`pOH=7-0.5pK_a+0.5 pK_b` is true for aqueous solution containing which pair of cation and anion :

Options

A. `C_6H_5NH_3^+,CH_3COO^(-)`
B. `NH_4^+,F^(-)`
C. Both (A) and (B)
D. None of these

Explanation

To solve the question, we need to analyze the equation given:

\[ \text{pOH} = 7 - 0.5 \text{pK}_a + 0.5 \text{pK}_b \]

This equation is generally applicable for solutions containing a weak acid and its conjugate base, or a weak base and its conjugate acid.

### Step-by-Step Solution:

1. **Understanding the Components**:
- The equation relates pOH to the dissociation constants of a weak acid (pK_a) and a weak base (pK_b).
- A weak acid partially dissociates in solution, while a weak base does not fully accept protons.

2. **Identifying the Pairs**:
- We need to identify which pairs of cations and anions correspond to weak acids and weak bases.
- The options provided are:
- A) C₆H₅NH₃⁺ (anilinium ion) and CH₃COO⁻ (acetate ion)
- B) NH₄⁺ (ammonium ion) and F⁻ (fluoride ion)

3. **Analyzing Option A**:
- **C₆H₅NH₃⁺ (Anilinium ion)**: This is the conjugate acid of aniline (C₆H₅NH₂), which is a weak base. Therefore, C₆H₅NH₃⁺ is a weak acid.
- **CH₃COO⁻ (Acetate ion)**: This is the conjugate base of acetic acid (CH₃COOH), which is a weak acid. Therefore, CH₃COO⁻ is a weak base.
- Conclusion: This pair consists of a weak acid and a weak base.

4. **Analyzing Option B**:
- **NH₄⁺ (Ammonium ion)**: This is the conjugate acid of ammonia (NH₃), which is a weak base. Therefore, NH₄⁺ is a weak acid.
- **F⁻ (Fluoride ion)**: This is the conjugate base of hydrofluoric acid (HF), which is also a weak acid. Therefore, F⁻ acts as a weak base.
- Conclusion: This pair also consists of a weak acid and a weak base.

5. **Final Conclusion**:
- Both pairs (A and B) consist of a weak acid and a weak base, thus satisfying the condition of the equation provided.
- Therefore, the correct answer is that both pairs are valid, and the answer is **both A and B are correct**.