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The first-order decomposition of H2O2 has a half-life of 360 min at 380 degC (653 K) and an activation energy of 200 kJ/mol. Find the time (in minutes) needed for 75% decomposition at 450 degC (723 K). Use [1/653 - 1/723] = 1.5*10⁻⁴, e³.6 = 36, R = 25/3 J/(K mol).

1. 20 min
2. 10 min
3. 5 min
4. 40 min

Correct answer: 20 min

Solution

Using Arrhenius, k(723)/k(653) = e^(Ea/R * [1/653-1/723]) = e³.6 = 36, so the rate is 36 times faster; the new half-life is 360/36 = 10 min, and 75% decomposition needs two half-lives = 20 min.

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