Chemistry • Year 11 • Module 4 • Lesson 10
Hess’s Law Applied — Heat of Combustion & Consolidation
Apply the three calculation methods, interpret real data on fuel efficiency, and evaluate which method is appropriate in each scenario.
1. Alcohol fuel comparison — interpret the data table
The table below shows thermochemical data for five alcohol fuels. Use it to answer questions 1.1–1.4. 8 marks
| Alcohol | Formula | M (g mol−1) | ΔHc (kJ mol−1) | Energy per gram (kJ g−1) |
|---|---|---|---|---|
| Methanol | CH3OH(l) | 32.04 | −726 | calculate |
| Ethanol | C2H5OH(l) | 46.07 | −1367 | 29.7 |
| Propan-1-ol | C3H7OH(l) | 60.10 | −2021 | 33.6 |
| Butan-1-ol | C4H9OH(l) | 74.12 | −2676 | calculate |
| Pentan-1-ol | C5H11OH(l) | 88.15 | −3329 | 37.8 |
Table 1. Standard enthalpies of combustion for C1–C5 alcohols. Source: NIST Webbook, standard conditions (25°C, 100 kPa).
1.1 Calculate the missing energy-per-gram values for methanol and butan-1-ol. Show the formula and working. 2 marks
1.2 Describe the trend in energy per gram as the alcohol chain lengthens from C1 to C5. Is this consistent with the trend in |ΔHc| per mole? Explain. 2 marks
1.3 A transport company is choosing between ethanol and butan-1-ol as a biofuel for its fleet. Purely on the basis of energy per gram, which fuel would give a greater driving range per kilogram of fuel carried? Justify using the data. 2 marks
1.4 A student claims: “Pentan-1-ol is the best alcohol fuel because it releases the most energy per mole.” Evaluate this claim with reference to the data above and at least one criterion other than energy per mole. 2 marks
2. Graph interpretation — energy per gram vs chain length
The graph below plots energy per gram (kJ g−1) for C1–C5 alcohols against carbon chain length. Answer questions 2.1–2.4. 9 marks
2.1 Describe the trend in energy per gram as the alcohol chain lengthens from C1 to C5 as shown by the graph. Include values in your answer. 2 marks
2.2 At what carbon chain length would the alcohol energy per gram be expected to reach the octane reference line (47.9 kJ g−1)? Estimate from the graph or explain using the trend. 2 marks
2.3 The graph shows a decreasing rate of increase in energy per gram as chain length grows (i.e., the curve levels off). Suggest a chemical reason for why the increase per extra CH2 group gets smaller as the chain gets longer. 2 marks
2.4 Shell Prelude FLNG (Floating Liquefied Natural Gas), anchored off the Kimberley coast of Western Australia, produces liquefied natural gas (LNG — primarily methane, CH4). Methane has ΔHc = −890 kJ mol−1 and M = 16.04 g mol−1. Calculate its energy per gram and compare it to ethanol (29.7 kJ g−1). Comment on why LNG is considered a superior industrial fuel on an energy-density basis. 3 marks
3. Case study — Bundaberg Sugar and bagasse combustion
Read the scenario below and answer questions 3.1–3.3. 8 marks
Scenario. The Bundaberg Sugar Mill (Queensland) burns bagasse — the fibrous residue of crushed sugarcane — to generate steam for both the milling process and electricity export to the grid. Bagasse is approximately 50% cellulose by dry mass; cellulose can be modelled as a repeating unit of glucose (C6H12O6, M = 180.16 g mol−1).
Relevant ΔH°f data (kJ mol−1): CO2(g) = −393.5 • H2O(l) = −285.8 • C6H12O6(s) = −1274.
The balanced combustion equation for glucose is: C6H12O6(s) + 6O2(g) → 6CO2(g) + 6H2O(l)
3.1 Using the ΔH°f data above, calculate ΔHc for glucose. Show full working. State which calculation method you are using and why this method is appropriate given the data provided. 4 marks
3.2 Calculate the energy per gram of glucose and compare it to ethanol (29.7 kJ g−1). Which releases more energy per kilogram? 2 marks
3.3 The Bundaberg Mill’s use of bagasse is described as “carbon-neutral.” Using your knowledge of the carbon cycle and your ΔHc result, explain what this claim means chemically. Is it completely accurate? 2 marks
4. Predict and justify
A student proposes comparing three methods to determine ΔHc for biodiesel (modelled as methyl oleate, C19H36O2): (i) bond energy method, (ii) ΔH°f method, and (iii) Hess’s Law using measured combustion data for related esters. 4 marks
4.1 Rank the three methods in order of expected accuracy for ΔHc of biodiesel (most to least accurate). Justify each ranking step with a specific reason. 3 marks
4.2 In practice, precise ΔH°f data for large ester molecules like methyl oleate may not be available in standard tables. Predict which method would then be the next-best alternative, and explain one limitation that remains. 1 mark
Q1 — Alcohol fuel data table
1.1 Methanol: 726 ÷ 32.04 = 22.7 kJ g−1. Butan-1-ol: 2676 ÷ 74.12 = 36.1 kJ g−1. Both use Eg = |ΔHc| ÷ M.
1.2 Energy per gram increases consistently from 22.7 (C1) to 37.8 (C5) kJ g−1 as chain length increases. This is consistent with the trend in |ΔHc| per mole (726 to 3329), but the per-gram increase is smaller and decelerating because each additional CH2 group adds proportionally less to Eg than it adds to M — the ratio improves because the OH group’s mass contribution becomes a smaller fraction of total molar mass.
1.3 Butan-1-ol (36.1 kJ g−1) gives greater driving range per kilogram than ethanol (29.7 kJ g−1) — it releases 21.5% more energy per gram, so a fuel tank of the same mass delivers more energy.
1.4 The claim is partially valid but incomplete. Pentan-1-ol does release the most energy per mole (3329 kJ mol−1) among these five alcohols, but energy per gram (37.8 kJ g−1) is only marginally higher than butan-1-ol (36.1 kJ g−1). Other criteria include: safety (higher flash point, lower vapour pressure); miscibility with existing petrol; production cost and availability; toxicity. “Best” requires multi-criteria evaluation, not just energy per mole.
Q2 — Graph interpretation
2.1 Energy per gram increases from 22.7 kJ g−1 (C1) to 37.8 kJ g−1 (C5). The rate of increase decreases with each additional CH2 group (C1→C2: +7.0; C2→C3: +3.9; C3→C4: +2.5; C4→C5: +1.7).
2.2 The trend is decelerating and approaching but not yet reaching 47.9 kJ g−1. Based on the diminishing increments, the alcohol line would reach the octane reference at approximately C9–C12 (long-chain alcohols approach alkane energy densities asymptotically). Accept any reasonable estimate between C8 and C12 with a justification referencing the decreasing increments.
2.3 Each additional CH2 group adds approximately 14 g mol−1 to M and adds ∼620 kJ mol−1 to |ΔHc| (roughly one C–C + two C–H bond energies × 2, less O2 bond breaking). The ratio Δ(|ΔHc|) / ΔM ≈ 620/14 ≈ 44 kJ g−1 — but as M grows, the −OH group’s oxygen atom makes up a smaller fraction of the total mass, so the per-gram energy gain per additional CH2 converges toward a constant, giving a levelling curve.
2.4 Methane: Eg = 890 ÷ 16.04 = 55.5 kJ g−1. This is well above ethanol (29.7 kJ g−1) and above octane (47.9 kJ g−1). LNG is considered a superior industrial fuel per unit mass because its very low molar mass combined with a moderate |ΔHc| per mole gives it an exceptionally high energy density per gram — important for industrial turbines and industrial heating applications where mass-to-energy efficiency is valued.
Q3 — Bundaberg bagasse case study
3.1 Method: ΔH°f method, because ΔH°f data is provided for all species. ΣΔH°f(products) = 6(−393.5) + 6(−285.8) = −2361.0 + (−1714.8) = −4075.8 kJ mol−1. ΣΔH°f(reactants) = 1(−1274) + 6(0) = −1274 kJ mol−1. ΔHc = −4075.8 − (−1274) = −2801.8 kJ mol−1.
3.2 Eg = 2801.8 ÷ 180.16 = 15.6 kJ g−1. Ethanol (29.7 kJ g−1) releases almost twice as much energy per kilogram. So ethanol is the superior fuel per unit mass compared to glucose/cellulose.
3.3 “Carbon-neutral” means the CO2 released during combustion equals the CO2 absorbed by the growing sugarcane via photosynthesis over the same growth cycle — the net atmospheric CO2 change is approximately zero over one growth cycle. This is not completely accurate: the process requires energy for harvesting, transport, milling, and disposal of ash, each producing some CO2 from fossil fuels. It is better described as “near carbon-neutral” or “low net carbon.”
Q4 — Predict and justify
4.1 Most accurate: (iii) Hess’s Law with measured combustion data, because it uses precise experimental values specific to real compounds rather than averages — accuracy depends on quality of input data, which here is high. Second: (ii) ΔH°f method, if ΔH°f data is available for such a large molecule; it uses experimentally measured compound-specific values. Least accurate: (i) bond energy method, because it uses average bond enthalpies across many molecular environments and assumes all species are gaseous — errors accumulate across the very large number of bonds in C19H36O2.
4.2 Next-best alternative: Hess’s Law (iii), using measured combustion data for related esters. Limitation: ΔH values for closely related esters must be available and must cancel cleanly to give the target reaction; errors in input data propagate into the final result.