Question

The mass of a substance liberated when charge $q$ flows through an electrolyte is proportional to
A. q
B. $\dfrac{1}{q}$
C. ${{q}^{2}}$
D. $\dfrac{1}{{{q}^{2}}}$

Answer 1

Hint: Faraday introduced a quantitative relation between the electricity passed and the mass of the substance deposited at a specific electrode. This relation is popularly known as Faraday’s first law of electrolysis. By applying these concepts we can easily find the solution to the given problem.

Complete Step by Step Answer:
When current is passed through the electrolyte, a chemical reaction occurs at the electrodes, this process is named electrolysis. Positively charged electrodes are called the anode and negatively charged electrodes are called the cathode.

The law that governs the deposition of ions on the electrodes with the passage of electricity is known as Faraday’s law of electrolysis. Faraday introduced two fundamental laws regarding electrolysis from his experiment.

To approach this question we only need to know about Faraday’s first law of electrolysis.
Faraday’s first law of electrolysis: The mass of a substance liberated is directly proportional to the number of charges flowing through an electrolyte.

Given the amount of charge $=q$
Let the mass of the substance $=m$
According to Faraday’s first law of electrolysis, $m$$\alpha $$q$
Or, $m=Z\times q$
Here $Z$ is proportionality constant and is also known as electrochemical equivalent.
When $q=1$ then $m=Z$
That is the electrochemical equivalent of any substance is the amount of that particular substance by mass liberated by passing unit coulomb electricity.
Hence the mass of a substance liberated when a charge $q$flows through an electrolyte is proportional $q$.
Thus, option (A) is correct.

Note: According to Faraday’s law the mass of a substance directly depends on the quantity of electricity passed but does not depend on the potential difference. This is because each ion deposited on the electrode and made molecular carries a specific amount of charge across the cell and thus is proportional to the passing charge through the electrolyte.