AIIMS 2018 Chemistry Effect of Catalyst MCQ Question

The ratio of the rate constants $\frac{K_B}{K_A}$ can be determined using the Arrhenius equation, $k = A e^{-\frac{E_a}{RT}}$. Given that the activation energy $E_{a,B}$ of B is lower than $E_{a,A}$ by 5.75 kJ/mol, we can express this as $E_{a,B} = E_{a,A} - 5.75$ kJ/mol. Substituting into the Arrhenius equation and simplifying gives $\frac{K_B}{K_A} = e^{\frac{5.75 \times 10^3}{RT}}$. At 300 K, this results in approximately $e^{10}$, which equals about 1000, making option C correct.

Options A (1), B (10), and D (100) are incorrect as they do not accurately reflect the exponential relationship derived from the difference in activation energies.