A-level chemistry · Chapter 11
Thermodynamics
Born–Haber cycles, entropy, Gibbs free energy
Lattice enthalpy of formation — the enthalpy change when one mole of a solid ionic compound is formed from its gaseous ions. Always exothermic (large and negative).
Born–Haber cycles
- Route 1 (direct): formation. Route 2: atomise both elements → ionise the metal → electron affinity of the non-metal → lattice formation. Hess: the routes are equal.
- NaCl check: ΔH°f −411 = (+107 atomisation Na) + (+496 IE₁) + (+122 atomisation ½Cl₂) + (−349 EA) + lattice → lattice ≈ −787 kJ mol⁻¹.
- Real lattices vs the perfect ionic model: agreement is good for NaCl; large differences (e.g. AgI) mean covalent character — a small, highly charged cation polarises the anion.
Entropy and feasibility
ΔG = ΔH − TΔS · feasible when ΔG ≤ 0 · switch-over at T = ΔH/ΔS- Entropy S rises with disorder: solid < liquid < gas, and with more moles of gas.
- Units trap: ΔS is usually J K⁻¹ mol⁻¹ — divide by 1000 before mixing with ΔH in kJ.
- An endothermic reaction can still be feasible if TΔS outweighs ΔH (why ice melts above 0 °C).
3.1.8.1The NaCl Born–Haber cycle, fully worked
Worked example. Find the lattice enthalpy of formation of NaCl (kJ mol⁻¹): ΔH°f(NaCl) = −411; atomisation Na +107; first ionisation Na +496; atomisation ½Cl₂ +122; electron affinity Cl −349.
- Formation route = atomise both + ionise + electron affinity + lattice formation.
- −411 = 107 + 496 + 122 + (−349) + ΔH(latt)
- ΔH(latt) = −411 − 376 = −787 kJ mol⁻¹
3.1.8.1Dissolving: lattice vs hydration
- ΔH(solution) = −ΔH(lattice formation) + Σ ΔH(hydration). For NaCl: +787 + (−406 −378) = ≈ +3 kJ mol⁻¹ — slightly endothermic, so dissolving is driven by the entropy increase.
- Hydration enthalpy is more exothermic for smaller, more highly charged ions (stronger ion–dipole attraction).
3.1.8.2ΔG worked example
Worked example — decomposing CaCO₃. ΔH = +178 kJ mol⁻¹, ΔS = +160 J K⁻¹ mol⁻¹.
- Convert: ΔS = 0.160 kJ K⁻¹ mol⁻¹.
- Feasible when ΔG ≤ 0: T ≥ ΔH/ΔS = 178 ÷ 0.160 ≈ 1110 K — why limekilns run hot.
Exam tip. Two classic traps: (1) J vs kJ in ΔS; (2) electron affinity questions — the FIRST is exothermic, the SECOND endothermic (forcing an electron onto an anion), and lattice enthalpy values quoted as "dissociation" flip the sign of everything.
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