Question

A sample contains a mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample is:

• A. $\frac{1}{\sqrt{32}}$
• B. $2\sqrt{2}$
• C. $\frac{1}{4}$
• D. $\frac{1}{2\sqrt{2}}$

Answer 1

Answer: (B)

$2\sqrt{2}$

Answer 2

The root mean square speed ($V_{\text{rms}}$) is given by:

$V_{\text{rms}} = \sqrt{\frac{3RT}{M_w}}$

where $M_w$ is the molar mass of the gas.

The ratio of root mean square speeds of helium ($V_{\text{He}}$) and oxygen ($V_{\text{O}_2}$) is:

$\frac{V_{\text{O}_2}}{V_{\text{He}}} = \sqrt{\frac{M_{w,\text{He}}}{M_{w,\text{O}_2}}}$

Substituting the values:

• $M_{w,\text{He}} = 4 \, \text{g/mol}$
• $M_{w,\text{O}_2} = 32 \, \text{g/mol}$

$\frac{V_{\text{O}_2}}{V_{\text{He}}} = \sqrt{\frac{4}{32}} = \frac{1}{2\sqrt{2}}$

The ratio $V_{\text{He}} / V_{\text{O}_2}$ is:

$\frac{V_{\text{He}}}{V_{\text{O}_2}} = \frac{2\sqrt{2}}{1}$