Formula from Chapter 9: molar mass dependence of rate of effusion

\(\dfrac{\mathrm{rate}_{\mathrm{effusion\ A}}}{\mathrm{rate}_{\mathrm{effusion\ B}}} = \sqrt{\dfrac{m_{\mathrm{B}}}{m_{\mathrm{A}}}} = \sqrt{\dfrac{M_{\mathrm{B}}}{M_{\mathrm{A}}}}\)     

\(\mathrm{rate}_{\mathrm{effusion\ \ce{N2}}}\) \(= 3.9\ \frac{\mathrm{mol}}{\mathrm{min}}\)


\(M_{\mathrm{\ce{N2}}}\) \(= M_{\mathrm{\ce{N2}}}\)

\(\ \ \ =28.014\ \frac{\mathrm{g}}{\mathrm{mol}}\)


\(M_{\mathrm{\ce{He}}}\) \(= M_{\mathrm{\ce{He}}}\)

\(\ \ \ =4.002602\ \frac{\mathrm{g}}{\mathrm{mol}}\)


\(\mathrm{rate}_{\mathrm{effusion\ \ce{He}}}\) \(= \sqrt{\dfrac{M_{\mathrm{\ce{N2}}}}{M_{\mathrm{\ce{He}}}}} \cdot \mathrm{rate}_{\mathrm{effusion\ \ce{N2}}}\)

\(\ \ \ =\sqrt{\dfrac{28.014\ \frac{\mathrm{g}}{\mathrm{mol}}}{4.002602\ \frac{\mathrm{g}}{\mathrm{mol}}}} \cdot 3.9\ \frac{\mathrm{mol}}{\mathrm{min}}\)

\(\ \ \ =\sqrt{6.99895} \cdot 3.9\ \frac{\mathrm{mol}}{\mathrm{min}}\)

\(\ \ \ =2.645552 \cdot 3.9\ \frac{\mathrm{mol}}{\mathrm{min}}\)

\(\ \ \ =10.3\ \frac{\mathrm{mol}}{\mathrm{min}}\)