Which of the following aqueous solutions remains neutral after electrolysis ?
1) `K_(2)SO_(4)`
2) `NaCl`
3) `AgNO_(3)`
4) `CuSO_(4)`

Options

A. `K_(2)SO_(4)`
B. `NaCl`
C. `AgNO_(3)`
D. `CuSO_(4)`

Explanation

To determine which of the following aqueous solutions remains neutral after electrolysis, we will analyze each option step by step:

### Step 1: Analyze K₂SO₄
1. **Dissociation:** K₂SO₄ dissociates into K⁺ and SO₄²⁻ ions in solution.
2. **Electrolysis:**
- At the **cathode**, K⁺ ions would typically be reduced, but the reduction potential of water (H₂O) is greater than that of K⁺. Therefore, water is reduced to produce H₂ gas and OH⁻ ions.
- At the **anode**, SO₄²⁻ ions do not oxidize water; instead, water is oxidized to produce O₂ gas and H⁺ ions.
3. **Products:** The overall reaction produces H₂, O₂, H⁺, and OH⁻ ions. The presence of both H⁺ and OH⁻ ions means that they will combine to form water, leaving the solution neutral.

### Step 2: Analyze NaCl
1. **Dissociation:** NaCl dissociates into Na⁺ and Cl⁻ ions in solution.
2. **Electrolysis:**
- At the **cathode**, Na⁺ ions are not reduced; instead, water is reduced to produce H₂ gas and OH⁻ ions.
- At the **anode**, Cl⁻ ions are oxidized to produce Cl₂ gas.
3. **Products:** The overall reaction produces H₂, Cl₂, and OH⁻ ions. The presence of OH⁻ ions indicates that the solution becomes basic.

### Step 3: Analyze AgNO₃
1. **Dissociation:** AgNO₃ dissociates into Ag⁺ and NO₃⁻ ions in solution.
2. **Electrolysis:**
- At the **cathode**, Ag⁺ ions are reduced to Ag metal.
- At the **anode**, water is oxidized to produce O₂ gas and H⁺ ions.
3. **Products:** The overall reaction produces Ag, O₂, and H⁺ ions. The presence of H⁺ ions indicates that the solution becomes acidic.

### Step 4: Analyze CuSO₄
1. **Dissociation:** CuSO₄ dissociates into Cu²⁺ and SO₄²⁻ ions in solution.
2. **Electrolysis:**
- At the **cathode**, Cu²⁺ ions are reduced to Cu metal.
- At the **anode**, water is oxidized to produce O₂ gas and H⁺ ions.
3. **Products:** The overall reaction produces Cu, O₂, and H⁺ ions. The presence of H⁺ ions indicates that the solution becomes acidic.

### Conclusion
After analyzing all four options:
- **K₂SO₄** is the only solution that remains neutral after electrolysis, as it produces equal amounts of H⁺ and OH⁻ ions that combine to form water.
- **NaCl** results in a basic solution.
- **AgNO₃** and **CuSO₄** both result in acidic solutions.

Thus, the answer is **K₂SO₄**.