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Question : 1 of 14
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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 A˚\text{\AA}.
Solution:  
Here, the diameter of an oxygen molecule, d=3A˚=3×10−10md = 3 \text{\AA} = 3 \times 10^{-10} \mathrm{m}
The radius of an oxygen molecule
r=d2=3×10−102mr = \frac{d}{2} = \frac{3 \times 10^{-10}}{2} \mathrm{m}
Molecular volume of one mole of oxygen, V′V'
= Volume of one molecule of oxygen × Avogadro number(N)(N)
=43πr3×N= \frac{4}{3} \pi r^{3} \times N
V′=43×3.14×(3×10−102)3×6.023×1023V' = \frac{4}{3} \times 3.14 \times \left( \frac{3 \times 10^{-10}}{2} \right)^{3} \times 6.023 \times 10^{23}
=8.52×10−6m3= 8.52 \times 10^{-6} \mathrm{m}^{3}
Actual volume occupied by one mole of oxygen gas at S.T.P.V=22, ⁣400cm3V = 22,\!400 \mathrm{cm}^{3}
=22, ⁣400×10−6m3= 22,\!400 \times 10^{-6} \mathrm{m}^{3}
∴ Fraction of molecular volume of the actual volume occupied by
O2=V′V\mathrm{O}_{2} = \frac{V'}{V}
=8.52×10−622, ⁣400×10−6= \frac{8.52 \times 10^{-6}}{22,\!400 \times 10^{-6}}
=3.8×10−4≃4×10−4= 3.8 \times 10^{-4} \simeq 4 \times 10^{-4}
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