Galvanic Cell: Nernst Voltage, Salt Bridge and Discharge

What is modelled

Two metal strips dip into solutions of their own ions in separate beakers; a salt bridge keeps each solution electrically neutral, and an external circuit carries electrons from the metal that oxidises (the anode, the lower half-cell potential) to the metal on which ions are reduced (the cathode). The page solves the cell with the Nernst equation, Ohm's law for the circuit and Faraday's laws for what happens to the plates and the solutions, and integrates the discharge with an adaptive time step (no concentration changes by more than 0.5 % per step).

Equations

• Half-cell potential: E = E° + (RT / zF) ln c, with standard reduction potentials E° from the CRC Handbook at 25 °C. The cell EMF is the difference of the two half-cell potentials; the lower one is the anode.
• Overall form: E = E°cell - (RT / nF) ln Q with n the lowest common multiple of the two ion charges and Q the reaction quotient; ΔG° = -nFE° = -RT ln K. At 25 °C, RT ln10 / F = 59.16 mV per decade.
• Circuit: I = E / (Rload + rint); the voltmeter across the load reads U = E - I rint (an ideal voltmeter on an open switch reads the EMF).
• Faraday: charge Q dissolves Q M / zF grams from the anode and plates the same number of moles on the cathode, changing each ion concentration by Q / (zFV).

Simplifications

Concentrations are used instead of activities (no Debye-Huckel correction), so real EMFs at 1 M differ by a few tens of millivolts; there is no overpotential, concentration polarisation, gas evolution, hydrolysis or side reaction, the internal resistance is a constant you choose, and the salt bridge only keeps charge balance. Magnesium and iron in real aqueous solution also react with water or oxygen. The moving dots show direction and relative current only; real electron drift is about a millimetre per second or less. The time warp lets a discharge that would last hours run in seconds.