Wet-process phosphoric acid: electrochemical removal of copper and cadmium

Wet-process phosphoric acid (about 42 wt% H3PO4, 10 kg/s) carries the metals its phosphate rock brought in: iron, zinc, nickel, copper and the cadmium that limits how the acid may be used in fertilizer. Two flow-through electrochemical cells remove the two noble enough to plate from strong acid. The first holds its cathode at -0.05 V vs SHE: copper's Nernst potential sits far above that, so copper plates at its mass-transfer limit (plug-flow law, 99% removed) while zinc, nickel, iron and cadmium, whose potentials lie below the cathode, stay dissolved. The second cell runs at -0.55 V and is told that only cadmium plates: mass transfer alone would take 99.4% of it, but at that potential and 323 K the Nernst floor holds about 2.6e-5 mol/L in solution, so the solver reports the equilibrium-limited 91% instead. Each cell's current comes from the metal's partial current and the current efficiency you give it; the copper and cadmium currents regenerate phosphoric acid (one proton per dihydrogen-phosphate counter-ion), and the rest of the charge evolves hydrogen beside the anode's oxygen, which the cell gas reports, with a flammability warning. Honesty notes: (1) the impurity levels are illustrative inputs, not a measured acid analysis; (2) iron-group metals (Fe, Ni) are thermodynamically able to plate at -0.55 V but deposit from strong acid only with large kinetic overpotentials that a thermodynamic ordering cannot see, so the second cell is restricted to cadmium by the user, not by the model; (3) the mass-transfer coefficient, cathode area, current efficiencies and cell voltages are illustrative inputs for a three-dimensional flow-through cathode, to be replaced with measured cell data; (4) real wet-process acid holds its iron mostly as Fe(III), whose reduction to Fe(II) at the cathode consumes current, and that shuttle is represented only through the low current efficiencies given; and (5) activity coefficients are taken as one, so the Nernst potentials order the metals rather than fix their electrode potentials.