The molecular radius of ${\mathrm{O}}_2$ is $2.88\times {10}^{-10}.$ Calculate the excluded volume per mol of ${\mathrm{O}}_2$.

$$\begin{gathered} \mathrm{r}=3.61\times {10}^{-10}\mathrm{m} \\ \mathrm{b}=4\mathrm{V} \end{gathered}$$ 

Excluded vol. per molecule is equal to four times times the volume of the molecule. Excluded vol. per mole is equal to 4N times the volumes of the molecule $=4\times \mathrm{N}\times \frac{4}{3}{\mathrm{\pi r}}^3$

$=4\times \left(6.023\times {10}^{23}\right)\times \frac{4}{3}\times 3.14\times {\left(3.61\times {10}^{-10}\right)}^3$

$=4749.60\times {10}^{-7}{\mathrm{m}}^3=0.48{\mathrm{dm}}^3$