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Cell
Applied voltage, electrolyte strength, temperature and geometry.
Electrodes
Electrode material sets the exchange current densities.
Layers
Model checks
The science
Voltage budget
The applied voltage must cover the reversible water-splitting voltage Erev(T) = (ΔH - TΔS) / 2F (1.23 V at 25 C), two Butler-Volmer overpotentials and the ohmic drop in the electrolyte: V = Erev + ηc + ηa + I R. For high overpotential η = (RT / αF) asinh(I / 2 I0), where the exchange current I0 depends strongly on the electrode material (platinum, nickel, graphite values are order-of-magnitude illustrations). The cell current is found by bisection on this budget.
Faraday's law and gas volumes
n(H2) = I t / 2F and n(O2) = I t / 4F, so hydrogen fills exactly twice the volume of oxygen. The dry gas volume collected over water uses V = nRT / (p - pw) with the Magnus vapour pressure pw(T). 100 % current efficiency is assumed.
Efficiency and heat
Voltage efficiency against the higher heating value is ηV = 1.48 V / V (thermoneutral voltage), and the heat released is I (V - 1.48). Below 1.48 V the cell absorbs heat from its surroundings.
Simplifications
Conductivity follows an illustrative curve peaking near 6 mol/L, no bubble screening, no gas crossover, no temperature dependence of ΔH and ΔS.
What to try
- Sweep the voltage from 1.0 V upwards: nothing happens until the reversible voltage plus overpotentials is exceeded.
- Switch to graphite and compare the current at the same voltage: the cathode overpotential bar grows.
- Dilute the electrolyte to 0.05 M and watch the ohmic bar take over the budget.
- Check the 2 : 1 ratio of hydrogen to oxygen volume in the tubes.