Equal volumes of following solutions are mixed. In which case the pH of resulting solution will be average value of pH of two solutions?

Options

A. `pH=2(HCl)and pH=12(NaOH)`
B. `pH=2(HCl)and pH=4(HCl)`
C. `pH=2(HCN)and pH=12(NaOH)(K_(a)of HCN=10^(-10))`
D. `pH=5(CH_(3)COOH)and pH=9(NH_(3))(aq)(K_(a)of HCN=10^(-10))`

Answer

To determine in which case the pH of the resulting solution will be the average value of the pH of two solutions when equal volumes are mixed, we need to analyze each option provided.

### Step-by-Step Solution:

1. **Understanding pH and Neutralization**:
- pH is a measure of the hydrogen ion concentration in a solution.
- When an acid and a base are mixed in equal volumes, they can neutralize each other, resulting in a solution with a pH of 7 (neutral).

2. **Analyzing the First Option**:
- Given: pH of HCl = 2 and pH of NaOH = 12.
- The average pH = (2 + 12) / 2 = 14 / 2 = 7.
- Since HCl and NaOH will neutralize each other, the resulting solution will indeed have a pH of 7.
- **Conclusion**: This option satisfies the condition.

3. **Analyzing the Second Option**:
- Given: pH of HCl = 2 and pH of HCl = 4.
- H⁺ concentration for pH 2 = 10^(-2) M and for pH 4 = 10^(-4) M.
- Total H⁺ concentration = 10^(-2) + 10^(-4) = 10^(-2) + 0.01 * 10^(-4) = 10^(-2) + 10^(-6).
- This does not lead to a pH of 3 (which would be the average of 2 and 4).
- **Conclusion**: This option does not satisfy the condition.

4. **Analyzing the Third Option**:
- Given: pH of HCl = 2 and pH of NaOH = 12.
- Similar to the first option, the average pH = (2 + 12) / 2 = 7.
- However, the resulting solution will not be neutral because HCl and NaOH will neutralize each other, but the resulting concentration will not yield a pH of 7.
- **Conclusion**: This option does not satisfy the condition.

5. **Analyzing the Fourth Option**:
- Given: pH of acetic acid = 5 and pH of ammonia = 9.
- The average pH = (5 + 9) / 2 = 14 / 2 = 7.
- Acetic acid (weak acid) and ammonia (weak base) will not completely neutralize each other, but the resulting solution can approximate a pH of 7.
- **Conclusion**: This option satisfies the condition.

### Final Answer:
The cases where the pH of the resulting solution will be the average value of the pH of the two solutions are **Option A (HCl and NaOH)** and **Option D (acetic acid and ammonia)**.