IB Chemistry SLTopic 4 — Energy from FuelsPaper 1 & 2Core idea~13 min read
Fuel Cells
Burning a fuel throws its electrons straight at oxygen and collects the energy as heat. A fuel cell separates the two halves of that reaction and makes the electrons travel round a circuit to reach the oxygen — so you collect the energy as electricity instead.
📚 What you need to know
A fuel cell is an electrochemical cell in which a fuel is oxidised at the anode and oxygen is reduced at the cathode, converting chemical energy directly into electrical energy.
Unlike a battery, the reactants are supplied continuously from outside, so the cell never goes flat and stores no energy itself.
In the alkaline hydrogen–oxygen cell the overall reaction is 2H2(g) + O2(g) → 2H2O(l), Eθ = +1.23 V.
Water is the only product, so there is no CO2, CO, soot or NOx.
The methanol cell uses methanol as the source of H+ instead, and does release CO2.
Fuel cells are more efficient than combustion because they skip the conversion of chemical energy into heat.
What a fuel cell is
Fuel cell
an electrochemical cell in which a fuel is oxidised at one electrode and oxygen is reduced at the other, generating a voltage
The distinction from a battery is the one examiners like. A battery is a sealed container of reactants: use them up and it goes flat, and it has to be recharged or replaced. A fuel cell holds no reactants at all — fuel and oxygen are piped in continuously and the products piped out, so it runs for as long as you keep feeding it. It converts energy; it does not store it.
Get the electrode names right, because the signs are the opposite of electrolysis. In any cell that produces a voltage: anode = oxidation = negative, cathode = reduction = positive. Electrons leave the anode, travel through the external circuit, and arrive at the cathode. Inside the electrolyte, anions travel towards the anode and cations towards the cathode.
The hydrogen–oxygen fuel cell
The electrons cannot cross the electrolyte, so they are forced through the wire. That detour is the current you use.
The cell is built from:
a reaction chamber with separate inlets for hydrogen and oxygen
two porous electrodes, coated with a catalyst to speed up the electron transfer
an electrolyte, here aqueous potassium or sodium hydroxide, which carries ions but not electrons
a semi-permeable membrane keeping the two gases apart, and an outlet for the water
With an alkaline electrolyte the two half-equations are:
Both half-equations use four electrons, so they can be added without any scaling — which is exactly why they are written that way.
WORKED EXAMPLE
Combine the two half-equations above to give the overall cell reaction, and calculate Eθ for the cell.
Step 1 — add them as written2H₂ + 4OH− + O₂ + 2H₂O → 4H₂O + 4OH−Step 2 — cancel what appears on both sides4OH− cancels completely; 2H₂O on the left cancels 2 of the 4 on the right; the 4e− cancel.2H₂(g) + O₂(g) → 2H₂O(l)Step 3 — the voltageEᵒ = Eᵒ(cathode) − Eᵒ(anode) = (+0.40) − (−0.83)Eᵒ cell = +1.23 VThe overall reaction is exactly the combustion of hydrogen. Same chemistry, same energy — delivered as electricity rather than as a flame.
Look at what the hydroxide ions are doing. They are made at the cathode and consumed at the anode, so the electrolyte is not used up — it just ferries charge across the gap to complete the circuit. Every ion that migrates left balances an electron that went right.
Why not just burn the hydrogen?
Every arrow is a conversion, and every conversion leaks. The fuel cell wins by having fewer arrows.
Burning hydrogen in an engine releases the same energy, but you then have to convert heat into motion and motion into electricity, losing a large fraction at each stage. A fuel cell makes the conversion in one step at ordinary temperatures, which is why it is so much more efficient. Running cool has a second benefit: no nitrogen oxides, which only form when air is heated to combustion temperatures.
Hydrogen fuel cells — in favour
Against
Water is the only product — no CO2, CO, soot or SO2
Hydrogen is highly flammable, so it is hazardous to handle
More efficient than combustion, since chemical energy becomes electrical directly
Very low energy density by volume, so it needs heavy, thick-walled, high-pressure tanks
Runs at near room temperature, so no NOx is produced
Most hydrogen is currently made from fossil fuels, which makes it non-renewable in practice
Runs continuously while fuel is supplied, with no recharging
Distribution and refuelling infrastructure barely exists
Used on spacecraft, where the product water is drinkable
Catalysts and materials are expensive
“Zero emission” needs a caveat, and saying so earns marks in an evaluation question. The cell emits only water, but if the hydrogen came from steam reforming of natural gas, carbon dioxide was released making it. Hydrogen is only genuinely clean if it is made by electrolysis using renewable electricity.
The methanol fuel cell
Hydrogen’s real problem is storage, so an obvious workaround is to carry the hydrogen inside a liquid molecule. A methanol cell works the same way but takes its H+ from methanol, using an acidic proton exchange membrane instead of an alkaline electrolyte.
Because the electrolyte is acidic, the mobile ion is H+ and it travels towards the cathode — the opposite direction to OH– in the alkaline cell.
This time the electron counts do not match — six against four — so one half-equation has to be scaled before they can be added.
WORKED EXAMPLE
Combine the two methanol half-equations to give the overall cell reaction.
Step 1 — match the electrons6 and 4 both divide into 12, but multiplying the cathode by 1.5 is quicker.1½O₂ + 6H⁺ + 6e− → 3H₂OStep 2 — add to the anode halfCH₃OH + H₂O + 1½O₂ + 6H⁺ + 6e− → CO₂ + 6H⁺ + 6e− + 3H₂OStep 3 — cancel6H⁺ and 6e− cancel; one H₂O on the left cancels one of the three on the right.CH₃OH + 1½O₂ → CO₂ + 2H₂OWhich is precisely the equation for the complete combustion of methanol from earlier in this topic. A fuel cell does not change the reaction — only the route.
Methanol cell compared with hydrogen
Better
Worse
Storage and transport
A liquid at room temperature, so no pressurised tanks; much higher energy density by volume
Emissions
Releases CO2, so it is not emission-free at the point of use
Performance
Lower voltage and power per unit mass; methanol crossing the membrane wastes fuel
Safety
Operates at low pressure and temperature
Methanol is toxic as well as flammable
Source
Can be made renewably from biomass
Usually made from fossil fuels at present
WORKED EXAMPLE
A hydrogen–oxygen fuel cell consumes 1.00 g of hydrogen. Calculate the mass of water produced and the amount of electrons transferred. (Mr: H2 = 2.02, H2O = 18.02)
Step 1 — moles of hydrogenn = 1.00 ÷ 2.02 = 0.495 molStep 2 — water, from 2H₂ + O₂ → 2H₂OThe ratio H₂ : H₂O is 1 : 1.0.495 × 18.02 = 8.928.92 g of waterStep 3 — electronsThe anode half-equation gives 4e− per 2H₂, so 2e− per H₂.0.495 × 2 = 0.990 mol e−Nine grams of drinking water from one gram of fuel — which is why spacecraft liked them.
Extension: multiply the moles of electrons by Faraday’s constant, 96500 C mol–1, and you get the charge that flowed: 0.990 × 96500 ≈ 9.55 × 104 C. Charge calculations like this belong to the HL electrochemistry topic, but the moles-of-electrons step above is the same one.
💡 Exam tip
Anode is oxidation and negative in a cell that produces a voltage. Write “oxidation at the anode” next to your working so you never invert it.
Before adding half-equations, make the electrons match, then cancel anything appearing on both sides — including water and H+.
Eθcell = Eθ(cathode) – Eθ(anode), and a working cell always gives a positive answer.
Asked why a fuel cell beats an engine? Say chemical energy is converted directly to electrical, with no heat stage to lose energy at.
For evaluation marks, distinguish emissions at the point of use from emissions during fuel production.
⚠️ Common mix-up
Using the electrolysis sign convention. Here the anode is negative, not positive.
Calling a fuel cell a battery. A battery stores its reactants and goes flat; a fuel cell is fed.
Adding half-equations without matching the electrons first. Six and four do not cancel.
Claiming hydrogen cells are entirely emission-free. That depends on how the hydrogen was made.
Forgetting the methanol cell produces CO2. Its overall equation is a combustion equation.
That completes Energy from Fuels, and with it the whole of Topic 4. You can now measure an enthalpy change in a cup, calculate one you could never measure at all, work out exactly what a fuel does to the atmosphere, and get the energy out of it without ever lighting a flame.
Want this explained one-to-one?
Book a free session with an experienced IB Chemistry tutor and get your trickiest topics made simple.
