Lattice Enthalpy (ΔHlatt)
The enthalpy change when one mole of a solid ionic compound is completely separated into its gaseous ions at infinite separation under standard conditions. Always positive (endothermic dissociation: MX(s) → M⁺(g) + X⁻(g)).
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
Born-Haber Cycle Calculation for MgCl₂
Data: ΔHf⦵ = −641 | ΔHat(Mg) = +148 | IE₁ + IE₂ = +2189 | ΔHat(Cl₂) = +242 (for 2 mol Cl) | EA(Cl) × 2 = −698 kJ mol⁻¹
Cycle balance: −641 = 148 + 2189 + 242 − 698 − ΔHlatt
∴ ΔHlatt(MgCl₂) = +2522 kJ mol⁻¹
Theoretical vs Experimental
Theoretical vs Experimental Lattice Enthalpy
If experimental > theoretical → the compound has significant covalent character (Fajans' rules: a small, highly charged cation polarises the anion's electron cloud).
NaCl: Close match (~1% difference → purely ionic model valid).
AgI: Large discrepancy (significant polarisation and covalent bonding character).
Born-Haber Cycle Traps
- For MgCl₂: multiply EA(Cl) by 2 and sum both IE₁ and IE₂ of Mg.
- The 2nd electron affinity of oxygen (O⁻ → O²⁻) is endothermic (+844 kJ mol⁻¹) due to electron-electron repulsion.
- State symbols on every single species in the Born-Haber cycle are mandatory.
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