Unit 2 Kinetics

2.2 Exercises

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Section 2.2 Exercises

  1. Doubling the concentration of a reactant increases the rate of a reaction four times. With this knowledge, answer the following questions:

    (a) What is the order of the reaction with respect to that reactant?
    (b) Tripling the concentration of a different reactant increases the rate of a reaction three times. What is the order of the reaction with respect to that reactant?

  2. How much and in what direction will each of the following affect the rate of the reaction: [latex]\text{CO}(g)\;+\;\text{NO}_2(g)\;{\longrightarrow}\;\text{CO}_2(g)\;+\;\text{NO}(g)[/latex] if the rate law for the reaction is [latex]\text{rate} = k[\text{NO}_2]^2[/latex]?

    (a) Decreasing the pressure of NO2 from 0.50 atm to 0.250 atm.
    (b) Increasing the concentration of CO from 0.01 M to 0.03 M.

  3. Regular flights of supersonic aircraft in the stratosphere are of concern because such aircraft produce nitric oxide, NO, as a byproduct in the exhaust of their engines. Nitric oxide reacts with ozone, and it has been suggested that this could contribute to depletion of the ozone layer. The reaction [latex]\text{NO}\;+\;\text{O}_3\;{\longrightarrow}\;\text{NO}_2\;+\;\text{O}_2[/latex] is first order with respect to both NO and O3 with a rate constant of 2.20 × 107 L/mol/s. What is the instantaneous rate of disappearance of NO when [NO] = 3.3 × 10−6 M and [O3] = 5.9 × 10−7 M?
  4. The rate constant for the radioactive decay of 14C is 1.21 × 10−4 year−1. The products of the decay are nitrogen atoms and electrons (beta particles):
    [latex]_{14}^{6}\text{C}\;{\longrightarrow}\;_{14}^{6}\text{N}\;+\;\text{e}^{-}[/latex]
    [latex]\text{rate} = k[_{14}^{6}\text{C}][/latex]

    What is the instantaneous rate of production of N atoms in a sample with a carbon-14 content of 6.5 × 10−9 M?

  5. Alcohol is removed from the bloodstream by a series of metabolic reactions. The first reaction produces acetaldehyde; then other products are formed. The following data have been determined for the rate at which alcohol is removed from the blood of an average male, although individual rates can vary by 25–30%. Women metabolize alcohol a little more slowly than men:
    [C2H5OH] (M) 4.4 × 10−2 3.3 × 10−2 2.2 × 10−2
    Rate (mol/L/h) 2.0 × 10−2 2.0 × 10−2 2.0 × 10−2

    Determine the rate equation, the rate constant, and the overall order for this reaction.

  6. Nitrosyl chloride, NOCl, decomposes to NO and Cl2.
    [latex]2\text{NOCl}(g)\;{\longrightarrow}\;2\text{NO}(g)\;+\;\text{Cl}_2(g)[/latex]

    Determine the rate equation, the rate constant, and the overall order for this reaction from the following data:

    [NOCl] (M) 0.10 0.20 0.30
    Rate (mol/L/h) 8.0 × 10−10 3.2 × 10−9 7.2 × 10−9
  7. Nitrogen(II) oxide reacts with chlorine according to the equation:
    [latex]2\text{NO}(g)\;+\;\text{Cl}_2(g)\;{\longrightarrow}\;2\text{NOCl}(g)[/latex]

    The following initial rates of reaction have been observed for certain reactant concentrations:

    [NO] (mol/L) [Cl2] (mol/L) Rate (mol/L/h)
    0.50 0.50 1.14
    1.00 0.50 4.56
    1.00 1.00 9.12

    What is the rate equation that describes the rate’s dependence on the concentrations of NO and Cl2? What is the rate constant? What are the orders with respect to each reactant?

  8. For the reaction [latex]\text{A}\;{\longrightarrow}\;\text{B}\;+\;\text{C}[/latex], the following data were obtained at 30 °C:

    [A] (M) 0.230 0.356 0.557
    Rate (mol/L/s) 4.17 × 10−4 9.99 × 10−4 2.44 × 10−3

    (a) What is the order of the reaction with respect to [A], and what is the rate equation?
    (b) What is the rate constant?

  9. The rate constant for the first-order decomposition at 45 °C of dinitrogen pentoxide, N2O5, dissolved in chloroform, CHCl3, is 6.2 × 10−4 min−1.

    [latex]2\text{N}_2\text{O}_5\;{\longrightarrow}\;4\text{NO}_2\;+\;\text{O}_2[/latex]

    What is the rate of the reaction when [N2O5] = 0.40 M?

  10. The following data have been determined for the reaction:

    [latex]\text{I}^{-}\;+\;\text{OCl}^{-}\;{\longrightarrow}\;\text{IO}^{-}\;+\;\text{Cl}^{-}[/latex]

    1 2 3
    [latex][\text{I}^{-}]_{\text{initial}}[/latex] (M) 0.10 0.20 0.30
    [latex][\text{OCl}^{-}]_{\text{initial}}[/latex] (M) 0.050 0.050 0.010
    Rate (mol/L/s) 3.05 × 10−4 6.20 × 10−4 1.83 × 10−4

    Determine the rate equation and the rate constant for this reaction.

Solutions

  1. (a) 2
    (b) 1
  2. (a) The process reduces the rate by a factor of 4.
    (b) Since CO does not appear in the rate law, the rate is not affected.
  3. 4.3 × 10−5 mol/L/s
  4. 7.9 × 10−13 mol/L/year
  5. rate = k; k = 2.0 × 10−2 mol/L/h (about 0.9 g/L/h for the average male); The reaction is zeroth-order.
  6. rate = k[NOC]2; k = 8.0 × 10−8 L/mol/s; second-order
  7. rate = k[NO]2[Cl]2; k = 9.12 L2 mol−2 h−1; second-order in NO; first-order in Cl2
  8. (a) The rate equation is second-order in A and is written as rate = k[A]2.
    (b) k = 7.88 × 10−13 L mol−1 s−1
  9. (a) 2.5 × 10−4 mol/L/min
  10. rate = k[I−][OCl−]; k = 6.1 × 10−2 L mol −1 s−1

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