Which of the following on adding will not change the pH of 100mL x M HCl (dil) solution:

Options

A. 100mL of pure water
B. 100 mL of 2xM HCl
C. 50 mL of pure water
D. 50 mL of xM HCl

Answer

To solve the question of which addition will not change the pH of a 100 mL x M HCl (dilute) solution, we need to analyze the effect of each option on the concentration of hydrogen ions (H⁺) in the solution.

### Step-by-Step Solution:

1. **Understanding pH and H⁺ Concentration**:
- The pH of a solution is defined as pH = -log[H⁺], where [H⁺] is the concentration of hydrogen ions in moles per liter (M).
- For the pH to remain unchanged, the concentration of H⁺ must remain constant.

2. **Analyzing Each Option**:
- **Option 1: Adding 100 mL of pure water**:
- When pure water is added, the total volume of the solution becomes 200 mL.
- The concentration of H⁺ will decrease because the same amount of H⁺ is now in a larger volume (dilution).
- **Conclusion**: This will change the pH.

- **Option 2: Adding 100 mL of 2x M HCl**:
- Adding 100 mL of 2x M HCl means we are increasing the concentration of H⁺ in the solution.
- The total volume becomes 200 mL, but the concentration of H⁺ will increase significantly.
- **Conclusion**: This will change the pH.

- **Option 3: Adding 50 mL of pure water**:
- Similar to option 1, adding 50 mL of pure water will dilute the solution.
- The total volume becomes 150 mL, leading to a decrease in H⁺ concentration.
- **Conclusion**: This will change the pH.

- **Option 4: Adding 50 mL of x M HCl**:
- Here, we are adding 50 mL of x M HCl to the existing 100 mL of x M HCl.
- The total volume will be 150 mL, but the concentration of H⁺ will remain the same (since we are adding the same concentration).
- **Conclusion**: This will not change the pH.

3. **Final Answer**:
- The only option that does not change the pH of the solution is **Option 4: Adding 50 mL of x M HCl**.