The aqueous solutions of the following substances were electrolysed. In which case, the pH of the solution does not change if inert electrodes are used.

Options

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

Answer

To determine in which case the pH of the solution does not change during electrolysis with inert electrodes, we need to analyze the behavior of the ions in each of the given solutions.

### Step-by-Step Solution:

1. **Understanding pH and Electrolysis**:
- pH is a measure of the concentration of hydrogen ions (H⁺) in a solution. If the concentration of H⁺ or hydroxide ions (OH⁻) changes during electrolysis, the pH will also change.

2. **Analyzing Each Substance**:
- **Silver Nitrate (AgNO₃)**: During electrolysis, silver ions (Ag⁺) are reduced at the cathode, and nitrate ions (NO₃⁻) do not participate in the reaction. The concentration of H⁺ ions may change due to the reduction of Ag⁺, which can lead to a change in pH.

- **Copper Sulfate (CuSO₄)**: Similar to silver nitrate, copper ions (Cu²⁺) are reduced at the cathode, and oxygen is evolved at the anode. The presence of H⁺ ions can change due to the reactions occurring, which can also lead to a change in pH.

- **Dilute Sodium Chloride (NaCl)**: Electrolysis of NaCl solution produces chlorine gas at the anode and hydrogen gas at the cathode. The generation of H₂ gas can alter the concentration of H⁺ ions, thus changing the pH.

- **Potassium Sulfate (K₂SO₄)**: In this case, during electrolysis, water is split into hydrogen and oxygen. At the cathode, water is reduced to produce hydrogen gas and hydroxide ions (OH⁻), while at the anode, water is oxidized to produce oxygen gas and H⁺ ions. The overall reaction does not change the concentration of H⁺ or OH⁻ ions significantly, maintaining the pH.

3. **Conclusion**:
- Among the given options, the electrolysis of potassium sulfate (K₂SO₄) does not change the pH of the solution because the production of H⁺ and OH⁻ ions is balanced, resulting in no net change in their concentrations.

### Final Answer:
The pH of the solution does not change during the electrolysis of **Potassium Sulfate (K₂SO₄)**.