The calculations to find out the amount of product formed in electrolysis are based on the following Faraday’s Laws:

#### First law:

The number of moles of product formed by an electric current is stoichiometrically equivalent to the number of moles of electrons supplied.

Once we know the number of moles of product formed, we can calculate the masses of the products, or if they are gases, their volumes.

For examples, Cu is refined electrolytically by using an impure form of copper metal (blister copper) as the anode in an electrolytic cell. The current supply causes the oxidation of blister copper to copper (II) ions.

Cu (blister) –> Cu^{2+} + 2e^{−}

These ions are then reduced at the cathode:

Cu^{2+} (aq) + 2e^{−} –> Cu(s)

From the stoichiometry of these chemical equations, we know that 2 mole electrons give one mol of Cu. Therefore, if 4.0 mole electrons is supplied, then the amount of copper produced is 2.0 mol. This law can also be stated in other way:

” The mass of a substance deposited or liberated at any electrode is directly proportional to the amount of charge passed ”

i.e., $\large w \propto q $

(where w is the mass of the substance deposited or liberated and q is the amount of charge passed).

This proportionality can be made into an equality by, w = z q

where z is the proportionality constant called the electrochemical equivalent.

It is the mass of the substance in grams deposited or liberated by passing one coulomb of charge.

The quantity of electricity passed through the electrolytic cell is normally measured as the current and the time for which the current flows. The charge passed through an electrolytic cell is the product of the current and the time for which it is supplied. Electric current is measured in the SI unit (ampere), A, the rate of flow of charge in coulombs per second (1A = 1CS^{−1}). Therefore, the charge supplied is,

Charge supplied = Current (A) x time(s)

Next, we use the fact that faraday’s constant F , is the magnitude of the charge per mole of electrons.

Charge = moles × F

$\large Moles \; of\; e^- = \frac{Charge \; supplied}{F}= \frac{Current \times time}{9.6485 \times 10^4 C mol^{-1}} $

So, by measuring the current and the time for which it flows, we can determine the moles of electrons supplied.

The amount of product in an electrolytic reaction is calculated from the stoichiometry of the half − reaction and the current and time for which the current flows.

### Also Read :

→ Electrolysis → Faraday’s second Law of Electrolysis → Electrode Potential → Electrochemical Series → Galvanic Cells → IUPAC Cell Representation → The Nernst Equation → Standard Electrode Potential |