Catalytic Electrodes: Making Hydrogen by Electrolysis

On a catalytic electrode the electrode itself is not consumed: it provides a surface on which species in solution gain or lose electrons. The Butler–Volmer equation still applies, and the exchange current density now measures how good a catalyst the surface is. Here you compare cathodes for the hydrogen evolution reaction, then build a water electrolyser and find the voltage it needs. Work through the three stages in order.

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Predict, then see: 2H⁺ + 2e⁻ ⇄ H₂,

Or explore freely:

Overpotential, η 0.00 V

The pictures show each surface at the molecular level. Two separate H⁺ ions (blue) arrive at neighbouring surface atoms; each takes one electron (black dot) from the electrode and becomes an adsorbed H atom (white), H⁺ + e⁻ → H; the two H atoms then join and leave as H₂. Two electrons per H₂, so the rate of hydrogen formation is |i|/(2F).
The text under each bar gives the rate for a single surface atom (taking about 1.5 × 10¹⁵ surface atoms per cm²). The animations run on a log scale of the true rate, so that all three surfaces can be seen at once; the text gives the true rate.
The bars use a log scale: each grid line is a factor of 1,000 in current density.
The faint part of each bar is i₀. Making η more negative lengthens every bar by the same amount; the catalyst decides where the bar starts.

Remember

A catalytic (inert) electrode is not oxidised or reduced itself; it transfers electrons to and from species in solution and remains unchanged.
Water electrolysis, 2H₂O → 2H₂ + O₂: hydrogen evolution (HER) at the cathode, 2H⁺ + 2e⁻ → H₂, E° = 0 V; oxygen evolution (OER) at the anode, 2H₂O → O₂ + 4H⁺ + 4e⁻, E° = +1.23 V.
E° depends only on the reaction; the catalyst changes i₀, and so the overpotential needed for a given current.
The same current passes through both electrodes. The electrode with the smaller i₀ needs the larger overpotential and limits the rate.
Voltage needed = 1.23 V + η_anode + |η_cathode|. Everything above 1.23 V is lost as heat.
10 mA cm⁻² is the benchmark current density used to compare electrocatalysts in research (it corresponds roughly to a 10 % efficient solar-driven water splitter). Commercial electrolysers run much harder: about 0.2–0.5 A cm⁻² (alkaline) and 1–2 A cm⁻² (PEM), which is why the overpotentials matter so much in practice.

Exchange current densities are those in the lecture tables (HER: Pt 10⁻³, Cu 10⁻⁶, Pb 10⁻¹¹ A cm⁻²; OER: IrO₂ 10⁻⁶, Pt 10⁻⁸, graphite 10⁻¹⁰ A cm⁻²). The model uses the Butler–Volmer equation with α = 0.5 and n = 2 for the HER and n = 4 for the OER, the number of electrons in each half-reaction. Real OER kinetics involve several steps, and real cells also lose voltage to the resistance of the electrolyte and to gas bubbles; these are left out.