A : pH of equimolar solution of `NH_4 CI and NH_4OH` does not change when small amount of HCI is added to it .
R : pOH of above solution is equal to `pK_b` of the buffer.

Options

A. If both Assertion & Reason are true and the reason in the corret explanation of the assertion, then mark
B. If both assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark
C. If Assertion is true statement but Reason is false then mark
D. If both Assertion and Reason are false statements , then mark

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Components**:
- We have an equimolar solution of \( NH_4Cl \) (ammonium chloride) and \( NH_4OH \) (ammonium hydroxide).
- \( NH_4Cl \) is a salt that dissociates into \( NH_4^+ \) ions and \( Cl^- \) ions in solution.
- \( NH_4OH \) is a weak base that partially dissociates in water.

2. **Buffer Solution**:
- The combination of a weak base (\( NH_4OH \)) and its conjugate acid (\( NH_4Cl \)) forms a buffer solution.
- A buffer solution resists changes in pH when small amounts of strong acids or bases are added.

3. **Effect of Adding HCl**:
- When a small amount of HCl (a strong acid) is added to the buffer solution, the \( H^+ \) ions from HCl react with the \( NH_4OH \) (the weak base) to form \( NH_4^+ \) ions.
- This reaction does not significantly change the concentration of \( NH_4OH \) or \( NH_4^+ \), thus the pH of the solution remains relatively constant.

4. **pH and pOH Relationship**:
- The pH of the buffer solution can be expressed using the Henderson-Hasselbalch equation:
\[ pH = pK_a + \log \left( \frac{[Base]}{[Acid]} \right) \]
- In this case, since the concentrations of \( NH_4OH \) and \( NH_4Cl \) are equal, the log term becomes zero, leading to:
\[ pH = pK_a \]
- Since \( pK_a + pK_b = 14 \) (for water at 25°C), we can say that the pOH of the solution is equal to \( pK_b \) of the buffer.

5. **Conclusion**:
- The assertion (A) is true because the pH does not change significantly upon the addition of HCl.
- The reason (R) is also true because the pOH of the solution is indeed equal to \( pK_b \) of the buffer.

### Final Answer:
Both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion.