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 different compounds during electrolysis in both molten and aqueous states, particularly focusing on the liberation of dihydrogen gas (H₂).

### Step-by-Step Solution:

1. **Understanding Electrolysis**:
- Electrolysis involves the breakdown of a compound into its ions when an electric current is passed through it. The reactions occur at two electrodes: the anode (positive electrode) and the cathode (negative electrode).

2. **Identifying the Anode and Cathode Reactions**:
- At the **anode**, oxidation occurs, meaning that electrons are lost. For dihydrogen gas to be liberated at the anode, we need a source of hydride ions (H⁻) that can be oxidized to form H₂ gas.
- At the **cathode**, reduction occurs, meaning that electrons are gained. Here, H⁺ ions from the aqueous solution can gain electrons to form H₂ gas.

3. **Analyzing the Compounds**:
- We need a compound that contains H⁻ ions in its molten state, which can be oxidized at the anode to produce H₂ gas.
- When in aqueous solution, the same compound should allow H⁺ ions to be reduced at the cathode to liberate H₂ gas.

4. **Considering Sodium Hydride (NaH)**:
- Sodium hydride (NaH) dissociates into Na⁺ and H⁻ ions in molten state.
- At the anode, the reaction would be:
\[ 2H⁻ \rightarrow H₂ + 2e⁻ \]
- In an aqueous solution, NaH dissociates into Na⁺ and H⁻ ions, and at the cathode, the reaction would be:
\[ 2H⁺ + 2e⁻ \rightarrow H₂ \]

5. **Conclusion**:
- Sodium hydride (NaH) is the compound that fits the criteria of liberating dihydrogen gas at the anode during molten electrolysis and at the cathode during aqueous electrolysis.

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