Question

What is the fraction of molecular volume to the actual volume occupied by oxygen gas at $STP$ ? Given, the diameter of oxygen molecule is $ 2\,\mathring{A} $ .

• A. $ 1.75\times 10^{-4} $
• B. $ 1.5\times 10^{-4} $
• C. $ 12\times 10^{-4} $
• D. $ 1.125\times 10^{-4} $

Answer 1

Answer: (D)

Volume of oxygen gas at STP $=22.4\, L$
$=22.4 \times 10^{-3} m^{3} \ldots$ (i)
$\Rightarrow $ Volume of oxygen molecules at STP
$=N_{0} \times \frac{4}{3} \pi r^{3}$
$=6.02 \times 10^{23} \times \frac{4}{3} \pi\left(10^{-10}\right)^{3}$
$=6.02 \times \frac{4}{3} \times \pi \times 10^{-7}$
$=25.20 \times 10^{-7} m^{3}$
$\Rightarrow \frac{\text { Volume (oxygen molecules at STP) }}{\text { Volume (oxygen gas at STP) }}$
$=\frac{25.20 \times 10^{-7}}{22.4 \times 10^{-3}}$
$=1.125 \times 10^{-4}$