Deck 15: Chemical Kinetics: the Rates of Chemical Reactions

Question 1

Which of the following units are consistent with the units of the reaction rate in a first order reaction?

A) $\frac { \mathrm { M } } { \mathrm { min } }$
B) $\frac { 1 } { \min }$
C) $\frac { 1 } { \mathrm { M } \cdot \mathrm { min } }$
D) $\frac { 1 } { \mathrm { M } ^ { 2 } \cdot \min }$
E) $\frac { \min } { \mathrm { M } }$

Answer 1

$\frac { \mathrm { M } } { \mathrm { min } }$

Question 2

If a reaction is second-order with respect to a particular reactant, when the concentration of that reactant is increased by a factor of 4, the reaction rate will _____.

A) increase by a factor of 16.
B) remain constant.
C) decrease by a factor of $\frac { 1 } { 16 }$ .
D) increase by a factor of 64.
E) decrease by a factor of $\frac { 1 } { 4 }$ .

Answer 2

increase by a factor of 16.

Question 3

Which of the following statements is correct for the first-order reaction: A → 2B?

A) The concentration of A decreases linearly with respect to time.
B) The concentration of A is constant with respect to time.
C) The natural logarithm of the concentration of A decreases linearly with respect to time.
D) The rate of reaction is constant with respect to time.
E) The rate constant, k, of the reaction decreases linearly with respect to time.

Answer 3

The natural logarithm of the concentration of A decreases linearly with respect to time.

Question 4

Given the initial rate data for the reaction A + B ? C, determine the rate expression for the reaction. $$\begin{array} { l l l } { [ \mathrm { A } ] , \mathrm { M } } & { [ \mathrm { B } ] , \mathrm { M } } & \Delta [ \mathrm { C } ] / \Delta t ( \text { initial) } \mathrm { M } / \mathrm { s } \\\hline 0.0418 & 0.122 & 2.73 \times 10 ^ { - 4 } \\0.0836 & 0.122 & 10.9 \times 10 ^ { - 4 } \\0.0418 & 0.488 & 2.73 \times 10 ^ { - 4 }\end{array}$$

A) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 5.35 \times 10 ^ { - 2 } \mathrm { M } ^ { - 2 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] [ \mathrm { B } ]$
B) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 1.27 \mathrm { M } ^ { - 2 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] ^ { 2 } [ \mathrm {~B} ]$
C) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 0.156 \mathrm { M } ^ { - 1 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] ^ { 2 }$
D) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 0.439 \mathrm { M } ^ { - 2 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] [ \mathrm { B } ] ^ { 2 }$
E) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 6.53 \times 10 ^ { - 3 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ]$

Question 5

How are the exponents in a rate law determined?

A) They are equal to the inverse of the coefficients in the overall balanced chemical equation.
B) They are determined by experimentation.
C) They are equal to the coefficients in the overall balanced chemical equation.
D) They are equal to the reactant concentrations.
E) They are equal to the ln(2) divided by the rate constant.

Question 6

Given the initial rate data for the reaction A + B ? C, determine the rate expression for the reaction. $$\begin{array} { l l l } { [ \mathrm { A } ] , \mathrm { M } } & { [ \mathrm { B } ] , \mathrm { M } } & \Delta [ \mathrm { C } ] / \Delta t \text { (initial) } \mathrm { M } / \mathrm { s } \\\hline 0.215 & 0.150 & 5.81 \times 10 ^ { - 4 } \\0.215 & 0.300 & 1.16 \times 10 ^ { - 3 } \\0.430 & 0.150 & 2.32 \times 10 ^ { - 3 }\end{array}$$

A) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 1.80 \times 10 ^ { - 2 } \mathrm { M } ^ { - 1 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] [ \mathrm { B } ]$
B) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 3.60 \times 10 ^ { - 2 } \mathrm { M } ^ { - 1 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] [ \mathrm { B } ]$
C) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 1.20 \times 10 ^ { - 1 } \mathrm { M } ^ { - 2 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] [ \mathrm { B } ] ^ { 2 }$
D) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 5.57 \times 10 ^ { - 1 } \mathrm { M } ^ { - 3 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] ^ { 2 } [ \mathrm {~B} ] ^ { 2 }$
E) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 8.37 \times 10 ^ { - 2 } \mathrm { M } ^ { - 2 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] ^ { 2 } [ \mathrm {~B} ]$

Question 7

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 8

The rate law for a reaction is rate = k[A]²[B]. Which of the following mixtures of reactants will give the smallest initial rate?

A) 1.0 M A and 1.0 M B
B) 2.0 M A and 0.50 M B
C) 0.50 M A and 0.50 M B
D) 0.125 M A and 3.0 M B
E) 1.5 M A and 0.50 M B

Question 9

What is the overall order of the reaction
NO(g) + O₃(g) ? NO₂(g) + O₂(g)
if the reaction proceeds via the rate expression given below. $- \frac { \Delta [ \mathrm { NO } ] } { \Delta t } = k [ \mathrm { NO } ] \left[ \mathrm { O } _ { 3 } \right]$

A) Zero-order
B) First-order
C) Second-order
D) Third-order
E) Fourth-order

Question 10

The average rate of disappearance of ozone in the following reaction is found to be 7.01 × 10^-3 atm/s
$2 \mathrm { O } _ { 3 } ( g ) \rightarrow 3 \mathrm { O } _ { 2 } ( g )$ What is the rate of appearance of $\mathrm { O } _ { 2 }$ during this interval?

A) 4.67 × 10^-3 atm/s
B) 7.01 × 10^-3 atm/s
C) 16.4 × 10^-3 atm/s
D) 172 × 10^-3 atm/s
E) 10.5 × 10^-3 atm/s

Question 11

For which of the following hypothetical rate laws would the units of the rate constant have the general form M-1·h−1?

A) Reaction rate = k[A]²
B) Reaction rate = k
C) Reaction rate = k[A]
D) Reaction rate = k[A]..
E) Reaction rate = k[A]⁴..

Question 12

The rate constant for a particular reaction is 0.0020 ^⋅s−1. What is the overall order of this reaction?

A) 0
B) 1
C) 2
D) 3
E) 4

Question 13

For a certain overall second-order reaction with the general form aA → products, the initial rate of reaction is 0.50 M·s−1 when the initial concentration of the reactant is 0.27 M. What is the rate constant for this reaction?

A) 0.039 M^-1·s−1
B) 6.9 M^-1·s−1
C) 0.50 M^-1·s−1
D) 0.54 M^-1·s−1
E) 25 M^-1·s−1

Question 14

The following data were obtained in a kinetics study of the hypothetical reaction A + B + C ? products. $$\begin{array} { l l l l } { [ \mathrm { A } ] _ { 0 } ( M ) } & { [ \mathrm { B } ] _ { 0 } ( M ) } & { [ \mathrm { C } ] _ { 0 } ( M ) } & \underline { \text { Initial Rate } } \left(10 ^ { - 3 } \underline { M / \mathrm { s } ) } \right. \\0.4 & 0.4 & 0.2 & 160 \\0.2 & 0.4 & 0.4 & 80 \\0.6 & 0.1 & 0.2 & 15 \\0.2 & 0.1 & 0.2 & 5 \\0.2 & 0.2 & 0.4 & 20\end{array}$$
Using the initial-rate method, what is the order of the reaction with respect to A?

A) zero-order
B) first-order
C) second-order
D) third-order
E) impossible to tell from the data given

Question 15

Given the initial rate data for the decomposition reaction, A ? B + C
Determine the rate expression for the reaction.
$$\begin{array} { l l } { [ \mathrm { A } ] , \mathrm { M } } & - \Delta [ \mathrm { A } ] / \Delta t \mathrm { M } / \mathrm { s } \\\hline0.084 & 12.4 \times 10 ^ { - 6 } \\0.063 & 9.3 \times 10 ^ { - 6 } \\0.042 & 6.2 \times 10 ^ { - 6 }\end{array}$$

A) $\frac { - \Delta [ \mathrm { A } ] } { \Delta t } = 1.5 \times 10 ^ { - 4 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ]$
B) $\frac { - \Delta [ \mathrm { A } ] } { \Delta t } = 1.5 \times 10 ^ { - 4 } \mathrm { M } ^ { - 1 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] ^ { 2 }$
C) $\frac { - \Delta [ \mathrm { A } ] } { \Delta t } = 1.8 \times 10 ^ { - 9 } \mathrm { M } ^ { - 1 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] ^ { 2 }$
D) $\frac { - \Delta [ \mathrm { A } ] } { \Delta t } = 1.2 \times 10 ^ { - 5 } \mathrm { Ms } ^ { - 1 }$
E) $\frac { - \Delta [ \mathrm { A } ] } { \Delta t } = 6.8 \times 10 ^ { 3 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ]$

Question 16

Which statement concerning relative rates of reaction is correct for the chemical equation given below? 2 CH₃OH(g) + 3 O₂(g) → 2 CO₂(g) + 4 H₂O(g)

A) The rate of disappearance of CH₃OH is equal to the rate of disappearance of O₂.
B) The rate of disappearance of CH₃OH is two times the rate of appearance of H₂O_.
C) The rate of disappearance of CH₃OH is half the rate of appearance of CO₂.
D) The rate of appearance of H₂O is two times the rate of appearance of CO₂.
E) The rate of appearance of H₂O is four times the rate of disappearance of CH₃OH.

Question 17

Given the initial rate data for the reaction A + B ? C, determine the rate expression for the reaction. $$\begin{array} { l l l } { [ \mathrm { A } ] , \mathrm { M } } & { [ \mathrm { B } ] , \mathrm { M } } & \Delta [ \mathrm { C } ] / \Delta t \text { (initial) } \mathrm { M } / \mathrm { s } \\\hline 0.0344 & 0.160 & 2.11 \times 10 ^ { - 2 } \\0.0516 & 0.160 & 3.17 \times 10 ^ { - 2 } \\0.0344 & 0.272 & 6.10 \times 10 ^ { - 2 }\end{array}$$

A) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 3.84 \mathrm { M } ^ { - 1 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] [ \mathrm { B } ]$
B) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 24.0 \mathrm { M } ^ { - 2 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] [ \mathrm { B } ] ^ { 2 }$
C) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 111 \mathrm { M } ^ { - 2 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] ^ { 2 } [ \mathrm {~B} ]$
D) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 189 \mathrm { M } ^ { - 2 } \mathrm {~s} ^ { - 1 } [ \mathrm {~A} ] ^ { 2 } [ \mathrm {~B} ]$
E) $\frac { \Delta [ \mathrm { C } ] } { \Delta t } = 0.285 \mathrm { M } ^ { - 1 } \mathrm {~s} ^ { - 1 } [ \mathrm {~B} ] ^ { 2 }$

Question 18

For the reaction provided, the rate of disappearance of I^-(aq) at a particular time and concentration is 2.4 × 10^-3 mol/L·s. IO₃^-(aq) + 5I^-(aq) + 6H⁺(aq) → 3I₂(aq) + 3H₂O(l)
What is the relative rate of appearance of I₂(aq)?

A) 4.0 × 10^-3 mol/L·s
B) 7 × 10^-3 mol/L·s
C) -1 × 10^-3 mol/L·s
D) 1 × 10^-3 mol/L·s
E) 7 × 10^-3 mol/L·s..

Question 19

Which of the following expressions does not represent a proper expression for the rate of this reaction?
2A + 3B ? F + 2G

A) $\frac { - \Delta [ \mathrm { A } ] } { \Delta \mathrm { t } }$
B) $\frac { - \Delta [ \mathrm { B } ] } { 3 \Delta \mathrm { t } }$
C) $\frac { \Delta [ F ] } { \Delta t }$
D) $\frac { \Delta [ \mathrm { G } ] } { 2 \Delta \mathrm { t } }$
E) $\frac { - \Delta [ \mathrm { A } ] } { 2 \Delta \mathrm { t } }$

Question 20

Which of the given relationships correctly compares the rates of the reactants and products for the reaction below?
2 NOCl(g) ? 2 NO(g) + Cl₂(g)

A) $- \frac { \Delta [ \mathrm { NOCl } ] } { \Delta t } = \frac { \Delta [ \mathrm { NO } ] } { \Delta t } + \frac { \Delta \left[ \mathrm { Cl } _ { 2 } \right] } { \Delta t }$
B) $\frac { \Delta [ \mathrm { NOCl } ] } { \Delta t } = \frac { \Delta [ \mathrm { NO } ] } { \Delta t } = \frac { \Delta \left[ \mathrm { Cl } _ { 2 } \right] } { \Delta t }$
C) $- \frac { 1 } { 2 } \frac { \Delta [ \mathrm { NOCl } ] } { \Delta t } = \frac { 1 } { 2 } \frac { \Delta [ \mathrm { NO } ] } { \Delta t } = \frac { \Delta \left[ \mathrm { Cl } _ { 2 } \right] } { \Delta t }$
D) $\frac { - 2 \Delta [ \mathrm { NOCl } ] } { \Delta t } = \frac { 2 \Delta [ \mathrm { NO } ] } { \Delta t } = \frac { \Delta \left[ \mathrm { Cl } _ { 2 } \right] } { \Delta t }$
E) $\frac { \Delta [ \mathrm { NOCl } ] } { \Delta t } = \frac { \Delta t } { \Delta [ \mathrm { NO } ] } = \frac { \Delta t } { \Delta \left[ \mathrm { Cl } _ { 2 } \right] }$

Question 21

A first-order chemical reaction is observed to have a rate constant of 24 min^-1. What is the corresponding half-life for the reaction?

A) 1.7 s
B) 1.7 min
C) 35 min
D) 2.5 s
E) 34.3 s

Question 22

In a first-order reaction, the half-life is 133 minutes. What is the rate constant?

A) 1.25 × 10^-4 s^-1
B) 5530 s^-1
C) 0.313 s^-1
D) 5.21 × 10^-3 s^-1
E) 8.68 × 10^-5 s^-1

Question 23

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 was the initial concentration of A?

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

Question 24

For the hypothetical reaction aA → products, the experimental data showed the following behavior (below). What is the reaction order with respect to reactant A?

A) zero order
B) first order
C) second order
D) third order
E) fourth order

Question 25

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

Question 26

For a certain reaction of the general form aA → products, a plot of the experimental data of 1/[A] versus time is linear. What is the reaction order with respect to the reactant (A)?

A) Second-order
B) First-order
C) Zero-order
D) Third-order
E) Fourth

Question 27

A first-order reaction is 40.0% complete at the end of 48.6 minutes. What is the value of the rate constant?

A) 1.89 × 10^-2 min^-1
B) 1.05 × 10^-2 min^-1
C) 53.0 min^-1
D) 95.1 min^-1
E) none of these

Question 28

A second-order reaction starts with an initial concentration of 0.100 mol/L of the reactant. If the rate constant is 1.4 × 10^-2 L/mol·s, what is the time required to decrease the initial concentration to 0.050 mol/L? 2A → B
Rate = k[A]²

A) 710 s
B) 1100 s
C) 49.5 s
D) 3.57 s
E) 2100 s

Question 29

For the second-order reaction below, the initial concentration of reactant A is 0.24 M. If the rate constant for the reaction is 1.5 × 10^-2 M^-1s^-1, what is the concentration of A after 265 seconds? 2A → B + C
Rate = k[A]²

A) 0.12 M
B) 0.19 M
C) 0.95 M
D) 4.0 M
E) 5.2 M

Question 30

At a given temperature, a first-order reaction has a rate constant of 2.1 × 10^-3 s^-1. How long will it take for the reaction to be 25% complete?

A) 660 s
B) 2100 s
C) 1500 s
D) 59 s
E) 140 s

Question 31

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 32

For the zero-order reaction A ? B + C, a graph of _____ versus time will generate a straight line.

A) [A]_t
B) $\ln \frac { [ \mathrm { A } ] _ { t } } { [ \mathrm {~A} ] _ { 0 } }$
C) ln[A]_t
D) $\frac { 1 } { [ \mathrm {~A} ] _ { t } }$
E) $\frac { \ln ( 2 ) } { [ \mathrm { A } ] _ { t } }$

Question 33

For the first-order decomposition of N₂O₅ at a high temperature, determine the rate constant if the N₂O₅ concentration decreases from 1.04 M to 0.62 M in 375 seconds.

A) 5.99 × 10^-4 s^-1
B) 1.59 × 10^-3 s^-1
C) 1.74 × 10^-3 s^-1
D) 1.38 × 10^-3 s^-1
E) 1.94 × 10² s^-1

Question 34

Hydrogen peroxide decomposes into water and oxygen in a first-order process. H₂O₂(aq) ? H₂O( $\ell$ ) + 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 35

For a certain reaction of the general form aA → products, the experimental data plotted as [A] versus time is linear. The slope of this plot must equal

A) -1.
B) the negative of the rate constant.
C) one over the rate constant.
D) the rate constant.
E) 1.

Question 36

Which of the following is not a correct representation of the integrated rate expression for a decomposition first-order reaction?

A) $\ln \frac { [ A ] _ { t } } { [ A ] _ { 0 } } = - k t$
B) $\ln \frac { [ A ] _ { 0 } } { [ A ] _ { t } } = k t$
C) $\ln [ A ] _ { t } = \ln [ A ] _ { 0 } - k t$
D) $\frac { [ A ] _ { t } } { [ A ] _ { 0 } } = e ^ { - k t }$
E) $\ln [ A ] _ { t } + \ln [ A ] _ { 0 } = k t$

Question 37

A student analyzed a first-order reaction and obtained the graph below. Unfortunately, the student forgot to label the axes. What are the correct labels for the x and y axes?

A) x axis = time, y axis = ln[A]
B) x axis = ln[time], y axis = [A]
C) x axis = ln[time], y axis = [A]..
D) x axis = time, y axis = 1/[A]
E) x axis = 1/time, y axis = 1/[A]

Question 38

What is the half-life of the first-order reaction if it takes 4.4 × 10^-2 seconds for a concentration to decrease from 0.50 M to 0.20 M?

A) 2.5 × 10^-2 s
B) 3.3 × 10^-2 s
C) 1.6 s
D) 21 s
E) 27 s

Question 39

The decomposition of phosphine, PH₃, follows first-order kinetics. 4 PH₃(g) → P₄(g) + 6 H₂(g)
The half-life for the reaction at 550 °C is 81.3 seconds. What percentage of phosphine remains after 195 seconds?

A) 2.2%
B) 9.8%
C) 19%
D) 42%
E) 58%

Question 40

For the reaction A ? B + C, which of the following equations corresponds to the integrated expression for a second-order decomposition reaction?

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

Question 41

In general, as temperature increases, the rate of a chemical reaction

A) decreases due to fewer collisions with proper molecular orientation.
B) increases for exothermic reactions, but decreases for endothermic reactions.
C) increases due to a greater number of effective collisions.
D) remains unchanged.
E) decreases due to an increase in the activation energy.

Question 42

For the formation of 1 mol of nitrosyl chloride at a given temperature, Δ_rH = -37 kJ/mol. NO(g) + ½ Cl₂(g) → NOCl(g)
The activation energy for this reaction is 81 kJ/mol. What is the activation energy for the reverse reaction?

A) 81 kJ/mol
B) 44 kJ/mol
C) 118 kJ/mol
D) -37 kJ/mol
E) -118 kJ/mol

Question 43

The rate constant at 366 K for a first-order reaction is 7.7 × 10^-3 s^-1 and the activation energy is 15.9 kJ/mol. What is the value of the frequency factor, A, in the Arrhenius equation? (R = 8.314 J/K⋅mol)

A) 0.0047 s^-1
B) 0.70 s^-1
C) 0.93 s^-1
D) 1.1 s^-1
E) 1.4 s^-1

Question 44

Below is a proposed mechanism for the decomposition of $$\begin{array} { l l } \mathrm { H } _ { 2 } \mathrm { O } _ { 2 } + I^- \rightarrow \mathrm { H } _ { 2 } \mathrm { O } + \mathrm { IO } ^ { - } & \text {slow } \\\mathrm { H } _ { 2 } \mathrm { O } _ { 2 } + \mathrm { IO } ^ { - } \rightarrow \mathrm { H } _ { 2 } \mathrm { O } + \mathrm { O } _ { 2 } + I^- & \text { fast }\end{array}$$
Which of the following statements is incorrect?

A) IO^- is a catalyst.
B) I^- is a catalyst.
C) The net reaction is 2H₂O₂ ? 2H₂O + O₂.
D) The reaction is first-order with respect to [I^-].
E) The reaction is first-order with respect to [H₂O₂].

Question 45

Calculate the activation energy, E_a, for N₂O₅(g) → 2 NO₂(g) + 1/2 O₂(g)
Given k (at 45.0 °C) = 5.79 × 10^-4 s^-1 and k (at 60.0 °C) = 3.83 × 10^-3 s^-1. (R = 8.314 J/K⋅mol)

A) 0.256 kJ/mol
B) 2.83 kJ/mol
C) 31.1 kJ/mol
D) 111 kJ/mol
E) 389 kJ/mol

Question 46

The Arrhenius equation, $k = A e ^ { - E _ { \mathrm { u } } / R T }$ expresses the dependence of the rate constant on the reaction temperature. The slope of a plot of ln(k) versus 1/T is equal to

A) $\frac { - E _ { a } } { R T }$
B) $- E _ { a }$
C) $E _ { a }$
D) $\ln ( A )$
E) $\frac { - E _ { a } } { R }$

Question 47

The reaction kinetics for a certain reaction are studied over several temperatures. Which of the following is/are not effected by a change in reaction temperature?

A) the reaction rate
B) the rate constant, k
C) the energy of activation, E_a
D) a and b
E) a, b, and c

Question 48

Molecules must overcome a barrier called the activation energy if they are to react. The highest energy point reached during the progress of a reaction is called the ____.

A) rate determining step
B) transition state
C) half-life
D) elementary step
E) intermediate state

Question 49

Consider the following proposed mechanism. If this mechanism for the overall reaction were correct, and if k₁ were much less than k₂, then the observed rate law would be 2A $\stackrel { \mathrm { k } _ { 1 } } { \longrightarrow }$ C + I
I + B $\stackrel { \mathrm { k } _ { 2 } } { \longrightarrow }$ C + D

A) rate = k₁[A]
B) rate = k₂[I][B]
C) rate = k₁[A]²
D) rate = k₁[A]² ? k₂[C][D]
E) rate = k₁k₂[A]²[I][B]

Question 50

The reaction, A + 2B ? B₂ + A, proceeds by the following mechanism: (A is a catalyst.) $$\begin{array} { l } \mathrm { A } + \mathrm { B } \rightarrow \mathrm { AB } &(slow)\\\mathrm { AB } + \mathrm { B } \rightarrow \mathrm { B } _ { 2 } + \mathrm { A }&(fast)\end{array}$$
What is the rate law expression for this reaction?

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

Question 51

A suggested mechanism for the decomposition of ozone is as follows:
O₃ ${ k } _ { 1 }$$\rightleftharpoons$
${ \mathrm { k } _ { - 1 } }$ O₂ + O fast equilibrium
O + O₃ $\stackrel { k _ { 2 } } { \longrightarrow }$ 2O₂ slow step
What is the rate law predicted by this mechanism?

A) Rate = $\frac { k _ { 1 } k _ { 2 } } { k _ { - 1 } } \left[ \mathrm { O } _ { 3 } \right] ^ { 2 } [ \mathrm { O } ]$
B) Rate = k₂[O] [O₃]
C) Rate = $\frac { k _ { 1 } k _ { 2 } } { k _ { - 1 } } \frac { \left[ \mathrm { O } _ { 3 } \right] ^ { 2 } } { \left[ \mathrm { O } _ { 2 } \right] }$
D) Rate = $\frac { k _ { 1 } } { k _ { - 1 } } \left[ \mathrm { O } _ { 3 } \right]$
E) Rate = $\frac { k _ { 1 } } { k _ { - 1 } } \frac { \left[ \mathrm { O } _ { 2 } \right] [ \mathrm { O } ] } { \left[ \mathrm { O } _ { 3 } \right] }$

Question 52

The Arrhenius equation, $k = A \mathrm { e } ^ { - E _ { \mathrm { u } } / R T }$ , relates the rate constant of reaction and temperature. A plot of ____ versus 1/T will yield a straight line with a slope of -E_a/R.

A) k₂/k₁
B) -E_a
C) ln(k)
D) $\mathrm { e } ^ { - E _ { \mathrm { u } } / R }$
E) 1/RT

Question 53

In a reaction coordinate diagram, reacting molecules are most unstable ______.

A) at their initial position
B) when they are about to collide
C) right after they collide
D) at the transition state

Question 54

Which of the following is the effect of adding a catalyst to a reaction?

A) Increase in the number of collisions between reactants
B) Lowering of the activation energy of a reaction
C) Increase in the equilibrium constant of a reaction
D) Decrease in the yield of the products
E) Increase in the enthalpy change of a reaction

Question 55

For a chemical reaction, the activation energy for the forward reaction is +181 kJ and the activation energy for the backward reaction is +62 kJ. What is the net energy change for the forward reaction?

A) -119 kJ
B) -62 kJ
C) +119 kJ
D) +181 kJ
E) +243 kJ

Question 56

The rate constant for a first-order reaction is 1.7 × 10^-2 s^-1 at 676 K and 3.9 × 10^-2 s^-1 at 880 K. Determine the activation energy of the reaction. (R = 8.314 J/K⋅mol)

A) 8.6 kJ/mol
B) 8.7 kJ/mol
C) 26 kJ/mol
D) 2400 kJ/mol
E) 21 kJ/mol

Question 57

Nitrogen dioxide reacts with carbon monoxide to produce nitrogen monoxide and carbon dioxide. NO₂(g) + CO(g) ? NO(g) + CO₂(g)
A proposed mechanism for this reaction is
2 NO₂(g) $\rightleftharpoons$ NO₃(g) + NO(g)
(fast, equilibrium)
NO₃(g) + CO(g) ? NO₂(g) + CO₂(g)
(slow)
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 58

A catalyst ____.

A) is used up in a chemical reaction
B) changes the potential energy change of the reaction
C) is always a solid
D) does not influence the reaction in any way
E) changes the activation energy of the reaction

Question 59

The rate constant for a reaction at 40.0°C is exactly 6 times that at 20.0°C. Calculate the Arrhenius energy of activation for the reaction. (R = 8.314 J/K⋅mol)

A) 6.00 kJ/mol
B) 8.22 kJ/mol
C) 68.3 kJ/mol
D) 14.9 kJ/mol
E) none of these

Question 60

A possible mechanism for the gas phase reaction of NO and H₂ is as follows: Step 1 2NO $\stackrel { k _ { 1 } } { \longrightarrow }$ N₂O₂
Step 2 N₂O₂ + H₂ $\stackrel { k _ { 2 } } { \longrightarrow }$ N₂O + H₂O
Step 3 N₂O + H₂ $\stackrel { k _ { 3 } } { \longrightarrow }$ N₂ + H₂O
Which of the following statements concerning this mechanism is not directly supported by the information provided?

A) Step 1 is the rate determining step.
B) N₂O₂ is an intermediate.
C) There is no catalyst in this reaction.
D) The rate expression for step 1 is rate = k[NO]².
E) All steps are bimolecular reactions.

Question 61

Termolecular elementary steps are rare. Why?

Question 62

Draw the reaction coordinate diagram for an exothermic reaction involving three mechanistic steps.

Question 63

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) A + B $\rightleftharpoons$ I (fast)
I + A ? C (slow)
B) A + B ? I (slow)
I + B ? C (fast)
C) 2B ? I (slow)
A + I ? C (fast)
D) 2B $\rightleftharpoons$ I (fast)
I + A ? C (slow)
E) A + 2B $\rightleftharpoons$ I (fast)
I + B ? C + B (slow)

Question 64

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

A) A + B $\rightleftharpoons$ 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 $\rightleftharpoons$ I (fast)
I + B ? C (slow)
E) Answers a and d are both correct.

Question 65

Which of the following steps must occur for an enzyme to catalyze a reaction?

A) The reactant, often called the substrate, must bind to the enzyme.
B) The chemical reaction must be halted.
C) The products of the reaction must attach to the enzyme.
D) The quantity of the enzymes in the reaction should keep increasing.
E) The reactant must bind to the product rather than the enzyme.

Question 66

The _____ of an elementary step is defined as the number of reactant molecules that come together in a reaction.

Question 67

How many mechanistic steps are depicted by in this potential energy diagram?

A) one step
B) two steps
C) three steps
D) four steps
E) five steps

Question 68

Carbon dating may be used to date (once living) materials that are between 100 and 40,000 years old. The half-life of the first-order decay of carbon-14 is 5730 years. What percentage of carbon-14 remains in a sample after 40,000 years.

Question 69

The pre-exponential, A, in the Arrhenius equation is called the ________ factor.

Question 70

Elementary steps in a reaction mechanism often include reaction _____. These (usually) short-lived species, which are at one point produced and then later consumed, do not appear in the overall chemical reaction.

Question 71

If a catalyst is present in a different phase from the reactants and products, it is referred to as a(n) ________ catalyst.

Question 72

Radioactive isotopes decay by ________-order kinetics.

Question 73

Circle the catalyst in the following mechanism.

Question 74

Which of the following statements is true of the Arrhenius equation?

A) The factor $e ^ { - E a / R T }$ always has a value more than 1.
B) Ea represents the fraction of molecules having the minimum energy required for a reaction.
C) It can be used to calculate E_a from the temperature dependence of the rate constant.
D) It can be used to calculate the rate constant if $e ^ { - E a / R T }$ is known.
E) The factor $e ^ { - E a / R T }$ always has a value more than 10.