Chemistry • Year 11 • Module 4 • Lesson 6
Bond Energy & Enthalpy Change
Build HSC Band 5–6 extended-response technique: evaluate bond energy calculations using real data, quantitative reasoning, and multi-criteria judgements.
1. Extended response — evaluate bond energy data for a real clean-energy decision (Band 5–6)
8 marks Band 5–6
Scenario: The Australian Government’s National Hydrogen Strategy (2019) identified hydrogen (H2) as a key clean-energy export. CSIRO researchers have compared H2 with methane (CH4) as fuels. The bond energy data table and chart below summarise key values.
| Fuel reaction (gaseous products) | Bond energies used (kJ mol−1) | ΔH (bond energy method) | ΔHc° experimental (liquid H2O) |
|---|---|---|---|
| H2(g) + ½O2(g) → H2O(g) | H–H = 436; O=O = 498; O–H = 460 | −235 kJ mol−1 | −286 kJ mol−1 |
| CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) | C–H = 414; O=O = 498; C=O = 743; O–H = 460 | −674 kJ mol−1 | −890 kJ mol−1 |
Additional data: Molar masses: H2 = 2 g mol−1; CH4 = 16 g mol−1. Energy per gram: H2 = 143 kJ g−1 (experimental); CH4 = 55 kJ g−1 (experimental).
Q1. Using the data provided, evaluate the accuracy of the bond energy method and the suitability of H2 as a replacement for CH4 as a fuel. In your response you must:
- Show the full bond energy calculation for H2 combustion to verify the −235 kJ mol−1 value.
- Compare the bond energy ΔH with the experimental ΔHc° for both fuels; calculate the percentage discrepancy for each fuel.
- Explain, using two specific reasons, why the bond energy values differ from experimental values.
- Using both per-mole and per-gram energy data, evaluate whether H2 is a suitable replacement for CH4 on energy grounds.
- Reach an evidence-based judgement that explicitly weighs at least two criteria (energy density, carbon emissions, or accuracy of bond energy data).
2. Multi-step calculation and interpretation — ethanol as a biofuel (Band 5–6)
7 marks Band 5–6
Context: Ethanol (C2H5OH) is used in Australian biofuel blends such as E10 (10% ethanol in petrol). Its structural formula is CH3CH2OH, which contains: 5 × C–H bonds, 1 × C–C bond, 1 × C–O bond, 1 × O–H bond.
Bond energies (kJ mol−1): C–H = 414; C–C = 347; C–O = 360; O–H = 460; O=O = 498; C=O = 743.
Balanced equation: C2H5OH(g) + 3O2(g) → 2CO2(g) + 3H2O(g).
(a) Using the structural formula information provided, calculate ΣB(reactants) for the combustion of ethanol. Show every bond and every multiplication. 2 marks
(b) Calculate ΣB(products) and hence determine ΔH. State whether the reaction is exothermic or endothermic. 2 marks
(c) The experimental ΔHc° for ethanol with liquid water as product is −1367 kJ mol−1. Calculate the percentage discrepancy between your bond energy answer and this experimental value. Then explain, using two specific reasons, why these values differ. 3 marks
Q1 — Evaluate bond energy accuracy and H2 as a clean fuel
Bond energy calculation for H2 (verification):
ΣB(reactants) = 1(436) + ½(498) = 436 + 249 = 685 kJ mol−1
ΣB(products) = 2(460) = 920 kJ mol−1
ΔH = 685 − 920 = −235 kJ mol−1 ✓ (matches table value) [1]
Percentage discrepancies:
H2: |−235 − (−286)| / 286 × 100 = 51/286 × 100 = 17.8% [1]
CH4: |−674 − (−890)| / 890 × 100 = 216/890 × 100 = 24.3% [1]
Two reasons for discrepancy:
Reason 1: Average bond enthalpies — tabulated bond energies (e.g. C–H = 414 kJ mol−1) are averages across many different molecules; the actual C–H bond energy in CH4 differs slightly from this average, and the error accumulates across all bonds in the calculation. [1]
Reason 2: Gaseous state assumption — bond energies are defined for species in the gaseous state, so the calculation uses H2O(g) as the product. The experimental ΔHc° uses H2O(l); the condensation of water vapour to liquid releases additional energy (~44 kJ per mole H2O not captured in the bond energy calculation). For H2 producing 1 mol H2O, this accounts for ~44 of the 51 kJ discrepancy; for CH4 producing 2 mol H2O, condensation contributes ~88 kJ of the 216 kJ discrepancy (the remainder comes from average bond enthalpies). [1]
Energy comparison per mole and per gram:
Per mole: CH4 (−890) releases significantly more energy than H2 (−286). On a per-mole basis, H2 is a lower-energy fuel. However, per gram: H2 = 143 kJ g−1 vs CH4 = 55 kJ g−1. H2 has nearly 3× the energy density per gram. [1]
Evidence-based judgement: H2 is a suitable replacement for CH4 on two key criteria. First, per-gram energy density: H2 delivers 143 kJ g−1 vs CH4’s 55 kJ g−1, making H2 a mass-efficient fuel for vehicles where weight matters. Second, carbon emissions: combustion of H2 produces only H2O with no CO2, directly addressing climate targets — a clear advantage over CH4. The bond energy data overestimates ΔH by 9–16% for both fuels, so neither fuel’s energy advantage is an artefact of the calculation method; the conclusion holds when experimental values are used. The suitability of H2 is therefore well-supported by the evidence. [1]
Q2 — Ethanol combustion calculation and interpretation
(a) ΣB(reactants):
C2H5OH: 5(414) + 347 + 360 + 460 = 2070 + 347 + 360 + 460 = 3237 kJ mol−1
3O2: 3(498) = 1494 kJ mol−1
ΣB(reactants) = 3237 + 1494 = 4731 kJ mol−1 [1 for correct bond identification; 1 for correct arithmetic total]
(b) ΣB(products) and ΔH:
2CO2: 2 × 2(743) = 4(743) = 2972 kJ mol−1
3H2O: 3 × 2(460) = 6(460) = 2760 kJ mol−1
ΣB(products) = 2972 + 2760 = 5732 kJ mol−1
ΔH = 4731 − 5732 = −1001 kJ mol−1 [1 for ΣB(products); 1 for correct ΔH and sign, exothermic]
(c) Percentage discrepancy and explanation:
% discrepancy = |−1001 − (−1367)| / 1367 × 100 = 366 / 1367 × 100 = 26.8% [1]
Reason 1: Average bond enthalpies — the C–H, C–C, and C–O bond energies in ethanol differ slightly from the averaged values used; with many bonds summed, these small deviations accumulate into a noticeable error [1].
Reason 2: Gaseous state assumption — the calculation used H2O(g) as the product; the experimental value assumes H2O(l). Condensation of 3 mol of water vapour releases approximately 3 × 44 = 132 kJ mol−1 of additional energy not captured by the bond energy method. Combined with errors from average bond enthalpies, this accounts for most of the 366 kJ discrepancy observed [1].