`pK_a` of a weak acid is 5.76 and `pK_b` of a weak base 5.25 . What will be the pH of the salt formed by the two ?

Options

A. `-7.255`
B. `7.005`
C. `10.25`
D. `4.25`

Answer

To find the pH of the salt formed by a weak acid and a weak base, we can use the following formula:

\[ \text{pH} = \frac{1}{2} \left( pK_a + pK_b \right) \]

### Step-by-Step Solution:

1. **Identify the given values**:
- \( pK_a \) of the weak acid = 5.76
- \( pK_b \) of the weak base = 5.25

2. **Calculate \( pK_w \)**:
- The value of \( pK_w \) (the ion product of water) at 25°C is 14.

3. **Use the formula for pH**:
- Substitute the values into the formula:
\[ \text{pH} = \frac{1}{2} \left( pK_a + pK_b \right) \]
- Therefore,
\[ \text{pH} = \frac{1}{2} \left( 5.76 + 5.25 \right) \]

4. **Calculate the sum of \( pK_a \) and \( pK_b \)**:
- \( 5.76 + 5.25 = 11.01 \)

5. **Divide by 2**:
- \( \text{pH} = \frac{11.01}{2} = 5.505 \)

6. **Final pH Calculation**:
- The pH of the salt formed by the weak acid and weak base is approximately 5.51.

### Final Answer:
The pH of the salt formed by the weak acid and weak base is approximately **5.51**.