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 determine which addition will not change the pH of a 100 mL x M HCl (dilute) solution, we need to analyze how each option affects the concentration of hydrogen ions (H⁺) in the solution. The pH is defined as:

\[ \text{pH} = -\log[\text{H}^+] \]

Where \([\text{H}^+]\) is the concentration of hydrogen ions in the solution. For the pH to remain unchanged, the concentration of H⁺ must remain the same.

### Step-by-Step Solution:

1. **Understanding the Initial Solution**:
- We have 100 mL of x M HCl. This means the concentration of H⁺ ions is x M because HCl is a strong acid and dissociates completely in water.

2. **Evaluating the Options**:
- **Option 1: Adding 100 mL of Pure Water**:
- When we add pure water, we are diluting the solution. The new volume becomes 200 mL, and the concentration of H⁺ ions will decrease. Therefore, the pH will change. **(Not the answer)**

- **Option 2: Adding 100 mL of 2x M HCl**:
- This addition increases the concentration of H⁺ ions because we are adding a stronger acid (2x M). The overall concentration of H⁺ will increase, thus changing the pH. **(Not the answer)**

- **Option 3: Adding 50 mL of Pure Water**:
- Similar to option 1, adding 50 mL of pure water will also dilute the solution. The new total volume will be 150 mL, which will decrease the concentration of H⁺ ions and change the pH. **(Not the answer)**

- **Option 4: Adding 50 mL of x M HCl**:
- Here, we are adding 50 mL of a solution that has the same concentration (x M) as the original solution. This means the total amount of H⁺ ions will increase, but since we are adding the same concentration, the overall concentration of H⁺ ions will remain effectively the same when considering the total volume. Therefore, the pH will remain unchanged. **(This is the correct answer)**

### Conclusion:
The addition that will not change the pH of the 100 mL x M HCl solution is **Option 4: Adding 50 mL of x M HCl**.

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