Chapter 12: Chemical Kinetics

Chapter 12: Chemical Kinetics

1. Distinguish among the initial rate, average rate, and instantaneous rate of a chemical reaction. Which of these rates usually has the largest value?

2. In the Haber process for the production of ammonia,

N2 (g) + 3H2 (g) → 2NH3 (g)

what is the relationship between the rate of production of ammonia and the rate of consumption of hydrogen?(ΔNH3 = -2/3 ΔH2)

3. What are the units for each of the following if the concentrations are expressed in moles per liter and the time in seconds?

a. rate of a chemical reaction

b. rate constant for a zero-order rate law

c. . rate constant for a first-order rate law

d. . rate constant for a second-order rate law

e. . rate constant for a third-order rate law

4. The rate law for the reaction

Cl2 (g) + CHCl3 (g) → HCl(g) + CCl4 (g)

is rate = k[Cl2]1/2[CHCl3]

What are the units for k, assuming time in seconds and concentration in mol/L?

5. The reaction

2NO(g) + Cl2 (g) → 2NOCl(g)

was studied at -10°C. The following results were obtained, where

Rate = -Δ[Cl2]

Δt

Initial Rate

[NO]0 (mol/L) [Cl2]0 (mol/L) (mol/L • min)

0.10 0.10 0.18

0.10 0.20 0.36

0.20 0.20 1.45

a. What is the rate law?

b. What is the value of the rate constant? (180)

6. The decomposition of nitrosyl chloride was studied:

2NOCl(g) ↔ 2NO(g) + Cl2 (g)

was studied at 25°C. The following results were obtained, where

Rate = -Δ[NOCl]

Δt

[NOCl0] Initial Rate

(molecules/cm3) (molecules/cm3 * s)

3.0* 1016 5.98* 104

2.0* 1016 2.66* 104

1.0* 1016 6.64* 103

4.0* 1016 1.06* 105

a. What is the rate law?

b. Calculate the value of the rate constant.(6.6 * 10-29)

c. Calculate the rate constant for the concentrations given in moles per lliter.(4.0 * 10-8)

7.The rate of the reaction between hemoglobin (Hb) and carbon monoxide (CO) was studied at 20.°C. The following data were collected with all concentration unites in µmol/L. A hemoglobin concentration of 2.21 µmol/L is equal to 2.21 * 10-6mol/L.)

[Hb]0 [CO]0 Initial Rate

(µmol/L) (µmol/L) (µmol/L *s)

2.21 1.00 0.619

4.42 1.00 1.24

4.42 3.00 3.71

a. Determine the orders of this reaction with respect to Hb and CO.

b. Determine the rate law.

c. Calculate the value of the rate constant.(0.280)

d. What would be the initial rate for an experiment with [Hb]0 = 3.36 µmol/L and [CO]0 = 2.40 µmol/L?

8. The decomposition of ethanol (C2H5OH) on an alumina (Al2O3) surface

C2H5OH(g) → C2H4 (g) + H2O (g)

was studied at 600 K. Concentration versus time data were collected for this reaction, and a plot of [A] versus time resulted in a straight line with a slope of -4.00 * 105mol/L * s.

a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction.(k = 4.00 * 10-5 )

b. If the initial concentration of was .00125 M, calculate the half-life for this reaction.(156 s)

c. How much time is required for all .00125 M of the C2H5OH to decompose?(313 s)

9. Experimental data for the reaction

A 2B + C

have been plotted in the following three ways (with concentration units of M).

What is the order of the reaction with respect to A and what is the initial concentration of A?

10. The radioactive isotope 32P decays by first-order kinetics and has a half-life of 14.3 days. How long does it take for 95.0% of a sample of 32P to decay?(62 days)

11. A first-order reaction is 38.5% complete in 480. s.

a. Calculate the rate constant.(1.01 * 10-3)

b. What is the value of the half-life?(686 s)

c. How long will it take for the reaction to go to 25%, 75%, and 95% completion?(280, 1370, 3000 s)

12. The rate law for the reaction

2NOBr (g) → 2NO(g) + Br2 (g)

at some temperature is

Rate = -Δ[NOBr] = k[NOBr]2

Δt

a. If the half-life for this reaction is 2.00 s when [NOBr]0 = 0.900 M, calculate the value of k for this reaction.(0.555)

b. How much time is required for the concentration of NOBr to decrease .100 M?(16 s)

13. Write the rate laws for the following elementary reactions.

a. CH3NC(g)→ CH3CN(g)

b. O3 (g) + NO(g)→ O2 (g) + NO2 (g)

c. O3 (g)→ O2 (g) + O (g)

d.O3 (g) + O (g)→ 2O2 (g)

14. A proposed mechanism for a reaction is

C4H9Br → C4H9+ + Br- (slow)

C4H9+ + H2O → C4H9OH2+ (fast)

C4H9OH2+ + H2O →C4H9OH +H3O+ (fast)

Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction? What are the intermediates in the proposed mechanism?

15. The mechanism for the reaction of nitrogen dioxide with carbon monoxide to form nitric oxide and carbon dioxide is thought to be

NO2 + NO2 → NO3 + NO

NO3 + CO → NO2 + CO2

Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction?

16. Each of the statements given below is false. Explain why.

a. The activation energy of a reaction depends on the overall energy change (ΔE) for the reaction.

b. The rate law for a reaction can be deduced from examination of the overall balanced equation for the reaction.

c. Most reactions occur by one-step mechanisms.

17. Draw a rough sketch of the energy profile for each of the following cases:

a. ΔE = +10 kJ/mol, Ea = 25 kJ/mol

b. ΔE = -10 kJ/mol, Ea = 50 kJ/mol

c. ΔE = -50 kJ/mol, Ea = 50 kJ/mol

18. The reaction

(CH3)3CBr + OH-→ (CH3)3COH + Br-

in a certain solvent is first order with respect to (CH3)3CBr and zero order with respect to OH-. In several experiments, the rate constant k was determined at different temperatures. A plot of ln(k) vs. 1/T was constructed resulting in a straight line with a slope value of -1.10 * 104 K and a y-intercept of 33.5. Assume k has units of s-1.

a. Determine the Ea for this reaction.(91.5 kJ / mol)

b. Determine the value of the frequency factor A.(3.54 * 1014)

c. Calculate the value of k at 25°C.(.00324)

19. At 25°C the first-order rate constant for a reaction is 2.0 * 103 s-1. The activation energy is 15.0 kJ/mol. What is the value of the rate constant at 75°C?(4800)

20. Why does a catalyst increase the rate of a reaction? What is the difference between a homogenous and heterogeneous catalyst? Would a given reaction necessarily have the same rate law for both a catalyzed and an uncatalyzed pathway? Explain.

21. One mechanism for the destruction of ozone in the upper atmosphere is

O3 (g) + NO(g) → NO2 (g) + O2 (g) (slow)

NO2 (g) + O(g) → NO(g) + O2 (g) (fast)

O3 (g) + O(g) → O2 (g) (overall)

a. Which species is a catalyst?

b. Which species is an intermediate?

c. Ea for the uncatalyzed reaction

O3 (g) + O(g) → O2 (g)

is 14.0 kJ. Ea for the same reaction when catalyzed is 11.9 kJ. What is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at 25°C? Assume that the frequency factor A is the same for each reaction.(2.3 * faster)

22. Most reactions occur by a series of steps. The energy profile for a certain reaction that proceeds by a two-step mechanism is:

On the energy profile, indicate

a. The positions of reactants and products

b. The activation energy for the overall reaction

c. ΔE for the reaction

d. Which point on the plot represents the energy of the intermediate in the two-step reaction?

e. Which step in the mechanism for this reaction is rate determining, the first or the second step? Explain.