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 $=22.4L$
$=22.4\times 10^{-3}{m}^3\dots$ (i)
$\Rightarrow$ Volume of oxygen molecules at STP
$=N_0\times \frac{4}{3}\pi r^3$
$=6.02\times 10^{23}\times \frac{4}{3}\pi {\left(10^{-10}\right)}^3$
$=6.02\times \frac{4}{3}\times \pi \times 10^{-7}$
$=25.20\times 10^{-7}{m}^3$
$\Rightarrow \frac{\text{ Volume (oxygen molecules at STP) }}{\text{ Volume (oxygen gas at STP) }}$
$=\frac{25.20\times 10^{-7}}{22.4\times 10^{-3}}$
$=1.125\times 10^{-4}$