Electrolysis of Water — the 2:1 rule

Concept — splitting water, and the 2:1 rule

Direct current through acidified water (dilute H₂SO₄, added so the water conducts) splits it: 2 H₂O → 2 H₂ + O₂. Reduction happens at the cathode (−), where hydrogen bubbles off; oxidation happens at the anode (+), where oxygen bubbles off. Because freeing one O₂ molecule needs four electrons but each H₂ needs only two, twice as many H₂ molecules form per coulomb — so the collected hydrogen is always exactly twice the volume of oxygen (2:1).

What the animation shows

Both carbon electrodes are immersed in one beaker of acidified water, each under an inverted collection tube. H⁺ ions drift to the cathode and SO₄²⁻ ions to the anode; electrons run through the outer wire. Bubbles rise into the tubes and the H₂ column grows at twice the rate of the O₂ column, so the gas levels stay locked at 2:1. Turn the switch OFF and the current is zero — all bubbling stops.

Half-reactions

• Cathode (−): 4 H⁺ + 4 e⁻ → 2 H₂  (z = 2 per H₂)
• Anode (+): 2 H₂O → O₂ + 4 H⁺ + 4 e⁻  (z = 4 per O₂)

Quantities

• I — current through the cell (A); zero when the switch is off.
• Q = I·t — charge passed (C).
• n(H₂) = Q/(z·F) — moles of gas by Faraday's law; z = 2 for H₂, z = 4 for O₂.
• V = n·Vₘ — gas volume, molar volume Vₘ = 24.0 L/mol (25 °C, 1 atm).
• F = 96485 C/mol — Faraday constant, charge per mole of electrons.

Sources

Atkins, Physical Chemistry (Faraday's laws of electrolysis); NCERT Chemistry (electrolysis of acidified water; Hofmann voltammeter demo); CODATA 2018 (F = 96485.33 C/mol); ideal-gas molar volume 24.0 L/mol at 298 K, 1 atm (22.4 L/mol at STP). Time is a scaled simulation clock.