Born–Haber Cycles HL Only

Full Notes

What Is a Born–Haber Cycle?

A Born–Haber cycle breaks down the formation of an ionic compound into a series of theoretical steps. It applies Hess’s Law to calculate one unknown energy change (often lattice enthalpy or enthalpy of formation).

Each step corresponds to a real or theoretical process in forming the ionic solid from its elements in standard states.

Standard Born–Haber Cycles Often Include

• Enthalpy of Formation (ΔH_f^⦵):
  Energy change when 1 mole of an ionic compound forms from its elements in standard states.
  Example: Na (s) + ½Cl₂ (g) → NaCl (s)


• Enthalpy of Atomisation (ΔH_at^⦵):
  Energy change when 1 mole of gaseous atoms forms from an element.
  Example:

  Na (s) → Na (g)
  ½Cl₂ (g) → Cl (g)

• 1st Ionisation Energy (IE):
  Energy required to remove 1 mole of electrons from 1 mole of gaseous atoms of an element (to form 1 moles worth of ions with a 1+ charge).
  Example: Na (g) → Na⁺ (g) + e⁻


• Bond Enthalpy:
  Energy required to break one mole of a covalent bond in gaseous molecules.
  Example: Cl₂ (g) → 2Cl (g)


• 1st Electron Affinity (EA):
  Energy change when 1 mole of gaseous atoms gains electrons to form 1 moles worth of ions with a 1− charge.
  Example: Cl (g) + e⁻ → Cl⁻ (g)


• Lattice Enthalpy (ΔH_latt^⦵):
  Energy change when 1 mole of an ionic lattice forms or dissociates from gaseous ions. This is often the unknown value we solve for.

Matt’s exam tip

You won’t be asked to construct a complete Born–Haber cycle in an exam, however you do need to be aware of how to construct them in order to understand how they work!

Example: Born–Haber Cycle for NaCl

1. Step 1: Formation of NaCl (ΔH_f^⦵):Na (s) + ½Cl₂ (g) → NaCl (s)
2. Step 2: Atomisation of Na (ΔH_at^⦵): Na (s) → Na (g)
3. Step 3: Atomisation of Cl₂ (ΔH_at^⦵):½Cl₂ (g) → Cl (g)
4. Step 4: Ionisation Energy of Na (IE₁):Na (g) → Na⁺ (g) + e⁻
5. Step 5: Electron Affinity of Cl (EA₁): Cl (g) + e⁻ → Cl⁻ (g)
6. Step 6: Lattice Enthalpy (ΔH_latt^⦵):Na⁺ (g) + Cl⁻ (g) → NaCl (s)

By rearranging these enthalpy changes and substituting experimental values into the cycle we can use Hess’s Law to calculate ΔH_latt^⦵.

Summary Table

Summary

• A Born–Haber cycle applies Hess’s Law to ionic compound formation.
• It includes enthalpy of formation, atomisation, ionisation, electron affinity, and lattice enthalpy.
• Lattice enthalpy is often the unknown calculated value.