Question

A mixture of $2$ moles of helium gas (atomic mass $=4u$), and $1$ mole of argon gas (atomic mass $=40u$) is kept at $300K$ in a container. The ratio of their rms speeds $\left[\frac{V_{rms}\left(helium\right)}{V_{rms}\left(argon\right)}\right]$, is close to:

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

Answer 1

The correct option is D $3.16$

As we know that $V_{rms}=\sqrt{\frac{3RT}{M}}$

$\frac{V_{rms}\left(He\right)}{V_{rms}\left(Ar\right)}=\sqrt{\frac{M_{Ar}}{M_{He}}}=\sqrt{\frac{40}{4}}=3.16$