Assertion: In the electrolysis of aqueous NaCl, Na is preferentially discharged at mercury cathode forming sodium amalgam.
Reason: It is due to the fact that hydrogen gas a high over voltage at mercury cathode.

Options

A. if both assertion and reason are true and the reason is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If assertion is true but reason is false
D. If the assertion and reason both are false.

Explanation

To solve the question regarding the assertion and reason about the electrolysis of aqueous NaCl at a mercury cathode, we can break down the explanation into clear steps.

### Step-by-Step Solution:

1. **Understanding Electrolysis of Aqueous NaCl**:
- When aqueous NaCl is electrolyzed, two main ions are present: Na⁺ (sodium ions) and H⁺ (hydrogen ions). The electrolysis process involves the reduction of these ions at the cathode.

2. **Identifying the Cathode Reaction**:
- At the cathode, the possible reactions are:
- Reduction of sodium ions: Na⁺ + e⁻ → Na (sodium metal)
- Reduction of hydrogen ions: 2H⁺ + 2e⁻ → H₂ (hydrogen gas)

3. **Standard Electrode Potentials**:
- The standard reduction potential for Na⁺ is significantly lower than that for H⁺. This means that under normal conditions, H⁺ would be reduced first to form hydrogen gas.

4. **Effect of Mercury Cathode**:
- When using a mercury cathode, the situation changes. Mercury has a high overvoltage for the evolution of hydrogen gas. This means that the energy barrier for the reduction of H⁺ to H₂ is increased.

5. **Resulting Preference for Sodium Discharge**:
- Due to the high overvoltage for hydrogen, the reduction of Na⁺ becomes preferential. As a result, Na⁺ is reduced first, leading to the formation of sodium amalgam (Na-Hg).

6. **Conclusion on Assertion and Reason**:
- The assertion states that Na is preferentially discharged at the mercury cathode forming sodium amalgam, which is true.
- The reason provided states that this is due to the high overvoltage for hydrogen gas at the mercury cathode, which is also true and correctly explains the assertion.

### Final Answer:
Both the assertion and reason are true, and the reason correctly explains the assertion.