Using the concept of an enthalpy cycle, explain why the standard enthalpy of formation of sodium chloride (NaCl) cannot be determined directly from its elements and how Hess's law allows this value to be obtained indirectly.

IB DP Chemistry Standard Level (2023 syllabus) — R1.2 Energy cycles in reactions · Explain · 4 marks · View as Markdown

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

The standard enthalpy of formation of an ionic compound such as sodium chloride cannot be measured directly in a laboratory because the reaction of sodium metal with chlorine gas does not proceed in a single, controllable step.

Model answer (4 marks)

1. The direct reaction Na(s)+½Cl₂(g)→NaCl(s) cannot be measured because it is not a single, controllable step under standard conditions – it is highly exothermic, violent and cannot be isolated in a calorimeter.
2. Hess’s law states that the enthalpy change for a reaction is independent of the pathway, as long as the initial and final states are the same.
3. A Born–Haber cycle (enthalpy cycle) is drawn linking Na(s) and Cl₂(g) to NaCl(s) through measurable steps: atomisation of Na and Cl₂, ionisation of Na, electron affinity of Cl, and lattice enthalpy of NaCl.
4. By summing the enthalpy changes of these steps (applying Hess’s law algebraically) the standard enthalpy of formation of NaCl is obtained: ΔHf°(NaCl)=ΔHatom(Na)+½ΔHatom(Cl₂)+ΔHion(Na)+½ΔHea(Cl)+ΔHlattice(NaCl).

Examiner tips

  • Use the exact phrase ‘direct reaction cannot be measured’ for point 1.
  • Show the Born–Haber cycle diagram or list the four steps clearly for point 3.
  • Write the algebraic sum for ΔHf in point 4.
  • Keep the answer concise – 4 points, no extra wording.

Common mistakes

  • Writing the reaction as Na(s)+Cl₂(g)→NaCl(s) instead of the correct stoichiometry.
  • Forgetting that the lattice enthalpy is negative (exothermic) in the cycle.
  • Mixing up the sign of the ionisation energy (it is endothermic).

Mark scheme (4 marks)

  1. The direct combination of sodium and chlorine does not occur in a single measurable step / the reaction cannot be carried out under standard conditions in a controlled way, so a direct calorimetric measurement is not possible.
  2. Hess's law states that the total enthalpy change for a reaction is independent of the route taken, provided the initial and final states are the same.
  3. An enthalpy cycle (Born–Haber cycle) is constructed linking the elements to NaCl via a series of measurable steps such as atomisation, ionisation, electron affinity, and lattice enthalpy.
  4. The standard enthalpy of formation is then calculated by summing the enthalpy changes of the alternative route / applying Hess's law algebraically so that ΔHf = sum of the individual step enthalpies around the cycle.

Key terms in this question

enthalpy cycle · Hess's law · standard enthalpy of formation

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