Question

Given molecular weight of hydrogen molecule is $M=2.016\times {10}^{-3}\text{kg/mol}$. Calculate the root - mean-square speed of hydrogen molecules $\left(H_2\right)$ in km/s at $373.15K\left({100}^{\circ }C\right)$. (Answer the nearest integer)

Answer 1

The mass of an $H_2$ molecule may be calculated from the molecular weight as
$m=\frac{M}{N_0}=\frac{2.016\times {10}^{-3}\text{kg/mol}}{6.02\times {10}^{23}{\text{mol}}^{-1}}=3.35\times {10}^{-27}\text{kg}$
Then $\frac{1}{2}m{v}_{rms}^2=\frac{3}{2}kT$
$v_{rms}=\sqrt{\frac{3kT}{m}}=\sqrt{\frac{3(1.38\times {10}^{-23})\left(373.15\right)}{3.35\times {10}^{-27}}}=2.15\text{km/s}$

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