Deck 11: Rate of Reaction

Question 1

The rate constant of a first-order decomposition reaction is 0.0147 s^-1.If the initial concentration of reactant is 0.178 M,what is the concentration of reactant after 30.0 seconds?

A) 8.72 × 10⁵ M
B) 0.0645 M
C) 0.115 M
D) 0.0785 M
E) 0.643 M

Answer 1

0.115 M

Question 2

Dinitrogen pentaoxide decomposes to nitrogen dioxide and oxygen according to the following balanced chemical equation and rate expression. 2N₂O₅(g)→ 4NO₂(g)+ O₂(g)
Rate = k[N₂O₅]
What is the overall reaction order?

A) 0
B) 1
C) 2
D) 5
E) 7

Answer 2

1

Question 3

The reaction A → B follows first-order kinetics with a half-life of 21.7 hours.If the concentration of A is 0.023 M after 48.0 hours,what is the initial concentration of A?

A) 0.0050 M
B) 0.051 M
C) 0.51 M
D) 0.11 M
E) 2.0 × 10² M

Answer 3

0.11 M

Question 4

For the first-order reaction below,the concentration of product B after 24.2 seconds is 0.322 M.If k = 8.75 × 10−² s−¹,what was the initial concentration of A? A → 2B
Rate = k[A]

A) 0.0341 M
B) 0.183 M
C) 1.34 M
D) 2.68 M
E) 29.3 M

Question 5

The rate of reaction for the formation of carbon monoxide is measured at 1.24 mol/L⋅hr.What is the rate of formation of carbon monoxide in units of mol/L⋅s? CH₃CHO(g)→ CH₄(g)+ CO(g)

A) 3.44 × 10−⁴ mol/L⋅s
B) 2.07 × 10−² mol/L⋅s
C) 1.24 mol/L⋅s
D) 74.4 mol/L⋅s
E) 4.64 × 10³ mol/L⋅s

Question 6

Which equation is used to calculate the half-life of the zero-order equation below? $\mathrm{A} \rightarrow 2 \mathrm{~B}$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ rate $=k$

A) $t_{1 / 2}=\frac{1}{2 k}$
B) $t_{1 / 2}=\frac{[\mathrm{A}]_{0}}{k}$
C) $t_{1 / 2}=\frac{[A]_{0}}{2 k}$
D) $t_{1 / 2}=\frac{k}{[\mathrm{~A}]_{0}}$
E) t_1/2 = k

Question 7

For the second-order reaction below,the initial concentration of A is 1.00 M.If the concentration of A is reduced to 0.43 M after 75 seconds,what is the rate constant? $2 \mathrm{~A} \rightarrow \mathrm{B} \quad\quad\quad\quad\quad \text { rate }=k[\mathrm{~A}]^{2}$

A) 5.2 × 10?⁴ L/mol?s
B) 5.7 × 10?³ L/mol?s
C) 7.6 × 10?³ L/mol?s
D) 1.1 × 10?² L/mol?s
E) 1.8 × 10?² L/mol?s

Question 8

For the second-order reaction below,the initial concentration of A is 1.34 M.If k = 7.61 × 10?⁴ M¹s?¹,what is the concentration of A after 18.3 minutes? $2 \mathrm{~A} \rightarrow \mathrm{B} \quad\quad\quad\quad\quad \text { rate }=k[\mathrm{~A}]^{2}$

A) 0.504 M
B) 0.581 M
C) 0.632 M
D) 0.836 M
E) 1.12 M

Question 9

Determine the overall reaction order for the chemical expression and rate expression below. 2NO(g)+ Cl₂(g)→ 2NOCl(g)
Rate = k[NO]² × [Cl₂]

A) 1
B) 2
C) 3
D) 4
E) 5

Question 10

For the second-order decomposition reaction, $2 \mathrm{~A} \rightarrow \mathrm{B}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { rate }=k[\mathrm{~A}]^{2}$
Which of the following relationships yields a straight line plot?

A) ln [A] versus k
B) ln [A]² versus t
C) ln [A] versus t
D) 1/[A] versus t
E) 1/[A] versus k

Question 11

The reaction of NO and O₂ produces NO₂. 2 NO(g)+ O₂(g)→ 2 NO₂(g)
The reaction is second-order with respect to NO(g)and first-order with respect to O₂(g).At a given temperature,the rate constant,k,equals 4.7 × 10² M^-2s^-1.What is the rate of reaction when the initial concentrations of NO and O₂ are 0.025 M and 0.015 M,respectively?

A) 2.6 × 10^-3 M/s
B) 4.4 × 10^-3 M/s
C) 0.18 M/s
D) 2.0 × 10^-8 M/s
E) 3.8 × 10² M/s

Question 12

Which of the following expressions corresponds to the integrated rate equation for a first-order decomposition reaction?

A) [A] = ?kt
B) [A] = [A]₀ ?kt
C) ln [A] = ln [A]₀ ?kt
D) $\frac{1}{[A]}=-k t$
E) $\frac{1}{[\mathrm{~A}]}=\frac{1}{[\mathrm{~A}]_{0}}-k t$

Question 13

Which equation is used to calculate the half-life of the first-order equation below? $\mathrm{A} \rightarrow 2 \mathrm{~B}$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { rate }=k[\mathrm{~A}]$

A) t_1/2 = 2 × ln k
B) t_1/2 = (ln k)/[A]_o
C) t_1/2 = ln (k/2)
D) t_1/2 = ln ([A]_o/k)
E) t_1/2 = (ln 2)/k

Question 14

For the reaction A + 2B ? C,the rate law is $\frac{\Delta[\mathrm{C}]}{\Delta t}=k[\mathrm{~A}]^{2} \times[\mathrm{B}]$ . What are the units of the rate constant where time is measured in seconds?

A) $\frac{1}{\mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}}$
B) $\frac{1}{(\mathrm{~mol} / \mathrm{L})^{2} \cdot \mathrm{s}}$
C) $\frac{1}{\mathrm{~s}}$
D) $\frac{(\mathrm{mol} / \mathrm{L})^{2}}{\mathrm{~s}}$
E) $\frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}}$

Question 15

The rate constant for the decomposition of cyclobutane is 2.08 × 10−² s−¹ at high temperatures. C₄H₈(g)→ 2C₂H₄(g)
How many seconds are required for an initial concentration of 0.100 M C₄H₈(g)to decrease to 0.0450 M?

A) 0.00114 s
B) 1.07 s
C) 2.64 s
D) 38.4 s
E) 874 s

Question 16

For the second-order reaction below,the rate constant of the reaction is 9.4 × 10^-3 M^-1s^-1.How much time (in seconds)is required to decrease the concentration of A from 2.16 M to 0.40 M? $2 \mathrm{~A} \rightarrow \mathrm{B} \quad\quad\quad\quad\quad \text { rate }=k[\mathrm{~A}]^{2}$

A) 2.0 × 10¹ s
B) 7.8 × 10¹ s
C) 1.8 × 10² s
D) 1.9 × 10² s
E) 2.2 × 10² s

Question 17

For the reaction below,if the rate of appearance of Br₂ is 0.180 mol/L⋅s,what is the rate of disappearance of NOBr? 2NOBr(g)→ 2NO(g)+ Br₂(g)

A) -0.360 mol/L⋅s
B) -0.090 mol/L⋅s
C) 0.090 mol/L⋅s
D) 0.180 mol/L⋅s
E) 0.360 mol/L⋅s

Question 18

At a high temperature,the first-order decomposition of N₂O₅(g)produces NO₂(g)and O₂(g).If the initial concentration of 0.400 M N₂O₅(g)is reduced to 0.169 M after 118 seconds,what is the rate constant for the reaction?

A) 1.96 × 10−³ s−¹
B) 2.29 × 10−³ s−¹
C) 4.37 × 10−³ s−¹
D) 7.30 × 10−³ s−¹
E) 1.37 × 10² s−¹

Question 19

What are the units of the rate constant for the rate expression for the following chemical equation? 2NO(g)+ Cl₂(g)→ 2NOCl(g)
Rate = k[NO]² × [Cl₂]

A) mol/L⋅s
B) mol²/L²⋅s
C) L/mol⋅s
D) L²/mol²⋅s
E) L³/mol³⋅s

Question 20

Which equation is used to calculate the half-life of the second-order equation below? $2 \mathrm{~A} \rightarrow \mathrm{B} \quad\quad\quad\quad\quad\quad\quad \text { rate }=k[\mathrm{~A}]^{2}$

A) $t_{1 / 2}=\frac{1}{k[A]_{0}}$
B) $t_{1 / 2}=\frac{\ln (2)}{k[A]_{0}}$
C) $t_{1 / 2}=\frac{\ln (2)}{k}$
D) $t_{1 / 2}=\frac{\ln (2)}{[A]_{0}}$
E) $t_{1 / 2}=\frac{k}{2[A]_{0}}$

Question 21

For a given reaction,the activation energy is 63.9 kJ/mol.If the reaction rate constant is 4.1 × 10^-3 L/mol⋅s at 32.0°C,what is the reaction rate constant at -5.0°C? (R = 8.31 J/K⋅mol)

A) 1.2 × 10^-3 L/mol⋅s
B) 1.4 × 10^-6 L/mol⋅s
C) 1.3 × 10^-4 L/mol⋅s
D) 4.0 × 10^-3 L/mol⋅s
E) 1.3 × 10^-1 L/mol⋅s

Question 22

The effect of a catalyst on a chemical reaction is to

A) enable an alternate path for the reaction that has a lower activation barrier.
B) increase the energy of the products.
C) increase the activation barrier for the forward reaction.
D) increase the energy of the reactants.
E) increase the frequency of collisions between reactants and products.

Question 23

What is the half-life of a first-order reaction if the rate constant is 6.2 × 10^-3 s^-1?

A) 8.9 × 10^-3 s
B) 0.097 s
C) 5.77 s
D) 1.1 × 10² s
E) 1.6 × 10² s

Question 24

A first-order reaction has a half-life of 4.54 seconds.How much time is required for the reactant to be reduced to 6.25% of its initial concentration?

A) 1.14 s
B) 9.08 s
C) 13.6 s
D) 18.2 s
E) 93.6 s

Question 25

All of the following statements are correct EXCEPT

A) a heterogeneous catalyst is in a different phase from the reaction mixture.
B) enzymes are protein molecules that catalyze reactions.
C) catalysts are not consumed in reactions.
D) a reaction mechanism describes the path of a reaction at the molecular level.
E) elementary steps in a reaction mechanism are always unimolecular.

Question 26

A possible reaction mechanism for the reaction of nitrogen dioxide with carbon monoxide is
$\begin{array}{l}2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}_{3}(g)+\mathrm{NO}(g)&(slow) \\\mathrm{NO}_{3}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{CO}_{2}(g)&(fast)\end{array}$

What is the overall reaction and the most probable rate law for the reaction?

A) NO₂(g)+ CO(g)? NO(g)+ CO₂(g);rate = k[NO₂]
B) NO₂(g)+ CO(g)? NO(g)+ CO₂(g);rate = k[NO₂]²
C) NO₂(g)+ CO(g)? NO(g)+ CO₂(g);rate = k[NO₃]×[CO]
D) 2NO₂(g)+ CO(g)? NO(g)+ CO₂(g);rate = k[NO₂]×[ NO₃]×[CO]
E) 2NO₂(g)+ CO(g)? NO(g)+ CO₂(g);rate = k[NO₃]×[CO]

Question 27

The correct form of the Arrhenius equation is

A) E_a = Ae?k/RT
B) $k=A e^{-E_{a} / R T}$
C) $k=A e^{-R T / E_{a}}$
D) E_a = Ae^k/RT
E) A = E_ae?k/RT

Question 28

The decomposition of formic acid follows first-order kinetics. HCO₂H(g)→ CO₂(g)+ H₂(g)
The half-life for the reaction at 550°C is 24 seconds.How many seconds does it take for the formic acid concentration to decrease by 87.5%?

A) 24 s
B) 36 s
C) 48 s
D) 72 s
E) 96 s

Question 29

For the first-order reaction below,the initial concentration of A is 0.80 M.What is the half-life of the reaction if the concentration of A decreases to 0.10 M in 54 seconds? $\mathrm{A} \rightarrow \mathrm{B}$$\quad$$\quad$$\quad$$\quad$$\quad$ rate $=k[\mathrm{~A}]$

A) 18 s
B) 24 s
C) 36 s
D) 48 s
E) 51 s

Question 30

For the first-order reaction below,the initial concentration of A is 0.240 M.If the concentration of A decreases to 0.0800 M after 21.8 hours,what is the half-life of the reaction? $\mathrm{A} \rightarrow \mathrm{B}$$\quad$$\quad$$\quad$$\quad$$\quad$ rate $=k[\mathrm{~A}]$

A) 0.0504 hrs
B) 1.28 hrs
C) 7.26 hrs
D) 10.4 hrs
E) 13.8 hrs

Question 31

For a given reaction,the rate constant doubles when the temperature is increased from 45.0°C to 73.0°C.What is the activation energy for this reaction? (R = 8.31 J/K⋅mol)

A) 0.676 kJ/mol
B) 9.85 kJ/mol
C) 16.1 kJ/mol
D) 22.6 kJ/mol
E) 65.4 kJ/mol

Question 32

The elementary steps for a catalyzed reaction are shown below.Identify the catalyst.Identify the reactive intermediate. H₂O₂(aq)+ I−(aq)→ H₂O(l)+ IO−(aq)
IO−(aq)+ H₂O₂(aq)→ H₂O(l)+ O₂(g)+ I−(aq)

A) The catalyst is H₂O(l);the reactive intermediate is I−(aq).
B) The catalyst is IO−(aq);the reactive intermediate is I−(aq).
C) The catalyst is I−(aq);the reactive intermediate is H₂O₂(aq).
D) The catalyst is I−(aq);the reactive intermediate is IO−(aq).
E) The catalyst is H₂O₂(aq);the reactive intermediate is I−(aq).

Question 33

A first-order reaction has a half-life of 2.10 hours.How much time is required for the reactant to be reduced to 33.0% of its initial concentration?

A) 2.45 hours
B) 2.89 hours
C) 3.36 hours
D) 3.93 hours
E) 4.21 hours

Question 34

A possible mechanism for the decomposition of ozone to oxygen in the atmosphere is $\begin{array}{l}\mathrm{O}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{O}_{2}(\mathrm{~g})+\mathrm{O}& \text { (fast equilibrium) } \\\mathrm{O}+\mathrm{O}_{3}(\mathrm{~g}) \rightarrow 2 \mathrm{O}_{2}(\mathrm{~g})& \text { (slow) }\end{array}$

What is a rate law that is consistent with this mechanism?

A) rate = k[O₃]
B) rate = k[O₃]²
C) rate = k[O₃] × [O]
D) rate = k[O₃]² × [O₂]
E) rate = k[O₃]² × [O₂]?¹

Question 35

Hydrogen peroxide decomposes into water and oxygen in a first-order process. H₂O₂(aq)→ H₂O(l)+ 1/2 O₂(g)
At 20.0°C,the half-life for the reaction is 3.92 × 10⁴ seconds.If the initial concentration of hydrogen peroxide is 0.52 M,what is the concentration after 7.00 days?

A) 1.2 × 10-⁵ M
B) 0.034 M
C) 0.074 M
D) 0.22 M
E) 0.52 M

Question 36

For a certain reaction,the activation energy is 52.1 kJ/mole.By what ratio will the rate constant change if the temperature is decreased from 175°C to 75°C?

A) 0.00402
B) 0.0179
C) 0.996
D) 121
E) 249

Question 37

The rate constant at 373 K for a certain reaction is 8.29 × 10−⁴ s−¹ and the activation energy is 12.0 kJ/mole.What is the value of the constant,A,in the Arrhenius equation?

A) 0.00832 s−¹
B) 0.0398 s−¹
C) 0.120 s−¹
D) 0.998 s−¹
E) 25.1 s−¹

Question 38

Nitrogen dioxide reacts with carbon monoxide to produce nitrogen monoxide and carbon dioxide.
$\begin{array}{l}2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{NO}_{3}(g)+\mathrm{NO}(g) &(fast, equilibrium)\\\mathrm{NO}_{3}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}_{2}(g)+\mathrm{CO}_{2}(g)&(slow) \end{array}$

What is a rate law that is consistent with the proposed mechanism?

A) rate = k[NO₂]²×[CO]× [NO]^-1
B) rate = k[NO₂]²×[CO]
C) rate = k[NO₂]×[CO]
D) rate = k[NO₃]×[CO]
E) rate = k[NO₂]²

Question 39

For the second-order reaction below,the concentration of product B after 132 seconds is 0.0281 M.If the initial concentration of A is 0.932 M,what is the rate constant? $2 \mathrm{~A} \rightarrow \mathrm{B} \quad\quad\quad\quad\quad \text { rate }=k[\mathrm{~A}]^{2}$

A) 1.43 × 10?⁵ L/mol?s
B) 4.71 × 10?⁴ L/mol?s
C) 5.22 × 10?⁴ L/mol?s
D) 6.63 × 10?³ L/mol?s
E) 96.4 L/mol?s

Question 40

The elementary steps for the catalyzed decomposition for dinitrogen monoxide are shown below.Identify the catalyst. NO(g)+ N₂O(g)→ N₂(g)+ NO₂(g)
2NO₂(g)→ 2NO(g)+ O₂(g)

A) NO(g)
B) N₂O(g)
C) N₂(g)
D) NO₂(g)
E) O₂(g)

Question 41

What did Henry Eyring develop that changed how scientists study rates of reactions?

A) The catalyst model
B) The transition-state model
C) The liquid-state model
D) The temperature dependence model
E) The enzyme model

Question 42

For the overall reaction 2A + B ? C
Which of the following mechanisms are consistent with a rate equation of rate = k[A]²×[B]?

A)
A + B ? I (fast)
I + A ? C (slow)
B)
A + B ? I (slow)
I + A ? C (fast)
C)
2A ? I (slow)
B + I ? C (fast)
D)
2A? I (fast)
I + B ? C (slow)
E) Answers a and d are both correct.

Question 43

Ozone in the upper atmosphere is important to life on earth because it converts harmful UV radiation to heat.How does the release of CFCs into the atmosphere affect the concentration of ozone in the upper atmosphere?

A) The Cl in the CFC catalyzes the decomposition of ozone decreasing its concentration.
B) The Cl in the CFC catalyzes the production of ozone increasing its concentration.
C) The NO₂ in the CFC catalyzes the decomposition of ozone decreasing its concentration.
D) The NO₂ in the CFC catalyzes the production of ozone increasing its concentration.
E) The CFC's change the ozone into photochemical smog.

Question 44

For the overall reaction A + 2B ? C
Which of the following mechanisms yields the correct overall chemical equation and is consistent with the rate equation below?
Rate = k[A]×[B]

A)
$\begin{array}{l}\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{I} &\text { (fast) } \\\mathrm{I}+\mathrm{A} \rightarrow \mathrm{C} &\text { (slow) }\end{array}$
B)
$\begin{array}{l}\mathrm{A}+\mathrm{B} \rightarrow \mathrm{I} &\text { (slow) } \\\mathrm{I}+\mathrm{B} \rightarrow \mathrm{C} &\text { (fast) }\end{array}$
C)
$\begin{array}{l}2 \mathrm{~B} \rightarrow \mathrm{I} &\text { (slow) } \\\mathrm{A}+\mathrm{I} \rightarrow \mathrm{C} &\text { (fast) }\end{array}$
D)
$\begin{array}{l}2 \mathrm{~B} \rightleftharpoons \mathrm{I}& \text { (fast) } \\\mathrm{I}+\mathrm{A} \rightarrow \mathrm{C} &\text { (slow) }\end{array}$
E)
$\begin{array}{l}\mathrm{A}+2 \mathrm{~B} \rightleftharpoons \mathrm{I} &\text { (fast) } \\\mathrm{I}+\mathrm{B} \rightarrow \mathrm{C}+\mathrm{B} &\text { (slow) }\end{array}$