For two acids A and B, `pK_(a) = 1.2 , pK_(b) = 2.8` respectively in value , then which is true

Options

A. A and B both are equally acidic
B. A is stronger than B
C. B is stronger than A
D. Neither A nor B is strong

Answer

To determine which acid is stronger between A and B based on their pKa values, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the pKa and pKb Values**:
- The pKa value indicates the strength of an acid; the lower the pKa, the stronger the acid.
- We are given:
- pKa of acid A = 1.2
- pKb of acid B = 2.8

2. **Convert pKb of Acid B to pKa**:
- To compare the strengths of both acids, we need to convert the pKb of acid B to pKa. We can use the relationship:
\[ pKa + pKb = 14 \]
- Therefore, for acid B:
\[ pKa_B = 14 - pKb_B = 14 - 2.8 = 11.2 \]

3. **Compare the pKa Values**:
- Now we have:
- pKa of acid A = 1.2
- pKa of acid B = 11.2
- Since 1.2 < 11.2, acid A is stronger than acid B.

4. **Calculate the Acid Dissociation Constants (Ka)**:
- The acid dissociation constant (Ka) can be calculated using the formula:
\[ Ka = 10^{-pKa} \]
- For acid A:
\[ Ka_A = 10^{-1.2} \approx 0.063 \]
- For acid B:
\[ Ka_B = 10^{-11.2} \approx 6.31 \times 10^{-12} \]

5. **Compare the Ka Values**:
- Since \(Ka_A > Ka_B\), this confirms that acid A is indeed stronger than acid B.

6. **Determine How Much Stronger Acid A is than Acid B**:
- To find out how many times stronger acid A is compared to acid B, we can divide the two Ka values:
\[ \text{Strength Ratio} = \frac{Ka_A}{Ka_B} = \frac{0.063}{6.31 \times 10^{-12}} \approx 10^{10.2} \approx 42 \text{ times} \]

### Conclusion:
- Acid A is stronger than acid B by approximately 42 times.