Deriving m = AIt/(nF) from the charge of ions

Step 1 of 4: Total charge = number of ions × charge per ion

Intuition

Measuring current and time is 'counting ions' with an ammeter — Faraday did exactly that in 1834, decades before the electron was discovered.

Q = I\,t = N_{\text{ion}}\,n\,e

Analysis

A current $I$ running for a time $t$ transfers charge $Q = It$ . Each ion of valence $n$ carries charge $ne$ (with $e = 1{,}6\cdot10^{-19}$ C), and to be neutralized (deposited/dissolved) at the electrode it must gain or lose $n$ electrons. If $N_{\text{ion}}$ ions are neutralized, the total charge through the circuit is $N_{\text{ion}}\,n\,e$ .