Worked Example 1. Formation Cycle
Enthalpy of Combustion from Enthalpies of Formation
Find ΔHr⦵ for: \(\text{CH}_4(\text{g}) + 2\text{O}_2(\text{g}) \rightarrow \text{CO}_2(\text{g}) + 2\text{H}_2\text{O}(\text{l})\)
Data: \(\Delta H_f^\ominus(\text{CH}_4) = -74\) | \(\Delta H_f^\ominus(\text{CO}_2) = -394\) | \(\Delta H_f^\ominus(\text{H}_2\text{O}) = -286\text{ kJ mol}^{-1}\)
\( \Delta H_r^\ominus = [(-394) + 2(-286)] - [(-74) + 0] \)
\( = -966 - (-74) = \mathbf{-892 \text{ kJ mol}^{-1}} \)
Worked Example 2. Bond Enthalpy
Enthalpy of Combustion from Average Bond Enthalpies
Combustion of methane: \(\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}\)
Bonds broken: \(4 \times \text{C--H}\) (\(4 \times 414 = 1656\)) + \(2 \times \text{O=O}\) (\(2 \times 498 = 996\)) = 2652 kJ
Bonds formed: \(2 \times \text{C=O}\) (\(2 \times 804 = 1608\)) + \(4 \times \text{O--H}\) (\(4 \times 463 = 1852\)) = 3460 kJ
\( \Delta H = 2652 - 3460 = \mathbf{-808 \text{ kJ mol}^{-1}} \)
(Less accurate than formation data because bond enthalpies are averages compiled across multiple molecules)
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 |
Thermochemical Calculation Sanity Checks
- Sign check: Ensure exothermic reactions carry a negative sign (−).
- Units: Always include kJ mol⁻¹.
- Stoichiometry: Multiply every ΔH by its balanced molar coefficient.
- State symbols: Write standard state symbols on every intermediate in energy cycles.
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