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At 300 K, 50% of the molecules in a gas sample possess kinetic energy equal to or above the activation energy Eₐ. At what temperature (in K) will only 25% of the molecules have energy equal to or above Eₐ?
- 150 K
- 200 K
- 250 K
- 300 K
Correct answer: 150 K
Solution
Using f = e^(-Eₐ/RT), forming the ratio of the 50% and 25% fractions and solving gives T2 = 150 K. Note ln(0.5)/ln(0.25) = 1/2, so Eₐ/(R*300) doubles, requiring the temperature to halve.
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