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Formula from Chapter 9: velocity of gas particle
\(u_{\mathrm{rms}} = \sqrt{\dfrac{2 \cdot E_{\mathrm{kin\ avg}} \cdot N_{\mathrm{A}}}{m_{\mathrm{particle}}}} = \sqrt{\dfrac{3 \cdot R \cdot T}{M_{\mathrm{particle}}}}\)
\(M_{\mathrm{\ce{N2}}}\)
\(= M_{\mathrm{\ce{N2}}}\)
\(\ \ \ =28.014\ \frac{\mathrm{g}}{\mathrm{mol}}\)
\(R\)
\(= 8.314\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}}\)
\(T\)
\(= 298.15\ \mathrm{K}\)
\(u_{\mathrm{rms}}\)
\(= \sqrt{\dfrac{3 \cdot R \cdot T}{M_{\mathrm{\ce{N2}}}}}\)
\(\ \ \ =\sqrt{\dfrac{3 \cdot 8.314\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}} \cdot 298.15\ \mathrm{K}}{28.014\ \frac{\mathrm{g}}{\mathrm{mol}}}}\)
\(\ \ \ =\sqrt{\dfrac{24.9420\ \frac{\mathrm{J}}{\mathrm{mol}\ \mathrm{K}} \cdot 298.15\ \mathrm{K}}{28.014\ \frac{\mathrm{g}}{\mathrm{mol}}}}\)
\(\ \ \ =\sqrt{\dfrac{7436.46\ \frac{\mathrm{J}}{\mathrm{mol}}}{28.014\ \frac{\mathrm{g}}{\mathrm{mol}}}}\)
\(\ \ \ =\sqrt{265.455\ \frac{\mathrm{J}}{\mathrm{g}}}\)
\(\ \ \ =515.22\ \frac{\mathrm{m}}{\mathrm{s}}\)