Explain why the dissolution of ammonium nitrate in water, a process that is endothermic, is nonetheless spontaneous at room temperature.

IB DP Chemistry Higher Level (2023 syllabus) — R1.4 Entropy and spontaneity (HL only) · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

When ammonium nitrate dissolves in water, the temperature of the solution decreases noticeably, yet the process proceeds without any external energy input.

Model answer (4 marks)

A spontaneous process requires ΔG<0.

For dissolution of NH4NO3:
1. ΔH>0 (endothermic – heat absorbed, temperature falls).
2. ΔS>0 – the ionic lattice breaks up into many ions and water molecules, increasing disorder.
3. ΔG=ΔH−TΔS. Although ΔH is positive, the TΔS term is larger and positive, so ΔG becomes negative.

Thus the large entropy increase drives the process, making it spontaneous at room temperature.

Examiner tips

  • State ΔG<0 as the criterion for spontaneity.
  • Mention ΔH>0 and ΔS>0 explicitly.
  • Use the equation ΔG=ΔH−TΔS and explain the sign of each term.
  • Show that TΔS dominates over ΔH to give ΔG<0.

Common mistakes

  • Saying the process is spontaneous because it is endothermic, ignoring ΔS.
  • Forgetting to include the TΔS term or its sign.
  • Using the wrong sign for ΔH or ΔS (e.g., ΔH<0).

Mark scheme (4 marks)

  1. A spontaneous process requires the total Gibbs energy change (ΔG) to be negative.
  2. The dissolution results in a large increase in entropy (positive ΔS) because ions and water molecules become more disordered when the ionic lattice disperses into solution.
  3. Using ΔG = ΔH − TΔS: because ΔH is positive (endothermic) but TΔS is also positive and sufficiently large, the TΔS term dominates.
  4. Therefore, the entropy-driven decrease in Gibbs energy provides the thermodynamic driving force, making the process spontaneous even though it is endothermic.

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