NEET (UG) 2025 — Question 82

Given: $k = 0.03 \text{ s}^{-1}$, initial concentration $[A]_0 = 7.2 \text{ mol L}^{-1}$, final concentration $[A]_t = 0.9 \text{ mol L}^{-1}$. Since the rate constant has units of s⁻¹, the reaction is first order. For a first-order reaction, half-life $t_{1/2} = \dfrac{0.693}{k} = \dfrac{0.693}{0.03} = 23.1 \text{ s}$. The concentration decreases by a factor of 8 from 7.2 to 0.9, which corresponds to 3 half-lives (because $7.2 \xrightarrow{1t_{1/2}} 3.6 \xrightarrow{2t_{1/2}} 1.8 \xrightarrow{3t_{1/2}} 0.9$). Therefore, total time $t = 3 \times t_{1/2} = 3 \times 23.1 = 69.3 \text{ s}$. Hence, the correct answer is A.