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8.E: Kinetics - Homework

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    Chemical Reaction Rates

    1. A study of the rate of dimerization of C4H6 gave the data shown in the table. Determine the average rate of dimerization between 0 s and 1600 s, and between 1600 s and 3200 s.
      Time (s) 0 1600 3200 4800 6200
      [C4H6] (M) 1.00 ×× 10−2 5.04 ×× 10−3 3.37 ×× 10−3 2.53 ×× 10−3 2.08 ×× 10−3
      answer
      5.03x10-3 M/s
      2.08x10-3 M/s

    Factors Affecting Reaction Rates

    1. Describe the effect of each of the following on the rate of the reaction of magnesium metal with a solution of hydrochloric acid: the molarity of the hydrochloric acid, the temperature of the solution, and the size of the pieces of magnesium.
      answer
      HCl molarity - will increase reaction rate
      Temperature - will increase reaction rate
      Size of Mg - will reduce reaction rate
    2. Go to the PhET Reactions & Rates interactive. Use the Single Collision tab to represent how the collision between monatomic oxygen (O) and carbon monoxide (CO) results in the breaking of one bond and the formation of another. Pull back on the red plunger to release the atom and observe the results. Then, click on “Reload Launcher” and change to “Angled shot” to see the difference.
      1. What happens when the angle of the collision is changed?
      2. Explain how this is relevant to rate of reaction.
    answer
    orientation is not correct for reaction to occur, slows down reaction rate

    Collision Theory

    1. Chemical reactions occur when reactants collide. What are two factors that may prevent a collision from producing a chemical reaction?
      answer
      collision energy and collision orientation
    2. What is the activation energy of a reaction, and how is this energy related to the activated complex of the reaction?
      answer
      the energy required for the collision to create the activated complex so that a reaction can occur.
    3. How does an increase in temperature affect rate of reaction? Explain this effect in terms of the collision theory of the reaction rate.
      answer
      increasing temperature increases the kinetic energy of the molecules so that there is more energy available in the collision.
    4. Use the PhET Reactions & Rates interactive simulation to simulate a system. On the “Single collision” tab of the simulation applet, enable the “Energy view” by clicking the “+” icon. Select the first A+BC⟶AB+CA+BC⟶AB+C reaction (A is yellow, B is purple, and C is navy blue). Using the “straight shot” default option, try launching the A atom with varying amounts of energy. What changes when the Total Energy line at launch is below the transition state of the Potential Energy line? Why? What happens when it is above the transition state? Why?
      answer
      there is not enough energy to overcome the activation energy barrier and no reaction occurs.  Above the transition state, there is enough energy for the reaction to overcome the activation energy barrier.

    Reaction Mechanisms

    1. In general, can we predict the effect of doubling the concentration of A on the rate of the overall reaction A+B⟶CA+B⟶C? Can we predict the effect if the reaction is known to be an elementary reaction?
      answer
      I depends upon knowing the rate law, which can be determined experimentally or if it is known to be an elementary reaction.  If this is an elementary reaction, doubling the concentration of A will double the reaction rate.
    2. Write the rate law for each of the following elementary reactions:
      1. \( \mathrm{O}_3 \stackrel{\text { sunlight }}{\longrightarrow} \mathrm{O}_2+\mathrm{O} \)
      2. \( \mathrm{O}_3+\mathrm{Cl} \longrightarrow \mathrm{O}_2+\mathrm{ClO} \)
      3. \( \mathrm{ClO}+\mathrm{O} \longrightarrow \mathrm{Cl}+\mathrm{O}_2 \)
      4. \( \mathrm{O}_3+\mathrm{NO} \longrightarrow \mathrm{NO}_2+\mathrm{O}_2 \)
      5. \( \mathrm{NO}_2+\mathrm{O} \longrightarrow \mathrm{NO}+\mathrm{O}_2 \)
      answer
      answer here

    Catalysis

     
    1. Consider this scenario and answer the following questions: Chlorine atoms resulting from decomposition of chlorofluoromethanes, such as CCl2F2, catalyze the decomposition of ozone in the atmosphere. One simplified mechanism for the decomposition is:

      \[\begin{aligned}
      & \mathrm{O}_3 \stackrel{\text { sunlight }}{\longrightarrow} \mathrm{O}_2+\mathrm{O} \\
      & \mathrm{O}_3+\mathrm{Cl} \longrightarrow \mathrm{O}_2+\mathrm{ClO} \\
      & \mathrm{ClO}+\mathrm{O} \longrightarrow \mathrm{Cl}+\mathrm{O}_2
      \end{aligned}\]

      1. Explain why chlorine atoms are catalysts in the gas-phase transformation:
        \[\mathrm{2O}_3 \stackrel{\text { sunlight }}{\longrightarrow} \mathrm{3O}_2 \]
        answer
        The chlorine atoms are used in the second step of the reaction but are reformed in the third step of the reaction, so the chlorine atoms are not consumed.
      2. Nitric oxide is also involved in the decomposition of ozone by the mechanism:

        \[ \begin{aligned}
        & \mathrm{O}_3 \stackrel{\text { sunlight }}{\longrightarrow} \mathrm{O}_2+\mathrm{O} \\
        & \mathrm{O}_3+\mathrm{NO} \longrightarrow \mathrm{NO}_2+\mathrm{O}_2 \\
        & \mathrm{NO}_2+\mathrm{O} \longrightarrow \mathrm{NO}+\mathrm{O}_2
        \end{aligned} \]

        Is NO a catalyst for the decomposition? Explain your answer.

        answer
        Yes, the NO is required for the second step of the reaction mechanism.  But is reformed in the third step.
    2. For each of the following pairs of reaction diagrams, identify which of the pair is catalyzed:
      1. In this figure, two graphs are shown. The x-axes are labeled, “Extent of reaction,” and the y-axes are labeled, “Energy (k J).” The y-axis of the first graph is marked off from 0 to 30 in intervals of 5. The y-axis of the second graph is marked off from 0 to 25 by intervals of 5. In a, a blue curve is shown. It begins with a horizontal region at about 12. The curve then rises sharply near the middle to reach a maximum of about 24 and similarly falls to another horizontal segment at 5. In b, the curve begins and ends similarly, but the maximum reached near the center of the graph is only 20.
      2. In this figure, two graphs are shown. The x-axes are labeled, “Extent of reaction,” and the y-axes are labeled, “Energy.” The y-axes are marked off from 0 to 50 in intervals of 5. In a, a blue curve is shown. It begins with a horizontal region at about 2. The curve then rises sharply near the middle to reach a maximum of about 43 and similarly falls to another horizontal segment at 15. In b, the curve begins and ends similarly, but the maximum reached near the center of the graph is only about 32.
      answer
      a) reaction b  b) reaction b  both have lower activation energies.
    3. For each of the following reaction diagrams, estimate the activation energy (Ea) of the reaction:
      1. This figure shows a graph. The x-axis is labeled, “Extent of reaction,” and the y-axis is labeled, “Energy (k J).” The y-axis is marked off from 0 to 40 at intervals of 5. A blue curve is shown. It begins with a horizontal region at 10. The curve then rises sharply near the middle to reach a maximum of 35 and similarly falls to another horizontal segment at 5.
      2. This figure shows a graph. The x-axis is labeled, “Extent of reaction,” and the y-axis is labeled, “Energy (k J).” The y-axis is marked off from 0 to 40 at intervals of 5. A blue curve is shown. It begins with a horizontal region at 10. The curve then rises sharply near the middle to reach a maximum of 20 and similarly falls to another horizontal segment at 5.
      answer
      a) 25 kJ/mole   b) 10 kJ/mole
     

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