IB Chemistry HLTopic 4 — Energy from FuelsPaper 1 & 2Core idea~12 min read
Fuel Cells
Every page so far has burnt the fuel. A fuel cell does something cleverer: it separates the oxidation from the reduction, forces the electrons to travel round an external circuit, and takes the energy out as electricity directly. No flame, no pistons, and no losing most of the energy as heat on the way.
📘 What you need to know
A fuel cell is an electrochemical cell in which a fuel is oxidised at one electrode and oxygen is reduced at the other, generating a potential difference.
The anode is where oxidation happens and is the negative electrode. The cathode is where reduction happens and is positive.
Electrons travel through the external circuit; ions travel through the electrolyte. Both are needed to complete the circuit.
The cell needs a reaction chamber with separate inlets for fuel and oxygen, an outlet for the products, an electrolyte, and a semi-permeable membrane keeping the two gases apart.
A fuel cell is not a battery. Nothing is stored: it runs continuously for as long as fuel and oxygen are fed in.
Hydrogen–oxygen cell, overall: 2H2(g) + O2(g) → 2H2O(l), with E°cell = +1.23 V. Water is the only product.
Methanol cell, overall: 2CH3OH(aq) + 3O2(g) → 2CO2(g) + 4H2O(l). Easier to store, but it emits CO2.
The half-equations depend on whether the electrolyte is alkaline (OH− migrates) or acidic (H+ migrates), but the overall reaction is the same either way.
What makes it different from burning
Burn hydrogen in air and the electrons pass straight from hydrogen to oxygen where the two molecules collide. You get the energy, but you get it as heat, and heat is an awkward form to work with.
A fuel cell keeps the two halves of that reaction physically apart. Hydrogen is oxidised at one electrode and releases electrons; oxygen is reduced at the other electrode and needs electrons. The only route between them is the wire you have connected, so the electrons have to travel through your circuit and do useful electrical work on the way.
This is the same trick as any voltaic cell you have met before. The novelty is only that the reactants are gases fed in continuously rather than solids and solutions sealed inside.
The membrane matters more than it looks. If hydrogen and oxygen mixed inside the cell they would simply react together, releasing the energy as heat and producing no current at all.
The parts, and what each is for
Reaction chamber with separate inlets for the fuel and for oxygen (usually just air).
Two porous electrodes, with a large surface area and often a catalyst, so the gases can meet the electrolyte and react quickly.
An electrolyte to carry ions between the electrodes. In the classic alkaline cell this is aqueous sodium or potassium hydroxide.
A semi-permeable membrane that lets ions through but keeps the two gases apart.
An outlet for the product — water, in the hydrogen cell.
The half-equations for the hydrogen cell
In an alkaline electrolyte, hydroxide ions are the species available, so they appear in both half-equations. At the anode, hydrogen is oxidised:
Add them together and cancel what appears on both sides — the 4e−, the 4OH−, and two of the four waters:
Overall
2H2(g) + O2(g) → 2H2O(l) E°cell = +1.23 V
Notice what the hydroxide is doing: it is consumed at the anode and regenerated at the cathode, so the electrolyte is not used up. It is carrying charge, not taking part in the net reaction.
WORKED EXAMPLE
Using the two half-cell potentials above, calculate E°cell for the alkaline hydrogen–oxygen fuel cell, and identify which electrode is the anode.
Step 1: The more positive potential is reduced, so it is the cathode+0.40 V (oxygen) is more positive than −0.83 V, so oxygen is reducedStep 2: The other half-cell must be the anodehydrogen is oxidised, so the hydrogen electrode is the anode − and it is negativeStep 3: Apply E°cell = E°cathode − E°anodeE°cell = (+0.40) − (−0.83)E°cell = +1.23 V, hydrogen electrode is the anodea positive E°cell confirms the reaction is spontaneous, as it must be
Change the electrolyte and the half-equations change
This catches people out badly. The same cell in an acidic electrolyte, such as a proton exchange membrane, has completely different-looking half-equations, because now it is H+ that is available rather than OH−:
Add those together and you get… exactly the same overall reaction, 2H2 + O2 → 2H2O, and the same +1.23 V. The electrolyte changes the route, not the destination.
In both cases the ion moves so as to cancel the charge building up: away from the electrode gaining positive charge, towards the one losing it.
🧩 Building a fuel-cell half-equation from scratch
Decide which species is oxidised (the fuel, at the anode) and which is reduced (oxygen, at the cathode).
Ask what ion the electrolyte provides: OH− if alkaline, H+ if acidic. That ion is allowed to appear.
Balance the atoms other than O and H first.
Balance oxygen using H2O, then hydrogen using H+ or OH−.
Balance the charge by adding electrons to whichever side needs them.
Scale the two half-equations so the electrons cancel, add them, and cancel anything appearing on both sides.
Why fuel cells are so efficient
This is the strongest argument for the technology, and it is a thermodynamic one rather than an engineering one.
A petrol engine converts chemical energy into heat, heat into mechanical work, and mechanical work into electricity. The middle step is the problem: converting heat into work has a hard theoretical ceiling, and real engines manage only 25–30% overall.
A fuel cell goes from chemical energy straight to electrical energy. There is no heat step to be limited by, so the ceiling is set by a different and much more generous quantity.
Real hydrogen fuel cells reach 50–60% rather than 83%, because of resistance in the electrolyte and slow reaction at the electrodes. Even so, that is roughly double a petrol engine.
WORKED EXAMPLE
1.00 g of hydrogen is consumed by a fuel cell operating at 1.23 V. Calculate the charge that passes and the electrical energy produced. Compare it with the 141.8 kJ of enthalpy available from burning the same mass (ΔHc = −285.8 kJ mol−1). Take F = 96 500 C mol−1.
Step 1: Moles of hydrogen, then moles of electronsn(H₂) = 1.00 ÷ 2.016 = 0.496 moleach H₂ releases 2 electrons at the anoden(e⁻) = 2 × 0.496 = 0.992 molStep 2: Charge, using Q = nFQ = 0.992 × 96 500 = 9.57 × 10⁴ CStep 3: Electrical energy, using W = QVW = 9.57 × 10⁴ × 1.23 = 1.18 × 10⁵ JQ = 9.57 × 10⁴ C, W = 118 kJStep 4: Compare with the enthalpy118 ÷ 141.8 × 100 = 83.0%so 83% of the chemical energy is available as electricity − the theoretical ceiling
Hydrogen: the honest assessment
Advantages
Disadvantages
Water is the only product, so there are no harmful emissions at the point of use
Hydrogen is highly flammable, so storage and handling carry real safety risks
Operates at or near room temperature, avoiding combustion entirely
Needs heavy, thick-walled pressurised tanks, adding cost, mass and complexity
No nitrogen oxides are formed, unlike in high-temperature combustion
Most hydrogen is currently made from fossil fuels, so it is not renewable in practice
Energy goes directly to electricity, so efficiency is roughly double an engine’s
Low energy density by volume, so containers must be large even though the mass is small
Used on spacecraft, where the water produced becomes drinking water for the crew
Until cheap, sustainable hydrogen production exists, wide use stays limited
Hydrogen is a carrier, not a source. There are no hydrogen mines. Every kilogram has to be made using energy from somewhere else — usually from natural gas at present. So a hydrogen car is exactly as clean as the electricity or fuel used to make its hydrogen. This is the same life-cycle argument that qualifies the carbon-neutral claim for biofuels.
The methanol fuel cell
Methanol solves hydrogen’s most annoying practical problem. It is a liquid at room temperature, so it can be stored and transported in an ordinary tank with no pressurisation at all. The cell works the same way, but the fuel supplying the hydrogen ions is methanol rather than hydrogen gas, and the electrolyte is acidic — typically a proton exchange membrane.
The electrons do not cancel as written — six against four — so the cathode equation has to be scaled by 1.5 first.
WORKED EXAMPLE
Combine the two half-equations above to give the overall equation for the methanol fuel cell, using whole-number coefficients.
Step 1: Match the electronsanode gives 6e⁻, cathode takes 4e⁻, so multiply the cathode by 1.51.5O₂ + 6H⁺ + 6e⁻ → 3H₂OStep 2: Add the two half-equationsCH₃OH + H₂O + 1.5O₂ + 6H⁺ + 6e⁻ → CO₂ + 6H⁺ + 6e⁻ + 3H₂OStep 3: Cancel what appears on both sidesthe 6H⁺ and 6e⁻ cancel; 3H₂O − 1H₂O leaves 2H₂OCH₃OH(aq) + 1.5O₂(g) → CO₂(g) + 2H₂O(l)Step 4: Double for whole numbers2CH₃OH(aq) + 3O₂(g) → 2CO₂(g) + 4H₂O(l)check: C 2 = 2, H 8 = 8, O 2 + 6 = 8 = 4 + 4 ✓
Methanol vs hydrogen
Better
Worse
Storage and transport
A liquid at room temperature, so no pressurised tank; higher energy density by volume
Toxic as well as flammable, so spills are more hazardous to people
Operating conditions
Runs at low pressure and temperature; the aqueous conditions give the membrane a longer lifespan
Lower voltage and power output per unit mass
Efficiency
—
Methanol crossover: the small polar molecule diffuses through the membrane and is oxidised at the cathode, wasting fuel and dropping the voltage
Emissions
Can be made from renewable biomass, so lower life-cycle emissions than hydrogen from fossil fuels
Produces carbon dioxide at the point of use; hydrogen produces only water
Cost
Fuel is cheap and easy to distribute using existing infrastructure
Needs expensive catalysts such as ruthenium and palladium
Worth noticing: the methanol cell still releases CO2, so it is not a zero-carbon technology. What it avoids is combustion — so no nitrogen oxides, no carbon monoxide and no soot, and roughly double the efficiency of burning the same methanol in an engine.
💡 Exam tip
Anode = oxidation, always, in every kind of cell. In a fuel cell the anode is the negative electrode.
Check the electrolyte before writing half-equations. Alkaline means OH− appears; acidic means H+ appears. Mixing them scores nothing.
Always scale so the electrons cancel before adding half-equations, and cancel species appearing on both sides.
Use E°cell = E°cathode − E°anode. A positive answer means a spontaneous reaction.
Say electrons move through the external circuit and ions through the electrolyte. Ions never travel through the wire.
If asked how a fuel cell differs from a battery, the answer is that reactants are supplied continuously and energy is not stored in the cell.
For evaluation marks on hydrogen, mention how the hydrogen was made. “No emissions” alone is an incomplete answer.
⚠ Common mix-up
Thinking the anode is positive. It is positive in electrolysis but negative in a fuel cell or any voltaic cell, because it is the source of electrons.
Saying a fuel cell “goes flat”. It does not discharge — it stops only when the fuel supply stops.
Using OH− in an acidic cell, or H+ in an alkaline one. The electrolyte dictates which is available.
Adding half-equations without matching the electrons. Six and four do not cancel; scale first.
Claiming hydrogen fuel cells are emission-free overall. They are clean at the point of use; the production of the hydrogen usually is not.
Saying the methanol cell produces only water. It produces carbon dioxide as well.
Calling combustion “inefficient because of friction”. The real limit is the heat-to-work step, which a fuel cell avoids altogether.
Forgetting the membrane. Without it the gases mix and react directly, giving heat instead of current.
Up next: Entropy and Spontaneity — enthalpy is only half the story. Some endothermic reactions happen anyway, and to explain why we need a second quantity.
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