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Formula from Chapter 9: molar mass dependence of rate of effusion
\(\dfrac{\mathrm{rate}_{\mathrm{effusion\ A}}}{\mathrm{rate}_{\mathrm{effusion\ B}}} = \sqrt{\dfrac{m_{\mathrm{B}}}{m_{\mathrm{A}}}} = \sqrt{\dfrac{M_{\mathrm{B}}}{M_{\mathrm{A}}}}\)
\(\mathrm{rate}_{\mathrm{effusion\ \ce{N2}}}\)
\(= 3.9\ \frac{\mathrm{mol}}{\mathrm{min}}\)
\(M_{\mathrm{\ce{N2}}}\)
\(= M_{\mathrm{\ce{N2}}}\)
\(\ \ \ =28.014\ \frac{\mathrm{g}}{\mathrm{mol}}\)
\(M_{\mathrm{\ce{He}}}\)
\(= M_{\mathrm{\ce{He}}}\)
\(\ \ \ =4.002602\ \frac{\mathrm{g}}{\mathrm{mol}}\)
\(\mathrm{rate}_{\mathrm{effusion\ \ce{He}}}\)
\(= \sqrt{\dfrac{M_{\mathrm{\ce{N2}}}}{M_{\mathrm{\ce{He}}}}} \cdot \mathrm{rate}_{\mathrm{effusion\ \ce{N2}}}\)
\(\ \ \ =\sqrt{\dfrac{28.014\ \frac{\mathrm{g}}{\mathrm{mol}}}{4.002602\ \frac{\mathrm{g}}{\mathrm{mol}}}} \cdot 3.9\ \frac{\mathrm{mol}}{\mathrm{min}}\)
\(\ \ \ =\sqrt{6.99895} \cdot 3.9\ \frac{\mathrm{mol}}{\mathrm{min}}\)
\(\ \ \ =2.645552 \cdot 3.9\ \frac{\mathrm{mol}}{\mathrm{min}}\)
\(\ \ \ =10.3\ \frac{\mathrm{mol}}{\mathrm{min}}\)