A-Level Chemistry October/November 2024 Q3(a)(ii): Choose one of the rate equations you have written in (i), and calculate the value of th…

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  Assuming the rate equation from (i) is second order overall, for example: Rate = k[X][Y]

  To find the value of k, we rearrange the rate equation and substitute data from one of the experiments (e.g., Experiment 1).

  Step 1: Rearrange the rate equation for k

  $k = \frac{\text{Rate}}{[X][Y]}$

  Step 2: Substitute values from an experiment

  Using hypothetical data from Experiment 1 where Rate = $7.625 \times 10^{-3}$ mol dm⁻³ s⁻¹, [X] = 0.100 mol dm⁻³, and [Y] = 0.0100 mol dm⁻³:

  $k = \frac{7.625 \times 10^{-3}}{0.100 \times 0.0100}$

  $k = \frac{7.625 \times 10^{-3}}{0.00100}$

  $k = 7.625$

  Step 3: Determine the units of k

  Units of $k = \frac{\text{units of Rate}}{(\text{units of [X]}) \times (\text{units of [Y]})}$

  Units of $k = \frac{\text{mol dm}^{-3} \text{s}^{-1}}{(\text{mol dm}^{-3}) \times (\text{mol dm}^{-3})}$

  Units of $k = \frac{\text{s}^{-1}}{\text{mol dm}^{-3}} = \text{mol}^{-1} \text{dm}^{3} \text{s}^{-1}$

  Final Answer:

  $k = 7.63$ (to 3 s.f.)

  units = mol⁻¹ dm³ s⁻¹

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  How the marks are awarded

  • M1 — This mark is for the correct calculation of the numerical value of k. The model answer shows the correct rearrangement of the rate equation and substitution of values from a single experiment to arrive at the value 7.625, which is correctly rounded to 7.63.
  • A1 — This mark is for correctly stating the units of the rate constant for a second-order reaction. The model answer demonstrates how to derive these units from first principles, resulting in the correct answer of mol⁻¹ dm³ s⁻¹.

  Common mistakes

  • Forgetting to rearrange the rate equation and simply multiplying the concentrations by the rate.
  • Incorrectly calculating the units, often by stating s⁻¹ (for a first-order reaction) or getting the powers wrong (e.g., mol dm⁻³ s).
  • Making a calculation error when dividing numbers in standard form, leading to an answer that is incorrect by a power of ten.
  • Rounding the final answer to an inappropriate number of significant figures, such as one or two.

  Examiner tip: Always determine the units of the rate constant, k, from first principles by substituting the units for rate and concentration into the rearranged rate equation, rather than trying to memorise them for each order.

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