R1.3 Energy from fuels

Combustion reactions

Combustion is the rapid reaction of a substance with oxygen, releasing energy as heat and light. Every combustion reaction is exothermic. Many elements burn in oxygen to form oxides, and almost all organic compounds burn to form oxides of carbon and hydrogen.

Combustion of reactive metals

Reactive metals burn brightly when heated in air or oxygen, forming solid ionic oxides. Magnesium ribbon burns with a brilliant white flame and leaves a white powder of magnesium oxide. Sodium burns with a yellow-orange flame and calcium with a brick-red one.

The formula of each oxide follows from the charges of the ions: ${{\mathrm{Mg}{\vphantom{X}}^{2+}}}$ and ${{\mathrm{O}{\vphantom{X}}^{2-}}}$ give ${{\mathrm{MgO}}}$, while two ${{\mathrm{Na}{\vphantom{X}}^{+}}}$ ions balance one ${{\mathrm{O}{\vphantom{X}}^{2-}}}$ in ${{\mathrm{Na}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$. Metal oxides are basic: those of groups 1 and 2 react with water to form hydroxides, a pattern described with the acid–base character of oxides across the periodic table.

Combustion of non-metals

Many non-metals also burn in oxygen, forming covalent oxides, most of which are gases. Carbon glows red and forms carbon dioxide; sulfur burns with a blue flame to form sulfur dioxide, a choking gas; hydrogen burns with an almost invisible pale blue flame (or a squeaky pop in a test tube) to form water. White phosphorus is so reactive that it catches fire in air at about 30 °C, and is stored under water.

Non-metal oxides are acidic. Sulfur dioxide dissolves in water to form an acidic solution, which is why sulfur impurities in coal contribute to acid deposition.

Comparing the combustion of metals and non-metals

The combustion of an s-block metal and of a p-block non-metal have features in common and important differences. The table compares magnesium and sulfur.

Combustion as a redox reaction

In every combustion reaction, oxygen gains electrons (its oxidation state falls from 0 to −2) and is reduced. The fuel loses electrons and is oxidized. Oxygen is therefore the oxidizing agent and the fuel is the reducing agent.

For a carbon compound, the oxidation state of carbon shows how far it is oxidized. In methane the oxidation state of carbon is −4; in carbon dioxide it is +4. Each carbon atom therefore loses the equivalent of eight electrons when methane burns completely. In ethanol, ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{2}}\mathrm{H}{\vphantom{X}}_{\smash[t]{5}}\mathrm{OH}}}$, the average oxidation state of carbon is −2, because one oxygen atom is already attached. Carbon in ethanol has less oxidation still to undergo, which is one reason ethanol releases less energy per gram than an alkane.

Why fuels need to be lit

A mixture of methane and air can be stored indefinitely at room temperature without reacting, even though the reaction is strongly exothermic. Combustion has a high activation energy: bonds such as ${{\mathrm{C}{-}\mathrm{H}}}$ and ${{\mathrm{O}{=}\mathrm{O}}}$ must start to break before new bonds can form, and very few molecules at room temperature collide with enough energy. A spark or flame supplies this energy to a small region. The heat released there raises the neighbouring molecules above the activation energy, so the reaction spreads through the fuel.

A high activation energy is a useful property in a fuel. It means the fuel can be stored, pumped and transported safely in air, and it burns only when and where it is ignited. A fuel with a very low activation energy, such as white phosphorus, would ignite on its own and could not be handled safely.

Complete combustion of hydrocarbons and alcohols

When a hydrocarbon or an alcohol burns in excess oxygen, all of its carbon is converted to carbon dioxide and all of its hydrogen to water. Any oxygen atoms in the fuel end up in these products too. Standard enthalpies of combustion refer to water formed as a liquid, so equations for combustion are usually written with ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}\mskip2mu (\mathrm{l})}}$.

Balancing combustion equations

Combustion equations are balanced in a fixed order, because oxygen appears in two products and, for an alcohol, in the fuel as well:

• Carbon: the number of ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ molecules equals the number of carbon atoms in the fuel.

• Hydrogen: the number of ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$ molecules is half the number of hydrogen atoms in the fuel.

• Oxygen last: count the oxygen atoms in the products, subtract any oxygen atoms in the fuel, and halve the result to get the number of ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$ molecules.

• Integer coefficients: if the ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$ coefficient is a fraction such as $\tfrac{25}{2}$

For any hydrocarbon ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{x }}\mathrm{H}{\vphantom{X}}_{\smash[t]{y }}}}$ these steps give a general equation, which is a quick check on an answer:

An alcohol already contains one oxygen atom per molecule, so it needs less oxygen from the air than the alkane with the same carbon skeleton. Ethanol needs 3 mol of ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$ per mole, while ethane needs 3.5 mol.

Enthalpies of combustion across a homologous series

The data booklet lists the standard enthalpy change of combustion, $\Delta H_{\text{c}}^{\ominus}$, for many fuels: the enthalpy change when one mole of the substance burns completely in oxygen under standard conditions. Within a homologous series the values follow a clear pattern.

Data: IB Chemistry data booklet (2025), section 14.

Each member differs from the next by one ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{2}}}}$ group. Burning that extra ${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{2}}}}$ means breaking one more ${{\mathrm{C}{-}\mathrm{C}}}$ bond, two more ${{\mathrm{C}{-}\mathrm{H}}}$ bonds and $1\tfrac{1}{2}$ more ${{\mathrm{O}{=}\mathrm{O}}}$ bonds, and forming two more ${{\mathrm{C}{=}\mathrm{O}}}$ bonds and two more ${{\mathrm{O}{-}\mathrm{H}}}$ bonds. The same bonds change each time, so each step adds roughly the same amount of energy, about 650 $\text{kJ mol}^{-1}$. The graph of $\Delta H_{\text{c}}^{\ominus}$ against the number of carbon atoms is therefore a straight line for both alkanes and alcohols.

Measuring the enthalpy of combustion of a liquid fuel

The enthalpy of combustion of an alcohol can be estimated in a school laboratory by burning it in a spirit burner under a can of water. The method is a form of calorimetry: the heat released by the fuel is assumed to be absorbed by the water.

• Measure a known volume (and so mass) of water into a copper can and clamp it a fixed, short distance above the wick.

• Weigh the spirit burner with its cap on, and record the initial temperature of the water.

• Light the wick, stir the water and let the flame heat it until the temperature has risen by about 20 °C.

• Put out the flame with the cap, record the highest temperature, and reweigh the burner straight away.

The energy transferred to the water is $Q = mc\Delta T$, where $m$ is the mass of water, $c = 4.18\ \text{J g}^{-1}\ \text{K}^{-1}$ and $\Delta T$ is the temperature rise. Dividing $Q$ by the amount of fuel burned gives the enthalpy change per mole, with a negative sign because the reaction is exothermic.

Results from a spirit burner are usually 30–50 % less exothermic than the data booklet values. The main sources of error are systematic, so repeating the experiment does not remove them:

More accurate values come from a bomb calorimeter, in which the fuel is burned in pure oxygen inside a sealed steel vessel surrounded by water, so very little heat escapes. Calorimetry methods and their errors are described more fully with the measurement of enthalpy changes.

Incomplete combustion

When the supply of oxygen is limited, there is not enough oxygen to convert all the carbon in a fuel to carbon dioxide. Incomplete combustion produces carbon monoxide, ${{\mathrm{CO}}}$, or carbon itself in the form of fine black particles called soot, together with water. Hydrogen is more easily oxidized than carbon, so water still forms.

Equations for incomplete combustion

There is no single equation for the incomplete combustion of a fuel, because the proportions of ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$, ${{\mathrm{CO}}}$ and ${{\mathrm{C}}}$ depend on how much oxygen is available. Equations are written for one stated product at a time. For methane:

The amount of oxygen needed falls from 2 mol to 1.5 mol to 1 mol per mole of methane. The same steps used for complete combustion balance these equations: fix carbon in the stated product, then hydrogen as water, then oxygen.

What incomplete combustion looks like

A Bunsen burner shows the difference clearly. With the air hole open, gas and air mix before burning, and the flame is blue, roaring and very hot. With the air hole closed, the gas meets oxygen only at the edge of the flame. The flame becomes larger, yellow and smoky. The yellow colour comes from tiny particles of carbon glowing in the heat, and a cold object held in the flame is quickly coated with black soot.

Less energy is released

Carbon monoxide and carbon are not fully oxidized: they can still burn to form carbon dioxide, releasing 283 $\text{kJ mol}^{-1}$ and 394 $\text{kJ mol}^{-1}$ respectively (data booklet). Energy that would have been released when they burned stays stored in them. The enthalpy diagram for methane shows the size of the loss.

Incomplete combustion therefore wastes fuel. A gas boiler or car engine that is badly adjusted burns more fuel for the same useful energy, and its soot coats the burners or pistons, making the combustion worse still.

Health and environmental effects

Carbon monoxide is a colourless, odourless and very toxic gas. It binds to the iron in haemoglobin, the oxygen-carrying protein in red blood cells, about 200–250 times more strongly than oxygen does. Haemoglobin that has bound carbon monoxide cannot carry oxygen, so the body's organs are starved of it. Low concentrations cause headaches, dizziness and tiredness; higher concentrations cause unconsciousness and death. Because the gas cannot be seen or smelt, poorly ventilated gas heaters, boilers and charcoal stoves are a common cause of accidental poisoning, which is why carbon monoxide detectors are fitted in many homes.

Soot is made of fine particles of carbon, often with unburned hydrocarbons stuck to them. The smallest particulates, less than about 2.5 μm across, are breathed deep into the lungs and contribute to asthma, bronchitis and heart disease. In the atmosphere, particulates also reflect and absorb sunlight, reducing the sunlight that reaches the ground, an effect called global dimming. Diesel engines, coal fires and the burning of wood and dung for cooking are major sources.

Why larger hydrocarbons burn incompletely more easily

Small hydrocarbons such as methane usually burn completely in a well-designed burner, while large ones such as diesel fuel and candle wax produce smoky flames. Three properties change as the carbon chain gets longer:

• More oxygen is needed per molecule. One molecule of methane needs 2 molecules of ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$; one molecule of octane needs 12.5, and one of hexadecane, ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{16}}\mathrm{H}{\vphantom{X}}_{\smash[t]{34}}}}$, needs 24.5. It becomes harder for every carbon atom to meet enough oxygen as the fuel burns.

• The proportion of carbon is higher. The ratio of hydrogen to carbon atoms falls from 4 : 1 in methane towards 2 : 1 in long chains, and is 1 : 1 in benzene. Hydrogen is oxidized first, so a fuel with relatively more carbon is more likely to leave carbon unburned.

• Larger molecules are less volatile. Stronger London (dispersion) forces between longer chains mean that large hydrocarbons are liquids or solids that vaporize less readily. Only vapour burns, and a liquid that vaporizes slowly mixes poorly with air.

Fossil fuels

Fossil fuels formed over millions of years from the remains of living things. Plants and plankton fixed carbon from the air by photosynthesis; when they died, some were buried before they decayed. Heat and pressure deep underground slowly turned the remains into coal (mostly from land plants in ancient swamps), crude oil and natural gas (mostly from marine plankton). Because they form far more slowly than they are used, fossil fuels are non-renewable.

• Coal is a solid made mostly of carbon, with some hydrogen, oxygen and impurities including sulfur (typically about 0.5–5 % by mass), nitrogen and minerals that form ash.

• Crude oil is a liquid mixture of hundreds of hydrocarbons, mostly alkanes, cycloalkanes and arenes. It is separated by fractional distillation into fractions such as petrol (gasoline), kerosene and diesel, which are used as fuels and as feedstock for plastics and other chemicals.

• Natural gas is mostly methane, with smaller amounts of ethane, propane, carbon dioxide and nitrogen.

Specific energy

To compare fuels, the energy released per gram is often more useful than the energy per mole, because fuels are bought, stored and carried by mass. This quantity is the specific energy.

The related quantity energy density is the energy released per unit volume, in $\text{kJ cm}^{-3}$ or $\text{kJ dm}^{-3}$. It equals the specific energy multiplied by the density of the fuel, and matters wherever space is limited, as in a car's fuel tank or an aircraft's wings.

The bar chart shows two patterns. Fuels with a higher proportion of hydrogen release more energy per gram: hydrogen atoms are light, and the ${{\mathrm{O}{-}\mathrm{H}}}$ bonds formed in water release a lot of energy. Fuels that already contain oxygen, such as the alcohols, release less, because part of the fuel is already oxidized and the oxygen atoms add mass without releasing energy.

Comparing coal, oil and natural gas

Each fossil fuel has its own balance of advantages and disadvantages. The table summarizes them, using specific energy, ease of storage and transport, the tendency to burn incompletely, the pollutants formed and the carbon dioxide released for each unit of energy.

Nitrogen oxides form in a different way from the other pollutants: their nitrogen comes from the air rather than from the fuel. At the high temperatures inside an engine or furnace, nitrogen and oxygen from the air react: ${{\mathrm{N}{\vphantom{X}}_{\smash[t]{2}}\mskip2mu (\mathrm{g}) {}+{} \mathrm{O}{\vphantom{X}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})\xrightarrow{}2\,\mathrm{NO}\mskip2mu (\mathrm{g})}}$. Sulfur dioxide, by contrast, comes from sulfur compounds in the fuel itself: ${{\mathrm{S}\mskip2mu (\mathrm{s}) {}+{} \mathrm{O}{\vphantom{X}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})\xrightarrow{}\mathrm{SO}{\vphantom{X}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})}}$. Power stations remove it from their flue gases by reacting it with a base, for example calcium oxide, ${{\mathrm{CaO}\mskip2mu (\mathrm{s}) {}+{} \mathrm{SO}{\vphantom{X}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})\xrightarrow{}\mathrm{CaSO}{\vphantom{X}}_{\smash[t]{3}}\mskip2mu (\mathrm{s})}}$.

Evaluating the carbon dioxide released by different fuels

All carbon-based fuels release carbon dioxide when they burn. The amount can be compared in three ways, which give different rankings, so a comparison must state which basis it uses:

• per mole of fuel, read directly from the equation (1 mol ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ per mole of methane, 8 mol per mole of octane);

• per gram of fuel, which is fairer when equal masses are burned;

• per kilojoule of energy released, which is the fairest comparison when the fuel is used to supply a fixed amount of energy.

Carbon dioxide from fossil fuels is the main cause of the rise in atmospheric carbon dioxide. Fossil fuel use and cement production released a record of about 37 billion tonnes of carbon dioxide in 2024: about 41 % from coal, 32 % from oil and 21 % from natural gas, with most of the remainder from cement. Coal's share of the emissions is larger than its share of the energy supplied, because it releases the most carbon dioxide per unit of energy.

Emissions data: Global Carbon Project, Global Carbon Budget 2024 (projected values for 2024).

The consequences of burning fossil fuels reach beyond chemistry. Environmentally, they include climate change, acid deposition and oil spills. Economically, fossil fuels have powered industrial growth and still provide cheap, reliable energy, but their reserves are concentrated in a few regions, so prices and supplies depend on international politics. Socially and ethically, air pollution from fuel combustion contributes to millions of premature deaths each year, and the countries that have emitted the least carbon dioxide are often those most exposed to the effects of climate change.

Carbon dioxide and the greenhouse effect

The Sun emits most of its energy as visible and near-ultraviolet radiation, which has short wavelengths. The atmosphere is largely transparent to this radiation, so most of it reaches the Earth's surface, apart from the part reflected by clouds, ice and the ground. The surface absorbs the rest and warms up. A warm surface emits energy as infrared radiation, which has much longer wavelengths.

Some gases in the atmosphere absorb infrared radiation. A greenhouse gas molecule that absorbs infrared gains energy, then re-emits infrared in a random direction, or passes the energy on to other molecules in collisions. Part of the energy that would have escaped to space is therefore sent back towards the surface, and the lower atmosphere and surface are warmer than they would be without these gases. This is the greenhouse effect.

The natural greenhouse effect is essential for life: without it, the average surface temperature of the Earth would be about −18 °C instead of about 15 °C. The concern is the enhanced greenhouse effect: the extra warming caused by increasing the concentrations of greenhouse gases through human activities, mainly the burning of fossil fuels. Rising temperatures drive climate change, including melting ice, rising sea levels and more frequent extreme weather.

The concentration of carbon dioxide in the atmosphere has been measured continuously at Mauna Loa in Hawaii since 1958. It was about 280 ppm (parts per million by volume) before the industrial revolution, and has risen faster with each decade.

The main greenhouse gases

The main greenhouse gases are water vapour, carbon dioxide, methane, dinitrogen monoxide and ozone, together with synthetic gases such as chlorofluorocarbons (CFCs) and sulfur hexafluoride. Nitrogen and oxygen, which make up 99 % of dry air, do not absorb infrared radiation. Why some molecules absorb infrared and others do not depends on how their bonds vibrate, which is explained in the HL study of infrared spectroscopy.

The effect of a greenhouse gas on climate depends on how strongly each molecule absorbs infrared radiation, at which wavelengths it absorbs (a gas that absorbs where other gases do not has more effect), how long it stays in the atmosphere and how much of it is present. The first three are combined in its global warming potential.

Over 100 years methane has a GWP of about 28, so each tonne of methane released causes roughly 28 times the warming of a tonne of carbon dioxide. Carbon dioxide still contributes far more to the enhanced greenhouse effect, because human activities release about a hundred times more of it by mass, and it persists in the atmosphere for centuries.

Reducing carbon dioxide emissions

Several approaches reduce the carbon dioxide added to the atmosphere by energy use:

• Using less energy through more efficient engines, power stations, buildings and appliances.

• Switching fuels, for example replacing coal with natural gas, which roughly halves the carbon dioxide released per unit of energy.

• Using renewable or low-carbon energy sources such as solar, wind, hydroelectric and nuclear power, and biofuels.

• Carbon capture and storage (CCS): carbon dioxide is removed from the flue gases of power stations or factories, for example by absorbing it in a basic solution, then compressed and pumped into porous rock deep underground.

• Using captured carbon dioxide as a feedstock to make other chemicals, such as urea or methanol.

• Economic measures such as carbon taxes and tradable emissions permits, which make releasing carbon dioxide more expensive.

Renewable energy and biofuels

Energy sources are classified by whether they can be replenished as fast as they are used.

Renewable sources such as solar and wind power release no carbon dioxide while they operate, but their output varies with the weather and time of day, so energy storage is needed. Non-renewable fossil fuels can supply energy on demand, but their reserves are limited and their combustion adds carbon dioxide to the atmosphere.

Photosynthesis

Green plants, algae and some bacteria make glucose from carbon dioxide and water by photosynthesis, using energy from sunlight absorbed by the green pigment chlorophyll. Oxygen is released as a by-product.

Photosynthesis is the reverse of the combustion of glucose, so it is endothermic. The energy absorbed from light is stored as chemical energy in the glucose, and much of it can later be released when the glucose, or a fuel made from it, is burned or respired.

Photosynthesis fixes carbon: it converts carbon from atmospheric carbon dioxide into carbon compounds in living things. Plants convert glucose into starch, cellulose, oils and the other compounds from which biofuels are made.

What a biofuel is

The key difference between a biofuel and a fossil fuel is the time since the carbon was fixed. Burning a biofuel returns to the atmosphere carbon dioxide that the crop removed from it while it grew. Burning a fossil fuel releases carbon that has been locked underground for millions of years, adding to the total in the atmosphere and oceans.

For this reason biofuels are sometimes described as carbon neutral. The description is only approximately true. Growing, harvesting, transporting and processing the crop use energy, much of it from fossil fuels, and fertilizer manufacture and use release carbon dioxide and dinitrogen monoxide. Clearing forest or peatland to grow fuel crops releases large amounts of stored carbon. A biofuel therefore has a lower carbon footprint than a fossil fuel, often much lower, but not zero.

Bioethanol, biodiesel and biogas

Three biofuels are produced on a large scale:

• Bioethanol is made by fermentation: yeast converts sugars from sugar cane, maize (corn) or sugar beet into ethanol and carbon dioxide in the absence of oxygen, and the ethanol is concentrated by distillation. It is used pure or blended with petrol.

• Biodiesel is made from vegetable oils (such as rapeseed, soya or palm oil) or waste cooking oil by reacting them with methanol, which converts the large oil molecules into smaller esters with properties similar to diesel.

• Biogas is a mixture of mainly methane and carbon dioxide, produced when bacteria break down manure, sewage or food waste in the absence of oxygen (anaerobic digestion).

Fermentation and the reaction of oils with methanol are described more fully with the reactions of organic compounds.

Advantages and disadvantages of biofuels

An evaluation of a biofuel separates the problems of producing the fuel from the problems of using it. The table includes both.

Blends of petrol and ethanol, such as E10 (10 % ethanol), are sold in many countries. Compared with pure petrol, a blend uses up fossil fuel more slowly and lowers net carbon dioxide emissions. Because ethanol already contains oxygen, the blend also burns more completely, producing less carbon monoxide, and it resists premature ignition (knocking) in the engine, giving a higher octane rating.

Case study: sugar-cane ethanol in Brazil

Brazil has the longest-running large-scale biofuel programme in the world. Its government launched the National Alcohol Programme (Proálcool) in 1975, after the oil crisis of 1973 had sharply raised the price of imported crude oil. Sugar cane grows well in Brazil's climate and contains sucrose that can be fermented directly, without first breaking down starch as maize requires.

All petrol sold in Brazil contains anhydrous ethanol; the minimum ethanol content was raised from 27.5 % to 30 % (E30) in August 2025. Most new cars are flex-fuel vehicles, which can run on any mixture of petrol and ethanol up to pure hydrated ethanol, and drivers choose at the pump according to price. The crushed cane fibre left after the sugar is extracted (bagasse) is burned to supply heat and electricity to the distilleries, which lowers the fossil energy used in production.

The programme shows both sides of the evaluation. It has reduced Brazil's oil imports and its carbon dioxide emissions from transport. It has also used millions of hectares of land, and the expansion of cane and other crops has been linked to pressure on savannah and forest land. Ethanol's lower specific energy means a car travels roughly 30 % less far on a tank of pure ethanol than on petrol.

Fuel cells

Burning a fuel in a power station or engine converts its chemical energy into electrical or kinetic energy in several steps, with energy lost as heat at each. A fuel cell converts the chemical energy of a fuel directly into electrical energy, with no flame.

Because it avoids the conversion to heat, a fuel cell is more efficient: hydrogen fuel cells typically convert around 40–60 % of the fuel's energy into electricity, while a petrol engine converts only about 20–35 % into useful work.

How a hydrogen fuel cell works

A fuel cell contains two porous electrodes, usually coated with a platinum catalyst, separated by an electrolyte that conducts ions but not electrons. The fuel and the oxygen never mix. Instead, the overall redox reaction is split into two half-reactions:

• At the anode (the negative electrode), the fuel is oxidized, releasing electrons into the external circuit.

• At the cathode (the positive electrode), oxygen is reduced, taking electrons from the external circuit.

• Electrons flow through the external circuit from anode to cathode and do useful work. Ions move through the electrolyte to complete the circuit.

In a fuel cell with an acidic electrolyte, hydrogen ions carry the charge from the anode to the cathode:

The overall equation is the same as for the combustion of hydrogen, but the energy appears as electrical energy rather than heat. To add the half-equations, the anode equation is multiplied by 2 so that the four electrons released match the four used at the cathode, and the hydrogen ions then cancel.

In a fuel cell with an alkaline electrolyte, such as aqueous potassium hydroxide, hydroxide ions carry the charge, moving from the cathode to the anode. The half-equations are written with ${{\mathrm{OH}{\vphantom{X}}^{-}}}$ and ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$ instead of ${{\mathrm{H}{\vphantom{X}}^{+}}}$:

Alkaline fuel cells powered the Apollo spacecraft that took astronauts to the Moon between 1968 and 1972.

The methanol fuel cell

Hydrogen is difficult to store, so fuel cells that use a liquid fuel are also used, for example in portable generators. In a direct methanol fuel cell with an acidic electrolyte, methanol reacts with water at the anode to form carbon dioxide:

The oxidation state of carbon rises from −2 in methanol to +4 in carbon dioxide, a loss of six electrons per molecule, which matches the six electrons in the anode half-equation. Unlike a hydrogen fuel cell, a methanol fuel cell releases carbon dioxide, although less per unit of electrical energy than burning the methanol would, because it is more efficient.

Deducing half-equations for a fuel cell

The half-equations for any fuel can be deduced in the same way as other redox half-equations. For an acidic electrolyte:

• Write the fuel and its oxidized product (carbon dioxide for a carbon compound).

• Balance atoms other than oxygen and hydrogen.

• Balance oxygen by adding ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$.

• Balance hydrogen by adding ${{\mathrm{H}{\vphantom{X}}^{+}}}$.

• Balance charge by adding electrons, ${{\mathrm{e}{\vphantom{X}}^{-}}}$ (on the right for the oxidation at the anode).

For an alkaline electrolyte, balance the equation in acid first, then add ${{\mathrm{OH}{\vphantom{X}}^{-}}}$ to both sides to turn each ${{\mathrm{H}{\vphantom{X}}^{+}}}$ into ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$, and cancel water that appears on both sides.

Fuel cells compared with other cells and with combustion

A fuel cell is a type of voltaic cell, but it differs from a primary cell such as an alkaline battery in where its reactants are kept.

The advantages and disadvantages of fuel cells compared with rechargeable batteries are discussed with electrochemical cells.

Hydrogen as a fuel

Hydrogen has the highest specific energy of any common fuel, about 142 $\text{kJ g}^{-1}$, and the only product of its reaction with oxygen is water. Fuel-cell cars such as the Toyota Mirai, first sold in 2014, emit only water vapour from their exhaust. Hydrogen is described as a "greener" fuel for these reasons, but it has serious drawbacks:

• Production. Hydrogen does not occur naturally as the element. Most hydrogen produced today comes from natural gas, by reacting methane with steam (${{\mathrm{CH}{\vphantom{X}}_{\smash[t]{4}} {}+{} \mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}\xrightarrow{}\mathrm{CO} {}+{} 3\,\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}}}$), which releases carbon dioxide. Hydrogen made by the electrolysis of water using renewable electricity ("green hydrogen") avoids this, but it is still more expensive.

• Storage and transport. As a gas, hydrogen has a very low energy density. Cars store it at about 700 times atmospheric pressure in strong, heavy tanks, and liquefying it requires cooling to about −253 °C.

• Safety. Hydrogen forms explosive mixtures with air over a wide range of compositions, and its small molecules leak easily through joints.

• Cost. Fuel cells use expensive platinum catalysts, and few hydrogen filling stations exist.

Applying the ideas in exam questions

Paper 1A: balancing the combustion of an alcohol

Paper 1A: biofuels and greenhouse gases

Paper 1B: the enthalpies of combustion of four alcohols

(Paper 1B style) A student used a spirit burner under a copper can to compare four alcohols. Each burner heated $100.0\ \text{g}$ of water through a temperature rise of $20.0\ \text{K}$. The burners were weighed before and after on a balance reading to $\pm 0.001\ \text{g}$; the thermometer reads to $\pm 0.1\ \text{K}$.

Paper 2: propane as a fuel

Paper 2: a methanol fuel cell and biodiesel

Self-check

• To do:

  I can write balanced equations, with state symbols, for the combustion of reactive metals and of non-metals such as carbon, sulfur, hydrogen and phosphorus.

• To do:

  I can compare the combustion of an s-block metal and a p-block non-metal, including the bonding and acid–base character of their oxides.

• To do:

  I can identify the oxidizing and reducing agents in a combustion reaction and use oxidation states to describe how far carbon is oxidized.

• To do:

  I can explain why a high activation energy is a useful property of a fuel.

• To do:

  I can write equations for the complete combustion of hydrocarbons, alcohols and other compounds of C, H and O, using integer coefficients when asked.

• To do:

  I can explain why the enthalpy of combustion increases by a roughly constant amount along a homologous series.

• To do:

  I can describe the spirit-burner method for the enthalpy of combustion of an alcohol, process its results and evaluate its errors.

• To do:

  I can write equations for incomplete combustion forming carbon monoxide or carbon, and describe what is observed.

• To do:

  I can explain the health effects of carbon monoxide and particulates and why incomplete combustion releases less energy.

• To do:

  I can explain why larger hydrocarbons have a greater tendency to burn incompletely.

• To do:

  I can describe the formation of coal, crude oil and natural gas, and compare their advantages and disadvantages.

• To do:

  I can calculate specific energy from an enthalpy of combustion, and energy density from specific energy and density.

• To do:

  I can compare the carbon dioxide released by different fuels per mole, per gram and per kilojoule.

• To do:

  I can explain the greenhouse effect and the enhanced greenhouse effect, and name greenhouse gases other than carbon dioxide.

• To do:

  I can contrast methane and carbon dioxide as greenhouse gases and outline what global warming potential depends on.

• To do:

  I can outline ways of reducing carbon dioxide emissions, including carbon capture and storage.

• To do:

  I can distinguish between renewable and non-renewable energy sources.

• To do:

  I can write the equation for photosynthesis and explain why biofuels have a lower net carbon dioxide impact than fossil fuels.

• To do:

  I can evaluate biofuels, separating the disadvantages of producing them from those of using them.

• To do:

  I can explain how a fuel cell converts chemical energy directly into electrical energy and why it is more efficient than combustion.

• To do:

  I can write and deduce half-equations for hydrogen fuel cells (acidic and alkaline) and methanol fuel cells.

• To do:

  I can compare a fuel cell with a primary cell, and discuss the advantages and challenges of hydrogen as a fuel.

Explanation

The answer is C.

Oxygen: the products contain $8 \times 2 + 9 \times 1 = 25$ oxygen atoms, so $\tfrac{25}{2}$ molecules of ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$ are needed:

Integer coefficients: multiply throughout by 2:

Check: C 16 = 16; H 36 = 36; O 50 = 32 + 18. The general formula gives $x + y/4 = 8 + 4.5 = 12.5$ for one mole of octane, as found.

(b) Products: ${{4\,\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ and ${{5\,\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$ (ten hydrogen atoms). Oxygen atoms in the products: $8 + 5 = 13$. Subtract the one in butan-1-ol: 12 atoms, or 6 molecules of ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$:

Both equations already have integer coefficients. A common slip is to forget the oxygen atom in the alcohol, which gives ${{6.5\,\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$ for butan-1-ol, the value for butane.

Enthalpy change per mole:

The mass of ethanol (0.62 g) has only two significant figures, so the answer is given to two.

Percentage error:

The experimental value is much less exothermic than the accepted value, which is typical of this method.

24.5

Specific energies:

Energy density of octane: $47.9\ \text{kJ g}^{-1} \times 0.703\ \text{g cm}^{-3} = 33.7\ \text{kJ cm}^{-3}$.

Methane releases more energy per gram, but as a gas at room temperature its energy density is about a thousand times lower than that of liquid octane unless it is compressed or liquefied.

The mass of ${{\mathrm{SO}{\vphantom{X}}_{\smash[t]{2}}}}$ is twice the mass of sulfur, because $M({{\mathrm{SO}{\vphantom{X}}_{\smash[t]{2}}}})$ is almost exactly twice $M({{\mathrm{S}}})$. A power station burning 10 000 tonnes of this coal a day would release about 80 tonnes of ${{\mathrm{SO}{\vphantom{X}}_{\smash[t]{2}}}}$ unless the flue gases were treated.

(b) ${{\mathrm{SO}{\vphantom{X}}_{\smash[t]{2}}\mskip2mu (\mathrm{g}) {}+{} \mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}\mskip2mu (\mathrm{l})\xrightarrow{}\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{SO}{\vphantom{X}}_{\smash[t]{3}}\mskip2mu (\mathrm{aq})}}$. The sulfurous acid formed contributes to acid deposition.

(c) Amount of methane: $n = \dfrac{1.00\ \text{dm}^3}{22.7\ \text{dm}^3\ \text{mol}^{-1}} = 0.0441\ \text{mol}$. Energy released $= 0.0441 \times 891 = 39.3\ \text{kJ}$. One gram of carbon releases $\dfrac{394}{12.01} = 32.8\ \text{kJ}$, so $1.00\ \text{dm}^3$ of methane at STP, with a mass of only $0.707\ \text{g}$, releases more energy than $1.00\ \text{g}$ of carbon.

(a) Per gram. $M({{\mathrm{CH}{\vphantom{X}}_{\smash[t]{4}}}}) = 16.05$ and $M({{\mathrm{C}{\vphantom{X}}_{\smash[t]{4}}\mathrm{H}{\vphantom{X}}_{\smash[t]{10}}}}) = 58.14\ \text{g mol}^{-1}$:

(b) Per kilojoule.

Methane releases less carbon dioxide on both bases, and the difference is larger per kilojoule (about 20 % less). Methane has the highest proportion of hydrogen of any hydrocarbon, so more of its energy comes from forming water rather than carbon dioxide.

A is the correct ratio but not an integer. B comes from ignoring the oxygen atom in the alcohol (the value for propane). D ignores the alcohol's oxygen and then doubles.

Ignore state symbols.

(b)

• ${{2\,\mathrm{C}{\vphantom{X}}_{\smash[t]{3}}\mathrm{H}{\vphantom{X}}_{\smash[t]{8}}\mskip2mu (\mathrm{g}) {}+{} 7\,\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})\xrightarrow{}6\,\mathrm{CO}\mskip2mu (\mathrm{g}) {}+{} 8\,\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}\mskip2mu (\mathrm{l})}}$ ✓

• CO is toxic: it binds to haemoglobin «more strongly than oxygen» and prevents the blood carrying oxygen ✓

Accept ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{3}}\mathrm{H}{\vphantom{X}}_{\smash[t]{8}} {}+{} \mathchoice{\textstyle\frac{7}{2}}{\frac{7}{2}}{\frac{7}{2}}{\frac{7}{2}}\,\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}\xrightarrow{}3\,\mathrm{CO} {}+{} 4\,\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$. Do not accept "CO is poisonous" alone for M2.

(c)

• $\dfrac{2219}{44.11} = 50.3$ «$\text{kJ g}^{-1}$» ✓

(d)

• propane: $\dfrac{3}{2219} = 1.35\times10^{-3}$ «mol ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ per kJ» AND ethanol: $\dfrac{2}{1367} = 1.46\times10^{-3}$ «mol ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ per kJ» ✓

• ethanol releases more «CO₂ per kJ» ✓

Accept answers in grams of ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ (59.5 and 64.4 g per MJ). M2 can be awarded by ECF from M1.

(e)

• ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$ absorbs infrared radiation emitted by the Earth's surface ✓

• and re-emits it in all directions, some back towards the Earth «warming the lower atmosphere» ✓

Do not accept "traps heat" or "reflects radiation" alone.