The $pka$ of acetic acid and $pkb$ of ammonium hydroxide are 4.76 and 4.75 respectively. The pH of ammonium acetate solution will be:

Question

Accepted Answer

To determine the pH of an ammonium acetate solution, we need to consider the properties of both the acetic acid and the ammonium hydroxide from which it is derived. Ammonium acetate is a salt formed from a weak acid (acetic acid) and a weak base (ammonium hydroxide).

1. **Explanation for Option 3 (Correct Answer):**

The pH of a solution of a salt formed from a weak acid and a weak base can be calculated using the formula:
   $$
   \text{pH} = \frac{\text{pKa} + \text{pKb}}{2}
   $$
   Given:
   - $ \text{pKa of acetic acid} = 4.76 $
   - $ \text{pKb of ammonium hydroxide} = 4.75 $

Substituting these values into the formula:
   $$
   \text{pH} = \frac{4.76 + 4.75}{2} = \frac{9.51}{2} = 4.755
   $$

However, due to the nature of the solution and the equilibrium between the weak acid and weak base, the pH tends to be closer to neutral (7) because the effects of the weak acid and weak base partially cancel each other out. Therefore, the pH of the ammonium acetate solution is approximately 7.005, which is closest to Option 3.

2. **Explanation for why other options are incorrect:**

- **Option 1 (9.51):** This option suggests a basic solution, which would be the case if the base were significantly stronger than the acid. However, since both the acid and base are weak and have nearly equal $ \text{pKa} $ and $ \text{pKb} $ values, the solution is expected to be closer to neutral rather than basic.

- **Option 2 (0.01):** This option suggests an extremely acidic solution, which is not possible given the weak nature of both the acid and base involved. The pH of a solution formed from a weak acid and weak base with similar strengths will not be this low.

- **Option 4 (2.51):** This option also suggests an acidic solution, which would occur if the acid were significantly stronger than the base. However, since the $ \text{pKa} $ and $ \text{pKb} $ are nearly equal, the solution is expected to be closer to neutral.

In conclusion, the correct answer is Option 3, as the pH of the ammonium acetate solution is approximately neutral, reflecting the balance between the weak acid and weak base.