3.12 Practice Problems

Attempt these problems as if they were real exam questions in an exam environment.

Only look up information if you get severely stuck. Never look at the solution until you have exhausted all efforts to solve the problem.


  1. Consider the following reaction.

    \[5\mathrm{Br^-}(aq) + \mathrm{BrO_3}(aq) + 6\mathrm{H^+}(aq) \longrightarrow \mathrm{3Br_2}(aq) + \mathrm{3H_2O}(l)\]

    If the rate of disappearance of Br(aq) at a particular moment during the reaction is 3.7 × 10–4, what is the rate of appearance (in M s–1) of Br2(aq) at that moment?

    1. 2.2 × 10–4
    2. 4.4 × 10–3
    3. 6.6 × 10–2
    4. 0.88
    5. 1.03

    Solution


  2. In the first 10.0 s of the following reaction, [I] drops from 1.000 M to 0.868 M. What is the average rate of reaction (in M s–1) in this time interval?

    \[\mathrm{H_2O_2}(aq) + 3\mathrm{I^-}(aq) + 2\mathrm{H^+}(aq) \longrightarrow \mathrm{I_3^-}(aq) + \mathrm{2H_2O}(l)\]

    1. –8.23 × 10–6
    2. –4.40 × 10–3
    3. 3.14 × 10–15
    4. 4.40 × 10–3
    5. 1.44

    Solution


  3. The balanced reaction below had an initial concentration of A of 4.09 M. After 40.0 s, the concentration of A was found to be 1.93 M. What is the average rate of reaction (in M s–1)?

    \[\mathrm{A}\longrightarrow \mathrm{B}\]

    1. 5.23 × 10–4
    2. 4.23 × 10–2
    3. 5.40 × 10–2
    4. 1.023
    5. 300.4

    Solution


  4. A reaction is second-order and has a single reactant, A. What is the rate constant (in M–1 s–1) if the reaction rate at 450 °C is 1.13 × 10–1 mol L–1 s–1 when A is 0.206 mol L–1?

    1. 0.001
    2. 0.11
    3. 2.66
    4. 1.33
    5. 11.34

    Solution


  5. The rate constant for a first-order decomposition of cyclobutane, C4H8, at 500 °C is 9.2 × 10–3 s–1. How long (in s) will it take for 20.0% of the reactant to decompose?

    1. 24
    2. 42
    3. 87
    4. 175
    5. 430

    Solution


  6. Molecular iodine dissociates at 625 K with a rate constant of 0.271 M s–1. What is the half-life (in s) of this reaction when [I2] = 1.05 M?

    1. 1.94
    2. 2.56
    3. 6.42
    4. 8.36
    5. 9.34

    Solution


  7. What is the half-life (in h) for the decomposition of O3 when the concentration is 2.42 × 10–6 M? The rate constant is 50.4 L mol–1 h–1.

    1. 4.80 × 10–8
    2. 0.014
    3. 623.15
    4. 8,199
    5. 2.86 × 105

    Solution


  8. A decomposition reaction of molecule X is performed and three plots are generated with the x-axis as time. You notice that the plot which gave a straight line of data points had 1/X on the y-axis. What is the order of the decomposition reaction?

    1. zeroth-order
    2. first-order
    3. second-order
    4. third-order
    5. none of these

    Solution


  9. What is the rate constant (in s–1) for a decomposition of molecule X if 95% of the reactant decomposed in 5.43 minutes?

    1. 9.2 × 10–3
    2. 0.55
    3. 1.2
    4. 68.2
    5. 174.9

    Solution


  10. What is the activation energy (in kJ) for a reaction that has a rate constant of 0.253 s–1 and a frequency factor of 1.06 × 1011 s–1 at 44.0 °C?

    1. –7.06 × 104
    2. 7.21
    3. 17.3
    4. 70.6
    5. 700.69

    Solution


  11. For the following reaction, the rate constant at 701 K is measured as 2.57 M–1 s–1 and at 895 K is measured as 567 M–1 s–1. What is the activation energy (in kJ mol–1 to one decimal place)?

    1. –1.4 × 10–2
    2. 4.9 × 10–3
    3. 1.5 × 102
    4. 8.3 × 102
    5. 2.6 × 103

    Solution


  12. What is the molecularity for the following elementary step?

    \[2\mathrm{N_2O}(g) + \mathrm{Cl_2}(g) \longrightarrow 2\mathrm{N_2}(g) + 2\mathrm{ClO}(g)\]

    1. Unimolecular
    2. Bimolecular
    3. Termolecular

    Solution


  13. Which rate law for an elementary step corresponds to a molecularity that is bimolecular?

    1. rate = k[A][B]2
    2. rate = k[A]
    3. rate = k[A]2[B]2
    4. rate = k[A]2
    5. none of these

    Solution


  14. What is the rate law for the following elementary step?

    \[\mathrm{NO}(g) + \mathrm{O_2}(g) \longrightarrow \mathrm{NO_2}(g)\]

    1. rate = k[NO][O2]3
    2. rate = k[NO]2[O2]
    3. rate = k[NO][O2]
    4. rate = [NO2]/[NO][O2]
    5. none of these

    Solution


  15. Consider the following two-step reaction mechanism.

    \[\begin{align*} \mathrm{Cl}(g) + \mathrm{O_3}(g) ~ &\longrightarrow ~ \mathrm{ClO}(g) + \mathrm{O_2}(g) \\ \mathrm{ClO}(g) + \mathrm{O}(g) ~ &\longrightarrow ~ \mathrm{Cl}(g) + \mathrm{O_2}(g) \end{align*}\]

    Identify the intermediate of reaction.

    1. O2
    2. ClO
    3. O
    4. Cl
    5. none of these

    Solution


  16. A single-reactant is found to have an decreasing half-life as the initial concentration of the reactant increases. What is the order of the reaction?

    1. zeroth
    2. first
    3. second

    Solution


  17. The rate constant for a decomposition reaction is 4.5 × 10–3 s–1. How long (in min) will it take for 75% of the reactant to decompose?

    1. 122.41
    2. 5.13
    3. 308.07
    4. 1.07
    5. 63.93

    Solution


  18. If a 5.0 M solution of substance A decomposes for 50 min and the remaining is found to be 0.5 M, what is the half life of this reaction (in h) if it follows first-order kinetics?

    1. 0.25
    2. 0.83
    3. 1.0
    4. 15.1
    5. 32.4

    Solution


  19. Choose the false statement regarding the Arrhenius equation and reaction rates.

    1. Increasing T results in a faster rate of reaction.
    2. Increasing the pre-exponential factor results in a larger k.
    3. Decreasing k results in a slower rate of reaction.
    4. Increasing Ea results in a faster rate of reaction.
    5. none of these

    Solution


  20. A two-step reaction mechanism describing an aqueous phase reaction has the following rate constants for each step: k1 = 1.843 and k2 = 0.0325. Each step is unimolecular and equimolar. A catalyst is used in the overall reaction. Which of the following statements is true?

    1. The catalyst is consumed in the second step of the reaction
    2. The catalyst lowers the activation energy for the first step of the reaction
    3. The catalyst lowers the activation energy for the second step of the reaction
    4. The catalyst shifts the equilibrium towards the products
    5. The catalyst is an intermediate of reaction

    Solution


  21. The mechanism for a chemical reaction is given below.

    \[\begin{alignat*}{3} \mathrm{(CH_3)_3CCl} ~ &\longrightarrow ~ \mathrm{(CH_3)_3C^+} + \mathrm{Cl^-} \quad &&k_1 \quad &&(E_{\mathrm{a}}~\text{is large}) \\ \mathrm{(CH_3)_3C^+} + \mathrm{OH^-} ~ &\longrightarrow ~ \mathrm{(CH_3)_3COH} \quad &&k_2 \quad &&(E_{\mathrm{a}}~\text{is small}) \end{alignat*}\]

    Which of the following statements is/are correct?

    Number Statement
    1 The overall balanced reaction is   (CH3)3CCl + OH → (CH3)3COH + Cl
    2 The chloride ion is a reaction intermediate
    3 The following experimental rate law is consistent with the mechanism: rate = k[(CH3)3CCl]


    1. 1 and 3
    2. 1
    3. 3
    4. 1, 2, and 3
    5. 1 and 2

    Solution


  22. What is the predicted rate law for the following reaction mechanism?

    \[\begin{align*} &\text{Step 1 (fast):} ~\mathrm{2NO}(g) \longrightarrow \mathrm{N_2O_2}(g)\\[1.5ex] &\text{Step 2 (slow):} ~\mathrm{H_2}(g) + \mathrm{N_2O_2}(g) \longrightarrow \mathrm{H_2O}(g) + \mathrm{N_2O}(g)\\[1.5ex] &\text{Step 3 (fast):} ~\mathrm{N_2O}(g) + \mathrm{H_2}(g) \longrightarrow \mathrm{N_2}(g) + \mathrm{H_2O}(g) \end{align*}\]

    1. rate = k[NO]2
    2. rate = k[N2O][H2]
    3. rate = k[H2][N2O2]
    4. rate = k[H2]2
    5. none of these

    Solution