DONATSciences and Maths
Chemistry · Practice book · Senior 6 · Unit 13 of 14

Rate laws and measurements

Senior 6 Chemistry · 14 questions with answers. Try each question on paper, then tap it to see the answer.

Unit 13 Rate laws and measurements

Key unit competence: Evaluate reaction rates and rate laws using kinetic theories, experimental data and reaction mechanisms.

Key ideas

  • Rate equation: rate = k[A]m[B]n, where k is the rate constant (depends on temperature) and m, n are the orders with respect to A and B (found only by experiment). Overall order = m + n. Units of k: zero order mol dm−3 s−1; first order s−1; second order dm3 mol−1 s−1.
  • Orders from initial rates: double [A] with [B] constant: rate unchanged (order 0), doubles (order 1), quadruples (order 2). Concentration–time graphs: zero order a straight line; first order a curve with a constant half-life; rate–concentration graphs: zero order horizontal, first order straight through the origin, second order a curve (parabola).
  • Integrated rate laws: zero order [A] = [A]0 − kt; first order ln[A] = ln[A]0 − kt and t½ = 0.693 ÷ k (independent of concentration); second order 1/[A] = 1/[A]0 + kt.
  • Collision theory and transition state theory (an activated complex at the top of the energy barrier). Arrhenius equation: k = Ae−Ea/RT; ln k = ln A − Ea/RT, so a plot of ln k against 1/T has gradient −Ea/R. For two temperatures: ln(k2/k1) = (Ea/R)(1/T1 − 1/T2).
  • A mechanism is a series of elementary steps. Molecularity is the number of particles in an elementary step (uni-, bi-, termolecular); order is experimental and may differ. The slowest step is the rate-determining step; species in it appear in the rate equation.
  • Example: hydrolysis of 2-bromo-2-methylpropane is first order (rate = k[RBr]): slow ionisation then fast attack by OH− (SN1). Hydrolysis of bromomethane is second order (rate = k[CH3Br][OH−], one step, SN2). NO2 + CO → NO + CO2 has rate = k[NO2]2: slow step 2NO2 → NO3 + NO.

Common misconceptions

  • "Orders can be read from the coefficients of the balanced equation." No: Orders are found by experiment; they match coefficients only for elementary steps.
  • "The half-life of every reaction is constant." No: Only first-order reactions have a constant half-life.
  • "Molecularity and order are the same thing." No: Molecularity applies to one elementary step and is a whole number; order is experimental for the overall reaction and can be 0 or fractional.

Worked examples

Example 1. Iodine reacts with propanone in acid: CH3COCH3 + I2 → CH3COCH2I + HI. Initial-rate data show: doubling [propanone] doubles the rate; doubling [H+] doubles the rate; doubling [I2] has no effect. Deduce the rate equation and comment on the mechanism.

Solution

Order 1 in propanone, 1 in H+, 0 in I2: rate = k[CH3COCH3][H+].

Overall order 2; units of k: dm3 mol−1 s−1.

Iodine is not in the rate equation, so it is not involved in the rate-determining step.

The slow step involves propanone and H+ (forming an enol); iodine reacts in a later fast step. H+ is a catalyst.

Example 2. Explain how to use the Arrhenius equation to find Ea from rate constants measured at several temperatures.

Solution

Measure k at five or more temperatures (e.g. by initial rates).

Calculate ln k and 1/T (T in kelvin) for each.

Plot ln k (y) against 1/T (x): a straight line with gradient = −Ea/R and intercept ln A.

Ea = −gradient × R (R = 8.314 J K−1 mol−1).

Practice questions

  1. Define order of reaction with respect to a reactant.

    Show answer

    The power to which the concentration of that reactant is raised in the experimentally found rate equation.

    Common mistake: Saying it is the coefficient in the equation.

  2. What is the rate constant?

    Show answer

    The constant of proportionality in the rate equation; it depends on temperature.

    Common mistake: Saying it is constant at all temperatures.

  3. Give the half-life expression for a first-order reaction.

    Show answer

    t½ = 0.693 ÷ k (ln 2 ÷ k).

    Common mistake: Writing t½ = k ÷ 0.693.

  4. Distinguish order from molecularity.

    Show answer

    Order is experimental and refers to the overall rate equation; molecularity is the number of particles in an elementary step.

    Common mistake: Saying they are always equal.

  5. What is the rate-determining step?

    Show answer

    The slowest step in a reaction mechanism, which controls the overall rate.

    Common mistake: Saying it is the first step.

  6. Sketch (describe) the rate–concentration graph for a second-order reaction.

    Show answer

    A curve rising more and more steeply (rate ∝ [A]2).

    Common mistake: Drawing a straight line.

  7. Write the Arrhenius equation.

    Show answer

    k = Ae−Ea/RT.

    Common mistake: Writing k = AEa/RT.

  8. How would you show a reaction is first order from a [A]–time graph?

    Show answer

    Measure successive half-lives: they are constant.

    Common mistake: Checking that the graph is a straight line.

  9. Why is the reaction mixture 'quenched' when following a rate by titration?

    Show answer

    To stop (or greatly slow) the reaction at a known time so the sample's composition stays fixed.

    Common mistake: Saying it speeds up the reaction.

  10. Give the units of k if rate = k[A][B]2 and rate is in mol dm−3 s−1.

    Show answer

    dm6 mol−2 s−1.

    Common mistake: Writing mol3 dm−9 s−1.

Matching and drag-and-drop

  1. Matching

    Match each item in column A with the correct answer in column B. Write the letter next to each number.

    Column AColumn B
    1. The units of k for a first-order reaction are:a. taking part in an elementary step
    2. A plot of [A] against time is a straight line for a reaction that is:b. zero order
    3. If doubling [A] quadruples the rate, the order with respect to A is:c. s−1
    4. Molecularity is the number of particles:d. 2
    Show answer

    1 → c (s−1) · 2 → b (zero order) · 3 → d (2) · 4 → a (taking part in an elementary step)

    • rate ÷ concentration.
    • [A] = [A]0 − kt.
    • 22 = 4.
    • e.g. bimolecular.

  2. Drag and drop

    Choose the correct word or phrase from the box for each gap. One word in the box is not needed.

    third order  ·  second order (SN2)  ·  dm3 mol−1 s−1  ·  3 half-lives
    1. The units of k for a second-order reaction are .
    2. For a first-order reaction, 1/8 of the reactant remains after .
    3. The hydrolysis of bromomethane by OH− is .
    Show answer

    1: dm3 mol−1 s−1 · 2: 3 half-lives · 3: second order (SN2)

    • rate ÷ concentration2.
    • (½)3 = 1/8.
    • One-step collision.

  3. Matching

    Match each item in column A with the correct answer in column B. Write the letter next to each number.

    Column AColumn B
    1. In the Arrhenius equation, A is the:a. 3
    2. The hydrolysis of 2-bromo-2-methylpropane by OH− is:b. first order (SN1)
    3. A plot of ln k against 1/T has a gradient of:c. pre-exponential (frequency) factor
    4. In rate = k[A]2[B], the overall order is:d. −Ea/R
    Show answer

    1 → c (pre-exponential (frequency) factor) · 2 → b (first order (SN1)) · 3 → d (−Ea/R) · 4 → a (3)

    • Related to collision frequency and orientation.
    • Slow ionisation of RBr.
    • ln k = ln A − Ea/RT.
    • 2 + 1.

  4. Drag and drop

    Choose the correct word or phrase from the box for each gap. One word in the box is not needed.

    the temperature changes  ·  −1  ·  0  ·  first order
    1. The rate constant k changes when .
    2. If doubling [A] has no effect on the rate, the order with respect to A is .
    3. A plot of rate against [A] that is a straight line through the origin shows .
    Show answer

    1: the temperature changes · 2: 0 · 3: first order

    • Arrhenius.
    • Rate independent of [A].
    • Rate = k[A].

Take the Unit 13 quiz → · Back to contents