9701 · 23.1
Lattice energy and Born-Haber cycles
A Born-Haber cycle is a clever energy diagram that breaks down the formation of an ionic solid into a series of simpler, measurable steps. By applying Hess's Law, we can calculate the lattice energy, which is too difficult to measure directly.
Need to know
What you need to know
- **Standard Lattice Energy (ΔH°_latt)**: Formation of 1 mole of solid ionic lattice from its gaseous ions. E.g., Na⁺(g) + Cl⁻(g) → NaCl(s). This is always **exothermic**.
- **Standard Enthalpy of Formation (ΔH°_f)**: Formation of 1 mole of a compound from its elements in their standard states. E.g., Na(s) + ½Cl₂(g) → NaCl(s). Can be exothermic or endothermic.
- **Standard Enthalpy of Atomisation (ΔH°_at)**: Formation of 1 mole of gaseous atoms from an element in its standard state. E.g., Na(s) → Na(g). This is always **endothermic**.
- **First Ionisation Energy (IE₁)**: Removal of 1 mole of electrons from 1 mole of gaseous atoms. E.g., Na(g) → Na⁺(g) + e⁻. This is always **endothermic**.
- **First Electron Affinity (EA₁)**: Addition of 1 mole of electrons to 1 mole of gaseous atoms. E.g., Cl(g) + e⁻ → Cl⁻(g). This is usually **exothermic** for non-metals.
Explanation
Building Ionic Crystals, Step by Step
- Lattice energy (ΔH°_latt) is the exothermic enthalpy change when one mole of a solid ionic lattice is formed from its gaseous ions. It's more exothermic for smaller ions with higher charges.
- A Born-Haber cycle applies Hess's law, stating the total enthalpy change is independent of the route taken. It equates the standard enthalpy of formation (ΔH°_f) with the sum of all steps in an alternative pathway.
- The magnitude of lattice energy is determined by the strength of electrostatic attraction. It becomes more exothermic (stronger) as ionic charges increase and ionic radii decrease.
- Comparing the experimental ΔH°_latt (from a Born-Haber cycle) with a theoretical value (from a pure ionic model) reveals covalent character. A large discrepancy suggests significant orbital overlap, often due to a highly polarising cation and a polarisable anion.