Explain why the lattice enthalpy of magnesium oxide (MgO) is much greater in magnitude than the lattice enthalpy of sodium chloride (NaCl), using Coulomb's law to support your answer.

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).

Lattice enthalpy is a key quantity used in Born–Haber cycles to assess the stability of ionic compounds. The lattice enthalpy of MgO is approximately −3791 kJ mol⁻¹, whilst that of NaCl is approximately −787 kJ mol⁻¹.

Model answer (4 marks)

The lattice enthalpy is proportional to the product of the charges of the ions and inversely proportional to the inter‑ionic distance (Coulomb’s law: ΔH_latt∝q_+q_−/r). In MgO the ions are Mg²⁺ and O²⁻, giving a charge product of 2×2=4. In NaCl the ions are Na⁺ and Cl⁻, giving a charge product of 1×1=1. Thus the electrostatic attraction in MgO is four times stronger. Additionally, Mg²⁺ and O²⁻ are smaller than Na⁺ and Cl⁻, so the inter‑ionic distance r in MgO is shorter. The combination of a larger charge product and a smaller r makes the electrostatic attraction in MgO much stronger, resulting in a lattice enthalpy of about –3791 kJ mol⁻¹ versus –787 kJ mol⁻¹ for NaCl.

Examiner tips

  • Use Coulomb’s law explicitly (q₁q₂/r) to link charge and distance to lattice enthalpy.
  • State the charge products (4 vs 1) and the relative ion sizes clearly.
  • Explain that a larger charge product and shorter distance give a more negative lattice enthalpy.

Common mistakes

  • Confusing lattice enthalpy sign (more negative means stronger attraction).
  • Omitting the ion size argument or the charge product comparison.

Mark scheme (4 marks)

  1. Lattice enthalpy depends on the charges of the ions and the distance between them (Coulomb's law / electrostatic attraction).
  2. Mg²⁺ and O²⁻ each carry a charge of 2+ and 2− respectively, giving a charge product of 4, compared with Na⁺ (1+) and Cl⁻ (1−) with a charge product of 1.
  3. Mg²⁺ and O²⁻ are smaller ions than Na⁺ and Cl⁻ respectively, so the interionic distance in MgO is shorter.
  4. Both the higher charge and the shorter interionic distance result in a much stronger electrostatic attraction in MgO, giving it a significantly larger (more negative) lattice enthalpy than NaCl.

Key terms in this question

lattice enthalpy · Coulomb's law

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