Chemistry End of Chapter Exercises

1. Describe how graphical methods can be used to determine the order of a reaction and its rate constant from a series of data that includes the concentration of A at varying times.
2. Use the data provided to graphically determine the order and rate constant of the following reaction: [latex]\text{SO}_2\text{Cl}_2\;{\longrightarrow}\;\text{SO}_2\;+\;\text{Cl}_2[/latex]
   

   Time (s)	0	5.00 × 103	1.00 × 104	1.50 × 104
   [SO2Cl2] (M)	0.100	0.0896	0.0802	0.0719
   Time (s)	2.50 × 104	3.00 × 104	4.00 × 104
   [SO2Cl2] (M)	0.0577	0.0517	0.0415
   Table 23.

3. Use the data provided in a graphical method to determine the order and rate constant of the following reaction:
   [latex]2P\;{\longrightarrow}\;Q\;+\;W[/latex]

   Time (s)	9.0	13.0	18.0	22.0	25.0
   [P] (M)	1.077 × 10−3	1.068 × 10−3	1.055 × 10−3	1.046 × 10−3	1.039 × 10−3
   Table 24.

4. Pure ozone decomposes slowly to oxygen, [latex]2\text{O}_3(g)\;{\longrightarrow}\;3\text{O}_2(g)[/latex]. Use the data provided in a graphical method and determine the order and rate constant of the reaction.
   

   Time (h)	0	2.0 × 103	7.6 × 103	1.00 × 104
   [O3] (M)	1.00 × 10−5	4.98 × 10−6	2.07 × 10−6	1.66 × 10−6
   Time (h)	1.23 × 104	1.43 × 104	1.70 × 104
   [O3] (M)	1.39 × 10−6	1.22 × 10−6	1.05 × 10−6
   Table 25.

5. From the given data, use a graphical method to determine the order and rate constant of the following reaction:
   [latex]2X\;{\longrightarrow}\;Y\;+\;Z[/latex]

   Time (s)	5.0	10.0	15.0	20.0	25.0	30.0	35.0	40.0
   [X] (M)	0.0990	0.0497	0.0332	0.0249	0.0200	0.0166	0.0143	0.0125
   Table 26.

6. What is the half-life for the first-order decay of phosphorus-32? ([latex]_{15}^{32}\text{P}\;{\longrightarrow}\;_{16}^{32}\text{S}\;+\;\text{e}^{-})[/latex]. The rate constant for the decay is 4.85 × 10⁻² day⁻¹.
7. What is the half-life for the first-order decay of carbon-14? [latex](_6^{14}\text{C}\;{\longrightarrow}\;_7^{14}\text{N}\;+\;\text{e}^{-})[/latex] The rate constant for the decay is 1.21 × 10⁻⁴ year⁻¹.
8. What is the half-life for the decomposition of NOCl when the concentration of NOCl is 0.15 M? The rate constant for this second-order reaction is 8.0 × 10⁻⁸ L/mol/s.
9. What is the half-life for the decomposition of O₃ when the concentration of O₃ is 2.35 × 10⁻⁶M? The rate constant for this second-order reaction is 50.4 L/mol/h.
10. The reaction of compound  A to give compounds  C and  D was found to be second-order in  A. The rate constant for the reaction was determined to be 2.42 L/mol/s. If the initial concentration is 0.500 mol/L, what is the value of t_1/2?
11. The half-life of a reaction of compound A to give compounds D and E is 8.50 min when the initial concentration of A is 0.150 mol/L. How long will it take for the concentration to drop to 0.0300 mol/L if the reaction is (a) first order with respect to A or (b) second order with respect to A?
12. Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of 3 × 10⁴ g/mol that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalyzed reactions can be complex, at low concentrations this reaction can be described by a rate equation that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: 1.0 L of a solution containing 0.15 µg (0.15 × 10⁻⁶ g) of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant.
    

    [Penicillin] (M)	Rate (mol/L/min)
    2.0 × 10−6	1.0 × 10−10
    3.0 × 10−6	1.5 × 10−10
    4.0 × 10−6	2.0 × 10−10
    Table 27.

13. Both technetium-99 and thallium-201 are used to image heart muscle in patients with suspected heart problems. The half-lives are 6 h and 73 h, respectively. What percent of the radioactivity would remain for each of the isotopes after 2 days (48 h)?
14. There are two molecules with the formula C₃H₆. Propene, [latex]\text{CH}_3\text{CH}=\text{CH}_2[/latex], is the monomer of the polymer polypropylene, which is used for indoor-outdoor carpets. Cyclopropane is used as an anesthetic:
    

    When heated to 499 °C, cyclopropane rearranges (isomerizes) and forms propene with a rate constant of

    5.95 × 10⁻⁴ s⁻¹. What is the half-life of this reaction? What fraction of the cyclopropane remains after 0.75 h at 499.5 °C?

15. Fluorine-18 is a radioactive isotope that decays by positron emission to form oxygen-18 with a half-life of 109.7 min. (A positron is a particle with the mass of an electron and a single unit of positive charge; the equation is [latex]_{518}^{9}\text{F}\;{\longrightarrow}\;_{18}^{8}\text{O}\;+\;\text{e}^{-}[/latex].) Physicians use ¹⁸F to study the brain by injecting a quantity of fluoro-substituted glucose into the blood of a patient. The glucose accumulates in the regions where the brain is active and needs nourishment.

    (a) What is the rate constant for the decomposition of fluorine-18?

    (b) If a sample of glucose containing radioactive fluorine-18 is injected into the blood, what percent of the radioactivity will remain after 5.59 h?

    (c) How long does it take for 99.99% of the ¹⁸F to decay?

16. Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for [latex]\frac{1}{64}[/latex] of the initial dose to remain in the athlete’s body?
17. Recently, the skeleton of King Richard III was found under a parking lot in England. If tissue samples from the skeleton contain about 93.79% of the carbon-14 expected in living tissue, what year did King Richard III die? The half-life for carbon-14 is 5730 years.
18. Nitroglycerine is an extremely sensitive explosive. In a series of carefully controlled experiments, samples of the explosive were heated to 160 °C and their first-order decomposition studied. Determine the average rate constants for each experiment using the following data:
    

    Initial [C3H5N3O9] (M)	4.88	3.52	2.29	1.81	5.33	4.05	2.95	1.72
    t (s)	300	300	300	300	180	180	180	180
    % Decomposed	52.0	52.9	53.2	53.9	34.6	35.9	36.0	35.4
    Table 28.

19. For the past 10 years, the unsaturated hydrocarbon 1,3-butadiene ([latex]\text{CH}_2=\text{CH}-\text{CH}=\text{CH}_2[/latex]) has ranked 38th among the top 50 industrial chemicals. It is used primarily for the manufacture of synthetic rubber. An isomer exists also as cyclobutene:
    

    The isomerization of cyclobutene to butadiene is first-order and the rate constant has been measured as 2.0 × 10⁻⁴ s⁻¹ at 150 °C in a 0.53-L flask. Determine the partial pressure of cyclobutene and its concentration after 30.0 minutes if an isomerization reaction is carried out at 150 °C with an initial pressure of 55 torr.