Born–Haber cycle: lattice enthalpy of MgCl₂

Worked example

Calculate the enthalpy of lattice formation of magnesium chloride. ΔfH(MgCl₂) = −641 kJ mol⁻¹; ΔatH(Mg) = 149 kJ mol⁻¹; first and second ionisation energies of Mg = 738 kJ mol⁻¹ and 1452 kJ mol⁻¹; ΔatH(Cl), per mole of Cl atoms, = 121 kJ mol⁻¹; first electron affinity of Cl = −348 kJ mol⁻¹.

1. 1. Weighted sum of 1·ΔfH(MgCl₂) − 1·ΔatH(Mg) − 1·IE₁(Mg) − 1·IE₂(Mg) − 2·ΔatH(Cl) − 2·EA₁(Cl) → Lattice formation enthalpy

   = −2526 kJ mol⁻¹

Answer: ΔLH (formation) = −2530 kJ mol⁻¹

Method

ΔLH = ΔfH − [ΔatH(Mg) + IE₁ + IE₂ + 2ΔatH(Cl) + 2EA₁(Cl)]. The ×2 terms are because one formula unit contains two Cl⁻ ions; ΔatH(Cl) is defined per mole of Cl atoms formed.

Common mistakes

• MgCl₂ has two chloride ions: atomise chlorine twice and add two electron affinities.
• Mg²⁺ needs both the first and the second ionisation energies.
• That is the lattice dissociation enthalpy. Lattice formation is exothermic, so it is negative.

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