Electrolysis — Faraday's laws (m = ZIt), industrial electrolysis (NaCl, Al): Foundations

This page builds every symbol used by the parent note one at a time, from absolute zero, in the order they depend on each other. Nothing below is used before it is drawn. By the last section you will have assembled the master law $m = Z I t$ — but only once each of $m$ , $Z$ , $I$ and $t$ has been earned.

1. Charge — the "stuff" that flows

How many marbles make one coulomb? Since one electron carries only $e = 1.602 \times 1 0^{- 19} C$ , it takes a staggering

$\frac{1 C}{1.602 \times 1 0 ^{- 19} C} \approx 6.24 \times 1 0^{18} electrons$

to make one coulomb. This is why we never count electrons directly — we count coulombs, and let $e$ do the translating.

The picture: imagine a pipe with tiny identical marbles (electrons) inside. Charge $Q$ is the total number of marbles that have gone past a line, but reported in coulombs (giant bundles of $6.24 \times 1 0^{18}$ marbles each) because a single marble is unimaginably small.

Why the topic needs it: electrolysis is driven by electrons landing on ions. To predict mass, we must first know how much electrical stuff arrived. That amount is $Q$ .

Figure — Electrolysis — Faraday's laws (m = ZIt), industrial electrolysis (NaCl, Al)

2. Current — how fast charge flows (and which way)

$I = \frac{Q}{t}$

Why divide charge by time? Because "flow" always means amount per time. A wide river and a thin stream can carry the same total water — what makes them different is water-per-second. Current is electricity-per-second.

Why this tool and not just "charge"? In a real cell you never measure total charge directly — you read an ammeter (current) and watch a clock (time). So we rebuild $Q$ from things we can measure:

$Q = I \cdot t$

Intuition The sign convention — which way does "positive current" point?

By historic convention, conventional current points in the direction positive charge would move — which is opposite to the way the (negative) electrons actually flow. Inside the wires, electrons stream out of the power supply's negative terminal toward one electrode; conventional current is drawn the other way. In this course we only need the consequences at the electrodes:

The electrode wired to the supply's negative terminal is flooded with electrons → it hands electrons out → reduction / deposition happens there.
The electrode wired to the supply's positive terminal has electrons pulled off it → oxidation / gas evolution happens there.

So the sign of the terminal predicts which electrode sees metal deposit and which sees gas bubble off — this is the whole point of tracking sign in electrolysis.

Look at figure s01: the same pipe, now with a clock and a flow arrow. Current is marbles crossing the line each second; the marbles (electrons) move against the conventional-current arrow.

3. Time $t$ and rearranging the flow

Now $Q = I t$ makes physical sense: coulombs = (coulombs per second) × (seconds). The units cancel to leave coulombs, which is exactly what we want.

4. The electron and the idea of "reduction / oxidation"

The picture: two metal plates dipped in a liquid full of charged particles (ions). One plate (wired to the negative terminal) hands out electrons; the other (wired to the positive terminal) collects them.

Reduction = gaining electrons (charge goes down / becomes more negative).
Oxidation = losing electrons.

Why the topic needs it: every product of electrolysis is made by an ion either gaining electrons (metal atoms forming) or losing them (gas forming). If you are shaky here, see Redox Reactions and Balancing.

5. Ions and their charge number $n$

The picture: $Cu^{2 +}$ is a copper atom "owing" 2 electrons. To become solid copper it must collect 2 electrons:

$Cu^{2 +} + 2 e^{-} \to Cu (n = 2)$

Silver only owes one:

$Ag^{+} + e^{-} \to Ag (n = 1)$

Why the topic needs $n$ : it is the exchange rate between electrons and atoms. If $n = 2$ , then two marbles buy one atom. This is the reason equal charge deposits different masses of different metals (Faraday's Second Law).

6. The mole and molar mass $M$

The picture: a mole is a box that always holds the same number of items. Weigh a full box of copper and it reads $63.5$ g; a full box of silver reads $108$ g. Same count, different weight.

Why the topic needs it: electrons are counted, atoms are counted, but we report mass in grams. Molar mass is the bridge from "how many atoms" to "how many grams".

$mass = moles \times M$

7. Faraday's constant $F$ — the exchange rate between coulombs and moles of electrons

Where does $96, 500$ come from? — it is not magic. One mole of electrons is $N_{A} = 6.022 \times 1 0^{23}$ electrons (section 6), and each electron carries the elementary charge $e = 1.602 \times 1 0^{- 19} C$ (section 1). Multiply the count by the charge-per-electron:

$F = N_{A} \times e = (6.022 \times 1 0^{23}) \times (1.602 \times 1 0^{- 19} C) \approx 96, 500 C/mol$

So $F$ is simply "how much charge is in one box of electrons" — Avogadro's number of the tiny packet $e$ , added up.

Why this specific number matters: we measure charge in coulombs, but chemistry counts in moles. $F$ is the single conversion factor between the two worlds. Divide any charge by $F$ and you get moles of electrons:

$moles of e^{-} = \frac{Q}{F} = \frac{I t}{F}$

The picture: a currency exchange booth. Hand over coulombs, receive moles-of-electrons at a fixed rate of $96, 500$ C per mole.

8. Putting it together: what $Z$ and $m$ mean

Read $Z = \frac{M}{n F}$ as a chain of the ideas above:

divide by $F$ : coulombs → moles of electrons,
divide by $n$ : moles of electrons → moles of atoms,
multiply by $M$ : moles of atoms → grams.

Every symbol in the parent note now traces back to a picture: marbles ( $Q$ , each a packet $e$ ), marbles-per-second ( $I$ ), a clock ( $t$ ), a box of atoms ( $M$ ), an exchange rate ( $F = N_{A} e$ ), and a swap ratio ( $n$ ).

9. Anode and cathode — where the action happens

Why the topic needs it: the parent's industrial half-reactions (Cl⁻ at the anode, Al³⁺ at the cathode) only make sense once you know which electrode does which job. Combine this with the sign convention of section 2: the electrode on the supply's negative terminal is the cathode (deposition); the positive terminal is the anode (evolution). For the spontaneous reverse of this — batteries — see Galvanic Cells and Standard Electrode Potentials.

Prerequisite map

The diagram below traces the same chain of ideas the page built, from the two physical constants at the top ( $e$ and $N_{A}$ ) down to the master law. Read it top-to-bottom: each box is only reachable once the boxes feeding into it are understood. The node "Q equals I times t" is the rebuilt-charge step from section 2; "coulombs to moles of e minus" is the $F$ division from section 7.

Quick self-check

Recall Why must time be in seconds?

Because current is defined as coulombs per second. Multiplying $I$ (C/s) by $t$ must give coulombs, which only works if $t$ is in seconds.

Recall What does dividing charge by

$F$ give you? Moles of electrons: $\frac{Q}{F}$ . $F$ is the exchange rate of $96, 500$ coulombs per mole of electrons, and it equals $N_{A} \times e$ .

Recall Which electrode sees metal deposit — the one on the positive or negative terminal?

The negative terminal: it floods that electrode with electrons, driving reduction (deposition). The positive terminal drives oxidation (gas evolution).

Recall Why does the same charge deposit different masses of Cu and Ag?

Because $n$ (electrons per atom) differs. Ag needs 1 electron per atom, Cu needs 2, so equal electrons build fewer Cu atoms — and each atom also has a different mass $M$ .

Equipment checklist

Test yourself — you should be able to state each aloud before reading the parent note.

Meaning of charge $Q$ and its unit ::: A count of electrical quantity; unit is the coulomb (C).
The elementary charge $e$ and marbles-per-coulomb ::: $e = 1.602 \times 1 0^{- 19}$ C; about $6.24 \times 1 0^{18}$ electrons make one coulomb.
Definition of current $I$ ::: Rate of charge flow, $I = Q / t$ , in amperes (C per second).
The sign convention at the electrodes ::: Negative terminal → cathode (deposition); positive terminal → anode (evolution); conventional current is opposite to electron flow.
How to get total charge from a meter reading ::: $Q = I \cdot t$ , with $t$ in seconds.
What "reduction" and "oxidation" mean ::: Gaining electrons (reduction) and losing electrons (oxidation).
Meaning of valency $n$ ::: Electrons exchanged per atom/molecule, e.g. $n = 2$ for $Cu^{2 +}$ .
What a mole and molar mass $M$ are ::: A fixed count ( $N_{A} = 6.022 \times 1 0^{23}$ ) of particles; $M$ is grams per mole.
Value and origin of Faraday's constant $F$ ::: $F = N_{A} \times e \approx 96, 500$ C per mole of electrons.
Formula for $Z$ ::: $Z = M / (n F)$ , mass deposited per coulomb.
The master equation and each symbol ::: $m = Z I t = \frac{M}{n F} I t$ .
Which electrode is cathode vs anode ::: Cathode = reduction (metals deposit); anode = oxidation (gases form).