Grade 12 Chemistry · Faraday's scales
Coulombs, counted as atoms
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Coulombs, counted as atoms

Michael Faraday's discovery, in one sentence: the metal an electrode grows is proportional to the charge you push through it. m=QMnFm = \dfrac{QM}{nF} — read aloud, m equals Q M over n F.

Name every letter before it works. mm is the mass deposited at the electrode, in grams. QQ is the charge passed, in coulombs. MM is the molar mass of the element plating out, in grams per mole. FF is the Faraday constant, 96500 C/mol96\,500\ \mathrm{C/mol} — the charge carried by one mole of electrons, and your paper will print it for you. And nn is the number of electrons per ion: 1 for Ag+\mathrm{Ag^{+}}, 2 for Cu2+\mathrm{Cu^{2+}}, 3 for Al3+\mathrm{Al^{3+}} — the ion's charge number, a pure count with no unit at all.

Be careful with that nn. It is NOT the nn of n=mMn = \dfrac{m}{M}, which is an amount in moles. Same letter, two jobs, one chapter — chemistry's oldest small cruelty. Read which formula the letter is standing in and you will never mix them again.

Do not memorise the fraction. Walk the route and it builds itself, in the order the electrons actually travel: coulombs divided by FF give moles of electrons; moles of electrons divided by nn give moles of metal, because every ion has to be handed nn of them; moles of metal times MM give grams. Two divisions and a multiplication. The formula is just those three steps stacked.