The passage of current through a solution of certain electrolyte results in the evolution of `H_2`(g) at cathode and `Cl_2`(g) at anode. The electrolytic solution is :

Options

A. `water`
B. `aq.H_2SO_4`
C. `aq. NaCl`
D. aq. `CuCl_2`

Answer

To determine the electrolytic solution where hydrogen gas is evolved at the cathode and chlorine gas at the anode, we can analyze the possible electrolytes based on their behavior during electrolysis.

### Step-by-Step Solution:

1. **Identify the Gases Evolved**:
- At the cathode, hydrogen gas (H₂) is evolved.
- At the anode, chlorine gas (Cl₂) is evolved.

2. **Consider Possible Electrolytes**:
- The options for the electrolytic solution could include:
- Water (H₂O)
- Aqueous H₂SO₄
- Aqueous NaCl
- Aqueous CuCl₂

3. **Analyze Water**:
- Water does not contain chloride ions (Cl⁻), so it cannot produce chlorine gas at the anode. Therefore, it is not the correct option.

4. **Analyze Aqueous H₂SO₄**:
- Aqueous H₂SO₄ does not contain chloride ions either, so it cannot produce chlorine gas at the anode. Thus, this option is also incorrect.

5. **Analyze Aqueous NaCl**:
- When NaCl is dissolved in water, it dissociates into Na⁺ and Cl⁻ ions.
- At the anode, the oxidation of chloride ions occurs:
\[ 2Cl^- \rightarrow Cl_2 + 2e^- \]
- The standard electrode potential for this reaction is -1.36 V.
- At the cathode, water can be reduced to produce hydrogen gas:
\[ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- \]
- The standard electrode potential for this reaction is -0.83 V.
- Since the potential for the reduction of water is less negative than that of chloride oxidation, hydrogen gas will be produced at the cathode.

6. **Analyze Aqueous CuCl₂**:
- Aqueous CuCl₂ dissociates into Cu²⁺ and Cl⁻ ions.
- At the anode, the oxidation of chloride ions occurs similarly to NaCl:
\[ 2Cl^- \rightarrow Cl_2 + 2e^- \]
- At the cathode, copper ions can be reduced:
\[ Cu^{2+} + 2e^- \rightarrow Cu \]
- The standard electrode potential for this reaction is +0.34 V, which is more positive than that of water. Therefore, copper will be deposited instead of hydrogen gas being evolved.

7. **Conclusion**:
- The only electrolyte that results in the evolution of hydrogen gas at the cathode and chlorine gas at the anode is **aqueous NaCl**.

### Final Answer:
The electrolytic solution is **aqueous NaCl**.

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