At 380°C, the half-life of the first-order decomposition of H2O2 is 360 min, and the activation energy of the reaction is 200 kJ mol−1. At 450°C, the half-life of the decomposition is 10.17 min. What is the time required for 75% decomposition of H2O2 at 450°C?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 20.3 min
The half-life at 450°C is given, so the activation energy and the 380°C data are not needed. For a first-order reaction the half-life does not depend on the starting concentration, so every half-life removes half of what is left.
First half-life: 100% → 50% of \( \ce{H2O2} \) left (50% decomposed).
Second half-life: 50% → 25% left (75% decomposed).
So 75% decomposition takes two half-lives:
\( \displaystyle t=2\,t_{1/2}=2\times10.17\ \mathrm{min}=20.3\ \mathrm{min} \)