Faraday's Law of Electrolysis (m = QM/nF)

Electroplating is stoichiometry done with a wire. Charge Q divided by the Faraday constant F = 96 485 C/mol gives the moles of electrons pushed through the cell; divide by n, the electrons each ion needs, and you have moles of metal; multiply by the molar mass M and you have grams on the cathode. Charge is usually the thing you control indirectly, through Q = It, so a steady current for a measured time is all the input a plating shop needs.

Michael Faraday established this in 1833–34 with nothing but jars, wires and a balance, and the vocabulary you use to describe it is his. He was uneasy with the existing terms, which assumed electricity was a fluid being carried, so he wrote to William Whewell at Cambridge asking for better ones. Whewell supplied Greek: ion, "that which goes"; anode, the way up; cathode, the way down; electrode, anion, cation, electrolyte. Faraday adopted the lot. What his measurements really showed — that a fixed quantity of electricity always liberates a fixed chemical equivalent — was the first hard evidence that charge itself comes in fixed lumps, sixty years before J. J. Thomson found the electron.

Worked case: copper plating, Cu²⁺ + 2e⁻ → Cu, with M = 63.55 g/mol and n = 2. Run 2.00 A for 30.0 minutes and Q = 2.00 × 1800 = 3600 C (exactly 1 A·h). Then m = 3600 × 63.55/(2 × 96 485) = 1.186 g of copper. Note that the same 3600 C would deposit 4.02 g of silver, because Ag⁺ needs only one electron and carries a heavier atom — the whole reason Faraday's "electrochemical equivalents" differ from element to element.