Kinetic theory (molecular speeds): At the stated temperatures, molecules of which gas have the highest average speed? Use proportionality v ∝ √(T/M) comparing temperature (K) and molar mass. Choose the correct option.
IIT JEE
Chemistry
Difficulty: Easy
Choose an option
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AH₂ at −73°C
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BCH₄ at 300 K
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CN₂ at 1,027°C
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DO₂ at 0°C
Answer
Correct Answer: H₂ at −73°C
Explanation
Given data
- Speed ∝ √(T/M) (T in kelvin; M in g·mol−1).
CalculationsH₂ at −73°C ⇒ T = 200 K, M = 2 ⇒ T/M = 100CH₄ at 300 K ⇒ M = 16 ⇒ T/M = 18.75N₂ at 1,027°C ⇒ T = 1300 K, M = 28 ⇒ T/M ≈ 46.4O₂ at 0°C ⇒ T = 273 K, M = 32 ⇒ T/M ≈ 8.53Highest T/M ⇒ highest speed: H₂ at −73°C.
Final AnswerH₂ at −73°C