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. 4.765
B. 5.012
C. 7.005
D. 6.098

Explanation

To calculate the pH of an ammonium acetate solution, we can use the relationship between the pKa of the weak acid (acetic acid) and the pKb of the weak base (ammonium hydroxide). The formula to find the pH of a salt formed from a weak acid and a weak base is given by:

\[ \text{pH} = 7 + \frac{1}{2}(\text{pK}_a - \text{pK}_b) \]

### Step-by-Step Solution:

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

2. **Calculate the difference between pKa and pKb:**
\[ \text{pK}_a - \text{pK}_b = 4.76 - 4.75 = 0.01 \]

3. **Substitute the values into the pH formula:**
\[ \text{pH} = 7 + \frac{1}{2}(0.01) \]

4. **Calculate \(\frac{1}{2}(0.01)\):**
\[ \frac{1}{2}(0.01) = 0.005 \]

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

### Final Answer:
The pH of the ammonium acetate solution is **7.005**.

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