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

The Correct Option is B

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:

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