GATE 2025 MT – Question 63
The reaction $A\to B$ follows first-order kinetics. At a given temperature, 20% conversion occurs in 223 s. The time to reach 50% conversion at the same temperature is ______ s (rounded to the nearest integer).
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Correct answer: 685 to 705
Explanation
First-order kinetics gives the unreacted fraction $C_A/C_{A0}=e^{-kt}$. At 223 s, 80% remains, so $k=-\ln(0.8)/223$.
For 50% conversion, $t_{1/2}=\ln2/k=223\ln2/[-\ln(0.8)]=692.69\ldots$ s. The answer is **693 s**.