Q: A first-order reaction has a rate constant $$k = 0.025\ \text{min}^{-1}. $$What is the half-life of the reaction?

$$t_{1/2} = \frac{0.693}{0.025} = 27.7\ \text{min}$$

Q: The decomposition of HI follows a second-order rate law: $$2\text{HI}(g) \rightarrow \text{H}_2(g) + \text{I}_2(g)$$ with $$k = 0.0308\ \text{M}^{-1}\text{s}^{-1}. If $$the initial concentration of HI is $$0.50\ \text{M}$$, how long does it take for the concentration to reach $$0.15\ \text{M}$$?

$$t = \frac{1}{k} \left( \frac{1}{[\text{HI}]_t} - \frac{1}{[\text{HI}]_0} \right) = \frac{1}{0.0308} \left( \frac{1}{0.15} - \frac{1}{0.50} \right) = 170\ \text{s}$$

Q: For the reaction $$\text{H}_2 + 2\text{ICl} \rightarrow 2\text{HCl} + \text{I}_2$$, the experimental rate law is $$\text{Rate} = k[\text{H}_2][\text{ICl}]. $$Which of the following mechanisms is consistent with this rate law?

Step 1: $$\text{H}_2 + \text{ICl} \rightarrow \text{HI} + \text{HCl} ($$slow); Step 2: $$\text{ICl} + \text{HI} \rightarrow \text{HCl} + \text{I}_2 ($$fast)

Q: A zero-order reaction has an initial concentration of $$[A]_0 = 0.10\ \text{M}$$ and a rate constant $$k = 2.0 \times 10$$^{-3}$$\ \text{M/s}. $$How long will it take for the concentration of A to decrease to $$0.02\ \text{M}$$?

$$t = \frac{[A]_0 - [A]_t}{k} = \frac{0.10 - 0.02}{2.0 \times 10$$^{-3}$$} = 40\ \text{s}$$

Q: In the mechanism for the destruction of stratospheric ozone, which species is the catalyst and which is the intermediate? Step 1: $$\text{Cl} \cdot + \text{O}_3 \rightarrow \text{ClO} \cdot + \text{O}_2$$ Step 2: $$\text{ClO} \cdot + \text{O} \rightarrow \text{Cl} \cdot + \text{O}_2$$ Overall: $$\text{O}_3 + \text{O} \rightarrow 2\text{O}_2$$

Catalyst: $$\text{Cl} \cdot$$; Intermediate: $$\text{ClO} \cdot$$

Question 1

A reaction is found to have a rate law of $$	ext{Rate} = k[	ext{A}]^2[	ext{B}]. If $$the concentration of A is doubled and the concentration of B is tripled, by what factor does the reaction rate increase?

Accepted Answer

The rate increases by a factor of 12.

Question 2

For the reaction $$2	ext{N}_2	ext{O}_5(g) ightarrow 4	ext{NO}_2(g) + 	ext{O}_2(g)$$, if the average rate of disappearance of $$	ext{N}_2	ext{O}_5 is$$ $$0.30\ 	ext{M/s}$$, what is the average rate of formation of $$	ext{NO}_2$$?

Accepted Answer

$$0.60\ 	ext{M/s}$$

Question 3

Which of the following statements about the rate law is correct?

Accepted Answer

The rate law must be determined experimentally.

Question 4

A first-order reaction has a rate constant $$k = 0.025\ 	ext{min}^{-1}. $$What is the half-life of the reaction?

Accepted Answer

$$t_{1/2} = \frac{0.693}{0.025} = 27.7\ 	ext{min}$$

Question 5

The decomposition of HI follows a second-order rate law: $$2	ext{HI}(g) ightarrow 	ext{H}_2(g) + 	ext{I}_2(g)$$ with $$k = 0.0308\ 	ext{M}^{-1}	ext{s}^{-1}. If $$the initial concentration of HI is $$0.50\ 	ext{M}$$, how long does it take for the concentration to reach $$0.15\ 	ext{M}$$?

Accepted Answer

$$t = \frac{1}{k} \left( \frac{1}{[	ext{HI}]_t} - \frac{1}{[	ext{HI}]_0} ight) = \frac{1}{0.0308} \left( \frac{1}{0.15} - \frac{1}{0.50} ight) = 170\ 	ext{s}$$

Question 6

Which of the following best describes the effect of a catalyst on a chemical reaction?

Accepted Answer

A catalyst provides an alternative pathway with a lower activation energy.

Question 7

The Arrhenius equation is $$k = Ae$$^{-E_a/RT}$$. If the rate constant k$ doubles when the temperature increases from 298$$\ 	ext{K}$$ to 308$$\ 	ext{K}$$, what is the approximate activation energy E_a$ in kJ/mol? (R = 8.314$$\ 	ext{J/mol}\cdot	ext{K}$$)

Accepted Answer

$$E_a = 53.7\ 	ext{kJ/mol}$$

Question 8

Which of the following is a requirement for a valid reaction mechanism?

Accepted Answer

The sum of the elementary steps must equal the overall reaction.

Question 9

For the reaction $$	ext{H}_2 + 2	ext{ICl} ightarrow 2	ext{HCl} + 	ext{I}_2$$, the experimental rate law is $$	ext{Rate} = k[	ext{H}_2][	ext{ICl}]. $$Which of the following mechanisms is consistent with this rate law?

Accepted Answer

Step 1: $$	ext{H}_2 + 	ext{ICl} ightarrow 	ext{HI} + 	ext{HCl} ($$slow); Step 2: $$	ext{ICl} + 	ext{HI} ightarrow 	ext{HCl} + 	ext{I}_2 ($$fast)

Question 10

A zero-order reaction has an initial concentration of $$[A]_0 = 0.10\ 	ext{M}$$ and a rate constant $$k = 2.0 	imes 10$$^{-3}$$\ 	ext{M/s}. $$How long will it take for the concentration of A to decrease to $$0.02\ 	ext{M}$$?

Accepted Answer

$$t = \frac{[A]_0 - [A]_t}{k} = \frac{0.10 - 0.02}{2.0 	imes 10$$^{-3}$$} = 40\ 	ext{s}$$

Question 11

Which of the following best explains why termolecular elementary steps are rare?

Accepted Answer

It is unlikely that three molecules will collide simultaneously with the correct orientation and sufficient energy.

Question 12

In the mechanism for the destruction of stratospheric ozone, which species is the catalyst and which is the intermediate?

Step 1: $$	ext{Cl} \cdot + 	ext{O}_3 ightarrow 	ext{ClO} \cdot + 	ext{O}_2$$
Step 2: $$	ext{ClO} \cdot + 	ext{O} ightarrow 	ext{Cl} \cdot + 	ext{O}_2$$
Overall: $$	ext{O}_3 + 	ext{O} ightarrow 2	ext{O}_2$$

Accepted Answer

Catalyst: $$	ext{Cl} \cdot$$; Intermediate: $$	ext{ClO} \cdot$$

Question 13

A reaction has an activation energy of $$40\ 	ext{kJ/mol}. At$$ $$25^\circ	ext{C}$$, what fraction of collisions have enough energy to react? Use $$R = 8.314\ 	ext{J/mol}\cdot	ext{K}$$ and $$T = 298\ 	ext{K}.$$

Accepted Answer

$$f = e$$^{-E_a/RT}$$ = e$$^{-40000/(8.314 	imes 298)}$$ = 9.7 	imes 10$$^{-8}$$

Question 14

Which of the following plots would yield a straight line for a first-order reaction?

Accepted Answer

A plot of $$\ln [A] vs$$. $$t$$

Question 15

For a reaction with the rate law $$	ext{Rate} = k[	ext{A}]^0$$, which of the following statements is true?

Accepted Answer

The rate is independent of the concentration of A.

Question 16

A certain pesticide degrades in the environment with a half-life of 10 years. How many years will it take for the concentration to decrease to $$1/16 of $$its original value?

Accepted Answer

40 years

Question 17

Which of the following is NOT a requirement for a chemical reaction to occur according to collision theory?

Accepted Answer

Molecules must be in the gas phase.

Chapter 14: Chemical Kinetics and Reaction Rates

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