Question

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $\bigg(\frac{ v_{rms}(helium)}{v_{rms(argon)}}\bigg)$ is

• A. 0.32
• B. 0.45
• C. 2.24
• D. 3.16

Answer 1

Answer: (D)

$v_{rms}=\sqrt{\frac{3RT}{M}} \, \, \, or \, \, v_{rms} \, \, \propto \, \frac{1}{\sqrt M}$
$\therefore \, \, \, \, \, \frac{(v_{rms})He}{(v_{rms})Ar}=\sqrt{\frac{M_{Ar}}{M_{He}}}=\sqrt{\frac{40}{4}}$
$ \, \, \, \, \, \, =\sqrt{10}=3.16$