisions with energy greater than or equal to the activation energy increase if the reaction temperature goes from 30°C to 60°C?

A)1.00
B)1.10
C)2.00
D)4.00
E)38.4

Question 41

Cyclobutane decomposes to ethene in a first-order reaction.From measurements of the rate constant (k)at various absolute temperatures (T),the accompanying Arrhenius plot was obtained (ln k versus 1/T).
a.Calculate the energy of activation,E_a.
b.Determine the value of the rate constant at 740.K.(In the plot,the units of k are s^-1. )

Question 42

When a catalyst is added to a reaction mixture,it

A)increases the rate of collisions between reactant molecules.
B)provides reactant molecules with more energy.
C)slows down the rate of the back reaction.
D)provides a new pathway (mechanism)for the reaction.
E)does none of these

Question 43

A chemical reaction of the general type
A $\to$ 2B
is first-order,with a rate constant of 1.52 $\times$ 10^-4 s^-1.
a.Calculate the half-life of A.
b.Assuming the initial concentration of A is 0.067 mol L^-1,calculate the time needed for the concentration to fall to 0.010 mol L^-1.

Question 44

You are studying the rate of the reaction 2A $\to$ B and have obtained measurements of the concentration of A at times t = 100,200,300,...... ,1000 seconds from the start of the reaction.Carefully describe how you would plot a graph and use it to
a.prove that the reaction is second-order with respect to A.
b.determine the second-order rate constant k.

Question 45

The elementary reaction HBr(g)+ Br(g) $\to$ H(g)+ Br₂(g)is endothermic.
a.Would you expect the rate constant for the back reaction to be smaller or larger than that for the forward reaction? Explain,briefly.
b.Draw a fully-labeled reaction energy diagram for this reaction,showing the locations of the reactants,products and transition state.

Question 46

You are required to determine the energy of activation (E_a)of a reaction.Briefly describe the experimental measurements you would make and how you would obtain the activation energy from a suitable linear plot of the experimental data.

Question 47

In the gas phase at 500.°C,cyclopropane reacts to form propene in a first-order reaction.The figure below shows the concentration of cyclopropane plotted versus time.Use the graph to calculate approximate values of
a.the rate of the reaction,600.seconds after the start.
b.the half-life of the reaction,t_1/2.

Question 48

Which of the following affects the activation energy of a reaction?

A)temperature of the reactants
B)concentrations of reactants
C)presence of a catalyst
D)surface area of reactants
E)reaction progress

Question 49

According to the collision theory of reaction rates,what are the three requirements which must be met before an elementary reaction between two molecules can occur?

Question 50

At 25.0°C,a rate constant has the value 5.21 $\times$ 10^-8 L mol^-1 s^-1.If the activation energy is 75.2 kJ/mol,calculate the rate constant when the temperature is 50.0°C.

Question 51

In the gas phase at 500.°C,cyclopropane reacts to form propene in a first-order reaction.The figure shows the natural logarithm of the concentration of cyclopropane (in mol/L)plotted versus time.
a.Explain how this plot confirms that the reaction is first order.
b.Calculate the first-order rate constant,k.
c.Determine the initial concentration of cyclopropane in this experiment.

Question 52

The gas-phase conversion of 1,3-butadiene to 1,5-cyclooctadiene,2C₄H₆ $\to$ C₈H₁₂ was studied,providing data for the plot shown below,of 1/[butadiene] versus time.
a.Explain how this plot confirms that the reaction is second order.
b.Calculate the second-order rate constant,k.
c.Determine the initial concentration of 1,3-butadiene in this experiment.

Question 53

Reaction intermediates differ from activated complexes in that

A)they are stable molecules with normal bonds and are frequently isolated.
B)they are molecules with normal bonds rather than partial bonds and can occasionally be isolated.
C)they are intermediate structures which have characteristics of both reactants and products.
D)they are unstable and can never be isolated.
E)all reactions involve reaction intermediates,but not all have activated complexes.

Question 54

Consider the following mechanism for the oxidation of bromide ions by hydrogen peroxide in aqueous acid solution.
H⁺ + H₂O₂
H₂O⁺-OH (rapid equilibrium)
H₂O⁺-OH + Br^- $\to$ HOBr + H₂O (slow)
HOBr + H⁺ + Br^- $\to$ Br₂ + H₂O (fast)
What is the overall reaction equation for this process?

A)2H₂O⁺-OH + 2Br^- $\to$ H₂O₂ + Br₂ + 2H₂O
B)2H⁺ + 2Br^- + H₂O₂ $\to$ Br₂ + 2H₂O
C)2H⁺ + H₂O₂ + Br^- + HOBr $\to$ H₂O⁺-OH + Br₂ + H₂O
D)H₂O⁺-OH + Br^- + H⁺ $\to$ Br₂ + H₂O
E)None of these choices is correct.

Question 55

The gas-phase reaction CH₃NC $\to$ CH₃CN has been studied in a closed vessel,and the rate equation was found to be: rate = - $\Delta$ [CH₃NC]/ $\Delta$ t = k[CH₃NC].Which one of the following actions is least likely to cause a change in the rate of the reaction?

A)lowering the temperature
B)adding a catalyst
C)using a larger initial amount of CH₃NC in the same vessel
D)using a bigger vessel,but the same initial amount of CH₃NC
E)continuously removing CH₃CN as it is formed

Question 56

The kinetics of the decomposition of dinitrogen pentaoxide is studied at 50°C and at 75°C.Which of the following statements concerning the studies is correct?

A)The rate at 75°C will be greater than the rate at 50°C because the activation energy will be lower at 75°C than at 50°C.
B)The rate at 75°C will be greater than the rate at 50°C because the activation energy will be higher at 75°C than at 50°C.
C)The rate at 75°C will be less than the rate at 50°C because the molecules at higher speeds do not interact as well as those at lower speeds.
D)The rate at 75°C will be greater than at 50°C because the concentration of a gas increases with increasing temperature.
E)The rate at 75°C will be greater than the rate at 50°C because the number of molecules with enough energy to react increases with increasing temperature.

Question 57

A catalyst accelerates a reaction because

A)it increases the number of molecules with energy equal to or greater than the activation energy.
B)it lowers the activation energy for the reaction.
C)it increases the number of collisions between molecules.
D)it increases the temperature of the molecules in the reaction.
E)it supplies energy to reactant molecules.

Question 58

What is the molecularity of the following elementary reaction?
NH₂Cl(aq)+ OH^-(aq) $\to$ NHCl^-(aq)+ H₂O(l)

A)unimolecular
B)bimolecular
C)termolecular
D)tetramolecular
E)The reaction order must be known before molecularity can be determined.

Question 59

Consider the following mechanism for the oxidation of bromide ions by hydrogen peroxide in aqueous acid solution.
H⁺ + H₂O₂
H₂O⁺-OH (rapid equilibrium)
H₂O⁺-OH + Br^- $\to$ HOBr + H₂O (slow)
HOBr + H⁺ + Br^- $\to$ Br₂ + H₂O (fast)
Which of the following rate laws is consistent with the mechanism?

A)Rate = k[H₂O₂][H⁺]²[Br^-]
B)Rate = k [H₂O⁺-OH][Br^-]
C)Rate = k[H₂O₂][H⁺][Br^-]
D)Rate = k[HOBr][H⁺][Br^-][H₂O₂]
E)Rate = k[Br^-]

Question 60

In the collision theory of reaction rates,the rate constant for a bimolecular reaction can be written as
k = z·p·exp(-E_a/RT)
In one sentence each,clearly explain the physical meaning (interpretation)of the following three factors which appear in the above expression:
a.z
b.p
c.exp(-E_a/RT)

Question 61

The half-life of a second-order reaction does not depend on the initial concentration of reactant.

Question 62

All second-order reactions are bimolecular reactions.

Question 63

All bimolecular reactions are second-order reactions.

Question 64

The units of the rate constant depend on the order of the reaction.

Question 65

The rate law cannot be predicted from the stoichiometry of a reaction.

Question 66

The half-life of a first-order reaction does not depend on the initial concentration of reactant.

Question 67

A transition state is a species (or state)corresponding to an energy maximum on a reaction energy diagram.

Question 68

For each of the following terms/concepts,give a brief explanation or definition.Where possible,use examples.
a.order of a reaction
b.elementary reaction
c.reaction intermediate

Question 69

An elementary reaction is a simple,one-step process.

Question 70

A reaction intermediate is a species corresponding to a local energy maximum on a reaction energy diagram.

Question 71

A $\to$ B
At very low pressures many such reactions occur by the following mechanism:

(A* represents a molecule with sufficient energy to overcome the activation energy barrier. )
a.Which of the three reactions above is/are elementary?
b.Where appropriate,identify the molecularity of the reactions.
c.Show that the proposed mechanism is consistent with reaction 1,the observed reaction.
d.Given the mechanism above,suggest a likely rate law for reaction (1).

Question 72

The units of the rate of reaction depend on the order of the reaction.

Question 73

Is a bimolecular reaction necessarily second-order? Is a second-order reaction necessarily bimolecular? Answer,with explanations and clarifications.

Question 74

Briefly list the features/properties common to all catalysts and how they work.Draw a labeled reaction energy diagram as part of your answer.

Question 75

The rate of a reaction is determined by the rate of the fastest step in the mechanism.

Question 76

The greater the energy of activation,E_a,the faster will be the reaction.