C1: Thermodynamics and Born-Haber Cycles

Year 1 / ASYear 2 / A-Level All Boards (AQA, Edexcel, OCR, WJEC, CCEA) AQA

Lattice enthalpy, Born-Haber cycles, entropy (ΔS), Gibbs free energy (ΔG = ΔH - TΔS), feasibility of reactions.

Exam Board:

📋 Key Definitions and Core Concepts

Lattice Enthalpy: Enthalpy change when one mole of solid ionic lattice forms from gaseous ions under standard conditions (exothermic).

Gibbs Free Energy: ΔG = ΔH - TΔS. A reaction is thermodynamically feasible when ΔG ≤ 0.

Born-Haber: ΔH_f = ΔH_at(metal) + IE(metal) + ΔH_at(non-metal) + EA(non-metal) + ΔH_latt.
Discrepancy between theoretical (ionic model) and experimental Born-Haber lattice enthalpies indicates covalent character due to polarization.
ΔG ≤ 0 temperature threshold: T = ΔH / ΔS (ensure units match: J/mol vs kJ/mol).

Exam-Style Question

Question:

For CaCO₃(s) → CaO(s) + CO₂(g), ΔH = +178 kJ/mol, ΔS = +161 J/(K·mol). Calculate the temperature above which decomposition is feasible.

Model Solution & Mark Scheme:

Feasible when ΔG ≤ 0 => T ≥ ΔH / ΔS.
ΔH = 178,000 J/mol.
T = 178,000 / 161 = 1105.6 K (833°C).

Q1: Why is lattice enthalpy of MgO much more exothermic than NaCl?

Show Model Answer

Answer: Mg²⁺ and O²⁻ have higher charges (+2/-2 vs +1/-1) and smaller ionic radii, generating much stronger electrostatic forces.

Q2: Explain why dissolving ammonium nitrate in water is endothermic yet spontaneous.

Show Model Answer

Answer: ΔH > 0 but solid-to-aqueous dissolution greatly increases entropy (ΔS >> 0). At 298 K, TΔS > ΔH, making ΔG = ΔH - TΔS < 0.

Physics & Maths Tutor -- Free notes, worksheets, and past paper questions by topic
Dr Frost Maths -- Free resources, slides, and interactive questions
BBC Bitesize -- BBC Bitesize revision resources