In simple terms
A friendly intro before the formal notes — no formulas yet.
How Much Energy, at What Cost?
Fuels are chemicals that lock away energy in their bonds. Burning them in oxygen releases that energy as heat. This lesson is about two questions: how much energy a fuel gives per gram, and what the burning does to the atmosphere — plus, for HL, what really decides whether a reaction happens at all.
Think of choosing a phone battery. You care about two things: how much charge it holds for its size and weight (that is a fuel's specific energy and energy density), and the hidden cost of making and disposing of it (that is a fuel's environmental impact — the CO₂, the soot, the carbon monoxide). A 'good' fuel, like a 'good' battery, is a trade-off between energy and cost, not just one number.
- 1
Identify the fuel and whether it is a fossil fuel (finite) or a biofuel (renewable biomass).
- 2
Decide whether combustion is complete (plenty of O₂ → CO₂ + H₂O) or incomplete (limited O₂ → CO and/or C soot + H₂O).
- 3
Compare fuels by energy: specific energy in kJ g⁻¹ (energy per gram) and energy density in kJ cm⁻³ (energy per volume).
- 4
Weigh the environmental cost: CO₂ and the enhanced greenhouse effect, toxic CO, and particulates.
- 5
(HL) Ask what drives it: combine ΔH and ΔS in ΔG = ΔH − TΔS to see if the reaction is spontaneous.
Explore the concept
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Key formulas
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Full topic notes
Formal explanation with the rigour you need for the exam.
Combustion, fossil fuels and biofuels
Combustion is an exothermic redox reaction in which a fuel reacts rapidly with oxygen, releasing energy as heat and light; its enthalpy change ΔH is always negative. The fuels we burn fall into two families. Fossil fuels — coal, crude oil (petroleum) and natural gas — formed over millions of years from the buried remains of ancient organisms. They are finite (non-renewable) and release carbon that has been locked underground for geological time. Biofuels — such as bioethanol from fermented sugars, biodiesel and biogas — come from recently living biomass. They are renewable, and because the carbon they release was only recently taken from the air by photosynthesis, they are often described as approximately carbon-neutral.
Combustion is exothermic and is a redox reaction: the fuel is oxidised, oxygen is reduced.
Fossil fuels (coal, oil, natural gas) are finite and add long-buried carbon to the atmosphere.
Biofuels (bioethanol, biodiesel, biogas) are renewable and roughly carbon-neutral, though growing and processing them still costs energy.
A useful fuel is judged on energy content, availability, renewability and pollution together — never on one factor alone.
Complete vs incomplete combustion
The products of burning a hydrocarbon depend entirely on how much oxygen is available. With a plentiful oxygen supply, combustion is complete: every carbon atom is oxidised all the way to carbon dioxide, and the only products are CO₂ and H₂O. The flame is clean and blue, and the maximum energy is released. When oxygen is limited, combustion is incomplete: the carbon is only partly oxidised, giving carbon monoxide (CO) and/or unburnt carbon as soot (C), together with water. The flame is smoky and yellow, and less energy is released because the fuel is not fully oxidised.
Complete combustion (excess O₂): products are CO₂ + H₂O only; clean blue flame; maximum energy released.
Incomplete combustion (limited O₂): products include CO and/or C (soot) plus H₂O; smoky yellow flame; less energy released.
Both CO and soot represent chemical energy that was never given out as heat — this is why incomplete combustion is less energy-efficient.
The exact incomplete-combustion equation depends on the oxygen supply; you may be asked to write one giving CO, or one giving C.
When a question asks for the products of incomplete combustion, do NOT just write 'CO₂ and water'. Name carbon monoxide (CO) and/or carbon (soot), and if asked to explain the energy difference, state that the fuel is only partially oxidised, so less energy is released than in complete combustion. Vague answers like 'it burns badly' earn nothing.
Comparing fuels: specific energy and energy density
To compare fuels fairly we standardise the energy they release. The specific energy (also called the calorific value) is the energy released per unit MASS of fuel, in kJ g⁻¹ (or MJ kg⁻¹); you obtain it by dividing the magnitude of the molar enthalpy of combustion by the molar mass, |ΔH_c| ÷ M. The energy density is the energy released per unit VOLUME of fuel, in kJ cm⁻³. Which one matters depends on the application: specific energy is decisive when mass is limited (an aircraft or a rocket), while energy density matters when storage volume is limited (a car's fuel tank). A fuel can score well on one and poorly on the other.
Environmental impact of burning fuels
Every combustion reaction has a cost. Complete combustion of any carbon-based fuel produces carbon dioxide, a greenhouse gas: CO₂ absorbs outgoing infrared radiation from the Earth's surface and re-emits it, trapping heat. Adding fossil-fuel CO₂ to the atmosphere strengthens this natural warming — the enhanced greenhouse effect — driving climate change. Incomplete combustion adds two further problems. Carbon monoxide (CO) is toxic: it binds to haemoglobin far more strongly than oxygen does, so it reduces the blood's capacity to carry oxygen. Particulates — tiny soot (carbon) particles — cause respiratory illness and smog and blacken surfaces. Comparing fuels therefore means weighing energy content against all of these emissions.
CO₂ (from complete combustion) is a greenhouse gas; extra CO₂ enhances the greenhouse effect and drives climate change.
CO (from incomplete combustion) is toxic because it binds strongly to haemoglobin, reducing oxygen transport.
Particulates (soot) from incomplete combustion cause respiratory problems and smog.
Comparing fuels: balance specific energy and energy density against renewability, availability and these pollutants.
(HL) What drives a reaction? Entropy
So far we have measured how much energy a fuel gives, but that does not fully explain why a reaction happens. Some spontaneous reactions are even endothermic. The missing idea is entropy, symbol S, a measure of how dispersed the energy and matter of a system are — loosely, its 'disorder'. Entropy increases when matter and energy spread out: gases have more entropy than liquids, which have more than solids; dissolving increases entropy; and, most usefully for predicting the sign of ΔS, a reaction that produces more moles of gas than it consumes has a positive ΔS. Combustion of a hydrocarbon in which the gas moles fall (for example forming liquid water) has a negative ΔS.
Entropy S has units J K⁻¹ mol⁻¹ — note the JOULES, not kilojoules.
ΔS > 0 when disorder rises: melting, boiling, dissolving, or producing more gas moles than are consumed.
ΔS < 0 when disorder falls: freezing, condensing, or producing fewer gas moles.
To predict the sign of ΔS quickly, count the change in moles of GAS across the equation.
(HL) Gibbs free energy and spontaneity
Enthalpy and entropy are combined into a single test for spontaneity by the Gibbs free energy change, ΔG = ΔH − TΔS, where T is the absolute temperature in kelvin. The sign of ΔG is what decides feasibility: a reaction is spontaneous when ΔG < 0, non-spontaneous when ΔG > 0, and at equilibrium when ΔG = 0. Because ΔH is in kJ mol⁻¹ but ΔS is in J K⁻¹ mol⁻¹, the single most common error is a units mismatch: you must convert ΔS from joules to kilojoules (divide by 1000) before multiplying by T, otherwise the TΔS term comes out one thousand times too large and the conclusion is wrong.
Model answer — marked the way our engine marks it
This is the showcase for the topic. In Paper 2, marks are analytic: each is tied to a specific line of working (a method mark, M, or an answer mark, A), and error-carried-forward (ECF) means a slip early on does not automatically cost you every later mark — but only if your method is written down. Study how each of the three marks below is earned by a specific line, and notice how the units step is itself worth a mark.
Common mistakes examiners penalise
Giving CO₂ and H₂O as the products of incomplete combustion — incomplete combustion produces carbon monoxide (CO) and/or soot (C) as well as water; CO₂ is the product of COMPLETE combustion.
Leaving ΔS in joules when using ΔG = ΔH − TΔS — ΔH is in kJ but ΔS is in J K⁻¹ mol⁻¹; convert ΔS to kJ (÷1000) first, or the TΔS term is 1000× too large.
Getting the sign rule for ΔG backwards — spontaneous means ΔG < 0 (negative), not positive. ΔG = 0 is equilibrium.
Mishandling the double negative in −TΔS — subtracting a negative ΔS ADDS to ΔG; write the substitution out fully to avoid a sign slip.
Judging feasibility from ΔH alone — an exothermic reaction is not automatically spontaneous; you must combine ΔH and ΔS through ΔG.
Comparing fuels on a single figure — a high specific energy does not make a fuel 'best' if it is scarce, hard to store, or highly polluting; weigh energy against renewability and emissions.
Blaming 'human error' for a low experimental energy value — name a specific cause such as heat loss to the surroundings or incomplete combustion instead.
Where this leads
The ideas here run through the rest of energetics. Specific energy connects directly to the calorimetry and q = mcΔT calculations of R1.1, where the same combustion is measured experimentally. The environmental discussion feeds into the wider chemistry of the atmosphere and green-chemistry themes. And for HL, ΔG = ΔH − TΔS is the bridge from thermochemistry to equilibrium and electrochemistry: the same sign of ΔG that decides whether a fuel burns spontaneously also decides which way a reaction lies at equilibrium and whether a cell reaction is feasible. Master the two habits of this topic — read the oxygen supply to get the right products, and convert ΔS to kJ before combining — and the harder energetics ahead becomes variations on a method you already own.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A camping stove burns 0.320 g of butane, C₄H₁₀. The standard enthalpy of combustion of butane is −2877 kJ mol⁻¹. (a) Calculate the energy released. (b) Calculate the specific energy of butane in kJ g⁻¹. [4]
- 1
Step 1 — molar mass of butane. g mol⁻¹. [M1: correct molar mass]
(HL) For the combustion of methane, CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), ΔH = −890 kJ mol⁻¹ and ΔS = −243 J K⁻¹ mol⁻¹. Determine ΔG at 298 K and state whether the reaction is spontaneous. [3]
- 1
Step 1 — convert ΔS to kJ. J K⁻¹ mol⁻¹ kJ K⁻¹ mol⁻¹ (divide by 1000). [M1: unit conversion + method]
(HL) A reaction has ΔH = −92.0 kJ mol⁻¹ and ΔS = −198 J K⁻¹ mol⁻¹. Determine whether the reaction is spontaneous at 298 K. [3]
- 1
Model answer — full working.
How it all connects
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Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
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Quick check
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Revision flashcards
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Combustion
An exothermic redox reaction in which a fuel reacts rapidly with oxygen, releasing energy as heat (and usually light). ΔH is always negative.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
- ✓
Combustion is exothermic and is a redox reaction: the fuel is oxidised, oxygen is reduced.
- ✓
Fossil fuels (coal, oil, natural gas) are finite and add long-buried carbon to the atmosphere.
- ✓
Biofuels (bioethanol, biodiesel, biogas) are renewable and roughly carbon-neutral, though growing and processing them still costs energy.
- ✓
A useful fuel is judged on energy content, availability, renewability and pollution together — never on one factor alone.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Get a Paper 2 answer marked: determine ΔG and whether a reaction is spontaneous, with full working
Get a Paper 2 answer marked: determine ΔG and whether a reaction is spontaneous, with full working
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Checkpoint
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