Question

The diameter of oxygen atom is $3\mathring{A}$. The fraction of molecular volume to the actual volume occupied by oxygen at STP is

• A. $6\times 10^{-28}$
• B. $6\times 10^{-23}$
• C. $4\times 10^{-10}$
• D. $8\times 10^{-4}$

Answer 1

Answer: (D)

The volume of an oxygen molecule has been taken as $2$ times that of one oxygen atom In $22.4L$ ie $22.4\times 10^{-3}{m}^3$ their are
$N_A=6.23\times 10^{23}$ molecules
Total volume of oxygen molecules
$=2\times \frac{4}{3}\pi r^3\times N_A$
$22.4\times 10^{-3}{m}^3$ is occupied by $N_A$ molecules.
$\therefore$ Fraction of volume occupied
$=\frac{2\times \frac{4}{3}\pi {\left(1.5\times 10^{-10}\right)}^3\times 6.2\times 10^{23}}{\left(22.4\times 10^{-3}\right)}$
$=8\times 10^{-4}$