Which of the following compounds liberates dihydrogen gas at anode when it is electrolysed in molten state but the same gas is liberated at cathode if its aqueous solution is electrolysed ?

Options

A. NaCl
B. NAH
C. `PH_4I`
D. `CuSO_4`

Answer

To solve the question, we need to analyze the behavior of the given compounds during electrolysis in both molten and aqueous states. The question specifically asks for a compound that liberates dihydrogen gas at the anode when electrolyzed in molten state, but at the cathode when electrolyzed in aqueous solution.

### Step-by-Step Solution:

1. **Understanding Electrolysis**:
- In electrolysis, an electric current is passed through a compound, causing it to decompose into its elements or ions. The reactions occur at two electrodes: the anode (positive electrode) and the cathode (negative electrode).

2. **Identifying the Compounds**:
- The given options are:
1. Sodium chloride (NaCl)
2. Sodium hydride (NaH)
3. pH 4 solution (acidic solution)
4. Copper sulfate (CuSO4)

3. **Analyzing Each Compound**:
- **Sodium Chloride (NaCl)**:
- In molten state: Na+ ions move to the cathode and Cl- ions to the anode. At the anode, Cl- ions are oxidized to Cl2 gas, not H2.
- In aqueous solution: H2 gas is not produced at either electrode.

- **Sodium Hydride (NaH)**:
- In molten state: Na+ ions move to the cathode and H- ions to the anode. At the anode, H- ions are oxidized to H2 gas.
- In aqueous solution: H+ ions are present, which can be reduced at the cathode to produce H2 gas.

- **pH 4 Solution**:
- This is an acidic solution with H+ ions. H2 gas would be produced at the cathode, but not at the anode.

- **Copper Sulfate (CuSO4)**:
- In molten state: Cu2+ ions move to the cathode and SO4^2- ions to the anode. H2 gas is not produced.
- In aqueous solution: H2 gas is produced at the cathode from H+ ions.

4. **Conclusion**:
- The only compound that fits the criteria of liberating dihydrogen gas at the anode in molten state and at the cathode in aqueous solution is **Sodium Hydride (NaH)**.

### Final Answer:
The correct answer is **Sodium Hydride (NaH)**.