Question

Assuming that $O_2$ molecule is spherical in shape with radius 2 Angstrom, the percentage of the volume of $O_2$ molecules to the total volume of gas at $STP$ is :

• A. 0.09 %
• B. 0.9 %
• C. 0.009 %
• D. 0.045 %

Answer 1

The correct option is A 0.09 %

The volume of 1 molecule of $O_2=\left(4/3\right)\pi r^3$

here $r=2A^o=2\times {10}^{-9}dm\Rightarrow volume=\left(4/3\right)\pi (2\times {10}^{-9}{)}^3$

Volume occupied by 1 mole $O_2=N_A\left(4/3\right)\pi (2\times {10}^{-9}{)}^3$

$N_A=$ Avogadro's number

Volume of 1 mole $O_2=6.023\times {10}^{23}\times \left(4/3\right)\times 3.14\times {(2\times {10}^{-9})}^3=0.202d{m}^3$

Volume occupied by $1mole$ gas at $STP$ $=22.4d{m}^3$

Percentage of volume of $O_2$ to the total volume of gas $=\frac{0.202\times 100}{22.4}=0.901$ %