Question

Given molecular weight of hydrogen molecule is $M=2.016\times {10}^{-3}kg/mol$. If the root-mean-square speed of hydrogen molecules $\left(H_2\right)$ at $373.15K\left({100}^{\circ }C\right)$ is $v_{rms}=\frac{x+210}{100}km/s$. Find $x$.

Answer 1

The mass of an $H_2$molecule may be calculated from the molecular weight as

$m=\frac{M}{N_0}=\frac{2.016\times {10}^{-3}kg/mol}{6.02\times {10}^{23}co{l}^{-1}}=3.35\times {10}^{-27}kg$

Then $\frac{1}{2}m{v}_{rms}^2=\frac{3}{2}kT$

$⟹v_{rms}=\sqrt{\frac{3kT}{m}}=2.15km/s$