Integrated Rate Laws and Mechanisms: Quiz

7 questions

  1. Question 1EasyFor a first-order reaction, which plot gives a straight line?
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    Answer: ln[A] against t

    ln[A] = ln[A]₀ − kt has the form y = c + mx, with slope −k.

  2. Question 2EasyA first-order reaction has a half-life of 20.0 min. What fraction remains after 60.0 min?
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    Answer: 1/8

    60.0 min is 3 half-lives: (½)³ = 1/8.

  3. Question 3MediumFor a second-order reaction with k = 0.100 M⁻¹ s⁻¹ and [A]₀ = 0.500 M, what is the first half-life?
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    Answer: 20.0 s

    t½ = 1/(k[A]₀) = 1/(0.100 M⁻¹ s⁻¹ × 0.500 M) = 20.0 s.

  4. Question 4MediumA plot of 1/[A] against time is a straight line with slope 0.0250 M⁻¹ s⁻¹. What is k?
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    Answer: 0.0250 M⁻¹ s⁻¹

    For second order, the slope of 1/[A] against t equals +k, with units M⁻¹ s⁻¹.

  5. Question 5MediumA mechanism is: step 1 NO₂ + NO₂ → NO₃ + NO (slow); step 2 NO₃ + CO → NO₂ + CO₂ (fast). What is the rate law?
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    Answer: rate = k[NO₂]²

    The slow step sets the rate, and it involves two NO₂ molecules.

  6. Question 6EasyIn the mechanism in the previous question, NO₃ is:
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    Answer: an intermediate

    It is made in step 1 and used up in step 2, so it does not appear in the overall equation.

  7. Question 7HardSuccessive half-lives of a reaction are 50 s, 100 s and 200 s. What is the order?
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    Answer: second

    Doubling half-lives are the signature of second order (t½ = 1/k[A]₀). First order gives constant half-lives; zero order gives shrinking ones.