Deck 13: Kinetics: Mechanisms and Rates of Reactions

Question 1

Explain the concepts of a mechanism and a rate-determining step in a chemical reaction.

Answer 1

A reaction mechanism is the exact molecular pathway that starting materials follow on their way to becoming products. The overall reaction is the sum of the elementary steps in the mechanism. The rate-determining step is the slowest step in the reaction mechanism. The overall reaction cannot go faster than the rate-determining step.

Question 2

Determine the rate of a reaction based on the rate of change of concentration of a reactant or a product.

Answer 2

The reaction rate can be expressed using the rate of change of concentration of any of the reagents.

Question 3

Determine the rate law, given the mechanism and knowledge of the relative rates of steps of a reaction.

Answer 3

A reaction rate depends on the concentrations of the reactants as expressed by the rate law for that reaction. The order of a reactant often differs from its stoichiometric coefficient.

Question 4

Determine rate laws from concentration versus time data.

Question 5

Show that the mechanism and rate law are closely related.

Question 6

Explain and quantify the effects of temperature on a reaction rate.

Question 7

Explain the mechanisms by which catalysts function.

Question 8

Which of the following are bimolecular processes?
I.
II. NO $\rarr$ ONNO
III. H₂C = CHCH₃ + H₂SO₄ $\rarr$ CH₃CH(OSO₂(OH))CH₃
IV.
V. H₂ $\rarr$ 2 H•

A) I and V
B) I, IV and V
C) II only
D) II and III
E) II, III and V

Question 9

Which of the following is an elementary reaction?

A) OH^- + H₃O⁺ $\rarr$ H₂O
B) 4NO₂ + O₂ $\rarr$ 2N₂O₅
C) CO + 2H₂ + CH₄ $\rarr$ C₂H₆ + H₂O
D) N₂ + 3H₂ $\rarr$ NH₃
E) 2NO + 2H₂ $\rarr$ N₂ + 2H₂O

Question 10

The formation of chlorocarbon solvents such as CH₂Cl₂ proceeds through the reaction of chlorine with methane. Which of the following is a unimolecular reaction in the mechanism?

A) CH₄ + Cl• $\rarr$ CH₃• + HCl
B) H₂ $\rarr$ 2 H•
C) CH₃• + Cl• $\rarr$ CH₃Cl
D) Cl₂ $\rarr$ 2 Cl•
E) CH₂Cl• + Cl• $\rarr$ CH₂Cl₂

Question 11

It has been suggested that the decomposition of NO₂ occurs via the following mechanism:
NO₂ $\rarr$ NO + O (Rxn I)
O + NO₂ $\rarr$ 2NO + O₂ (Rxn II)
Predict the rate determining step.

A) Rxn II; this reaction is bimolecular, bimolecular reactions are always slower than unimolecular reactions.
B) Rxn I; unimolecular reactions are always slower than bimolecular reactions.
C) Rxn I; O is highly reactive and thus Rxn II will be very fast.
D) Rxn II; NO₂ is highly reactive and thus Rxn I will be very fast.
E) Rxn I and II are both elementary reactions and will proceed at equal rates.

Question 12

You are running late for a basketball game on your campus and you are thinking about what will be the rate determining step for attending the basketball game? Which of the following will be your rate determining step?

A) purchasing a ticket
B) locating a seat in the stands
C) walking/driving to the game
D) waiting for the players to arrive
E) giving your ticket to the doorman

Question 13

Which of the following sketches shows the proper orientation of molecules for CO₂ reacting with NO to make NO₂ and CO?

A)

B)

C)

D)

E)

Question 14

The synthesis of nitrogen monoxide proceeds by the reaction of ammonia with oxygen as shown in the following unbalanced reaction:
NH₃(g) + O₂(g) $\rarr$ NO(g) + H₂O(g)If O₂ is being consumed at a rate of 32 mole/sec, what is the rate of NO production?

A) 38. mole/sec
B) 1.9 x 10³ mole/minute
C) 15 x 10³ mole/minute
D) 32 mole/minute
E) 1.4 x 10⁵ mole/hour

Question 15

Consider the aqueous phase reaction between the dichromate anion and iron (II) cations:14 H₃O⁺(aq) + Cr₂O₇^2- + 6Fe²⁺(aq) $\rarr$ 2Cr³⁺(aq) + 21H₂OWhat is the reaction rate expressed in terms of changing H₃O⁺ concentration?

A) Reaction rate =
B) Reaction rate = -
C) Reaction rate = -
D) Reaction rate =

Question 16

Consider the aqueous phase reaction between hydrogen gas and liquid bromine:H₂(g) + Br₂(g) $\rarr$ 2HBr(g)Which of the following expressions accurately express the rate of the above reaction?
I. Reaction rate =
II. Reaction rate =
III. Reaction rate =
IV. Reaction rate =

A) I and III
B) I and II
C) II and IV
D) III and IV
E) I only

Question 17

Consider the aqueous phase reaction between the dichromate anion and iron (II) cations:14 H₃O⁺(aq) + Cr₂O₇^2- + 6Fe²⁺(aq) $\rarr$ 2Cr³⁺(aq) + 21H₂OWhat is the rate of increase of Cr³⁺ concentration expressed in terms of changing H₃O⁺ concentration?

A)
B)
C)
D)

Question 18

Cyclohexane is manufactured from the reaction of benzene with hydrogen:
C₆H₆(g) + 3 H₂(g) $\rarr$ C₆H₁₂(g)
If the initial concentration of hydrogen was 1.5 M and 5 minutes later the hydrogen concentration is 0.34 M, what is the average rate of disappearance of hydrogen?

A) 0.30 M/min
B) 0.20 M/min
C) 1.16 M/min
D) 0.23 M/min
E) 0.68 M/min

Question 19

Cyclohexane is manufactured from the reaction of benzene with hydrogen:
C₆H₆(g) + 3 H₂(g) $\rarr$ C₆H₁₂(g)
If the initial concentration of hydrogen was 1.5 M and 5 minutes later the hydrogen concentration is 0.34 M, what is the average rate of appearance of cyclohexane?

A) 0.39 M/min
B) 7.7 x 10^-2 M/min
C) 4.6 M/s
D) 3.9 x 10^{- 2} M/hr
E) 2.3 M/min

Question 20

NO₂ decomposes to form NO and O₂. The concentration of NO₂ is monitored and found to be 2.1x10^-2 M after 15 seconds and 1.8 x10^-2 M after 20 seconds. What is the average rate of appearance of O₂ over this time period?

A) 6.0x10^-4 M/s
B) 1.2x10^-3 M/s
C) 3.0x10^-4 M/s
D) 3.0x10^-3 M/s
E) 1.5x10^-4 M/s

Question 21

Why does the rate of a reaction generally slow with time?

A) The reaction mixture gets warmer.
B) The number of product molecules decreases.
C) The number of collisions of reactants decreases.
D) The number of product molecules increases.
E) The temperature of the reaction vessel decreases.

Question 22

The rate of a reaction

A) increases with the concentration of reactants.
B) decreases with the concentration of reactants.
C) is independent of concentration.
D) is a function of reaction stoichiometry.
E) cannot be determined based on the balanced chemical reaction.

Question 23

For the reaction I^-(aq) + OCl^-(aq) $\rarr$ IO^-(aq) + Cl^-(aq) in basic solution, it was found that

A) This reaction is first order overall.
B) This reaction is third order overall.
C) This reaction is second order overall.
D) This reaction is first order in [OH^-] concentration.
E) The rate law is incorrect as OH^- is neither a reactant nor a product.

Question 24

A 1.66 x 10^-4 mole sample of ²³⁹Pu undergoes 9 x 10⁷ decays per second obeying first-order kinetics. How many decays per second would be expected from a 5.46 x 10^-1 mole sample?

A) 9 x 10⁸ decays/second
B) 3 x 10⁹ decays/second
C) 9 x 10¹⁰ decays/second
D) 3 x 10¹¹ decays/second
E) 9 x 10¹¹ decays/second

Question 25

The reaction A + 2B $\rarr$ products was found to have the rate law;
rate = k[A] [B]². While holding the concentration of A constant, the concentration of B was increased from 0.010M to 0.030M. Predict by what factor the rate of reaction will increase.

A) 3
B) 6
C) 9
D) 30
E) 27

Question 26

The first-order rate constant for the decomposition of trioxane (C₃H₆O₃) is known to be 3.05 x 10^-4 s^-1 at 519ºK. What is the half life of trioxane at 519ºK?

A) 3.28 x 10³ s
B) 6.93 x10³ s
C) 0.693 hour
D) 0.631 hour
E) 0.328 hour

Question 27

Butadiene reacts to form its dimmer according to the following reaction: Concentration versus time data were collected for this reaction and a plot of 1/[C₄H₆] resulted in a straight line with slope 6.14 x10^-2 M s^-1. The integrated for of the rate law is

A)
B)
C)
D)
E)

Question 28

It is determined that the charcoal in a fire pit used as an ancient hearth has lost about 42.3% of the initial ¹⁴C. How old was the fire pit if ¹⁴C has a half life of 5730 years?

A) 2210 years
B) 4430 years
C) 4550 years
D) 5250 years
E) 7750 years

Question 29

The following reaction takes place at 80.1°C:
Ru(NH₃)₅Cl²⁺ (aq) + H₂O (l) $\rarr$ Ru(NH₃)₅(H₂O)³⁺ (aq) + Cl^- (aq)
The following time and concentration data are collected: Which of the following is the correct value of the rate constant?

A) 3.28 1/M•s
B) 4.19 1/s
C) 419 1/s
D) 328 1/M•s
E) 328 1/s

Question 30

Nitrous oxide, N₂O, decomposes on metal surfaces readily at high temperatures following first-order kinetics for the equation:
2 N₂O (g) $\rarr$ 2 N₂ (g) + O₂ (g)
The following data are obtained for a reaction at 850°C: What was the initial concentration of N₂O (t = 0)?

A) 0.0885 M
B) 0.0940 M
C) 0.101 M
D) 0.112 M
E) 0.123 M

Question 31

The following are initial rate data for
2 NO + 2 H₂ (\rarr\) N₂ + 2 H₂O What is the rate law?

A) Rate = k[NO]
B) Rate = k[H₂]
C) Rate = k[NO][H₂]
D) Rate = k[NO]²[H₂]
E) Rate = k[NO][H₂]²

Question 32

The reaction of NO with O₂ to give oxygen is known to follow a third order rate law(rate = k[NO]²[O₂]). Two possible mechanisms are shown below: Which of these two mechanisms is a more acceptable mechanism, based on the criteria given above?

A) Mechanism 1 because it is simpler
B) Mechanism 1 because its rate law is the same as the known rate law
C) Mechanism 2 because it only involves 2 steps
D) Mechanism 2 because only bimolecular processes are involved
E) Mechanism 1 because no unstable species are formed

Question 33

The following mechanism has been suggested for the decomposition of ozone, O₃.O₃(g) O₂(g) + O(g) (fast equilibrium)
O(g) + O₃(g) $\rarr$ 2 O₂(g) (slow)
Consider the following statements in light of this mechanism:
I. The rate law is second order in O_3.
II. The rate does not depend on the concentration of O_2.
III. The reaction slows with increased O₂ concentration.
IV. The rate law is second order.
V. Substances reacting with O atoms will speed up the reaction.Which of the above statements are true?

A) II and V
B) II only
C) I and IV
D) I and III
E) II, IV and V

Question 34

What is the rate law associated with the following mechanism:
HCl + HCl H₂Cl₂
HCl + CH₃CHCH₂ CH₃CHClCH₃
H₂Cl₂ + CH₃CHClCH₃ $\rarr$ CH₃CHClCH₃ +2 HCl
Net: HCl(g) + CH₃CHCH₂(g) $\rarr$ CH₃CHClCH₃ (g)

A) rate = k[HCl]²[CH₃CHCH₂]
B) rate = k[HCl]³[CH₃CHCH₂]
C) rate = k[H₂Cl₂][CH₃CHClCH₃]
D) rate = k[HCl][CH₃CHCH₂]
E) rate = k[HCl]²

Question 35

Hydrogen and iodine react to form HI. One possible mechanism is shown below:I₂(g) 2 I(g)
H₂(g) + 2 I(g) $\rarr$ 2 HI(g)
Consider the following statements in light of this mechanism:
I. The rate law overall is second order.
II. The iodine atom is an intermediate.
III. The first step is the rate determining step.
IV. The second step is the fast step.
V. The second step is rate determining.
Which of the above statements are true?

A) II, III and IV
B) II and V
C) all except V
D) I and II only
E) I, II and V

Question 36

Heterogeneous catalysts are used in industrial processes because
I. they utilize more of the catalyst atoms.
II. it is easier to separate the products from the catalyst.
III. higher operating temperatures are readily obtained.
IV. they are more selective.Which of the above statements are true?

A) I, II and III
B) II and III
C) III and IV
D) I and IV
E) II and IV

Question 37

In which order do the following steps typically occur for reactions facilitated by heterogeneous catalysts:
I. Desorption of material
II. Adsorption on materials on catalyst surface
III. Reaction to form products
IV. Movement of bound species over catalyst surface

A) II, I, III, IV
B) II, IV, III, I
C) II, I, IV, III
D) II, III, IV, I
E) IV, II, III, I

Question 38

Which of the following does NOT occur during a reaction facilitated by a heterogeneous catalyst?

A) rejuvenation of catalyst via desorption of products
B) migration of bound reactants over catalyst surface
C) bond reorganization at catalyst surface
D) absorption of reactants on catalyst surface
E) weakening of or breaking of bonds and formation of bonds/interactions with catalyst

Question 39

The saturation behaviour of enzyme systems (E + S) suggests that

A) reactions in the pocket/active site are not rate limiting.
B) binding to the active site will never be rate limiting.
C) release of product will never be rate limiting.
D) bimolecular reactions cannot happen.
E) different steps in a mechanism can be rate determining based on concentration.

Question 40

Write the overall equation of reaction for the following mechanism and identify the reaction intermediates:
Cl₂ $\rightarrow$ 2 Cl•
Cl• + CO $\rightarrow$ COCl
COCl + Cl₂ $\rightarrow$ COCl₂ + Cl•
2 Cl• $\rightarrow$ Cl₂

Question 41

Write the overall equation of reaction for the following mechanism and identify the reaction intermediates:
2 NO₂ $\rightarrow$ NO₃ + NO
NO₃ + CO $\rightarrow$ CO₂ + NO₂

Question 42

The industrial production of 2-propanol involves the reaction of propene with sulphuric acid and then water. Write the second step of the mechanism if the following is the first step:

Question 43

Draw a molecular picture showing the termolecular process in which two NO molecules collide with an O₂ molecule to give two molecules of NO₂.

Question 44

Hydrogen peroxide decomposes according to the equation:
2 H₂O_2(aq) $\rightarrow$ 2 H₂O_(l) + O_2(g)
At 27°C and 1 atm, a 50.0 ml sample of hydrogen peroxide decomposes at a rate that produces 10.0 ml/sec of O_2(g). Assuming ideal behavioura) Determine the moles of oxygen produced per second.b) Determine the change in molarity of H₂O₂ per second.

Question 45

The following concentration vs. time data were collected for the reaction:
A + 2B $\rightarrow$ C Calculate for A, B and C for the following time differences:(a) 0 and 60 s,(b) 900 and 960 s,(c) What is the rate of the reaction for part

Question 46

Consider the following three molecular pictures that represent the relative numbers of the two reactants involved in one step of the depletion of stratospheric ozone by chlorine atoms: The equation for the elementary reaction and a molecular picture of the reaction process are shown below:Cl• + O₃ $\rightarrow$ ClO + O₂ If the three samples represented by A, B and C are at the same temperature, what are the rates of reaction of B and C compared to that of A?

Question 47

The reaction of NO₂ with CO to give CO₂ and NO can proceed through different mechanisms. What first step would be consistent with the following rate law?Rate = k[NO₂][CO]

Question 48

What are the units of a rate constant for a reaction that has an overall order of 3?

Question 49

The reaction of NO₂ with CO to give CO₂ and NO can proceed through different mechanisms. What rate law would be consistent for the following first step?
2 NO₂ $\rightarrow$ NO + NO₃

Question 50

The rate law for the reaction of NO with O₂ to give NO₂ is shown below:rate = k [NO]²[O₂]
a) If all other conditions are kept constant, what will be the effect on the rate if the concentration of NO is doubled?
b) If all other conditions are kept constant, what will be the effect on the rate if the concentration of O₂ is doubled?

Question 51

At moderate temperatures, the rate law for the reaction of NO₂ and CO to give CO₂ and NO follows the rate law shown below:rate = k [NO₂]² In which flask will the reaction be faster and how much faster?

Question 52

Radioactive decay follows first-order kinetics. Some smoke detectors use the isotope ²⁴¹Am that has a half-life of 432.2 years. In how many years will 95% of the ²⁴¹Am have decayed?

Question 53

Trioxane undergoes decomposition to formaldehyde at elevated temperatures.C₃H₆O₃ (g) $\rightarrow$ 3 CH₂O (g)The following data was collected for the gas phase reaction at 519ºK: Determine the order of the decomposition in trioxane and the rate constant at 519ºK.

Question 54

Ammonium cyanate undergoes rearrangement to form urea in aqueous solution.NH₄NCO(aq) $\rightarrow$ CO(NH₂)₂ (aq)The following data was collected: Determine the order of the reaction and the rate constant.

Question 55

Sucrose, cane sugar, reacts with water in acid solution to give glucose and fructose, which have the same chemical formula.
C₁₂H₂₂O₁₁ (aq) + H₂O (l) $\rightarrow$ 2 C₆H₁₂O₆ (aq)
The following data were obtained at room temperature for sucrose: Use graphical means to determine the order of the reaction and write the rate law with the numerical value of the rate constant with time units of seconds.

Question 56

Rate data were collected for the following reaction at a constant temperature.2ClO_2(aq) + 2 OH^-1_(aq) $\rightarrow$ ClO₃^-1_(aq) + ClO₂^-1_(aq) + H₂O_(l) a) Determine the rate law for this reaction.b) Determine the rate constant with appropriate units.

Question 57

Nitrous oxide, N₂O, decomposes on metal surfaces readily at high temperatures following first-order kinetics for the equation:
2 N₂O (g) $\rightarrow$ 2 N₂ (g) + O₂ (g)
The following data are obtained for a reaction at 850°C: Determine the rate constant and half-life for the reaction.

Question 58

The following are initial rate data for 2 NO + 2 H₂ $\rightarrow$ N₂ + 2 H₂O The rate law is determined to be: rate = k[NO]²[H₂]. With this information determine k using the data from experiment 2.

Question 59

Assume that the following first-order reaction has a rate constant k = 0.0137/min:
SO₂Cl₂ $\rightarrow$ SO₂ + Cl₂
Given the initial [SO₂Cl₂] = 0.42 M, how many minutes will it take for [SO₂Cl₂] = 0.19 M?

Question 60

The three reactions below, with identical reaction stoichiometry, must all share the same third order rate law found for the reaction of NO and O₂. True or False, and why?
2 NO(g) + O₂(g) $\rarr$ 2 NO₂(g)2
NO(g) + Cl₂(g) $\rarr$ 2 NOCl(g)2
NO(g) + F₂(g) $\rarr$ 2 NOF(g)

Question 61

Nitrogen dioxide, NO₂ will react with carbon monoxide, CO, to form nitric oxide, NO, and carbon dioxide, CO₂. A proposed mechanism is:
2NO₂ $\rarr$ NO₃ + NO
NO₃ + CO $\rarr$ NO₂ + CO₂
Experiments indicate that the rate of the reaction is independent of the CO concentration. Identify the rate determining step and derive the rate law consistent with the mechanism and experimental observation.

Question 62

A proposed mechanism for the following reaction, A₂ + B₂ $\rightarrow$ 2AB, isA₂ 2AA + B₂ $\rightarrow$ AB + B slowB +A₂ $\rightarrow$ AB + ADetermine the rate law.

Question 63

The reaction of nitrogen dioxide and fluorine is:2 NO₂ + F₂ $\rightarrow$ 2 NO₂FOne proposed mechanism has two steps; the first step is rate determining: What is the experimentally determined rate law?

Question 64

The rate law for the reaction2 H₂ (g) + 2 NO (g) $\rightarrow$ N₂ (g) + 2 H₂O (g)is rate = k[H₂ ][NO]². Which of the following mechanisms can be ruled out because the derived rate law is NOT consistent with the observed rate law?Mechanism 1H₂ + NO $\rightarrow$ N + H₂O (slow)N + NO $\rightarrow$ N₂ + O (fast)O + H₂ $\rightarrow$ H₂O (fast)Mechanism 2H₂ + 2 NO $\rightarrow$ N₂O + H₂O (slow)N₂O + H₂ $\rightarrow$ N₂ + H₂O (fast)Mechanism 32 NO N₂O₂ (fast equilibrium)N₂O₂ + H₂ $\rightarrow$ N₂O + H₂O (slow)N₂O + H₂ $\rightarrow$ N₂ + H₂O (fast)

Question 65

For the following reaction A + B $\rightarrow$ C + D, the rate law is determined to be Rate = k[A]²a) Of the five proposed mechanisms shown below, which is consistent with the experimentally determined rate law?
1. 2 A $\rightarrow$ Z (slow)2 B + Z $\rightarrow$ 2 C + 2 D (fast)
2. A + B $\rightarrow$ C + D (slow)
3. 2 B $\rightarrow$ N (slow)2 A + N $\rightarrow$ 2 C + 2 D (fast)
4. A $\rightarrow$ X (slow)B + X $\rightarrow$ C + D (fast)
5. B $\rightarrow$ M (slow)A + M $\rightarrow$ C + D (fast)b)
Are there any intermediates in the mechanism you chose and if so what?

Question 66

In the formation of dinitrogentetroxide, two NO₂ molecules react to make an N-N bond.2 NO₂ $\rightarrow$ 2 N₂O₄Draw molecular pictures superimposed on a diagram of energy vs. reaction coordinate that illustrates this process.

Question 67

The following rate constants were obtained at the stated temperatures for the first-order reaction:A $\rightarrow$ B Find the activation energy (in kJ/mole) for this reaction.

Question 68

Nitrogen dioxide molecules undergo oxygen exchange with an activation energy of 100 kJ/mole. By how much will the reaction rate constant increase if temperature is increased from 25^oC to 75^oC?

Question 69

A particular first-order reaction is characterized by activation energy of 50 kJ/mole. At what temperature would the rate of the reaction be 10 times that at 298^oK?

Question 70

The reaction of ozone with oxygen atoms to give oxygen has an activation energy of 17.1 kJ/mole with a rate constant at 298^oK, k = 4.8 x 10⁶ 1/M•s. Calculate the rate constant for this reaction at 315^oK.

Question 71

The reaction of ozone with oxygen atoms to produce molecular oxygen has a rate constant of 4.8x10⁶ 1/M s at 25^oC. A 20 degree increase in temperature results in a rate constant of 7.4x10⁶ 1/M s. What is the rate constant at 100^oC?

Question 72

The activation energy for the high temperature conversion cyclopropane to propene is 270 kJ mol^-1. At what temperature would the rate constant for this reaction be ten times that of 500^oC?

Question 73

The rate constant of the reaction, O (g) + N₂ (g) $\rightarrow$ NO (g) + N (g), is 9.7 x 10¹⁰1/M•s at 800^oK and has an activation energy of 315 kJ/mole. What is the value of the rate constant at 700^oK?

Question 74

For a large number of reactions in organic chemistry, an increase in temperature 10°C over room temperature will double the rate. What activation energy does this correspond to?

Question 75

For a hypothetical reaction, the activation energy is E_act = 50.2 kJ/mol and it has an Arrhenius constant of 22.3 M^-1s^-1. Determine what the rate constant would be if the temperature was 400 $\degree$ C.

Question 76

Consider the following energy-reaction coordinate diagram. Give the names for the quantities indicated by A, B and C.

Question 77

Write the overall equation of reaction for the following mechanism and identify any reaction intermediates and any catalysts.
H₂O₂ + I^-1 $\rightarrow$ H₂O + OI^-1
H₂O₂ + OI^-1 $\rightarrow$ H₂O + O₂ + I^-1