Lattice energy cannot be measured directly, but a Born-Haber cycle finds it from steps you can measure: atomising the elements, ionising the metal, adding electrons to the non-metal, and the enthalpy change of formation.
The lattice energy is the enthalpy change when 1 mol of an ionic compound is formed from its gaseous ions under standard conditions, e.g. Na+(g) + Cl−(g) → NaCl(s); it is always exothermic. A Born-Haber cycle is a Hess cycle linking it to measurable steps: enthalpy change of atomisation of each element, ionisation energies of the metal, electron affinities of the non-metal and the enthalpy change of formation. For NaCl: LE = −411 − (+107 + 496 + 122 − 349) = −787 kJ mol−1. Lattice energy becomes more exothermic when the ions have higher charge and smaller radius, because the electrostatic attraction between them is stronger.
Match each enthalpy term to its equation in the simulator. Every definition is for 1 mol of the species named, under standard conditions.
| Term | Example equation | Sign |
|---|---|---|
| enthalpy change of atomisation, ΔHat | Na(s) → Na(g); ½Cl2(g) → Cl(g) | always + (bonds broken) |
| first ionisation energy, IE1 | Mg(g) → Mg+(g) + e− | + (+736) |
| second ionisation energy, IE2 | Mg+(g) → Mg2+(g) + e− | + (+1450) |
| first electron affinity, EA1 | Cl(g) + e− → Cl−(g) | usually − (−349) |
| second electron affinity, EA2 | O−(g) + e− → O2−(g) | + (+798) |
| lattice energy, ΔHlatt | Na+(g) + Cl−(g) → NaCl(s) | always − |
Build the Born-Haber cycle step by step in the simulator. The two routes from the elements to the solid must have the same total enthalpy change.
| Step | NaCl / kJ mol−1 | MgO / kJ mol−1 |
|---|---|---|
| atomise the metal | +107 | +148 |
| ionise the metal | +496 (IE1) | +736 + 1450 (IE1 + IE2) |
| atomise the non-metal | +122 | +248 (½ × 496) |
| add electrons | −349 (EA1) | −141 + 798 (EA1 + EA2) |
| enthalpy change of formation | −411 | −602 |
| lattice energy | −787 | −3841 |
Four quick checks. Each correct answer earns XP and records this skill on your profile.
Which equation represents the lattice energy of sodium chloride?
Why is the second electron affinity of oxygen endothermic?
What is the enthalpy change of atomisation of chlorine if the Cl–Cl bond energy is +244 kJ mol−1?
Which compound has the most exothermic lattice energy?
Compare the lattices in the simulator: smaller, more highly charged ions sit closer together and attract more strongly.
| Compound | Ions | Lattice energy / kJ mol−1 | Reason |
|---|---|---|---|
| NaCl | Na+, Cl− | −787 | reference |
| NaBr | Na+, Br− | −747 | larger anion, less exothermic |
| KCl | K+, Cl− | −718 | larger cation, less exothermic |
| MgCl2 | Mg2+, Cl− | −2521 | 2+ cation, smaller than Na+ |
| MgO | Mg2+, O2− | −3841 | both ions doubly charged |
Lattice energy goes from gaseous ions to the solid, so it is negative; do not reverse it. Use ½ the bond energy for the atomisation of Cl or O, and remember MgO needs both IE1 + IE2 and EA1 + EA2, with EA2 positive. For MgCl2, the chlorine steps are doubled.
Unlocks once the four checks above are done. Worth more XP, written to A Level Paper 4 standard.
Use the data to find the lattice energy of NaCl. ΔHf −411; ΔHat(Na) +107; IE1(Na) +496; ΔHat(Cl) +122; EA1(Cl) −349 (all kJ mol−1).
Using ΔHf(NaCl) −411, ΔHat(Na) +107, IE1(Na) +496, Cl–Cl bond energy +244 and LE −787 (all kJ mol−1), what is the first electron affinity of chlorine?
Which change makes the lattice energy of an ionic compound MORE exothermic?
For MgO, ΔHf = −602, ΔHat(Mg) +148, IE1 + IE2 = +2186, ΔHat(O) +248, EA1 −141, EA2 +798 (all kJ mol−1). What is the lattice energy of MgO?
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