A Born-Haber cycle breaks the formation of an ionic compound into individual energy steps. This allows us to calculate lattice enthalpy — a quantity that cannot be measured directly.
Key Definition
Lattice enthalpy (ΔHlat) is the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions. It is always exothermic (negative).
Na⁺(g) + Cl⁻(g) → NaCl(s) ΔHlat < 0
The Steps in a Born-Haber Cycle
| Step | Name | Sign | Example (NaCl) |
|---|---|---|---|
| 1 | Atomisation of metal | + (endo) | Na(s) → Na(g) |
| 2 | Atomisation of non-metal | + (endo) | ½Cl₂(g) → Cl(g) |
| 3 | Ionisation energy (IE) | + (endo) | Na(g) → Na⁺(g) + e⁻ |
| 4 | Electron affinity (EA) | − (exo)* | Cl(g) + e⁻ → Cl⁻(g) |
| 5 | Lattice enthalpy | − (exo) | Na⁺(g) + Cl⁻(g) → NaCl(s) |
*First electron affinity is usually exothermic; second EA is endothermic.
Born-Haber Cycle for NaCl
Applying Hess's Law
ΔHf = ΔHat(Na) + ΔHat(Cl) + IE₁(Na) + EA(Cl) + ΔHlat
Rearranging to find lattice enthalpy:
ΔHlat = ΔHf − ΔHat(Na) − ΔHat(Cl) − IE₁(Na) − EA(Cl)
Think About It
Lattice enthalpy becomes more exothermic when ions are smaller and have higher charges. Why?
Smaller ions and higher charges mean stronger electrostatic attraction between the ions (Coulomb's Law: F ∝ q₁q₂/r²). More energy is released when these ions come together to form the lattice.