R1.3 Energy from fuels | IB DP Chemistry

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🎯What you need to be able to do

Deduce equations for combustion reactions, including those of hydrocarbons and alcohols.
Deduce equations for the incomplete combustion of hydrocarbons and alcohols, and state what is observed.
Evaluate the amount of carbon dioxide added to the atmosphere when different fuels burn, and explain the link between carbon dioxide levels and the greenhouse effect.
Compare fossil fuels in terms of their tendency to undergo incomplete combustion and their energy released per unit mass.
Understand the difference between renewable and non-renewable energy sources, and consider the advantages and disadvantages of biofuels.
Deduce half-equations for the electrode reactions in hydrogen and methanol fuel cells.

📚The chemistry

Complete combustion

Combustion is reaction with oxygen, and it is exothermic. Reactive metals, non-metals and organic compounds all burn:

\[ 2\mathrm{Mg}(s) + \mathrm{O_2}(g) \rightarrow 2\mathrm{MgO}(s) \qquad \mathrm{S}(s) + \mathrm{O_2}(g) \rightarrow \mathrm{SO_2}(g) \]

For an organic compound of carbon, hydrogen and (possibly) oxygen, complete combustion in excess oxygen always gives carbon dioxide and water. That single fact lets you write any such equation without memorising it:

\[ \mathrm{C_3H_8}(g) + 5\mathrm{O_2}(g) \rightarrow 3\mathrm{CO_2}(g) + 4\mathrm{H_2O}(l) \]

\[ \mathrm{C_2H_5OH}(l) + 3\mathrm{O_2}(g) \rightarrow 2\mathrm{CO_2}(g) + 3\mathrm{H_2O}(l) \]

Balance in a fixed order: carbon first, then hydrogen, then oxygen last. Oxygen goes last because it is the only element appearing in two products, so it is the only one you can adjust freely at the end. If the compound already contains oxygen, count it — ethanol supplies one oxygen atom of its own, which is why it needs three \( \mathrm{O_2} \) and not four.

Incomplete combustion

In a limited supply of oxygen, combustion is incomplete and gives carbon monoxide and/or carbon (soot) instead of, or as well as, carbon dioxide:

\[ 2\mathrm{CH_4}(g) + 3\mathrm{O_2}(g) \rightarrow 2\mathrm{CO}(g) + 4\mathrm{H_2O}(l) \]

\[ \mathrm{CH_4}(g) + \mathrm{O_2}(g) \rightarrow \mathrm{C}(s) + 2\mathrm{H_2O}(l) \]

Observations: a yellow or orange sooty flame rather than a clean blue one, and black deposits on the underside of the vessel. Two consequences matter:

Less energy is released per mole of fuel, because the carbon is not fully oxidised. This is the main reason calorimetry with a spirit burner under-reads (R1.1).
Carbon monoxide is toxic. It binds to haemoglobin far more strongly than oxygen does, and irreversibly on the timescale that matters, so the blood can no longer transport oxygen. It is colourless and odourless, which is what makes faulty gas appliances lethal.

Larger hydrocarbons undergo incomplete combustion more readily, because a higher proportion of carbon by mass requires proportionally more oxygen to burn cleanly — which is why a candle smokes and a Bunsen burner on full air does not.

Fossil fuels

Coal, crude oil and natural gas are all non-renewable: they formed over hundreds of millions of years from buried organic matter, and are being consumed vastly faster than they form.

Coal
mostly carbon · highest carbon per unit energy
most \( \mathrm{CO_2} \) released · most soot and \( \mathrm{SO_2} \)
easy to transport and store

Crude oil
liquid hydrocarbons · intermediate
energy-dense, easily transported, the feedstock for the whole petrochemical industry

Natural gas
mainly methane · highest hydrogen-to-carbon ratio
least \( \mathrm{CO_2} \) per unit energy · burns cleanest
hardest to transport and store

Comparing fuels quantitatively is what the syllabus means by “evaluate the amount of carbon dioxide added”. Two figures matter and must not be confused: the energy released per unit mass (or per mole), and the amount of \( \mathrm{CO_2} \) produced per unit of energy released. Methane wins on the second because much of its energy comes from burning hydrogen to water rather than carbon to carbon dioxide.

The greenhouse effect. Carbon dioxide, water vapour and methane absorb infrared radiation because their vibrations change the molecular dipole moment (S3.2); \( \mathrm{N_2} \) and \( \mathrm{O_2} \) are symmetric diatomics and cannot. Solar radiation reaching the Earth is mostly short-wavelength and passes through; the warmed surface re-radiates at longer, infrared wavelengths, which greenhouse gases absorb and re-emit in all directions, warming the lower atmosphere. Burning fossil fuels transfers carbon that was locked away for millions of years into the atmosphere as \( \mathrm{CO_2} \), increasing the concentration and hence the effect. The ocean acidification consequence is in S3.1.

Biofuels

Biofuels are produced from the biological fixation of carbon over a short period of time through photosynthesis — which is the exact wording that makes them renewable. The reactants and products of photosynthesis should be known:

\[ 6\mathrm{CO_2}(g) + 6\mathrm{H_2O}(l) \xrightarrow{\ \text{light}\ } \mathrm{C_6H_{12}O_6}(aq) + 6\mathrm{O_2}(g) \]

Fossil fuels came from photosynthesis too. The distinction is entirely one of timescale: a biofuel crop reabsorbs the carbon dioxide released by its predecessor within a growing season, whereas fossil carbon took hundreds of millions of years to fix and is returned in a century.

Advantages
renewable · approximately carbon neutral in principle · can be grown locally, improving energy security · lower sulfur content, so less acid rain · biodegradable if spilled

Disadvantages
competes with food production for land and water · may drive deforestation · energy is consumed in farming, fertiliser and processing, so not truly carbon neutral · lower energy density than petrol · ethanol absorbs water and is corrosive to some engines

“Carbon neutral” deserves the qualifier. In principle the \( \mathrm{CO_2} \) released on burning equals the \( \mathrm{CO_2} \) absorbed during growth. In practice the fertiliser, machinery, processing and transport are usually powered by fossil fuels, so the net saving is real but smaller than the simple argument suggests. Being able to make that qualification is exactly the AO3 skill the question is testing.

Fuel cells

A fuel cell converts chemical energy from a fuel directly into electrical energy. Unlike a battery it is not consumed and does not need recharging: fuel is supplied continuously from outside and the cell runs as long as it is fed.

Hydrogen fuel cell (acidic electrolyte):

Negative electrode (oxidation)
\( \mathrm{H_2}(g) \rightarrow 2\mathrm{H^{+}}(aq) + 2\mathrm{e^{-}} \)

Positive electrode (reduction)
\( \mathrm{O_2}(g) + 4\mathrm{H^{+}}(aq) + 4\mathrm{e^{-}} \rightarrow 2\mathrm{H_2O}(l) \)

Overall
\( 2\mathrm{H_2}(g) + \mathrm{O_2}(g) \rightarrow 2\mathrm{H_2O}(l) \)

In an alkaline electrolyte the same cell is written differently: \( \mathrm{H_2} + 2\mathrm{OH^{-}} \rightarrow 2\mathrm{H_2O} + 2\mathrm{e^{-}} \) and \( \mathrm{O_2} + 2\mathrm{H_2O} + 4\mathrm{e^{-}} \rightarrow 4\mathrm{OH^{-}} \). Read the question to see which electrolyte you are given.

Methanol fuel cell (acidic):

\[ \mathrm{CH_3OH}(l) + \mathrm{H_2O}(l) \rightarrow \mathrm{CO_2}(g) + 6\mathrm{H^{+}}(aq) + 6\mathrm{e^{-}} \]

\[ \tfrac{3}{2}\mathrm{O_2}(g) + 6\mathrm{H^{+}}(aq) + 6\mathrm{e^{-}} \rightarrow 3\mathrm{H_2O}(l) \]

The advantage of methanol is that it is a liquid at room temperature and so is far easier to store and transport than hydrogen; the disadvantage is that it produces carbon dioxide, which hydrogen does not. The use of proton exchange membranes will not be assessed.

“Hydrogen fuel cells are completely clean.” The cell emits only water, which is true and worth saying. But most hydrogen is currently produced by steam reforming of natural gas, which releases carbon dioxide, and hydrogen produced by electrolysis is only as clean as the electricity used. A full evaluation must consider where the fuel came from — and questions on this sub-topic are usually asking for exactly that judgement, not for the half-equations alone.

✏️Worked example

(a) Write balanced equations for the complete combustion of butane, \( \mathrm{C_4H_{10}} \), and of methanol, \( \mathrm{CH_3OH} \).
(b) Write an equation for the incomplete combustion of butane producing carbon monoxide only, and state two observations that would indicate incomplete combustion.
(c) Methane releases 891 kJ mol⁻¹ on complete combustion and butane 2878 kJ mol⁻¹. Determine which produces less carbon dioxide per kilojoule of energy released.
(d) Write the two electrode half-equations for a hydrogen fuel cell with an acidic electrolyte, and give one advantage and one disadvantage of hydrogen compared with methanol as a fuel-cell fuel.

(a) Carbon first, then hydrogen, then oxygen.

Butane: 4 C give 4 \( \mathrm{CO_2} \); 10 H give 5 \( \mathrm{H_2O} \). Oxygen atoms needed: \( 4 \times 2 + 5 = 13 \), so \( \tfrac{13}{2}\mathrm{O_2} \). Doubling to clear the fraction:

\[ 2\mathrm{C_4H_{10}}(g) + 13\mathrm{O_2}(g) \rightarrow 8\mathrm{CO_2}(g) + 10\mathrm{H_2O}(l) \]

Methanol: 1 C gives 1 \( \mathrm{CO_2} \); 4 H give 2 \( \mathrm{H_2O} \). Oxygen atoms needed \( = 2 + 2 = 4 \), but methanol supplies one, so only 3 more are needed, giving \( \tfrac{3}{2}\mathrm{O_2} \):

\[ 2\mathrm{CH_3OH}(l) + 3\mathrm{O_2}(g) \rightarrow 2\mathrm{CO_2}(g) + 4\mathrm{H_2O}(l) \]

(b) With carbon monoxide as the only carbon product, each carbon needs one oxygen instead of two:

\[ 2\mathrm{C_4H_{10}}(g) + 9\mathrm{O_2}(g) \rightarrow 8\mathrm{CO}(g) + 10\mathrm{H_2O}(l) \]

Observations: a yellow/orange, sooty, luminous flame instead of a clean blue one; black solid deposited on the base of the apparatus; and less heat released for the same amount of fuel.

(c) Work out the carbon dioxide produced per kilojoule for each.

Methane: \( \mathrm{CH_4} + 2\mathrm{O_2} \rightarrow \mathrm{CO_2} + 2\mathrm{H_2O} \) — one mole of \( \mathrm{CO_2} \) per 891 kJ.

\[ \frac{1}{891} = 1.12 \times 10^{-3}\ \mathrm{mol\ CO_2\ per\ kJ} \]

Butane: from the equation, one mole of butane gives four moles of \( \mathrm{CO_2} \) and releases 2878 kJ.

\[ \frac{4}{2878} = 1.39 \times 10^{-3}\ \mathrm{mol\ CO_2\ per\ kJ} \]

Methane produces less carbon dioxide per unit of energy — about 20% less. The reason is its higher hydrogen-to-carbon ratio: a greater share of the energy comes from oxidising hydrogen to water rather than carbon to carbon dioxide.

(d)

\[ \text{negative electrode: } \ \mathrm{H_2}(g) \rightarrow 2\mathrm{H^{+}}(aq) + 2\mathrm{e^{-}} \]

\[ \text{positive electrode: } \ \mathrm{O_2}(g) + 4\mathrm{H^{+}}(aq) + 4\mathrm{e^{-}} \rightarrow 2\mathrm{H_2O}(l) \]

Advantage of hydrogen: the only product at the cell is water, so no carbon dioxide is emitted at the point of use, whereas the methanol cell releases \( \mathrm{CO_2} \). Disadvantage: hydrogen is a gas of very low density, so it is difficult and energy-expensive to store and transport — requiring high pressure or cryogenic temperatures — while methanol is a liquid that can use existing fuel infrastructure.

Check it. For any combustion equation, count oxygen atoms on both sides as the last step: in the butane equation, left \( 13 \times 2 = 26 \), right \( 8 \times 2 + 10 = 26 \) ✓. For the methanol equation, left \( 2 \times 1 + 3 \times 2 = 8 \), right \( 2 \times 2 + 4 = 8 \) ✓. In (c), sanity-check the conclusion against chemistry you already know: methane has the highest H : C ratio of any hydrocarbon, so it must come out best on carbon dioxide per unit energy — if your arithmetic said butane, you have probably forgotten the factor of four.

Comparing carbon dioxide per mole of fuel rather than per unit of energy. Butane releases four moles of \( \mathrm{CO_2} \) against methane’s one, which looks like a factor of four — but butane also releases more than three times as much energy, so the honest comparison is much closer. Whenever a question asks you to evaluate fuels, ask “per what?” before calculating: per mole, per gram and per kilojoule can rank the same fuels differently, and the third is almost always the one that matters.

📝Practise

Work through these on paper, then reveal the answer.

1. Write balanced equations for the complete combustion of (a) pentane \( \mathrm{C_5H_{12}} \), (b) propan-1-ol \( \mathrm{C_3H_7OH} \), (c) sulfur, and (d) magnesium.

(a) 5 C → 5 \( \mathrm{CO_2} \); 12 H → 6 \( \mathrm{H_2O} \); oxygen atoms \( = 10 + 6 = 16 \), so 8 \( \mathrm{O_2} \): \( \mathbf{C_5H_{12} + 8O_2 \rightarrow 5CO_2 + 6H_2O} \). (b) Propan-1-ol is \( \mathrm{C_3H_8O} \): 3 C → 3 \( \mathrm{CO_2} \); 8 H → 4 \( \mathrm{H_2O} \); oxygen atoms needed \( = 6 + 4 = 10 \), of which the alcohol supplies one, so 9 more, i.e. 4.5 \( \mathrm{O_2} \). Doubling: \( \mathbf{2C_3H_7OH + 9O_2 \rightarrow 6CO_2 + 8H_2O} \). (c) \( \mathbf{S + O_2 \rightarrow SO_2} \). (d) \( \mathbf{2Mg + O_2 \rightarrow 2MgO} \). In every case check the oxygen count last, since it appears in two products.

2. Explain why a Bunsen burner with the air hole closed gives a yellow, sooty flame that deposits carbon on a beaker, while with the air hole open the flame is blue and clean.

With the air hole closed, the methane has access only to the oxygen that diffuses in at the flame surface, so the supply of oxygen is limited and combustion is incomplete. The carbon is not fully oxidised, giving carbon monoxide and carbon as well as carbon dioxide, for example \( \mathrm{CH_4} + \mathrm{O_2} \rightarrow \mathrm{C} + 2\mathrm{H_2O} \). The yellow luminous colour comes from glowing carbon particles heated in the flame, and those particles deposit as soot on any cool surface. With the air hole open, air is drawn in and premixed with the gas, so there is an excess of oxygen, combustion is complete, and the products are carbon dioxide and water only — a clean blue flame with no soot. The complete flame is also hotter, because full oxidation of the carbon releases considerably more energy per mole of fuel.

3. Compare coal and natural gas as fuels under three headings: carbon dioxide released per unit of energy, other pollutants produced, and ease of transport and storage.

Carbon dioxide per unit energy: coal is much worse. Coal is largely carbon, so essentially all its energy comes from oxidising carbon to \( \mathrm{CO_2} \). Natural gas is mainly methane, with a high hydrogen-to-carbon ratio, so a large part of its energy comes from oxidising hydrogen to water — which produces no carbon dioxide at all. Other pollutants: coal contains sulfur compounds which burn to \( \mathrm{SO_2} \), a cause of acid rain; it also produces soot and ash and, being a solid with a high proportion of carbon, undergoes incomplete combustion readily, generating carbon monoxide. Natural gas burns much more cleanly and contains little sulfur. Transport and storage: here coal has the advantage — it is a solid, so it is easy and cheap to store and move in bulk without pressurisation. Natural gas requires pipelines, or liquefaction at very low temperature for shipping, both of which are expensive and energy-intensive.

4. Ethanol from sugar cane is often described as carbon neutral. Explain the argument, and give two reasons why the description is an overstatement.

The argument: the sugar cane grows by photosynthesis, \( 6\mathrm{CO_2} + 6\mathrm{H_2O} \rightarrow \mathrm{C_6H_{12}O_6} + 6\mathrm{O_2} \), absorbing carbon dioxide from the atmosphere. When the ethanol made from it is burned, \( \mathrm{C_2H_5OH} + 3\mathrm{O_2} \rightarrow 2\mathrm{CO_2} + 3\mathrm{H_2O} \), the same carbon is returned. Over a growing season the two balance, so in principle no net carbon dioxide is added — unlike a fossil fuel, whose carbon was removed from the atmosphere hundreds of millions of years ago. Why it is an overstatement. (i) Fossil fuels are consumed at every other stage: ploughing, planting and harvesting use diesel machinery, fertilisers are manufactured from natural gas, and the fermentation, distillation and transport of the ethanol all require energy that is usually not renewable. (ii) Land-use change: if forest or grassland is cleared to grow the crop, a large stock of stored carbon is released at once, and it may take decades of production to repay that debt. Other acceptable points: nitrous oxide released from fertilised soils is itself a potent greenhouse gas; and the crop competes with food production for land and water, which is an ethical rather than a carbon objection but a real one.

5. Write the electrode half-equations and the overall equation for a hydrogen fuel cell with an alkaline electrolyte, and explain how a fuel cell differs from a rechargeable battery.

Negative electrode (oxidation): \( \mathrm{H_2}(g) + 2\mathrm{OH^{-}}(aq) \rightarrow 2\mathrm{H_2O}(l) + 2\mathrm{e^{-}} \). Positive electrode (reduction): \( \mathrm{O_2}(g) + 2\mathrm{H_2O}(l) + 4\mathrm{e^{-}} \rightarrow 4\mathrm{OH^{-}}(aq) \). Overall (double the first and add): \( 2\mathrm{H_2}(g) + \mathrm{O_2}(g) \rightarrow 2\mathrm{H_2O}(l) \) — the same overall reaction as in the acidic cell, as it must be, since the electrolyte is not consumed. Difference from a rechargeable battery: in a secondary cell the reactants are stored inside the cell and are gradually used up; when they are exhausted the cell must be recharged by driving the reaction backwards with an external supply, and it can only be discharged and recharged a finite number of times. In a fuel cell the reactants are supplied continuously from outside and the products are removed continuously, so the cell itself is not consumed and never needs recharging — it produces electricity for as long as fuel is fed to it.

6. Methanol releases 726 kJ mol⁻¹ on complete combustion and octane, \( \mathrm{C_8H_{18}} \), releases 5470 kJ mol⁻¹. Compare the two on energy released per gram and on carbon dioxide produced per kilojoule. (\( M \): methanol 32.05, octane 114.26.)

Energy per gram. Methanol: \( \dfrac{726}{32.05} = \mathbf{22.7\ kJ\,g^{-1}} \). Octane: \( \dfrac{5470}{114.26} = \mathbf{47.9\ kJ\,g^{-1}} \). Octane releases more than twice as much energy per gram, which is why petrol rather than methanol fills a fuel tank — energy density per unit mass and volume is what determines the range of a vehicle. Carbon dioxide per kilojoule. Methanol gives 1 mol \( \mathrm{CO_2} \) per mole burned: \( \dfrac{1}{726} = 1.38 \times 10^{-3}\ \mathrm{mol\,kJ^{-1}} \). Octane gives 8 mol \( \mathrm{CO_2} \) per mole: \( \dfrac{8}{5470} = 1.46 \times 10^{-3}\ \mathrm{mol\,kJ^{-1}} \). The two are close, with methanol marginally better — about 5% less carbon dioxide per unit of energy. The point of the comparison: the two measures rank the fuels differently and answer different questions. Octane is far better if you care about mass carried; methanol is slightly better per unit of energy delivered on carbon dioxide, and much better if it is made from a renewable source rather than from crude oil.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

The IPCC assessment report summaries for policymakers — the authoritative source on the link between carbon dioxide concentration and warming, and readable at this level.
RSC Learn Chemistry — the comparison of the enthalpies of combustion of a homologous series of alcohols, which is a good IA starting point and connects this sub-topic to R1.1.
PhET — The Greenhouse Effect, which shows infrared photons being absorbed and re-emitted by \( \mathrm{CO_2} \) and passing straight through \( \mathrm{N_2} \), the point that connects this to infrared spectroscopy.