AIIMS 2019 Chemistry First Order Reactions MCQ Question

For a first-order reaction, the relationship between the rate constant (k), time (t), and the fraction of reaction completed can be described by the equation:

$$t = \frac{2.303}{k} \log \left( \frac{[A]_0}{[A]} \right)$$

When 2/3 of the reaction is complete, 1/3 of the reactant remains, so $[A] = \frac{1}{3}[A]_0$. Substituting this into the equation gives:

$$t = \frac{2.303}{4.3 \times 10^{-4}} \log(3) \approx 2.5 \times 10^3 \text{ sec}$$

Thus, option D is correct. The other options are incorrect because they do not match the calculated time period based on the provided rate constant and the fraction of the reaction completed.