The pH of a buffer solution of 0.1 M `NH_4OH` and 0.1 M `NH_4Cl" is "(pK_b= 4.0)`

Options

A. 1
B. 4
C. 10
D. 13

Answer

To find the pH of the buffer solution containing 0.1 M ammonium hydroxide (NH₄OH) and 0.1 M ammonium chloride (NH₄Cl), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components**:
- Ammonium hydroxide (NH₄OH) is a weak base.
- Ammonium chloride (NH₄Cl) is the salt formed from the weak base and a strong acid (HCl).

2. **Determine the Type of Buffer**:
- Since we have a weak base (NH₄OH) and its corresponding salt (NH₄Cl), this is a basic buffer solution.

3. **Use the pOH Formula for Basic Buffers**:
- The formula for the pOH of a basic buffer is given by:
\[ pOH = pK_b + \log\left(\frac{[\text{Salt}]}{[\text{Base}]}\right) \]
- Here, the salt is NH₄Cl and the base is NH₄OH.

4. **Substitute the Values**:
- Given that the concentration of both the salt and the base is 0.1 M, we can substitute these values into the equation:
\[ pOH = pK_b + \log\left(\frac{0.1}{0.1}\right) \]
- Since \(\frac{0.1}{0.1} = 1\), we know that \(\log(1) = 0\).

5. **Calculate pOH**:
- Substitute the values into the equation:
\[ pOH = 4 + 0 = 4 \]

6. **Convert pOH to pH**:
- We know that:
\[ pH + pOH = 14 \]
- Therefore, we can find pH:
\[ pH = 14 - pOH = 14 - 4 = 10 \]

7. **Final Answer**:
- The pH of the buffer solution is **10**.