A buffer solution is prepared by mixing 0.1 M ammonia and 1.0 M ammonium chloride. At 298 K, the `pK_(b)` of `NH_(4)OH` is 5.0. The pH of buffer is :

Options

A. 10
B. 9
C. 6
D. 8

Explanation

To find the pH of the buffer solution prepared by mixing 0.1 M ammonia (NH₃) and 1.0 M ammonium chloride (NH₄Cl), we can use the Henderson-Hasselbalch equation. However, since we are given the pK_b value, we will first calculate the pOH and then convert it to pH.

### Step-by-step Solution:

1. **Identify the components of the buffer:**
- Base (NH₃): 0.1 M
- Salt (NH₄Cl): 1.0 M

2. **Use the given pK_b value:**
- pK_b of NH₄OH (which is the same as the conjugate acid of NH₃) = 5.0

3. **Calculate pOH using the formula:**
\[ \text{pOH} = \text{pK}_b + \log\left(\frac{[\text{Salt}]}{[\text{Base}]}\right) \]
Plugging in the values:
\[ \text{pOH} = 5.0 + \log\left(\frac{1.0}{0.1}\right) \]

4. **Calculate the logarithm:**
\[ \log\left(\frac{1.0}{0.1}\right) = \log(10) = 1 \]

5. **Substitute back to find pOH:**
\[ \text{pOH} = 5.0 + 1 = 6.0 \]

6. **Convert pOH to pH:**
Using the relation \( \text{pH} + \text{pOH} = 14 \):
\[ \text{pH} = 14 - \text{pOH} = 14 - 6.0 = 8.0 \]

### Final Answer:
The pH of the buffer solution is **8.0**.