Hydrogen Fuel Cells and Clean Energy

A hydrogen fuel cell is a galvanic cell that converts the chemical energy of hydrogen and oxygen directly into electricity, with water as the only product: 2H₂ + O₂ → 2H₂O, with a standard potential of 1.23 V. In brief: unlike a battery, a fuel cell does not run down as long as fuel and oxygen are supplied, and a stack of 50 cells operating at 0.7 V per cell and 28.6 A produces about 1 kW while consuming about 54 g of hydrogen per hour.

Fuel cells promise efficient and clean power for vehicles, buildings and spacecraft, if the hydrogen is made without releasing carbon dioxide. This article explains how a fuel cell works, derives its theoretical voltage and efficiency, compares the main types, covers the production and storage of hydrogen and provides an example calculation of hydrogen consumption.

How does a hydrogen fuel cell work?

In the most common type, the proton exchange membrane (PEM) fuel cell, the reactions are:

• Anode (oxidation): 2H₂ → 4H⁺ + 4e⁻ (platinum catalyst).
• Cathode (reduction): O₂ + 4H⁺ + 4e⁻ → 2H₂O.
• Overall: 2H₂ + O₂ → 2H₂O.

Hydrogen is fed to the anode and oxygen (from air) to the cathode. The membrane, a polymer such as Nafion, conducts protons but not electrons, so the electrons are forced to flow through the external circuit and do electrical work. Protons pass through the membrane to the cathode, where they combine with oxygen and electrons to form water. A single cell makes only about 0.6–0.8 V in operation, so many cells are connected in series to form a stack.

What are the voltage and the efficiency?

From the standard electrode potentials, E° = 1.23 V − 0.00 V = 1.23 V. The free energy change for H₂ + ½O₂ → H₂O(l) is ΔG° = −nFE° = −2 × 96,485 × 1.23 = −237 kJ/mol, and the enthalpy change is ΔH° = −286 kJ/mol. Since a fuel cell converts the free energy into electrical work, the maximum thermodynamic efficiency is ΔG/ΔH = 237 / 286 = 0.83, or 83 %.

Real cells are less efficient, since there are losses from slow electrode reactions (activation overpotential), resistance in the membrane and limits on the transport of gases. At 0.70 V per cell, the voltage efficiency is 0.70 / 1.23 = 57 %, and the overall efficiency about 0.83 × 0.57 ≈ 47 %. This is still higher than the 25–35 % typical of a gasoline engine, and unlike a heat engine, a fuel cell is not limited by the Carnot efficiency.

Types of fuel cells

High-temperature cells can use other fuels, such as natural gas, because the high temperature makes catalysts and reforming easier. In an alkaline cell, the reactions are H₂ + 2OH⁻ → 2H₂O + 2e⁻ at the anode and O₂ + 2H₂O + 4e⁻ → 4OH⁻ at the cathode.

How much hydrogen does a fuel cell use?

Worked example: a 1 kW stack

A stack of 50 cells in series operates at 0.70 V per cell. It must deliver 1000 W.

1. Stack voltage: 50 × 0.70 = 35.0 V.
2. Current: I = P / V = 1000 / 35.0 = 28.6 A (the same current flows through all cells in series).
3. Each H₂ molecule supplies 2 electrons, so the hydrogen consumption is I × N / (2F) = 28.6 × 50 / (2 × 96,485) = 0.00741 mol/s.
4. The mass is 0.00741 × 2.016 = 0.0149 g/s, or 53.8 g per hour.

For comparison, 1 kg of hydrogen contains about 120 MJ of lower heating value (141.8 MJ on the higher heating value basis), or about 33 kWh. A fuel-cell car may use roughly 1 kg of hydrogen per 100 km, and 1 kg of hydrogen has about the same energy as one US gallon (3.8 liters) of gasoline.

Where does hydrogen come from?

• Steam reforming of natural gas: CH₄ + H₂O → CO + 3H₂, followed by the water–gas shift. It supplies most of today’s hydrogen, and releases about 9–10 kg of CO₂ per kg of H₂, so the product is sometimes called “gray” hydrogen.
• Electrolysis of water: 2H₂O → 2H₂ + O₂ using electricity. If the electricity comes from wind, solar or other low-carbon sources, the hydrogen is called “green”.
• Other routes: reforming with carbon capture (“blue” hydrogen), biomass gasification and thermochemical cycles.

Hydrogen has a very high energy per mass but a low energy per volume, so it must be stored compressed (typically at 700 bar in cars), as a liquid at −253 °C or in materials that absorb it.

What are the challenges?

• Cost and materials: platinum catalysts and membranes are expensive.
• Hydrogen production: the cleanliness depends on the source of the energy.
• Storage and distribution: hydrogen leaks easily and embrittles some metals.
• Round-trip efficiency: converting electricity to hydrogen and back to electricity typically returns only about 30–40 % of the original energy, much less than a battery.
• Durability: membranes and catalysts degrade with time.

How did fuel cells develop?

William Grove, a Welsh judge and scientist, demonstrated the first hydrogen–oxygen “gas voltaic battery” in 1839, with platinum electrodes in dilute sulfuric acid. Francis Thomas Bacon developed a practical alkaline fuel cell in the 1950s, which was used by NASA in the Apollo missions, where its product water was drunk by the astronauts. PEM cells were developed at General Electric in the 1960s for the Gemini program. Mass-produced fuel-cell cars, such as the Toyota Mirai, were introduced in the 2010s.

Which mistakes are common?

• Calling a fuel cell a battery: it is supplied with fuel and does not store the reactants inside.
• Assuming that hydrogen is always a clean fuel: it depends on how it is made.
• Mixing up the cell voltage and the stack voltage: the voltages of cells in series add up.
• Ignoring the efficiency losses: real cells give 0.6–0.8 V, not 1.23 V.
• Thinking that hydrogen burns inside the fuel cell: the reaction is electrochemical and takes place at low temperature.