Butler-Volmer: Hydrogen Reactions

About This Visualisation

What decides how fast a reaction goes at an electrode? Mostly two things: how hard you push, and what the electrode is made of.

Push the slider away from the centre and watch the electrode: you are either making hydrogen gas or using it up. The graph records how fast.

Show the maths

The curve is the Butler-Volmer equation, which describes both hydrogen evolution (HER) and hydrogen oxidation (HOR) at the same electrode:

i = i₀ [exp(α_anFη/RT) − exp(−α_cnFη/RT)]

Hydrogen evolution (η < 0): 2H⁺ + 2e⁻ → H₂ (reduction, cathodic)
Equilibrium (η = 0): no net current flow
Hydrogen oxidation (η > 0): H₂ → 2H⁺ + 2e⁻ (oxidation, anodic)

i₀ is the exchange current density — how fast the reaction already runs in both directions when nothing is pushing it. It is what makes one electrode material better than another. Here α_a = α_c = 0.5, n = 2 and T = 298 K.

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How hard are you pushing? Overpotential (η): 0.000 V

−0.3 V +0.3 V

How far you have pushed the electrode from its resting voltage. Negative pushes electrons in, positive pulls them out.

Start here:

Electrode material:

At rest (no net reaction)

Real-World Applications

Water electrolysis (negative overpotential): production of green hydrogen for energy storage and fuel cells. Used in alkaline, PEM and solid oxide electrolysers.
Hydrogen fuel cells (positive overpotential): converting hydrogen back to electricity for vehicles, backup power and portable electronics.
Catalyst development: the exchange current density (i₀) is why platinum is used despite the cost. Finding earth-abundant materials with a similarly high i₀ is an active research problem.