Born-Haber Cycles (AQA A-Level Chemistry): Revision Notes

5.1.2 Born-Haber Cycles

Overview

The Born-Haber cycle is an application of Hess's Law, which states that the enthalpy change of a reaction is independent of the path taken. This approach is particularly useful for calculating lattice enthalpies, which cannot be measured directly.

A Born-Haber cycle allows us to indirectly determine the lattice enthalpy of an ionic compound by considering a series of enthalpy changes leading to the formation of the compound from their elements in their standard states.

Key Components of a Born-Haber Cycle

The Born-Haber cycle for an ionic compound includes several enthalpy changes:

1. Enthalpy of Formation ($ΔfH°$) – Enthalpy change when one mole of an ionic compound is formed from its elements in their standard states.
2. Enthalpy of Atomisation ($ΔatH°$) – Enthalpy change when one mole of gaseous atoms forms from the element in its standard state.
3. Ionisation Enthalpy ($ΔieH°$) – Enthalpy change when electrons are removed from one mole of gaseous atoms to form ions.
4. Electron Affinity ($ΔeaH°$) – Enthalpy change when electrons are added to one mole of gaseous atoms to form anions.
5. Lattice Enthalpy ($ΔlattH°$) – Enthalpy change when one mole of an ionic compound is formed from its gaseous ions. This can be calculated indirectly using the Born-Haber cycle.

Born-Haber Cycles with Group 2 Elements

Born-Haber cycles for compounds containing Group 2 elements, such as magnesium chloride ($MgCl₂$), require additional steps compared to Group 1 compounds due to differences in ion charges.

Second Ionisation Energy of Mg

Since Mg forms $Mg²⁺$ions, the second ionisation energy must be considered:

$$\text{Mg}^+ \rightarrow \text{Mg}^{2+} + e^-$$

Atomisation of Chlorine and Electron Affinity

Because two moles of $Cl⁻$ions are formed for each mole of $Mg²⁺$, both the atomisation of chlorine and the electron affinity of chlorine are multiplied by 2:

Atomisation of Cl

$$\text{Cl}_2(g) \rightarrow 2\text{Cl}(g)$$

Electron Affinity

$$2 \times (\text{Cl}(g) + e^- \rightarrow \text{Cl}^-(g))$$