Question

Assuming O₂ molecule is spherical in shape and has molecular radii as 150pm calculate :
1) volumeof single molecule of the gas.
2) % of empty space in 1 mole of O₂ at NTP

Answer 1

Dear Tikeya,

$$\begin{gathered} Volumeofasphere=\frac{4}{3}\mathrm{\pi }{\mathrm{r}}^3 \\ \mathrm{Volume}\mathrm{of}\mathrm{a}\mathrm{single}\mathrm{oxygen}\mathrm{molecule}=\frac{4}{3}\times \frac{22}{7}\times (150\times {10}^{-10}{)}^3 \\ =1.414\times {10}^{-23}{\mathrm{cm}}^3 \\ \mathrm{Since}1\mathrm{mole}\mathrm{of}\mathrm{the}\mathrm{gas}\mathrm{contains}\mathrm{avogadro}\mathrm{number}\mathrm{of}\mathrm{molecules} \\ \mathrm{Volume}\mathrm{of}1\mathrm{mole}\mathrm{of}\mathrm{the}\mathrm{gas}=1.414\times {10}^{-23}\times 6.022\times {10}^{23} \\ =8.515{\mathrm{cm}}^3 \\ \mathrm{Volume}\mathrm{of}1\mathrm{mole}\mathrm{of}\mathrm{any}\mathrm{gas}\mathrm{occupies}22.4\mathrm{L}=22400{\mathrm{cm}}^3 \\ \mathrm{Thus}\mathrm{the}\mathrm{empty}\mathrm{space}=22400-8.515=22391.49{\mathrm{cm}}^3 \\ \%\mathrm{of}\mathrm{empty}\mathrm{space}=\frac{22391.49}{22400}\times 100=99.96\% \end{gathered}$$