Ncert Exercises & Solutions

13.1 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.

Radius of an oxygen molecule, r = $\frac{d}{2} = \frac{3}{2} =$ 1.5 Å = 1.5 × $10^{- 8} cm$

The actual volume occupied by 1 mole of oxygen gas at STP = 22400 ${cm}^{3}$

Molecular volume of oxygen gas is given by, $V = \frac{4}{3} {πr}^{3} N$

Where N is Avogadro’s number = 6.023 × $10^{23}$ molecules/mole

$V = \frac{4}{3} \times 3.14 \times {(1.5 \times 10^{- 8})}^{3} \times 6.023 \times 10^{23} = 8.51 {cm}^{3}$

The ratio of the molecular volume to the actual volume of oxygen $= \frac{8.51}{22400}$ = 3.8 × $10^{- 4}$