The rms speed of oxygen molecules is 460 m/s at 0ºC.The molecular weight of oxygen is 8 times the molecular weight of helium.The rms speed of helium at 40ºC is approximately
A)3.68 km/s
B)1.84 km/s
C)1.40 km/s
D)880 m/s
E)440 m/s

Question

Quizplus · Accepted Answer

The rms speed of a gas is proportional to the square root of the temperature and inversely proportional to the square root of the molecular weight. Therefore, the rms speed of helium at 40ºC is:$$v_{rms,He} = v_{rms,O2} 	imes \sqrt{\frac{T_{He}}{T_{O2}}} 	imes \sqrt{\frac{M_{O2}}{M_{He}}}$$$$v_{rms,He} = 460 m/s 	imes \sqrt{\frac{313 K}{273 K}} 	imes \sqrt{\frac{32 g/mol}{4 g/mol}}$$$$v_{rms,He} = 1400 m/s = 1.40 km/s$$

The Rms Speed of Oxygen Molecules Is 460 M/s at 0ºC.The