Edexcel International A Level (IAL) Chemistry (YCH11) - Unit 4 - 12.13 Born-Haber cycles-Study Notes - New Syllabus

12.13 Born–Haber Cycles and Related Calculations

A Born–Haber cycle is an energy cycle used to calculate lattice energy or other unknown enthalpy changes in ionic compounds. It applies Hess’s Law by breaking the formation of an ionic solid into a series of steps involving atoms, ions and electrons.

Key Idea (Hess’s Law)

The total enthalpy change is independent of the pathway taken, so the sum of enthalpy changes in a cycle is zero.

Typical Steps in a Born–Haber Cycle

For an ionic compound such as \( \mathrm{NaCl} \):

\( \mathrm{Na(s) + \frac{1}{2}Cl_2(g) \rightarrow NaCl(s)} \)

The cycle includes:

• Enthalpy of formation (\( \mathrm{\Delta_f H} \))
• Atomisation of metal: \( \mathrm{Na(s) \rightarrow Na(g)} \)
• Atomisation of non-metal: \( \mathrm{\frac{1}{2}Cl_2(g) \rightarrow Cl(g)} \)
• Ionisation energy: \( \mathrm{Na(g) \rightarrow Na^+(g) + e^-} \)
• Electron affinity: \( \mathrm{Cl(g) + e^- \rightarrow Cl^-(g)} \)
• Lattice energy: \( \mathrm{Na^+(g) + Cl^-(g) \rightarrow NaCl(s)} \)

Energy Cycle Relationship

\( \mathrm{\Delta_f H = \Delta_{at}H (metal) + \Delta_{at}H (non-metal) + IE + EA + \Delta_{latt}H} \)

Rearranged to find lattice energy:

\( \mathrm{\Delta_{latt}H = \Delta_f H – (other\ enthalpy\ changes)} \)

Important Notes

• Pay attention to signs (endothermic = positive, exothermic = negative).
• Include all steps: atomisation, ionisation, electron affinity.
• Multiply values according to stoichiometry.

Diagrammatic Representation (Concept)

The Born–Haber cycle is typically drawn as an energy level diagram showing:

• Direct route: elements → ionic solid (enthalpy of formation).
• Indirect route: elements → gaseous atoms → gaseous ions → ionic solid.

Key Features

• Used to calculate lattice energy or unknown enthalpy changes.
• Based on Hess’s Law.
• Involves multiple energy steps (atomisation, IE, EA).
• Requires careful handling of signs and coefficients.