Worked Example 1. Formation Cycle
Find ΔHr⦵ for: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)
Data: ΔHf⦵(CH₄) = −74 | ΔHf⦵(CO₂) = −394 | ΔHf⦵(H₂O) = −286
\( \Delta H_r^\ominus = [(-394) + 2(-286)] - [(-74) + 0] \)
\( = -966 - (-74) = \mathbf{-892 \text{ kJ mol}^{-1}} \)
Worked Example 2. Bond Enthalpy
Combustion of methane: CH₄ + 2O₂ → CO₂ + 2H₂O
Bonds broken: 4×C–H (4×414 = 1656) + 2×O=O (2×498 = 996) = 2652 kJ
Bonds formed: 2×C=O (2×804 = 1608) + 4×O–H (4×463 = 1852) = 3460 kJ
\( \Delta H = 2652 - 3460 = \mathbf{-808 \text{ kJ mol}^{-1}} \)
(Less accurate than formation data because bond enthalpies are averages)
Quick Reference. Which Formula?
| Given Data | Formula |
|---|---|
| ΔHf⦵ values | ΔHr = Σ(products) − Σ(reactants) |
| ΔHc⦵ values | ΔHr = Σ(reactants) − Σ(products) |
| Bond enthalpies | ΔH = Σ(broken) − Σ(formed) |
| Born-Haber data (HL) | ΔHf = ΔHat + IE + EA − ΔHlatt |
| Solution data (HL) | ΔHsol = ΔHlatt + ΣΔHhyd |
⚠️ Final Exam Checklist
- ✅ Correct sign on final answer (exothermic = negative)
- ✅ Units: kJ mol⁻¹
- ✅ Stoichiometric coefficients applied to every ΔH value
- ✅ State symbols on all species in Born-Haber diagrams