Unit 2 Kinetics

2.1 Exercises

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Section 2.1 Exercises

  1. What is the difference between average rate, initial rate, and instantaneous rate?
  2. In the nuclear industry, chlorine trifluoride is used to prepare uranium hexafluoride, a volatile compound of uranium used in the separation of uranium isotopes. Chlorine trifluoride is prepared by the reaction [latex]\text{Cl}_2(g)\;+\;3\text{F}_2(g)\;{\longrightarrow}\;2\text{ClF}_3(g)[/latex]. Write the equation that relates the rate expressions for this reaction in terms of the disappearance of Cl2 and F2 and the formation of ClF3.
  3. A study of the rate of the reaction represented as [latex]2\text{A}\;{\longrightarrow}\;\text{B}[/latex] gave the following data:
    Time (s) 0.0 5.0 10.0 15.0 20.0 25.0 35.0
    [A] (M) 1.00 0.952 0.625 0.465 0.370 0.308 0.230

    (a) Determine the average rate of disappearance of A between 0.0 s and 10.0 s, and between 10.0 s and 20.0 s.
    (b) Estimate the instantaneous rate of disappearance of A at 15.0 s from a graph of time versus [A]. What are the units of this rate?  (This question is for students who have taken calculus.  Questions of this type is outside the scope of CHEM 1523.)
    (c) Use the rates found in parts (a) and (b) to determine the average rate of formation of B between 0.00 s and 10.0 s, and the instantaneous rate of formation of B at 15.0 s.

  4. 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.
  5. 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.

    (a) What happens when the angle of the collision is changed?
    (b) Explain how this is relevant to rate of reaction.

  6. In the PhET Reactions & Rates interactive, on the Many Collisions tab, set up a simulation with 15 molecules of A and 10 molecules of BC. Select “Show Bonds” under Options.

    (a) Leave the Initial Temperature at the default setting. Observe the reaction. Is the rate of reaction fast or slow?
    (b) Click “Pause” and then “Reset All,” and then enter 15 molecules of A and 10 molecules of BC once again. Select “Show Bonds” under Options. This time, increase the initial temperature until, on the graph, the total average energy line is completely above the potential energy curve. Describe what happens to the reaction.

Solutions

  1. The instantaneous rate is the rate of a reaction at any particular point in time, a period of time that is so short that the concentrations of reactants and products change by a negligible amount. The initial rate is the instantaneous rate of reaction as it starts (as product just begins to form). Average rate is the average of the instantaneous rates over a time period.
  2. [latex]\text{rate} = +\frac{1}{2}\;\frac{{\Delta}[\text{CIF}_3]}{{\Delta}t} = -\frac{{\Delta}[\text{Cl}_2]}{{\Delta}t} = -\frac{1}{3}\;\frac{{\Delta}[\text{F}_2]}{{\Delta}t}[/latex]
  3. (a) average rate, 0 − 10 s = 0.0375 mol L−1 s−1; average rate, 10 − 20 s = 0.0225 mol L−1 s−1; (b) instantaneous rate, 15 s = 0.0500 mol L−1 s−1; (c) average rate for B formation = 0.0188 mol L−1 s−1; instantaneous rate for B formation = 0.0250 mol L−1 s−1
  4. Higher molarity increases the rate of the reaction. Higher temperature increases the rate of the reaction. Smaller pieces of magnesium metal will react more rapidly than larger pieces because more reactive surface exists.
  5. (a) Depending on the angle selected, the atom may take a long time to collide with the molecule and, when a collision does occur, it may not result in the breaking of the bond and the forming of the other.
    (b) Particles of reactant must come into contact with each other before they can react.
  6. (a) very slow
    (b) As the temperature is increased, the reaction proceeds at a faster rate. The amount of reactants decreases, and the amount of products increases. After a while, there is a roughly equal amount of BC, AB, and C in the mixture and a slight excess of A.

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