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 the \( pK_b \) is 4.88, we can use the relationship between \( pK_a \) and \( pK_b \) for a conjugate acid-base pair. The relationship is given by:

\[ pK_a + pK_b = 14 \]

### Step 1: Write down the given information
We know that:
- \( pK_b = 4.88 \)

### Step 2: Use the relationship to find \( pK_a \)
Using the formula mentioned above, we can rearrange it to find \( pK_a \):

\[ pK_a = 14 - pK_b \]

### Step 3: Substitute the value of \( pK_b \)
Now, substitute \( pK_b \) into the equation:

\[ pK_a = 14 - 4.88 \]

### Step 4: Perform the calculation
Now, calculate the value:

\[ pK_a = 14 - 4.88 = 9.12 \]

### Conclusion
Thus, the value of \( pK_a \) for the 0.01 M aqueous solution of quinoline is:

\[ \boxed{9.12} \]

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