IB ChemistryReactivity 1R1.2R1.2.2
R1.2.2HL

Born-Haber Cycles

Constructing energy cycles for ionic compounds. Lattice enthalpy from experimental data.

🟣 This is Higher Level (HL) content.

📘 Lattice Enthalpy (IB Definition)

The enthalpy change when one mole of a solid ionic compound is completely separated into gaseous ions at infinite separation. Always positive (endothermic dissociation).

The 5 Components

Step Process Sign
Atomisation (metal) Solid metal → gaseous atoms + (endo)
Atomisation (non-metal) ½X₂(g) → X(g). Half bond dissociation + (endo)
Ionisation energy M(g) → M⁺(g) + e⁻ (can be 1st + 2nd for M²⁺) + (endo)
Electron affinity X(g) + e⁻ → X⁻(g) Usually − (exo)
Enthalpy of formation Elements → ionic solid (the "shortcut" route) Usually − (exo)

Worked Example. MgCl₂

Born-Haber Cycle for MgCl₂

Mg(s) + Cl₂(g) Mg(g) + Cl₂(g) Mg(g) + 2Cl(g) Mg²⁺(g) + 2e⁻ + 2Cl(g) Mg²⁺(g) + 2Cl⁻(g) MgCl₂(s) ΔH(at, Mg) = +148 ΔH(at, Cl₂) = +242 IE₁ + IE₂ = +2189 2×EA(Cl) = -698 -ΔH(latt) = -2522 ΔH(f) = -641

Data: ΔHf⦵ = −641 | ΔHat(Mg) = +148 | IE₁ + IE₂ = +2189 | ΔHat(Cl₂) = +242 (for 2 mol Cl) | EA(Cl) × 2 = −698

Cycle: −641 = 148 + 2189 + 242 − 698 − ΔHlatt

∴ ΔHlatt = +2522 kJ mol⁻¹

Theoretical vs Experimental

If experimental > theoretical → the compound has significant covalent character (Fajans' rules: small, highly charged cation polarises the anion's electron cloud).

NaCl: close match (purely ionic). AgI: large discrepancy (significant covalent character).

⚠️ Examiner Traps

  • For MgCl₂: multiply EA(Cl) by 2 and include both IE₁ and IE₂
  • 2nd EA of O²⁻ is endothermic (+844 kJ mol⁻¹). Students always get the sign wrong
  • State symbols on every species are mandatory for full marks
← R1.2.1 Energy CyclesR1.2.3 Enthalpy of Solution (HL) →