Manganese Electrowinning (2D) — cell cross-section, Faraday law and energy

• Low current density wastes most charge on hydrogen: efficiency collapses, energy per tonne soars.
• Very high density raises voltage (resistance and overpotential): energy rises again. The best value sits in between.
• Let the catholyte deplete without feed: [Mn²⁺] falls and efficiency drops; add feed to hold it.
• Toggle the selenium modifier and compare energy per tonne.

Faraday’s law of electrolysis: m = η I t M / (n F) with M = 54.938 g/mol, n = 2 electrons per Mn²⁺, F = 96 485 C/mol and current efficiency η (share of charge that deposits Mn instead of evolving H₂). Deposit thickness = m / (ρ A) with ρ = 7.2 g/cm³.

Cell voltage V = E_dec + b log₁₀(j/j₀) + j d / κ + V_diaphragm: decomposition voltage (Mn²⁺ + H₂O → Mn + ½O₂ + 2H⁺, about 2.4 V, Nernst-shifted by concentration), Tafel overpotential, solution resistance and the diaphragm. Specific energy W = V n F / (η M) (3.6×10⁶ J per kWh).

Current efficiency uses an empirical shape (rises with j as manganese outcompetes hydrogen, falls at low [Mn²⁺] and high temperature, improves with selenium). All coefficients are illustrative, tuned to typical industrial ranges (300–500 A/m², 5–6 V, 5000–9000 kWh/t), not data from a specific plant. Electrowinning is hazardous in practice (acid mist, hydrogen); this page is an educational model.