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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 Å.

Q13.1 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 Å.

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Diameter of an oxygen molecule, d = 3 Å.

The actual volume of a mole of oxygen molecules Vactual is

\\V_{actual}=N_{A}\frac{4}{3}\pi \left ( \frac{d}{2} \right )^{3}\\ V_{actual}=6.023\times 10^{23}\times \frac{4}{3}\pi \times \left ( \frac{3\times 10^{-10}}{2} \right )^{3}\\ V_{actual}=8.51\times 10^{-6}m^{3}\\ V_{actual}=8.51\times 10^{-3}litres

The volume occupied by a mole of oxygen gas at STP is Vmolar = 22.4 litres

\\\frac{V_{actual}}{V_{molar}}=\frac{8.51\times 10^{-3}}{22.4}\\ \frac{V_{actual}}{V_{molar}}=3.8\times 10^{-4}

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