Subjective Type

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 $$\displaystyle{{3 \mathring A}}$$.

Solution

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 $$\displaystyle =\frac{8.514\times 10^{-3}}{22.4}=3.8\times 10^{-4}$$

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