To which of the solution, addition of water would not effect the `pH` ? .

Options

A. `100 mL of 0.2 M CH_(3) COOH + 100mL of 0.1 M NaOH`
B. `100 mL of 0.2 M CH_(3) COOH + 100mL of 0.2 M NaOH`
C. `200 mL of 0.2 M CH_(3) COOH + 100mL of 0.1 M NaOH`
D. `100 mL of 0.2 M CH_(3) COOH + 200mL of 0.1 M NaOH`

Explanation

To determine which solution's pH would not be affected by the addition of water, we need to identify buffer solutions among the given options. Buffer solutions are characterized by their ability to maintain a relatively constant pH when diluted or when small amounts of acid or base are added.

### Step-by-Step Solution:

1. **Understanding Buffer Solutions**:
- A buffer solution is typically made from a weak acid and its conjugate base (or a weak base and its conjugate acid). The pH of a buffer solution is given by the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
- In this equation, the ratio of the concentrations of the salt and acid remains constant even when the solution is diluted, meaning the pH does not change.

2. **Analyzing Each Option**:
- **Option A**: 100 mL of 0.2 M CH₃COOH (acetic acid) + 100 mL of 0.1 M NaOH
- Here, acetic acid and sodium hydroxide react to form sodium acetate (CH₃COONa), creating a buffer solution. The pH will remain constant upon dilution.
- **Option B**: 100 mL of 0.2 M CH₃COOH + 100 mL of 0.2 M NaOH
- In this case, the moles of acetic acid and sodium hydroxide are equal, leading to complete neutralization and the formation of sodium acetate. However, this solution is not a buffer in the traditional sense, as it does not have both components in significant amounts after neutralization. Thus, the pH will change upon dilution.
- **Option C**: 200 mL of 0.2 M CH₃COOH + 100 mL of 0.1 M NaOH
- Similar to Option A, the resulting solution will still contain both acetic acid and sodium acetate, making it a buffer solution. The pH will remain constant upon dilution.
- **Option D**: 100 mL of 0.2 M CH₃COOH + 200 mL of 0.1 M NaOH
- Here, there will be complete neutralization, leading to a basic salt solution. The pH will depend on the concentration of the salt formed and will change upon dilution.

3. **Conclusion**:
- The options that represent buffer solutions, where the addition of water would not affect the pH, are **Option A** and **Option C**.

### Final Answer:
The correct options are **A and C**.