23.1 Lattice Energy and Born–Haber Cycles

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Define and use enthalpy change of atomisation (ΔH°at) and lattice energy (ΔH°latt)
  2. Define first electron affinity (EA₁), explain the factors that affect electron affinities, and describe and explain trends in electron affinities of Group 16 and Group 17 elements
  3. Construct and use Born–Haber cycles for ionic solids (limited to +1 and +2 cations; −1 and −2 anions)
  4. Carry out calculations using Born–Haber cycles
  5. Explain, in qualitative terms, how ionic charge and ionic radius affect the size of a lattice energy

1. Enthalpy Change of Atomisation

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What is it?

The standard enthalpy change of atomisation (ΔH°at) is the enthalpy change when 1 mole of gaseous atoms is formed from an element in its standard state (its normal physical state at 298 K and 101 kPa).

In plain English: it is the energy needed to turn a solid, liquid, or diatomic gas element into separate, individual gas atoms — one mole of them.

ΔH°at is always positive (endothermic) — you always have to put energy in to break the bonds holding atoms together.

Important detail about standard state

The standard state is the physical form an element exists in at 298 K and 101 kPa. For example:

  • Sodium exists as a solid → Na(s)
  • Chlorine exists as a diatomic gas → Cl₂(g)
  • Bromine exists as a liquid → Br₂(l)

Because atomisation always produces 1 mole of gaseous atoms, you may need to use a fraction of a molecule.

Example equations

ElementEquationΔH°at
SodiumNa(s) → Na(g)+107 kJ mol⁻¹
Chlorine½Cl₂(g) → Cl(g)+122 kJ mol⁻¹
Bromine½Br₂(l) → Br(g)positive value
LithiumLi(s) → Li(g)+161 kJ mol⁻¹

Notice that for chlorine, you write ½Cl₂ — not Cl₂ — because you only want 1 mole of Cl atoms, and Cl₂ contains 2 atoms per molecule.

Exam tip: Always include correct state symbols. The product must always be (g) for a gaseous atom.

2. Lattice Energy

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What is it?

Lattice energy (ΔH°latt) is the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions.

In plain English: it is the energy released when positively and negatively charged gas ions come together to form a solid ionic crystal (called a lattice).

ΔH°latt is always negative (exothermic) — forming a lattice always releases a large amount of energy because the strong electrostatic forces of attraction between opposite charges pull the ions together very powerfully.

The large negative value tells us that the ionic lattice is very stable compared to its separate gaseous ions.

Example equations

For sodium chloride (NaCl):

Na+(g)+Cl−(g)→NaCl(s)ΔHlatt∘=−787 kJ mol−1\text{Na}^+(g) + \text{Cl}^-(g) \rightarrow \text{NaCl}(s) \quad \Delta H^\circ_{latt} = -787 \text{ kJ mol}^{-1}

For magnesium chloride (MgCl₂):

Mg2+(g)+2Cl−(g)→MgCl2(s)ΔHlatt∘=−2526 kJ mol−1\text{Mg}^{2+}(g) + 2\text{Cl}^-(g) \rightarrow \text{MgCl}_2(s) \quad \Delta H^\circ_{latt} = -2526 \text{ kJ mol}^{-1}

For magnesium oxide (MgO):

Mg2+(g)+O2−(g)→MgO(s)ΔHlatt∘=−3923 kJ mol−1\text{Mg}^{2+}(g) + \text{O}^{2-}(g) \rightarrow \text{MgO}(s) \quad \Delta H^\circ_{latt} = -3923 \text{ kJ mol}^{-1}

Key point: Lattice energy cannot be measured directly by a single experiment. We calculate it using an energy cycle called a Born–Haber cycle.

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