Born–Haber cycle (enthalpy balance) (ΔHf° = ΔHsub + IE + ½D + EA + ΔHlatt (gaseous ions → solid lattice))
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ΔHf° = ΔHsub + IE + ½D + EA + ΔHlatt (gaseous ions → solid lattice)
What each symbol means
| Symbol | What it stands for |
|---|---|
| D | Bond dissociation enthalpy of halogen (per mole of X₂) (kJ mol⁻¹) |
| \mathrm{EA} | Electron gain enthalpy of halogen atom (often negative if exothermic) (kJ mol⁻¹) |
| \mathrm{IE} | Ionization enthalpy of metal (g → M⁺ + e⁻) (kJ mol⁻¹) |
| ΔH_f^\circ | Standard molar enthalpy of formation of the ionic solid (kJ mol⁻¹) |
| ΔH_{\mathrm{sub}} | Enthalpy of sublimation of metal (s → g) (kJ mol⁻¹) |
| ΔH_{\mathrm{latt}} | Lattice enthalpy: M⁺(g) + X⁻(g) → MX(s); exothermic → negative (kJ mol⁻¹) |
When to use this
Hess cycle for 1 mol MX(s) from elements in standard states. All steps gas-phase after sublimation unless noted. EA is usually written as actual ΔH (Cl: negative). Lattice formation step releases energy → ΔHlatt < 0 in this bookkeeping.