JEE Main 2024 — Electrochemistry Question with Solution

To determine the quantity of silver deposited when one coulomb of charge is passed through $${\mathrm{AgNO}}_3$$ solution, we need to refer to Faraday's laws of electrolysis, especially to the concept of the electrochemical equivalent. The electrochemical equivalent (ECE) of a substance is the amount of the substance that is deposited or dissolved at an electrode during electrolysis by one coulomb of charge.

The electrochemical equivalent of a substance can be calculated using the formula:

$$E=\frac{M}{nF}$$

where:

• $E$ is the electrochemical equivalent of the substance in grams per coulomb ($g/C$).
• $M$ is the molar mass of the substance in grams per mole ($g/mol$).
• $n$ is the number of electrons involved in the oxidation or reduction reaction (the valency).
• $F$ is the Faraday constant, approximately $96485C/mol$, which is the charge of one mole of electrons.

In the case of silver ($\mathrm{Ag}$) being deposited from ${\mathrm{AgNO}}_3$, when silver ion (${\mathrm{Ag}}^{+}$) is reduced to metallic silver ($\mathrm{Ag}$), the reaction involves one electron ($n=1$). The molar mass of silver (Ag) is approximately $107.868g/mol$. Using this information:

$$E=\frac{107.868g/mol}{1\cdot 96485C/mol}\approx 0.001118g/C$$

This means that for every coulomb of charge passed through the solution, $0.001118\mathrm{g}$ of silver is deposited.

Given the options:

• Option A: $0.1$ g atom of silver - This is incorrect because the calculation shows a much smaller amount is deposited per coulomb.
• Option B: 1 chemical equivalent of silver - This does not directly relate to the amount deposited per coulomb.
• Option C: $1\mathrm{g}$ of silver - This is incorrect as it overestimates the amount deposited by a large margin.
• Option D: 1 electrochemical equivalent of silver - This is correct, as it directly relates to the amount of a substance deposited by one coulomb of charge, based on the formula and calculation shown.

Therefore, the correct answer is Option D: 1 electrochemical equivalent of silver.