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 $\left(\frac{v_{rms}\left(helium\right)}{v_{rms}\left(argon\right)}\right)$ is?

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

Answer 1

The correct option is D $3.16$

$V_{rms}=\sqrt{\frac{3RT}{M}}$

$V_{rms}$ for helium $=\sqrt{\frac{3RT}{4}}$

$V_{rms}$ for argon $=\sqrt{\frac{3RT}{40}}$

$\frac{V_{rms}\left(helium\right)}{V_{rms}\left(Argon\right)}=\sqrt{10}$

$=3.16$