A Hall-Héroult cell is sized by Faraday’s law: aluminum takes 3 electrons per atom, so 1 kg needs about 2,980 ampere-hours at 100% current efficiency, and at 93% efficiency and 4.5 V that is 14.4 kWh. At the carrier’s 0.6-1.0 A/cm², a 3,000 A cell needs 3,000-5,000 cm² of anode face. Compare tapped metal with the Faraday figure every shift, because a shortfall is the only direct measure of how well the cell is running.
Part of Hall-Héroult Electrolysis
The arithmetic behind the electrolytic cell’s temperature, current, voltage and alumina limits, and how to use it as a control check.
The Governing Numbers Come From Physics, Not A Tolerance Table
The carrier’s operating table: temperature 950-980 °C, 4-5 V per cell, 500-5,000 A, current density 0.6-1.0 A/cm², alumina 2-6% in the bath. These are the only operating figures in the corpus. No source here gives acceptable limits on bath composition, anode-cathode spacing or temperature drift, so this article states the arithmetic that follows from the physics and marks everything else as unsourced.
Worked Example 1: Metal Per Ampere-Hour
Faraday’s constant is 96,485 C/mol (recalled). Aluminum is Al³⁺, so z = 3, and its molar mass is 26.98 g/mol (recalled).
- Charge per mole of aluminum: 3 × 96,485 = 289,455 C = 289,455 / 3,600 = 80.4 A·h.
- Metal per ampere-hour: 26.98 / 80.4 = 0.3356 g.
- Charge per kilogram: 1,000 / 0.3356 = 2,980 A·h.
Worked Example 2: Energy Per Kilogram
Energy = ampere-hours × volts. At 100% efficiency and 4.5 V: 2.98 kAh × 4.5 V = 13.4 kWh/kg. At current efficiency 0.93 (assumed; the Phase 5 article quotes 92-95%): 13.4 / 0.93 = 14.4 kWh/kg. At the carrier’s voltage limits: 2.98 × 4.0 / 0.93 = 12.8 kWh/kg, and 2.98 × 5.0 / 0.93 = 16.0 kWh/kg. The carrier’s “roughly 15 kWh” lies in this band.
Worked Example 3: Anode Area And Carbon Burn
For 3,000 A at 0.6-1.0 A/cm²: 3,000 / 1.0 = 3,000 cm² and 3,000 / 0.6 = 5,000 cm². The carrier’s boxes of 0.5-1 m by 0.3-0.5 m have floors of 1,500-5,000 cm², so the smallest box supports only 900-1,500 A at that density.
Carbon: 2Al₂O₃ + 3C → 4Al + 3CO₂. 3 × 12.01 = 36.0 g of carbon per 4 × 26.98 = 107.9 g of aluminum, so 0.334 kg C per kg Al; the carrier’s “roughly 0.4” is above the floor, the difference being extra burn I recall but cannot size. CO₂ released: 3 × 44.01 = 132.0 g per 107.9 g, or 1.22 kg per kg of aluminum.
Using The Numbers As Control
Current efficiency check. Suppose a cell carries 3,000 A for 8 hours. Faraday yield: 3,000 × 8 × 0.3356 = 8,054 g = 8.05 kg. At 93%, expect 7.49 kg. If only 6.0 kg is tapped, efficiency = 6.0 / 8.05 = 75%. Something is wrong: I recall that an overheated bath dissolves metal back into the electrolyte and burns it at the anode, and that this is the usual cause, but the corpus does not say.
Voltage log. Record cell voltage every hour. A steady 4-5 V (carrier) is normal. I recall that a sudden large voltage rise signals alumina starvation (the “anode effect”), which also releases fluorocarbon gases, so feed alumina to keep within the carrier’s 2-6%; no figure for the voltage spike is in the corpus.
Temperature. Keep the bath within 950-980 °C (carrier). A bath that is colder than needed freezes crust over the metal; one that is hotter loses efficiency. Both statements are from my recall.
What Is Not Sourced
Bath ratio, additive percentages, anode-to-cathode distance, crust practice, alumina feed rate, tapping frequency and failure thresholds. A cell run without them is run by trial, which at 3,000 A and 960 °C is costly.
Common Mistakes
- Reading energy per kilogram as a minimum. A small cell loses proportionally more heat; the carrier says 15-20 kW per kg/h.
- Counting only current. Volts times amp-hours is the energy.
Safety
Current and bath
A cell carries thousands of amps; a tool laid across the busbars is vaporised. Keep a DC disconnect outside the splash zone, remove rings and metal jewellery, never touch anode and cathode together, and keep all feed and tools dry. Fluoride fume and CO/CO₂ from the anode: see Cryolite Flux.
What’s Next
- Learn next: Carbon Electrode Production - the anodes whose burn the arithmetic above sizes
- Combine with: Cathode Lining - the other half of the cell