It is directly proportional to its equivalent mass which is Atomic mass/ valency

Faraday's second law of electrolysis states that the mass of a substance deposited or liberated on an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte. It can be mathematically represented as:

m ∝ Q

where m is the mass of the substance deposited, and Q is the quantity of electricity passed (measured in coulombs).

Explanation:
To understand why the correct answer is option 'C' (Atomic mass/Valency), let's break down the equation for Faraday's second law:

m ∝ Q

The quantity of electricity passed (Q) is related to the number of moles of electrons (n) transferred during the electrolysis process. This relationship is given by Faraday's first law of electrolysis:

Q = nF

where F is the Faraday constant, which represents the charge of one mole of electrons (F = 96,485 C/mol).

Substituting this relationship into the equation for Faraday's second law:

m ∝ nF

Since n represents the number of moles of electrons transferred, it is also related to the stoichiometry of the reaction. For a balanced redox reaction between ions in solution, the ratio of moles of electrons transferred (n) to moles of substance consumed or produced (x) is given by the stoichiometric coefficient (a):

n/x = a

Therefore, we can rewrite the equation as:

m ∝ aF

Now, considering that the mass of a substance deposited on an electrode is directly proportional to its molar mass (M), we can rewrite the equation as:

m ∝ aFM

Finally, the valency of an ion (z) represents the number of electrons transferred in the redox reaction. For example, in the case of a monovalent ion (z = 1), one electron is transferred. For a divalent ion (z = 2), two electrons are transferred, and so on.

Therefore, we can further rewrite the equation as:

m ∝ aF/z

Since the proportionality constant is not provided, we can introduce the constant of proportionality (k) to obtain an equation:

m = k(aF/z)

Now, comparing this equation with the given options, we can see that option 'C' (Atomic mass/Valency) is the correct answer.

m = (M/z) * (F/a)

In conclusion, Faraday's second law of electrolysis states that the mass deposited on an electrode is directly proportional to the atomic mass divided by the valency of the substance. This law is derived from the relationships between quantity of electricity, stoichiometry of the reaction, molar mass, and valency of the ions involved in the electrolysis process.