Chemistry 192 Problem Set 11 Spring, 2020

1. In problem set 10 we found the reaction

2N2O5(g) −→ 4NO2(g) + O2(g)

−1 to be ﬁrst order in N2O5 with a rate constant 0.174 min at 298K. If the concentration of N2O5 is 0.357 M at time t = 0, determine that time at which the concentration of N2O5 would be 0.100 M. 2. Problem 23, page 968, textbook.

3. The gas-phase decomposition of sulfuryl chloride into sulfur dioxdie and chlorine gas proceeds according to the reaction

SO2Cl2(g) −→ SO2(g) + Cl2(g)

and is ﬁrst order in SO2Cl2. At time t = 0 pure SO2Cl2 is placed in a reaction vessel, and the total pressure is measured to be 1.107 bar. As a function of time the following data are obtained for the total pressure as a function of time

Time (hours) 0 3.00 Pressure (bar) 1.107 1.479

Calculate the rate constant for the reaction.

4. Nitrogen pentoxide decomposes according to the reaction

2N2O5(g) −→ 4NO2(g) + O2(g)

This reaction is found to be ﬁrst order with respect to N2O5(g) with a rate constant k = 4.8 × 10−4s−1.

(a) What is the half-life of the reaction?

1 (b) Initially, 1.0 bar of pure N2O5(g) are introduced into a reaction vessel. Calculate the total pressure in the vessel after 1000 seconds.

5. In the gas phase at 470.K, acetic anhydride [(CH3CO)2O] decomposes into ethenone (C2H2O) and acetic acid (CH3COOH) according to the balanced reaction

(CH3CO)2O(g) −→ C2H2O(g) + CH3COOH(g).

The decomposition of acetic anhydride obeys ﬁrst-order kinetics with a rate constant k = 2.90 × 10−4 s−1 at 470.K. Pure gas-phase acetic anhydride is placed in a container of ﬁxed volume at 470.K and the initial pressure is measured to be 2.25 bar. Calculate the total pressure in the container after 1000. seconds has elapsed.

6. The gas-phase decomposition of ethylene oxide into gas-phase methane and carbon monoxide C2H4O(g) −→ CH4(g) + CO(g) −4 −1 is found to be first order in C2H4O with a rate constant k = 2.05×10 s at 298K. A container of fixed volume is filled with pure C2H4O. After the decomposition reaction proceeds for 1253. seconds the total pressure in the container is found to be PT =3.09 bar. Calculate the initial pressure in the container before the reaction has begun.

7. The gas-phase decomposition reaction of nitrous oxide (laughing gas) 1 N O −→ N + O 2 (g) 2(g) 2 2(g)

is first-order in N2O; i.e. R = k[N2O], where R is the rate. At 1000.K, pure nitrous oxide is placed in a container of fixed volume with an initial total pressure of 1.00 bar. After 2.00 seconds, the total pressure rises to 1.39 bar. Calculate the first-order rate constant for the decomposition of nitrous oxide at 1000.K.

8. The reaction

CH3CH(OH)CHCH2 −→ H2O + CH3CHCHCH2

is found to be ﬁrst order in CH3CH(OH)CHCH2 with an activation energy of 241 kJ mol−1. By what factor is the rate of this reaction increased if the temperature is raised from 25◦C to 100◦C?

9. The decomposition of ethylene oxide into methane and carbon dioxide in the gas phase

(CH2)2O(g) −→ CH4(G) + CO(g)

3 is found to follow ﬁrst-order kinetics with a half life of t1/2 = 3.38 × 10 s at 688. K 2 and a half life of t1/2 = 1.53 × 10 s at 750.K. Assuming Arrhenius behavior calculate the activation energy and the pre-exponential for the reaction.

2 10. For the reaction at 508K

HI(g) −→ 1/2H2(g) + 1/2I2(g)

the half-life is 135 minutes when the initial HI pressure is .1 bar and 13.5 minutes when the pressure is 1.0 bar. Show that the reaction is second order.

11. The gas-phase reaction

NO2(g) + CO(g) −→ NO(g) + CO2(g)

obeys second-order kinetics d[NO ] − 2 = k[NO ]2. dt 2 At 298.K the half life of nitrogen dioxide is measured to be 0.198 minutes when the initial concentration is 2.00 M and the half life is measured to be 7.00 ×10−2 minutes at 310.K when the initial concentration is 3.00 M. Calculate the activation energy of the reaction and determine the pre-exponential.

12. The decomposition of sulfuryl chloride in the gas phase

SO2Cl2(g) −→ SO2(g) + Cl2(g)

5 ◦ 2 is ﬁrst order in SO2Cl2 with measured half lives of 2.3 × 10 s at 600. K and 5.4 × 10 s at 700.◦K. Calculate the activation energy for the reaction.

13. The rate law for the gas-phase reaction

NO2(g) + CO(g) −→ NO(g) + CO2(g)

is d[NO ] − 2 = k[NO ]2. dt 2 At 350K the rate constant for the reaction is measured to be 29.0 M−1min−1 and at −1 −1 375K the rate constant is found to be 73.7 M min . Calculate the half life of NO2 for the reaction at T =362K when the initial concentration of NO2 is 2.75 M. 14. The gas-phase reaction N2O4(g) −→ 2NO2(g)

is ﬁrst order in dinitrogen tetroxide, N2O4. The half life of dinitrogen tetroxide is 1.36 ×10−7 s at 303K and 3.61 × 10−8 s at 323 K. A container is ﬁlled with pure dinitrogen tetroxide gas at 315 K with an initial concentration of 2.50 M. Calculate −7 the concentration of NO2(g) at 315 K, 1.00 × 10 s after the pure N2O4 gas has been placed in the container.

3 15. What activation energy implies a reaction rate to be doubled for a 10◦C temperature rise from 25◦C to 35◦C?

16. The reaction 2O3(g) −→ 3O2(g) is believed to follow the following mechanism:

k1 O3(g) −→ O2(g) + Og

k−1 O2(g) + Og −→ O3(g)

k O3(g) + O(g) −→ 2O2(g) (slow) Use the steady-state approximation for the concentration of O to determine the rate law implied by this mechanism. What is the order of the reaction and the molecularity of the slow step?

17. The proposed mechanism for the gas-phase reaction

2NO(g) + H2(g) −→ N2O(g) + H2O(g)

is k1 fast 2NO(g) −→ N2O2(g)

k−1 fast N2O2(g) −→ 2NO(g)

k2 slow N2O2(g) + H2(g) −→ N2O(g) + H2O(g). Derive the rate law associated with the mechanism, and simplify the rate law using the relation k−1 >> k2[H2]. Give the order of the reaction and the molecularity of the slow step.

18. The gas-phase reaction 1 N O −→ 2NO + O 2 5(g) 2(g) 2 2(g) is believed to occur by the following mechanism:

k1 N2O5(g) −→ NO2(g) + NO3(g) (fast)

k−1 NO2(g) + NO3(g) −→ N2O5(g) (fast)

k2 NO2(g) + NO3(g) −→ NO2(g) + O2(g) + NO(g) (slow)

k3 NO(g) + N2O5(g) −→ 3NO2(g) (fast). Derive the rate law associated with this mechanism.

4 19. A proposed mechanism for the balanced gas-phase reaction

2NO(g) + O2(g)) −→ 2NO2(g)

is k1 NO(g) + O2(g) −→ NO3(g) fast

k−1 NO3(g) −→ NO(g) + O2(g) fast

k2 NO(g) + NO3(g) −→ 2NO2(g) slow Use the steady-state approximation on the reactive intermediate to deduce the rate law implied by the proposed mechanism.