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.

Difficulty: Easy

H₂ at −73°C
CH₄ at 300 K
N₂ at 1,027°C
O₂ at 0°C

Correct Answer: H₂ at −73°C

Explanation:

Given data

Speed ∝ √(T/M) (T in kelvin; M in g·mol⁻¹).

Calculations
H₂ 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 Answer
H₂ at −73°C

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