Electrolysis_of_water

# Electrolysis of water  ## Microsims — three.js ### Electrolysis of water (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Electrolysis_of_water.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Electrolysis of water — three.js microsim"></iframe> </div> **Open it full-screen:** [Electrolysis_of_water.html](https://wikitube-3d-microsims.netlify.app/Electrolysis_of_water.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Hydronium]] - [[Haber_process]] - [[Fuel_cell]] - [[Interstellar_medium]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Overview On 2 May 1800, six weeks after Volta described his pile, William Nicholson and Anthony Carlisle passed its current through water in London and collected hydrogen at one wire and oxygen at the other, two volumes to one. That was the first electrolysis of water, and among the first chemical facts established with electricity. Everything since is an argument about the price. The price has a floor and it is thermodynamic, not technical. For H2O(l) -> H2 + 1/2 O2 at 25 C and 1 bar, dG = +237.1 kJ/mol; divide by 2F = 192 971 C/mol and the reversible cell potential is **1.229 V**. Below it the reaction does not go slowly, it does not go at all. Real low-temperature cells are driven at 1.8 to 2.0 V, and every millivolt of the difference is overpotential -- a loss with a name, a place in the cell, and a bill. ## The physics Two reference voltages, not one. dG = +237.1 kJ/mol is the *work* required; dH = +285.8 kJ/mol is the *total energy*, and the difference, T dS = 48.7 kJ/mol, is heat. At 1.229 V exactly the cell runs reversibly on electricity alone, absorbing that heat from its surroundings: it gets cold. At dH/2F = **1.481 V**, the *thermoneutral voltage*, the extra work covers the heat exactly and the cell neither takes heat in nor gives it out; above that it runs hot and needs cooling, which is where every commercial low-temperature stack sits. The sim computes both from enthalpy and entropy, so the threshold tracks temperature -- 1.18 V at 80 C, 0.98 V for steam at 800 C -- and enforces the floor literally: below E_rev the current is zero, not small. Above the floor, V_applied = E_rev + eta_anode + eta_cathode + i*R + eta_conc and the three losses sit in three places -- hence the staircase across the cell. **Activation** overpotential is charge-transfer kinetics, almost all of it the oxygen evolution reaction at the anode. OER moves *four* electrons and makes an O=O bond through adsorbed OH*, O* and OOH*; because their binding energies are not independent, the OH*/OOH* scaling relation puts a floor of 0.3 to 0.4 V under any simple oxide catalyst, and nobody has beaten it. Hydrogen evolution moves two electrons through one adsorbed H* and on platinum is nearly free -- the same asymmetry that dominates the cathode of a [[Fuel_cell]]. **Ohmic** loss is ionic resistance in electrolyte and separator, linear in current, proportional to thickness over conductivity. **Concentration** overpotential is reactant failing to reach the surface, which in a liquid cell mostly means gas blanketing the electrode. Kinetics obey Butler-Volmer, inverted here to eta = (RT/alpha F) asinh(j / 2 j0). The exchange current density j0 separates a good catalyst from a bad one, spanning ten orders of magnitude between OER on a cheap oxide and HER on platinum. Far from equilibrium this collapses to Tafel's law, eta = b log10(j/j0) with b = 2.303 RT/alpha F, so activation grows only **logarithmically** with current while the ohmic term grows **linearly**. A 60 mV/decade slope buys ten times the current for another 60 mV; eventually iR wins, and where they cross is where a real electrolyser sits. Then stoichiometry. 2 H2O -> 2 H2 + O2, so hydrogen leaves the cathode at exactly twice the volumetric rate of oxygen -- and the sim does not assert it. Each electrode fills its own bubbles from its own Faraday rate with a common quantum of gas, so V(H2)/V(O2) converges on 2.000 as a *measurement*, bubble count shown. Three technologies, three bargains: **alkaline** KOH between nickel electrodes across a diaphragm, cheap and mature; **PEM**, a polymer membrane on iridium oxide and platinum, high current density but iridium; **SOEC**, steam at 600 to 1000 C through a ceramic oxide-ion conductor. SOEC's advantage is honest rather than magic -- dG falls with temperature while dH barely moves, so the *electrical* requirement drops, E_rev 0.98 V at 800 C against 1.23 V at 25 C, and the balance arrives as heat. A hot cell can therefore read over 100 per cent efficient on either heating value. Not an error: part of the energy did not arrive through the wires, and the HUD says so. **The HHV/LHV trap, plainly.** Efficiency is energy in the hydrogen over electricity spent, and there are two accepted numerators, because the product water may be counted as liquid or as vapour: HHV (higher heating value) = 285.8 kJ/mol = 141.8 MJ/kg -> 1.481 V LHV (lower heating value) = 241.8 kJ/mol = 120.0 MJ/kg -> 1.253 V The two differ by **18 per cent, always**. An "80 per cent efficient" electrolyser on LHV is about 68 per cent on HHV, and that single unstated ambiguity produces most of the contradictory figures in circulation. An LHV efficiency is measured against a fuel whose condensation heat you have agreed to discard. Give both bases whenever you give one, labelled, as the sim does every frame. Measured HHV efficiencies of stacks: alkaline 50.5-78.8 per cent, PEM 47.5-78.8, AEM 57.1-69.1, solid oxide 71.6-87.6, lower after compression (OIES, ET48, 2025). Scale is the last honest number. World hydrogen demand is about 100 Mt a year and **under 1 per cent of it is low-emissions**. Installed electrolyser capacity was **2 GW at end-2024**, some 65 per cent in China, with over 1 GW more through July 2025 (IEA, *Global Hydrogen Review 2025*) -- a rounding error against a hundred-megatonne market. This is a technology at the start of its scale-up, and every overpotential here is a cost it has to pay -- including for the ammonia of the [[Haber_process]]. ## Controls -> what each maps to | Control | Maps to | Range / values | Physical meaning | |---|---|---|---| | V applied | cell voltage | 800 to 2400 mV, default 1900 | The whole experiment; everything above 1.229 V is overpotential | | Tech | electrolyser technology | Alkaline / PEM / SOEC | Rebuilds catalysts, separator, temperature range and units | | Medium | electrolyte medium | acidic (H+) / alkaline (OH-) | Changes carrier and half reactions, not thermodynamics; ion traffic reverses | | T | cell temperature | 20-95 C alkaline, 20-90 PEM, 600-1000 SOEC | Lowers E_rev, speeds kinetics, raises conductivity at once | | Gap | gap or membrane thickness | 0.5-5.0 mm / 25-250 um / 5-100 um | The ohmic step is linear in it; the drawn gap is logarithmic, the physics is not | | Catalyst | exchange current density multiplier | 10 x log10 of the factor, -20 to +20 | Multiplies both j0: the anode step moves, the cathode hardly at all | | bubble losses | shadowing and void fraction | on / off | The cost of gas covering the electrode and filling the gap | | profile panel | -- | on / off | The staircase, the budget bar, the live gas collection | | running | -- | on / off | Pauses bubbles, ions and electrons; the model still solves | The HUD's headline live quantity is the voltage budget -- E_rev plus each loss, summing to the applied voltage -- with efficiency on both bases beneath it. ## Learning objective After playing, a learner can distinguish the reversible potential from the thermoneutral voltage and say what the difference is physically, name the four-electron OER as the dominant loss and why the ohmic term overtakes it, and quote an efficiency on both bases without being fooled by either. ## Limits and connections The thermodynamics is computed, not tabulated. The liquid branch uses constant heat capacities and lands within 0.2 mV of the LeRoy, Bowen and LeRoy (1980) correlation at 25 and 80 C. The steam branch is a quadratic in T fitted to the JANAF Gibbs energy of H2O(g), dH following from Gibbs-Helmholtz so the pair is consistent by construction. The kinetics is where the fitting lives and it should be named. Exchange current densities here are *apparent* values referred to the geometric area, not intrinsic values for flat metal: a porous layer has a roughness factor of 100 to 1000, and intrinsic numbers would over-predict the anode overpotential by 0.2 V. Transfer coefficients reproduce measured Tafel slopes rather than a mechanism. The shape of every curve is real; the placement is calibrated. Three drawing compromises are on screen. The electrode separation is a monotone logarithmic mapping -- a 125 um membrane between 3 cm plates would be invisible -- while the physics uses the true centimetres. One drawn bubble stands for 70 to 240 real ones, though the ratio survives that. And the efficiency yardstick is frozen at 298 K values while the cell temperature moves: one that moved with the cell would flatter it. Bubble coverage is area shadowing plus a Bruggeman void-fraction term with the gas fraction taken as 0.4 times coverage: the form is right, the coefficient is a choice. Not modelled: crossover, degradation, balance of plant, compression, and the gap between a 10 cm2 laboratory cell and a stack. Run this chemistry backwards and it is a [[Fuel_cell]]; the ion carrying the current in acid is [[Hydronium]].  **Part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]]** — main article for section 10, *Electrolysis: the canon in reverse*. Related sections: [[Properties_of_water]] · [[Fuel_cell]] · [[Hydrogen_economy]] · [[Hydroelectricity]].   **Microsim — three.js (Wikitube framework):** *Electrolysis of water* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Electrolysis_of_water.html" data-title="Electrolysis of water"></div> *Built from `MICROSIM_GUIDE/specs/sims/Electrolysis_of_water.json`; part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Electrolysis_of_water) : [Wikitube](https://en.wikitube.io/wiki/Electrolysis_of_water) ## Previous hub tags Tree parent: [[Hydrogen]]. Legacy hubs: `HYDROGEN`. --- *Created 2026-08-05 - append-only - authored to WIKI_REPOPULATION_PROTOCOL v1.0 section 5 - portal-microsim-pass (PORTAL_Hydrogen batch 2) - 0 deletions*