Born–Haber cycles and lattice enthalpy (HL)

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The enthalpy change when **1 mol** of a **solid ionic compound** is converted into its **gaseous ions** (e.g. NaCl(s) → Na⁺(g) + Cl⁻(g)); **endothermic (+)**.

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There is **no single experiment** that turns a solid into a gas of free ions, so it is found **indirectly** via a Born–Haber cycle and Hess's law.

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A closed **enthalpy cycle** linking ΔH_{f}⊖ of an ionic solid to atomisation, bond dissociation, ionisation energy, electron affinity and lattice enthalpy — solved with **Hess's law**.

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**Endothermic (+)** — energy is needed to make gaseous atoms from an element.

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**Always endothermic (+)** — removing an electron works against the nuclear attraction.

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**Usually exothermic (−)** for the first electron added to a gaseous atom.

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**Endothermic (+)** — an electron is forced onto an already-negative ion.

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$\Delta H_{lat}^{\ominus} = \Delta H_{atom}^{\ominus} + \Delta H_{IE}^{\ominus} + \Delta H_{EA}^{\ominus} - \Delta H_{f}^{\ominus}$.

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**Bigger charge → larger** lattice enthalpy (stronger electrostatic attraction); the **dominant** factor. MgO ≫ NaCl.

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**Smaller ions → larger** lattice enthalpy — the ions sit closer together, so attraction is stronger. NaF > NaI.

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Forgetting that subtracting a **negative** ΔH_{f}⊖ **adds** its magnitude — write every value with its sign in brackets.

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**kJ mol⁻¹** (kilojoules per mole).