Hydrogen from Water Electrolysis: Faraday's Law
Water is electrolyzed with a steady current of 2.00 A for 1.00 hour. The cathode half-reaction is 2H2O + 2e- -> H2 + 2OH-. What volume of hydrogen gas is produced at STP? (F = 96485 C/mol; molar volume at STP = 22.414 L/mol.)
Given
Current I = 2.00 A
Time t = 1.00 h = 3600 s
Faraday constant F = 96485 C/mol
Half-reaction: 2H2O + 2e- -> H2 + 2OH- (2 electrons per H2)
Molar volume of an ideal gas at STP = 22.414 L/mol.
Find
The volume of H2 gas produced at STP.
Principle
Faraday's law links electric charge to chemical amount: charge Q = current x time, and moles of electrons = Q / F. The balanced half-reaction then converts moles of electrons to moles of product — here 2 electrons make 1 H2 molecule. The ideal-gas molar volume converts moles of gas to liters at STP.
Formula
Solution
Compute the total charge: Q = I x t = 2.00 A x 3600 s = 7200 C.
Convert charge to moles of electrons: n(e-) = 7200 C / 96485 C/mol = 0.0746 mol e-.
Use the half-reaction stoichiometry: 2 mol e- produce 1 mol H2, so n(H2) = 0.0746 / 2 = 0.0373 mol.
Convert to volume at STP: V = 0.0373 mol x 22.414 L/mol = 0.836 L.
Unit check
Amperes times seconds gives coulombs (A x s = C); C / (C/mol) = mol of electrons; dividing by the 2:1 stoichiometric ratio gives mol of H2; mol x L/mol = L. Every step ends in the expected unit.
What this means physically
Running 2 amps for an hour pushes 0.0746 mol of electrons through the cell, which can only make half that many moles of H2 — under a liter at STP. This shows why industrial hydrogen production needs enormous currents: gas volume scales directly with charge, and the Faraday constant is very large.
The most common error is treating moles of electrons as moles of H2 directly, forgetting the 2:1 ratio — that mistake doubles the answer to 1.67 L. Always write the balanced half-reaction (2H+ + 2e- -> H2) to get the electron-to-product ratio right.