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How is the energy content of a fuel measured and compared?

Define and calculate the enthalpy of combustion of fuels, and compare fuels by their energy content per gram and per mole.

How the enthalpy of combustion measures the energy released when a fuel burns completely, and how to calculate and compare the energy content of fuels per mole and per gram.

Generated by Claude Opus 4.78 min answer

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  1. What this dot point is asking
  2. Defining enthalpy of combustion
  3. Measuring it by calorimetry
  4. Comparing fuels
  5. Biofuels and fossil fuels

What this dot point is asking

You must define enthalpy of combustion, calculate it from data, and compare fuels on a per-mole and per-gram basis.

Defining enthalpy of combustion

Complete combustion of a hydrocarbon gives carbon dioxide and water:

CxHy+(x+y4)O2→x CO2+y2 H2O\text{C}_x\text{H}_y + \left(x + \tfrac{y}{4}\right)\text{O}_2 \rightarrow x\,\text{CO}_2 + \tfrac{y}{2}\,\text{H}_2\text{O}

Measuring it by calorimetry

The heat released by burning a known mass of fuel is found from the temperature rise of a known mass of water:

q=mcΔTq = mc\Delta T

with c=4.18 J g−1 ∘C−1c = 4.18\ \text{J g}^{-1}\,{}^\circ\text{C}^{-1} for water. Dividing by the moles of fuel burned gives the molar enthalpy of combustion.

Comparing fuels

A fair comparison can be made per mole or per gram:

  • Per mole values rise with molecular size (more bonds to break and form), so larger molecules release more energy per mole - but this can be misleading because their molar masses differ.
  • Per gram (specific energy) is often the fairer comparison for transport fuels, because vehicles carry fuel by mass/volume. Dividing the molar value by the molar mass gives energy per gram.

Biofuels and fossil fuels

Topic 4 also asks you to weigh fuels as resources. Fossil fuels are non-renewable and add net CO2\text{CO}_2 to the atmosphere. Biofuels (such as ethanol from fermentation, or biodiesel) are renewable and closer to carbon-neutral because the CO2\text{CO}_2 released was recently absorbed by the source plants - though their energy content per gram is typically lower than petrol or diesel.

Exam-style practice questions

Practice questions written in the style of SACE Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

2024 SACE Stage 24 marksWrite the thermochemical equation for the complete combustion of C17H34O2(l). (Energy released = 9950 kJ mol-1.)
Show worked answer →

Balance the combustion equation, then attach the enthalpy change.

  1. Complete combustion gives CO2 and H2O. Carbon: 17 CO2. Hydrogen: 34 H, so 17 H2O. Oxygen needed on the right = 34 (from CO2) + 17 (from H2O) = 51; the molecule supplies 2, so O2 supplies 49, meaning 24.5 O2.

  2. C17H34O2(l) + 24.5O2(g) -> 17CO2(g) + 17H2O(l)

  3. Combustion is exothermic, so delta H is negative: delta H = -9950 kJ mol-1.

Final: C17H34O2(l) + 24.5O2(g) -> 17CO2(g) + 17H2O(l), delta H = -9950 kJ mol-1. Marks for correct products, the carbon and hydrogen balance, the oxygen coefficient, and the correct sign and value of delta H.

2022 SACE Stage 22 marksDiesel from fossil fuels includes C18H38 and C14H30. Incomplete combustion produces carbon (soot). Explain why more soot is produced during the combustion of C18H38 than during the combustion of C14H30.
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Soot forms when there is insufficient oxygen for complete combustion, and larger molecules need more oxygen.

  1. C18H38 has a higher carbon content and requires more oxygen per molecule to combust completely than the shorter C14H30.

  2. With the same air supply, the larger C18H38 molecule is more likely to undergo incomplete combustion (relatively less oxygen available per carbon atom), producing more unburnt carbon (soot). One mark for the larger molecule needing more oxygen, one for linking the oxygen shortfall to more incomplete combustion/soot.

2022 SACE Stage 23 marksDiesel has energy density 45 MJ kg-1 and density 0.85 kg L-1; biodiesel has energy density 38 MJ kg-1 and density 0.88 kg L-1. Calculate the volume, in L, of biodiesel required to produce the same amount of energy as the complete combustion of 60 L of diesel.
Show worked answer →

Find the energy from the diesel, then the volume of biodiesel that supplies it.

  1. Mass of diesel = 60 x 0.85 = 51 kg. Energy = 51 x 45 = 2295 MJ.

  2. Energy per litre of biodiesel = 38 x 0.88 = 33.44 MJ L-1.

  3. Volume of biodiesel = 2295 / 33.44 = 68.6 L (about 69 L). One mark for the diesel energy, one for the biodiesel energy per litre, one for the final volume.

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