Question

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 k in a container. The ratio of their rms speeds rms rms v (helium) v ((argon) , is close to

Answer 1

Answer:

The ratio of their rms speeds is 3.16:1.

Explanation:

Root mean square speed is given by:

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

RMS speed of helium = $v_{rms}=\sqrt{\frac{3R\times 300 K}{4 u}}$

RMS speed of argon = $v'_{rms}=\sqrt{\frac{3R\times 300 K}{40 u}}$

$\frac{v_{rms}}{v'_{rms}}=\frac{\sqrt{\frac{3R\times 300 K}{4 u}}}{\sqrt{\frac{3R\times 300 K}{40 u}}}=\sqrt{\frac{10}{1}}=3.16:1$

The ratio of their rms speeds is 3.16:1.