STATEMENT-1: Faraday is the charge that liberates 1 eq. of metal at cathode.
and STATEMENT-2: Passage of 1 Faraday charge through aq. `MgCl_(2)` liberates 12g Mg at cathode.

Options

A. STATEMENT-1 is True, STATEMENT-2 is True, STATEMENT -2 is correct explanation for STATEMENT-1
B. STATEMENT 1 is True, STATEMENT-2 Is True, STATEMENT -2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT - 1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True

Answer

To analyze the question, we need to evaluate both statements given about Faraday's laws of electrolysis and the electrochemical behavior of magnesium chloride.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- **Statement**: "Faraday is the charge that liberates 1 eq. of metal at cathode."
- **Analysis**: Faraday's law states that the amount of substance liberated at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte. One Faraday (approximately 96485 coulombs) is indeed the charge required to liberate one equivalent of a substance at the cathode. Therefore, this statement is **true**.

2. **Understanding Statement 2**:
- **Statement**: "Passage of 1 Faraday charge through aq. MgCl₂ liberates 12g Mg at cathode."
- **Analysis**: To determine if this statement is true, we need to calculate how much magnesium is liberated when 1 Faraday of charge is passed through an aqueous solution of magnesium chloride (MgCl₂).
- The molar mass of magnesium (Mg) is approximately 24 g/mol.
- The electrochemical reaction for magnesium ions (Mg²⁺) is:
\[ \text{Mg}^{2+} + 2e^- \rightarrow \text{Mg} \]
- This indicates that 2 moles of electrons (2 Faradays) are required to liberate 1 mole of magnesium.
- Therefore, 1 Faraday will liberate:
\[ \text{Mass of Mg} = \frac{24 \text{ g/mol}}{2} = 12 \text{ g} \]
- Hence, this statement is also **true**.

3. **Conclusion**:
- Both statements are true. However, Statement 2 is not a correct explanation for Statement 1 because Statement 1 discusses the general principle of Faraday's law, while Statement 2 provides a specific example related to magnesium. Thus, the correct answer is that both statements are true, but Statement 2 does not explain Statement 1.

### Final Answer:
- **Statement 1 is true, Statement 2 is true, but Statement 2 is not a correct explanation for Statement 1.**