Yes, it's exactly what everybody wanted- a relationship between mole concept and electrolysis. As we discussed in the previous post, ions are discharged at electrodes in electrolysis. We can use mole concept to calculate the mass of substances discharged at an electrode during electrolysis.
Michael Faraday (1791-1867) carried out a lot of early work on electrolysis. In 1834, he discovered that the mass of substance discharged at an electrode during electrolysis is directly proportional to the quantity of electricity passing through the electrolytic cell.
So,
m ∝ Q
where:
Q = quantity of electricity in coulombs
m = mass of substance
If you aren't familiar with coulombs, they measure electric charge are calculated by multiplying electric current by time:
Q = I × t
I = electric current in amperes
t = time in seconds
Electric current is measured in amperes, and the coulomb is a measure of the amount of electricity that passes through a given point when an electric current of one ampere flows for one second.
Through experimentation, it was found that one mole of electrons (Avogadro's number of electrons) has a charge of 96500 Coulombs. This is known as the Faraday Constant, 96500 C/mol.
From this, we know that when one mole of a singly charged ion is discharged at an electrode, this happens:
X⁺ + e⁻ → X
Y⁻ → Y + e⁻
So, for these processes to occur, 96500 C must be transferred (1 mol of electrons must be added or subtracted).
Likewise, for a doubly charged ion to be discharged at an electrode, the following occurs:
X²⁺ + 2e⁻ → X
Y²⁻ → Y + 2e⁻
The process requires 2×96500 C to be transferred and 2 mol of electrons must be added or taken away.
Hence, for 1 mol of an ion Xⁿ⁺ or Yⁿ⁻ to be discharged at an electrode, n × 96500 C (and n mol of electrons) must be transferred through the electrolyte.
For example: What mass of magnesium is deposited at the cathode by the passage of 2 amperes through molten magnesium chloride for 30 minutes?
Q = I×t
Q = 2 A × (30 × 60)s
Q = 3600 C
Using the equation for the discharge of the magnesium ion:
Mg²⁺ + 2e⁻ → Mg
2 mol of electrons are required to form 1 mol of magnesium (24g) so:
2 × 96500 C → 24 g of Magnesium
Since we know that 3600 C are transferred, we can find how many moles of Magnesium were deposited based on what fraction of 2 × 96500 C is 3600 C.
3600/(2×96500) =0.01865 mol
We convert it to grams by multiplying it by the molar mass:
24 g/mol × 0.01865 mol = 0.45 g of Magnesium
Example 2: What mass of chlorine gas is liberated by the passage of 4.32 × 10⁴ C?
Writing the equation:
2Cl⁻ → Cl₂(g) + 2e⁻
Hence, 2 mol of electrons, or 2 × 96500 C liberates 1 mol of chlorine molecules. So:
4.32 × 10⁴ C liberates 4.32 × 10⁴ C/2 × 96500 = 0.224 mol chlorine molecules
Finding the mass:
0.224 mol × 71 g/mol = 15.904 g