The value of `pK_(b)` for quinoline base is 4.88 then the value of `pK_(a)` of 0.01 M of its aqueous solution is

Options

A. 4.88
B. 9.12
C. 0.01
D. 14

Answer

To find the value of \( pK_a \) for the quinoline base given that \( pK_b \) is 4.88, we can use the relationship between \( pK_a \), \( pK_b \), and \( pK_w \).

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between \( pK_a \), \( pK_b \), and \( pK_w \) at 25°C is given by the equation:
\[ pK_a + pK_b = pK_w \]
where \( pK_w \) is the ion product of water at 25°C, which is 14.

2. **Identify Given Values**:
From the problem, we know:
\[ pK_b = 4.88 \]

3. **Substitute into the Equation**:
We can rearrange the equation to solve for \( pK_a \):
\[ pK_a = pK_w - pK_b \]

4. **Calculate \( pK_a \)**:
Substitute the known values into the equation:
\[ pK_a = 14 - 4.88 \]
\[ pK_a = 9.12 \]

5. **Conclusion**:
Therefore, the value of \( pK_a \) for the 0.01 M aqueous solution of quinoline is:
\[ \boxed{9.12} \]