A-Level Chemistry October/November 2024 Q2(e): Calculate the value of the entropy change, AS, for the solution of compound T at 298 K.…

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  The relationship between Gibbs free energy, enthalpy change, and entropy change is given by the equation: $\Delta G = \Delta H - T\Delta S$

  To find the entropy change, $\Delta S$, we rearrange the equation: $T\Delta S = \Delta H - \Delta G$ $\Delta S = \frac{\Delta H - \Delta G}{T}$

  Using the values for the solution of compound T at $T = 298 \text{ K}$ (values for $\Delta G$ and $\Delta H$ are taken from previous parts of the question): $\Delta G = +6000 \text{ J mol}^{-1}$ $\Delta H = +30000 \text{ J mol}^{-1}$

  Substitute these values into the rearranged equation: $\Delta S = \frac{30000 - 6000}{298}$ $\Delta S = \frac{24000}{298}$ $\Delta S = +80.5369... \text{ J K}^{-1} \text{mol}^{-1}$

  The value of the entropy change, $\Delta S$, to 3 significant figures is: $\Delta S = +80.5 \text{ J K}^{-1} \text{mol}^{-1}$

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  How the marks are awarded

  • M1 — The first mark is for correctly stating the Gibbs free energy equation, $\Delta G = \Delta H - T\Delta S$, or showing its direct use by substituting the correct values, as seen in the calculation step $\Delta S = \frac{30000 - 6000}{298}$.
  • A1 — The final answer mark is for calculating the correct numerical value of +80.5. The answer is correctly rounded to 3 significant figures and includes the correct positive sign.

  Common mistakes

  • Forgetting to convert energy units if they are given in kJ mol⁻¹ instead of J mol⁻¹, which would lead to an answer that is incorrect by a factor of 1000.
  • Incorrectly rearranging the Gibbs equation, for example to $\Delta S = (\Delta G - \Delta H) / T$, which results in a sign error for the final answer (e.g., -80.5).
  • Rounding the final answer to an incorrect number of significant figures, such as two significant figures (81) instead of the required minimum of three.
  • Using the temperature in degrees Celsius (25 °C) instead of Kelvin (298 K), a common mistake if the conversion is not explicitly stated.

  Examiner tip: Always write down the governing equation, rearrange it algebraically for the unknown variable before substituting numbers, and meticulously check that all quantities have consistent SI units.

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