Question

Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be $3\mathring{A}$.

Answer 1

Diameter (size) of oxygen molecule $=3\mathring{A}$

Radius of oxygen molecule, $r=\frac{3}{2}\mathring{A}=1.5\times {10}^{-10}m$

Therefore, volume of 1 mole of oxygen gas at S.T.P

$=\frac{4}{3}{\pi r}^3\times N$

$=\frac{4}{3}\times \pi \times (1.5\times {10}^{-10}{)}^3\times 6.0225\times {10}^{23}$

$=8.514\times {10}^{-6}{m}^3=8.514\times {10}^{-3}$ litre

Fraction of the molecular volume occupied $=\frac{8.514\times {10}^{-3}}{22.4}=3.8\times {10}^{-4}$