Explain why the lattice enthalpy of magnesium oxide is significantly greater in magnitude than that of sodium chloride, using the Born–Haber cycle concept and relevant periodic trends.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Magnesium oxide (MgO) and sodium chloride (NaCl) both adopt the rock salt crystal structure, yet their standard lattice enthalpies differ considerably: MgO has a lattice enthalpy of approximately −3850 kJ mol⁻¹ compared to approximately −787 kJ mol⁻¹ for NaCl.
Model answer (4 marks)
MgO has a much larger lattice enthalpy because the ions carry higher charges and are smaller.
1. MgO is formed from Mg²⁺ and O²⁻, whereas NaCl is formed from Na⁺ and Cl⁻ – the charge product (z⁺z⁻) is 4 for MgO and 1 for NaCl.
2. In the Born–Haber cycle the lattice enthalpy is proportional to z⁺z⁻/r, so the higher charge gives a stronger Coulombic attraction.
3. The ionic radii are also smaller: Mg²⁺ (≈0.72 Å) < Na⁺ (≈1.02 Å) and O²⁻ (≈1.40 Å) < Cl⁻ (≈1.81 Å). The inter‑ionic distance r⁺+r⁻ is therefore shorter in MgO.
4. A shorter r increases the electrostatic attraction (force ∝1/r²), further lowering the lattice enthalpy.
Thus, the combination of higher charges and smaller radii makes the lattice enthalpy of MgO far more exothermic than that of NaCl.
1. MgO is formed from Mg²⁺ and O²⁻, whereas NaCl is formed from Na⁺ and Cl⁻ – the charge product (z⁺z⁻) is 4 for MgO and 1 for NaCl.
2. In the Born–Haber cycle the lattice enthalpy is proportional to z⁺z⁻/r, so the higher charge gives a stronger Coulombic attraction.
3. The ionic radii are also smaller: Mg²⁺ (≈0.72 Å) < Na⁺ (≈1.02 Å) and O²⁻ (≈1.40 Å) < Cl⁻ (≈1.81 Å). The inter‑ionic distance r⁺+r⁻ is therefore shorter in MgO.
4. A shorter r increases the electrostatic attraction (force ∝1/r²), further lowering the lattice enthalpy.
Thus, the combination of higher charges and smaller radii makes the lattice enthalpy of MgO far more exothermic than that of NaCl.
Examiner tips
- Show the charge product first, then explain how it enters the lattice enthalpy equation; link to Born–Haber cycle.
- Mention both charge and radius effects explicitly; use the words ‘higher charge’ and ‘smaller radius’ to match the mark scheme.
- Keep the answer concise – 4 points, one sentence each.
- Use correct chemical symbols and units (kJ mol⁻¹).
Common mistakes
- Confusing lattice enthalpy with lattice energy; writing the wrong sign. Assuming only charge matters and ignoring ionic radii. Using the wrong ionic radii or not stating the inter‑ionic distance explicitly.
Mark scheme (4 marks)
- MgO involves 2+ and 2− ions whereas NaCl involves 1+ and 1− ions, so the ionic charges (charge product) are greater in MgO.
- Greater ionic charges lead to stronger electrostatic (Coulombic) attraction between oppositely charged ions in the lattice.
- The ionic radius of Mg²⁺ is smaller than that of Na⁺, and the ionic radius of O²⁻ is smaller than that of Cl⁻, so the interionic distance (r⁺ + r⁻) in MgO is shorter.
- A shorter interionic distance further increases the electrostatic attraction (force ∝ 1/r²), so both the higher charge and the smaller ionic radii act together to make the lattice enthalpy of MgO much more exothermic than that of NaCl.
Key terms in this question
lattice enthalpy · Born–Haber cycle
Related
- All IB DP Chemistry Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →