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Kinetics: Rates of Reactions

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1. The rate of formation of oxygen in the reaction

2N2O5(g) −−> 4NO2(g) + O2(g)

is 2.28 (mol O2)*L-1*s-1. What is the rate at which N2O5 is used?

A) -9.12 (mol N2O5)*L-1*s-1

B) -1.14 (mol N2O5)*L-1*s-1

C) -4.56 (mol N2O5)*L-1*s-1

D) -0.57 (mol N2O5)*L-1*s-1

E) -2.28 (mol N2O5)*L-1*s-1

2. The rate of formation of oxygen in the reaction

2N2O5(g) −−> 4NO2(g) + O2(g)

is 1.45 (mol O2)*L-1*s-1. What is the rate at which N2O5 is used?

A) -1.45 (mol N2O5)*L-1*s-1

B) -0.725 (mol N2O5)*L-1*s-1

C) -2.90 (mol N2O5)*L-1*s-1

D) -5.80 (mol N2O5)*L-1*s-1

E) -1.45 (mol N2O5)*L-1*s-1

3. Given:

2NO2(g) + F2(g) −−> 2NO2F(g) rate = -Δ[F2]/Δt

The rate of the reaction can also be expressed as

A) Δ[NO2F]/Δt

B) -Δ[NO2]/Δt

C) -2Δ[NO2]/Δt

D) 1/2Δ[NO2F]/Δt

E) 1/2Δ[NO2]/Δt

4. For the reaction

2NO2(g) −−> 2NO(g) + O2(g)

initial rate = k[NO2]o2. For concentration in M and time in s, the units of the rate constant k are

A) M-2*s-1

B) M-1*s-1

C) s-1

D) M2*s-1

E) M*s-1

5. Given:

2N2O5(g) −−> 4NO2(g) + O2(g) rate = k[N2O5]

The overall order of the reaction is

A) 1

B) 0

C) 2

D) 3

E) 7

6. Given:

4Fe2+(aq) + O2(aq) + 2H2O(l) −−> 4Fe3+(aq) + 4OH-(aq) rate = k[Fe2+][OH-]2[O2]

The overall order of the reaction and the order with respect to O2 are

A) 4 and 2.

B) 4 and 1.

C) 5 and 1.

D) 3 and 1.

E) 7 and 1.

7. Given:

2A(g) + B(g) −−> C(g) + D(g)

When [A] = [B] = 0.10 M, the rate is 2.0 M*s-1; for [A] = [B] = 0.20 M, the rate is 8.0 M*s-1; and for [A] = 0.10 M, [B] = 0.20 M, the rate is 2.0 M*s-1. The order of the reaction is

A) 2

B) 4

C) 1

D) 0

E) 1.5

8. If the rate of a reaction increases by a factor of 64 when the concentration of reactant increases by a factor of 4, the order of the reaction with respect to this reactant is

A) 3

B) 4

C) 2

D) 16

E) 1

9. For the reaction

2A + B −−> products

determine the overall order of the reaction given the following data:

Initial Concentration, M Initial Rate, M*s-1

A B

0.10 0.10 2.0 ∗ 10-2

0.20 0.10 8.0 ∗ 10-2

0.30 0.10 1.8 ∗ 10-1

0.20 0.20 8.0 ∗ 10-2

0.30 0.30 1.8 ∗ 10-1

A) 2

B) 3

C) 0

D) 1

E) 1.5

10. If the rate of reaction increases by a factor of 2.3 when the concentration of reactant increases by a factor of 1.5, the order of the reaction with respect to this reactant is

A) 2

B) 1

C) 3

D) 4

E) 1.5

11. The reaction

2NO(g) + 2H2(g) −−> N2(g) + 2H2O(g)

is first-order in H2 and second-order in NO. Starting with equal concentrations of H2 and NO, the rate after 50% of the H2 has reacted is what percent of the initial rate?

A) 12.5%

B) 25.0%

C) 37.5%

D) 18.8%

E) 50.0%

12. The reaction

2NO(g) + Br2(g) −−> 2NOBr(g)

is second-order in NO and first-order in Br2. If the initial concentrations of NO and Br2 are 0.0200 M and 0.0100 M, respectively, the rate after 50% of the Br2 has reacted is what percent of the initial rate?

A) 12.5%

B) 37.5%

C) 18.8%

D) 2.50%

E) 50.0%

13. For the reaction

C2H6(g) −−> 2CH3(g) rate = k[C2H6]

If k = 5.50 ∗ 10-4 s-1 and [C2H6]initial = 0.0200 M, calculate the rate of reaction after 1 hour.

A) The rate of reaction is zero since the reaction is complete.

B) 1.52 ∗ 10-6 M*s-1

C) 5.50 ∗ 10-4 M*s-1

D) 2.76 ∗ 10-3 M*s-1

E) 1.10 ∗ 10-5 M*s-1

14. Consider the following:

2A −−> A2 rate = k[A]2

If the rate constant is 1.43 M-1*s-1 and the initial concentration of A is 0.0180 M, calculate the time for the rate of consumption of A to drop to 1.25 ∗ 10-5 M*s-1.

A) 80.0 s

B) 197 s

C) 236 s

D) 159 s

E) 99.0 s

15. Given: 4PH3(g) −−> P4(g) + 6H2(g) rate = k[PH3]

If the rate constant is 0.0278 s-1, calculate the percent of the original PH3 which has reacted after 76.0 s.

A) 87.9%

B) 12.1%

C) 47.3%

D) 97.9%

E) 2.10%

16. Consider the following reaction:

2N2O(g) −−> 2N2(g) + O2(g) rate = k[N2O]

For an initial concentration of N2O of 0.50 M, calculate the concentration of N2O remaining after 2.0 min if k = 3.4 ∗ 10-3 s-1.

A) 0.17 M

B) 0.66 M

C) 0.33 M

D) 0.55 M

E) 0.50 M

17. Consider the following reaction:

2N2O(g) −−> 2N2(g) + O2(g) rate = k[N2O]

For an initial concentration of N2O of 0.50 M, calculate the concentration of N2O remaining after 1.0 min if k = 3.4 ∗ 10-3 s-1.

A) 0.50 M

B) 0.63 M

C) 0.82 M

D) 0.41 M

E) 0.31 M

18. Consider the following reaction:

2N2O(g) −−> 2N2(g) + O2(g) rate = k[N2O]

For an initial concentration of N2O of 0.50 M, calculate the concentration of N2O remaining after 2 min if k = 6.8 ∗ 10-3 s-1.

A) 0.30 M

B) 0.49 M

C) 0.44 M

D) 0.22 M

E) 0.15 M

19. A first-order reaction has a rate constant of 0.00300 s-1. The time required for 75% reaction is

A) 231 s

B) 201 s

C) 41.7 s

D) 462 s

E) 95.9 s

20. A first-order reaction has a rate constant of 0.00300 s-1. The time required for 85% reaction is

A) 23.5 s

B) 316 s

C) 632 s

D) 54.2 s

E) 275 s

21. For a first-order reaction, after 230 s, 10% of the reactants remain. Calculate the rate 2222constant for the reaction.

A) 0.000458 s-1

B) 0.510 s-1

C) 0.0195 s-1

D) 100 s-1

E) 0.0100 s-1

22. For a first-order reaction, after 2.00 min, 20% of the reactants remain. Calculate the rate constant for the reaction.

A) 0.00186 s-1

B) 0.00582 s-1

C) 0.0134 s-1

D) 0.000808 s-1

E) 74.6 s-1

23. For a first-order reaction, after 5.00 s, 10% of the reactants remain. Calculate the rate constant for the reaction.

A) 2.17 s-1

B) 0.00915 s-1

C) 0.200 s-1

D) 0.461 s-1

E) 0.0211 s-1

24. Consider the following reaction:

2N2O5(g) −−> 4NO2(g) + O2(g) rate = k[N2O5]

Calculate the time for the concentration of N2O5 to fall to one-fourth its initial value if the rate constant for the reaction is 5.20 ∗ 10-3 s-1.

A) 66.6 s

B) 267 s

C) 33.3 s

D) 533 s

E) 133 s

25. Consider the following reaction:

2N2O5(g) −−> 4NO2(g) + O2(g) rate = k[N2O5]

Calculate the time for the concentration of N2O5 to fall to one-sixth its initial value if the rate constant for the reaction is 5.20 ∗ 10-3 s-1.

A) 2070 s

B) 800 s

C) 22.2 s

D) 345 s

E) 57.4 s

26. Given: SO2Cl2(g) −−> SO2(g) + Cl2(g) rate = k[SO2Cl2]

If 70% of the SO2Cl2 has reacted after 80 s, calculate the rate constant.

A) 0.0053 s-1

B) 5.3 s-1

C) 0.0045 s-1

D) 0.015 s-1

E) 0.029 s-1

27. The following data were obtained for the disappearance of A at 25oC:

[A], M Time, s

0.090 0

0.069 5

0.054 10

0.042 15

0.032 20

0.025 25

0.019 30

What is the order of the reaction and the rate constant?

28. The following data were obtained for the disappearance of A at 44.3oC:

[A], M Time, s

0.568 30

0.509 70

0.443 120

0.337 220

0.257 320

0.193 420

0.127 570

Determine the order of this reaction, and calculate the rate constant and half-life.

29. Given: 2H2O2(aq) −−> 2H2O(l) + O2(g) rate = k[H2O2]

If 75% of the H2O2 has reacted after 40 min, calculate the rate constant.

A) 0.0072 s-1

B) 0.035 s-1

C) 0.069 s-1

D) 0.000012 s-1

E) 0.00058 s-1

30. Given: A −−> P rate = k[A]

If 20% of A reacts in 5.12 min, calculate the time required for 60% of A to react.

A) 30.7 min

B) 21.0 min

C) 48.3 min

D) 11.7 min

E) 15.4 min

31. Consider the following reaction:

2N2O(g) −−> 2NO(g) + O2(g) rate = k[N2O]

If 46% of N2O reacts in 1.0 s, what is the rate constant?

A) 0.78 s-1

B) 0.34 s-1

C) 0.62 s-1

D) 3.8 s-1

E) 0.27 s-1

32. For the reaction

cyclopropane −−> propene

a plot of ln[cyclopropane] versus time in seconds gives a straight line with slope -2.8 ∗ 10-4 s-1 at 500oC. What is the rate constant for this reaction?

A) 5.6 ∗ 10-4 s-1

B) 1.7 ∗ 10-2 s-1

C) 1.2 ∗ 10-4 s-1

D) 6.4 ∗ 10-4 s-1

E) 2.8 ∗ 10-4 s-1

33. For the first-order reaction

2N2O(g) −−> 2NO(g) + O2(g)

the rate constant is 3.4 s-1. Calculate the percent N2O remaining after 1 second.

A) 3.3%

B) 30%

C) 87%

D) 20%

E) 66%

34. For the first-order reaction

2N2O(g) −−> 2NO(g) + O2(g)

the rate constant is 3.4 s-1. The time required for 75% reaction is

A) 85 ms

B) 0.41 s

C) 37 ms

D) 0.18 s

E) 2.6 s

35. A first-order reaction has a rate constant of 26 s-1. If the initial concentration of reactant is 0.082 M, how long will it take for the reactant to reach 0.0010 M?

A) 0.074 s

B) 2.2 s

C) 0.097 s

D) 0.038 s

E) 0.17 s

36. Consider the following reaction:

2N2O5(g) −−> 4NO2(g) + O2(g) rate = k[N2O5]

If the initial concentration of N2O5 is 0.80 M, the concentration after 2 half-lives is

A) 0.55 M

B) 0.20 M

C) 0.35 M

D) 0.40 M

E) 0.28 M

37. Consider the following reaction:

2N2O5(g) −−> 4NO2(g) + O2(g) rate = k[N2O5]

If the initial concentration of N2O5 is 0.80 M, the concentration after 4 half-lives is

A) 0.10 M

B) 0.20 M

C) 0.063 M

D) 0.050 M

E) 0.025 M

38. A compound decomposes with a half-life of 8.0 s and the half-life is independent of the concentration. How long does it take for the concentration to decrease to one-sixteenth of its initial value?

A) 24 s

B) 32 s

C) 40 s

D) 130 s

E) 64 s

39. For a first-order reaction, what fraction of the starting material will remain after 4 half-

lives?

A) 1/16

B) 1/9

C) 1/4

D) 1/8

E) 1/3

40. A first-order reaction has a half-life of 1.10 s. If the initial concentration of reactant is 0.142 M, how long will it take for the reactant concentration to reach 0.00100 M?

A) 0.127 s

B) 4.50 s

C) 7.87 s

D) 1.59 s

E) 3.09 s

41. A first-order reaction has a rate constant of 0.021 s-1. What is the half-life for this reaction?

A) 0.69 s

B) 0.015 s

C) 14 s

D) 33 s

E) 0.030 s

42. Given: 2A + B −−> P rate = k[A]

Which of the following is true?

A) The overall order of the reaction is 3.

B) t1/2 = 0.693/k

C) [A] = 1/(k ∗ t1/2)

D) 1/[A] = kt

E) ln[A] = k/t

43. For a first-order reaction, a straight line is obtained from a plot of

A) ln(t) vs. [A]

B) [A] vs. t

C) 1/[A] vs. t

D) ln(1/t) vs. [A]

E) ln[A] vs. t

44. Given: 4PH3(g) −−> P4(g) + 6H2(g) rate = k[PH3]

If the rate constant for this reaction is 0.0278 s-1, what is the half-life?

A) 99.6 s

B) 36.0 s

C) 18.0 s

D) 24.9 s

E) 49.8 s

45. Consider the following reaction:

2N2O(g) −−> 2NO(g) + O2(g) rate = k[N2O]

If the half-time for the reaction is 910 ms, the rate constant is

A) 0.69 s-1

B) 1.3 s-1

C) 0.32 s-1

D) 0.76 s-1

E) 1.1 s-1

46. For a certain first-order reaction the rate constant is 0.92 s-1. What percent of reactant remains after 5 half-lives?

A) 3.1%

B) 6.3%

C) 25%

D) 74%

E) 2.5%

47. The rate law for the decomposition of hydrogen peroxide is

rate = k[H2O2]

If the half-life for this reaction is 7.0 min, what is the concentration of H2O2 after 10 minutes when the initial concentration of hydrogen peroxide is 0.20 M?

A) 0.027 M

B) 0.18 M

C) 0.14 M

D) 0.074 M

E) 0.043 M

48. Iodine-131 can be used to measure the activity of the thyroid gland. If the rate of decay of a sample containing I-131 is 2.15 ∗ 105 disintegrations per minute initially, and 6.43 ∗ 104 disintegrations per minute after 2 weeks, calculate the half-life of I-131.

A) 9.70 days

B) 18.5 days

C) 14.0 days

D) 4.02 days

E) 8.04 days

49. An "old rock" was found to have 395 C-14 disintegrations per hour and a contemporary rock 503 C-14 disintegrations per hour. If the half-life of C-14 is 5.73 ∗ 103 years, estimate the age of the "old rock." The decay of C-14 is first-order.

A) 10800 years

B) 8260 years

C) 1230 years

D) 4500 years

E) 2000 years

50. The isotope I-131 has a half-life of 8.05 days. What fraction of the initial concentration of iodine-131 remains after 3 weeks. The decay of I-131 is first-order.

A) 0.164

B) 0.836

C) 0.0861

D) 0.124

E) 0.383

51. A second-order reaction has a rate constant of 1.25 M-1*s-1. If the initial reactant concentration is 1.0 M, calculate the time required for 90% reaction.

A) 0.13 s

B) 17 s

C) 7.2 s

D) 0.89 s

E) 1.3 s