Electrolysis and Faraday's Laws of Electrolysis

Electrolysis is the process of using an externally supplied electric current to drive a non-spontaneous redox reaction — the reverse of what a galvanic cell does. The device used is an electrolytic cell: two electrodes dipped in an electrolyte (molten or in solution), connected to an external power source. Because the power source forces electrons in a particular direction, the electrode connected to its positive terminal becomes the electrolytic cell's anode (positive, where oxidation still occurs) and the electrode connected to its negative terminal becomes the cathode (negative, where reduction still occurs) — the electrode polarities are opposite to a galvanic cell's, but the underlying oxidation-at-anode/reduction-at-cathode definitions never change.

Faraday's first law of electrolysis states that the mass, $m$, of any substance liberated or deposited at an electrode is directly proportional to the total quantity of electric charge, $Q$, passed through the electrolyte: $m \propto Q$, i.e. $m = ZQ = ZIt$, where $Z$ (the electrochemical equivalent) is a constant specific to that substance and electrode reaction. This follows directly from the fixed stoichiometry of the relevant half-reaction: since a fixed number of moles of electrons ($n$, from the balanced half-reaction) is required to produce one mole of the substance, and charge is simply $Q = n_eF$ (moles of electrons times the Faraday constant), passing more charge always means proportionally more moles of electrons, and hence proportionally more product.

Faraday's second law of electrolysis states that when the same quantity of charge is passed through different electrolytes (connected in series, so exactly the same charge flows through each), the masses of the different substances deposited are directly proportional to their chemical equivalent weights (atomic mass divided by the charge on the ion). This follows because the same charge always corresponds to the same fixed number of moles of electrons, but that fixed number of electrons deposits fewer moles of a higher-charge ion (which needs more electrons per ion) than of a lower-charge ion — for instance, the same charge deposits fewer moles of $\text{Cu}$ (from $\text{Cu}^{2+}$, needing 2 electrons per ion) than of $\text{Ag}$ (from $\text{Ag}^{+}$, needing only 1). …