The `pK_(a)` of acetic acid and `pK_(b)` of ammonium hydroxide are `4.76` and `4.75` respectively. Calculate the pH of ammonium acetate solution.

Options

A. `9.51`
B. `7.005`
C. `7.00`
D. `6.9`

Answer

To calculate the pH of an ammonium acetate solution using the given \( pK_a \) of acetic acid and \( pK_b \) of ammonium hydroxide, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- \( pK_a \) of acetic acid (CH₃COOH) = 4.76
- \( pK_b \) of ammonium hydroxide (NH₄OH) = 4.75

2. **Write the relationship for pH of a buffer solution:**
The pH of a solution containing a weak acid and its conjugate base can be calculated using the formula:
\[ \text{pH} = 7 + \frac{1}{2}(pK_a - pK_b) \]

3. **Substitute the values into the formula:**
\[ \text{pH} = 7 + \frac{1}{2}(4.76 - 4.75) \]

4. **Calculate the difference:**
\[ 4.76 - 4.75 = 0.01 \]

5. **Calculate half of the difference:**
\[ \frac{1}{2}(0.01) = 0.005 \]

6. **Add this value to 7:**
\[ \text{pH} = 7 + 0.005 = 7.005 \]

7. **Final result:**
The pH of the ammonium acetate solution is **7.005**.