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 for basic buffers.

### Step-by-Step Solution:

1. **Identify the Components of the Buffer:**
- The buffer consists of a weak base (ammonia, NH₃) and its conjugate acid (ammonium ion, NH₄⁺ from ammonium chloride, NH₄Cl).

2. **Write the Henderson-Hasselbalch Equation:**
- For a basic buffer, the equation is:
\[ pOH = pK_b + \log\left(\frac{[\text{Salt}]}{[\text{Base}]}\right) \]
- Here, the salt is NH₄Cl and the base is NH₃.

3. **Substitute the Known Values:**
- Given:
- \( pK_b = 5.0 \)
- Concentration of salt (NH₄Cl) = 1.0 M
- Concentration of base (NH₃) = 0.1 M
- Substitute these values into the equation:
\[ pOH = 5.0 + \log\left(\frac{1.0}{0.1}\right) \]

4. **Calculate the Logarithm:**
- Calculate the logarithm:
\[ \log\left(\frac{1.0}{0.1}\right) = \log(10) = 1 \]
- Now substitute this back into the equation:
\[ pOH = 5.0 + 1 = 6.0 \]

5. **Calculate the pH:**
- Use the relationship between pH and pOH:
\[ pH + pOH = 14 \]
- Substitute \( pOH \):
\[ pH + 6.0 = 14 \]
- Solve for pH:
\[ pH = 14 - 6.0 = 8.0 \]

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