Faraday's Law

Electroplating runs on a simple exchange: electrons for metal atoms. Current is just charge flowing per second, so multiplying current (amps) by time (seconds) gives total charge in coulombs. Divide that charge by Faraday's constant, 96485 C per mole of electrons, and you get moles of electrons delivered. From there the half-reaction tells you the exchange rate. Ag+ + e- → Ag needs one electron per silver atom, so moles of electrons equal moles of silver. Cu2+ + 2e- → Cu needs two electrons per copper atom, so you get only half as many moles of copper as moles of electrons. Multiply moles of metal by molar mass and you have the mass deposited.

This is electrochemistry's version of stoichiometry, with electrons playing the role of a reactant you measure electrically instead of by mass. It threads together everything in the unit: free energy and cell voltage tell you whether and how strongly a reaction wants to run, while Faraday's law tells you how much actually happens when you force current through for a set time. The same constant, F, that converts moles of electrons to charge here also connects cell potential to delta G elsewhere in the unit.

Working backward is just as common: given a target mass, find the time or current needed. The algebra is identical, just rearranged, which is why it helps to always solve for moles of electrons first before touching the stoichiometry of the specific metal.