Gibbs free-energy change and feasibilityAQA A-Level Chemistry: Subtopic test

1. 1
   Whether a reaction is feasible at a given temperature depends on the balance between its enthalpy change and its entropy change, expressed by the equation ΔG = ΔH − TΔS, where T is the temperature in kelvin. A student has values of ΔH in kJ mol⁻¹ and ΔS in J K⁻¹ mol⁻¹ for several reactions.

   (a)

   Which statement gives the condition for a reaction to be feasible?

   [1 mark]

   • AΔG must be positive
   • BΔG must be zero or negative
   • CΔH must be negative
   • DΔS must be negative

   (b)

   To use ΔG = ΔH − TΔS correctly with these units, what must the student do?

   [1 mark]

   • AUse the values as they are
   • BMultiply ΔS by 1000
   • CConvert the temperature to °C
   • DDivide ΔS by 1000 to convert it to kJ K⁻¹ mol⁻¹

   (c)

   A reaction has a negative ΔH and a positive ΔS. State the sign of ΔG at all temperatures and explain your answer.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Dinitrogen tetroxide decomposes reversibly: N₂O₄(g) → 2NO₂(g). For this reaction ΔH = +57.0 kJ mol⁻¹ and ΔS = +176 J K⁻¹ mol⁻¹.

   (a)

   Calculate ΔG for the decomposition of N₂O₄ at 298 K.

   [1 mark]

   • A−4.6 kJ mol⁻¹
   • B+109.4 kJ mol⁻¹
   • C+4.6 kJ mol⁻¹
   • D−52 391 kJ mol⁻¹

   (b)

   Above which temperature is the decomposition of N₂O₄ feasible?

   [1 mark]

   • A324 K
   • B0.324 K
   • C51 K
   • D3.09 × 10⁻³ K

   (c)

   Use the equation ΔG = ΔH − TΔS to explain why increasing the temperature makes the decomposition of N₂O₄ more feasible.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In the Haber process, N₂(g) + 3H₂(g) → 2NH₃(g), the enthalpy change is ΔH = −92 kJ mol⁻¹ and the entropy change is ΔS = −199 J K⁻¹ mol⁻¹ for the reaction as written.

   (a)

   Calculate ΔG for the Haber process at 298 K. State whether the reaction is feasible at this temperature.

   [3 marks]

   (b)

   Calculate the temperature above which the Haber process is no longer feasible. Explain why the reaction becomes less feasible at higher temperatures.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Iron(II) oxide can be reduced by carbon in a furnace: FeO(s) + C(s) → Fe(s) + CO(g). For this reaction ΔH = +161 kJ mol⁻¹ and ΔS = +158 J K⁻¹ mol⁻¹. The furnace operates at 1300 K.

   (a)

   Calculate the minimum temperature at which carbon can reduce iron(II) oxide, and explain why the reduction becomes feasible only above this temperature.

   [6 marks]

   (b)

   Calculate ΔG for the reduction at 800 K and at 1300 K. Evaluate whether the furnace is suitable for producing iron by this reaction.

   [6 marks]

   Total for question 4: 12 marks

End of questions