Faraday's laws of electrolysis
/ FAIR-uh-dayz /
If you want to plate exactly one gram of silver onto a spoon, how much electricity do you need, and for how long? Faraday's laws are the simple accounting that answers this: they connect the amount of charge you push through a cell to the amount of substance it deposits or dissolves.
There are two laws, and together they boil down to one idea. The first law says the mass of product is proportional to the total electric charge passed (current multiplied by time). The second law says that for a fixed charge, the mass of different substances produced is in proportion to their equivalent weights — roughly, how many electrons each ion needs. So depositing an ion that needs two electrons takes twice the charge per atom as one that needs only one.
These laws are why electrolysis is so controllable. They let an engineer dial in a current and a time and predict the yield to the gram, which is exactly what aluminium smelters and electroplaters rely on. The bookkeeping is exact because charge transfer happens one electron at a time — counting electrons is the same as counting atoms reacted.
Plating copper from a solution, each copper ion needs two electrons. To lay down one mole of copper (about 64 grams) you must pass two moles of electrons — that is, about 193,000 coulombs of charge.
Two electrons per copper ion, so a mole of copper costs two moles of electrons.
The bridge between charge and amount of substance is the Faraday constant — the charge on one mole of electrons. Faraday's laws are really just this constant applied to a real cell.