Q: Americium-241 ($$^{241}\mathrm{Am}) is $$used in smoke detectors and decays by emitting alpha particles with a half-life of 432.6 years. What is the rate constant $$k$$ for this decay, and what are its units?

$$k = \frac{0.693}{432.6\ \mathrm{years}} = 1.60 \times 10$$^{-3}$$\ \mathrm{years}^{-1}$$; units: $$\mathrm{years}^{-1}$$

Q: A smoke detector contains 1.00 $$\muCi of$$ $$^{241}\mathrm{Am}. $$How much activity remains after 30.0 years? Use $$k = 1.60 \times 10$$^{-3}$$\ \mathrm{years}^{-1}.$$

$$A = 1.00\ \mu\mathrm{Ci} \times e$$^{-1.60 \times 10^{-3}$$ \times 30.0} = 0.953\ \mu\mathrm{Ci}$$

Question 1

Americium-241 ($$^{241}\mathrm{Am}) is $$used in smoke detectors and decays by emitting alpha particles with a half-life of 432.6 years. What is the rate constant $$k$$ for this decay, and what are its units?

Accepted Answer

$$k = \frac{0.693}{432.6\ \mathrm{years}} = 1.60 	imes 10$$^{-3}$$\ \mathrm{years}^{-1}$$; units: $$\mathrm{years}^{-1}$$

Question 2

A smoke detector contains 1.00 $$\muCi of$$ $$^{241}\mathrm{Am}. $$How much activity remains after 30.0 years? Use $$k = 1.60 	imes 10$$^{-3}$$\ \mathrm{years}^{-1}.$$

Accepted Answer

$$A = 1.00\ \mu\mathrm{Ci} 	imes e$$^{-1.60 	imes 10^{-3}$$ 	imes 30.0} = 0.953\ \mu\mathrm{Ci}$$

Question 3

For a first-order reaction, which of the following correctly expresses the half-life $$t_{1/2} in $$terms of the rate constant $$k$$?

Accepted Answer

$$t_{1/2} = \frac{0.693}{k}$$

Question 4

A reaction $$3A \rightarrow 2B + C is $$monitored, and a plot of $$1/[A] vs. $$time is linear. What is the order of the reaction with respect to $$A$$?

Accepted Answer

Second order

Question 5

Given the rate law $$	ext{rate} = k[S_8$]^2$$ for the reaction $$2Al + S_8$ ightarrow Al_2S_3$$, what happens to the rate if the concentration of $$S_8 is $$tripled?

Accepted Answer

The rate increases by a factor of 9

Question 6

Which of the following statements about reaction mechanisms is TRUE?

Accepted Answer

A bimolecular step involves two reactant molecules colliding in a single step.

Question 7

For a reaction with the rate law $$	ext{rate} = k[N_2$][H_2$]^2[Fe]$$, what is the overall order of the reaction?

Accepted Answer

Fourth order

Question 8

The activation energy for a reaction is $$36.8\ \mathrm{kJ/mol}. If $$the rate constant at $$18.3^\circ\mathrm{C} is$$ $$k_1$$, what equation would you use to calculate the rate constant $$k_2 at$$ $$35.4^\circ\mathrm{C}$$?

Accepted Answer

$$\ln\left(\frac{k_1$}{k_2$}\right) = \frac{E_a}{R}\left(\frac{1}{T_2$} - \frac{1}{T_1$}\right)$$

Question 9

Which of the following is a requirement for an effective collision between reactant molecules?

Accepted Answer

Sufficient energy and proper orientation

Question 10

In the mechanism for ammonia synthesis, $$Fe$$ acts as a catalyst. Which of the following best describes the role of a catalyst in a reaction mechanism?

Accepted Answer

It is present at the start and end of the reaction, but is not consumed.

Question 11

For a zero-order reaction, what are the units of the rate constant $$k$$?

Accepted Answer

$$\mathrm{M}\,\mathrm{time}^{-1}$$

Question 12

Given the following mechanism:

$$Fe + N_2$ \rightarrow $$FeN_2$$
$$FeN_2$$ + H_2$ \rightarrow FeN_2H_2$$
$$FeN_2H_2 + H_2$ \rightarrow FeNH + NH_3$
$$FeNH + $$H_2$$ \rightarrow Fe + $$NH_3$$

Which species is an intermediate?

Accepted Answer

$$FeN_2$$

Question 13

For the reaction $$2Al + S_8$ ightarrow Al_2S_3$$ with $$	ext{rate} = k[S_8$]^2$$, what is the order with respect to $$Al$$?

Accepted Answer

Zero order

Question 14

A reaction has a rate law $$	ext{rate} = k[A]^2. If $$the initial concentration of $$A is$$ $$0.50\ \mathrm{M}$$, what is the half-life $$t_{1/2}$$?

Accepted Answer

$$t_{1/2} = \frac{1}{k[A]_0}$$

Question 15

Which of the following best explains why alpha particle sources in smoke detectors are considered safe for home use?

Accepted Answer

Alpha particles have very low penetration and are stopped by the plastic casing.

Question 16

For the exothermic reaction $$N_2 + 3H_2$$ \rightarrow 2NH_3$$ catalyzed by Fe$, which of the following would increase the rate of ammonia formation the most?

Accepted Answer

Increasing the concentration of $$H_2$$

Question 17

Which of the following is TRUE about the rate-determining step in a reaction mechanism?

Accepted Answer

It is the slowest step and limits the overall reaction rate.

Question 18

If the concentration of $$S_8 is $$quartered and $$Al is $$tripled in the reaction $$2Al + S_8$ ightarrow Al_2S_3$$ with $$	ext{rate} = k[S_8$]^2$$, what happens to the rate?

Accepted Answer

The rate decreases by a factor of 16

Question 19

Which of the following best describes the relationship between the slope of a linear plot and the rate constant for a first-order reaction?

Accepted Answer

The slope of $$\ln([A]) vs. $$time is $$-k$$

Question 20

Which of the following is a correct statement about enzymes in biological systems?

Accepted Answer

Enzymes are catalysts and substrates are reactants.

General Chemistry II Exam 2 Study Guidance: Kinetics, Radioactivity, and Reaction Mechanisms

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