Question

Calculate the root mean square speed of hydrogen molecule at STP.

Answer 1

$c=\sqrt{\frac{3PV}{M}}$
$P=1atm=101.3kPa$
$V=22.4d{m}^3$
$M=2gmo{l}^{-1}=0.002kgmo{l}^{-1}$
Substituting the values,
$c=\sqrt{\frac{3\times 101.3\times 22.4}{0.002}}=1844.91m{s}^{-1}$.
Alternative method:
$c=\sqrt{\frac{3RT}{M}}$
$R-8.314kPad{m}^3{K}^{-1}mo{l}^{-1};T=273K$;
$M=0.002kgmo{l}^{-1}$
Substituting the values,
$c=\sqrt{\frac{3\times 8.314\times 273}{0.002}}=1845.15m{s}^{-1}$.