A reaction is catalysed by `H^(+)` ion. In presence of HA, rate constant is `2 xx 10^(–3)" min"^(–1)` and in presence of HB rate constant is `1 xx 10^(–3)" min"^(–1)`. HA and HB being strong acids, we may conclude that

Options

A. HB is stronger acid than HA
B. HA is stronger acid than HB.
C. relative strength HA and HB is 2.
D. HA is weaker than HB and relative strength is 0.5.

Answer

To solve the problem, we need to analyze the information given about the rate constants of a reaction catalyzed by \( H^+ \) ions in the presence of two different strong acids, HA and HB.

### Step-by-Step Solution:

1. **Identify the Rate Constants**:
- The rate constant in the presence of HA is \( k_{HA} = 2 \times 10^{-3} \, \text{min}^{-1} \).
- The rate constant in the presence of HB is \( k_{HB} = 1 \times 10^{-3} \, \text{min}^{-1} \).

2. **Compare the Rate Constants**:
- We see that \( k_{HA} \) is twice \( k_{HB} \):
\[ k_{HA} = 2 \times k_{HB} \]
- This indicates that the reaction rate in the presence of HA is greater than in the presence of HB.

3. **Understand the Implication of Rate Constants**:
- The rate of a reaction is directly proportional to the rate constant when all other factors are constant.
- Since \( k_{HA} > k_{HB} \), the presence of HA leads to a faster reaction rate compared to HB.

4. **Determine the Strength of the Acids**:
- Since both HA and HB are strong acids, the one that produces a greater concentration of \( H^+ \) ions will be the stronger acid.
- The fact that HA results in a higher rate constant suggests that it provides a greater effective concentration of \( H^+ \) ions compared to HB.

5. **Conclusion**:
- Therefore, we can conclude that HA is a stronger acid than HB because it leads to a higher rate of reaction due to a greater concentration of \( H^+ \) ions.

### Final Conclusion:
- HA is stronger than HB.