Assuming oxygen molecule to be spherical in shape, calculate the volume of a single molecule of oxygen if its radius is 150 pm. Also calculate the percentage of empty space in one mole of the gas at STP.

Explanation

As oxygen molecule is spherical, therefore, volume of one molecule
`=(4)/(3)pir^(3)=(4)/(3)xx(22)/(7)(150xx10^(-10)cm)^(3)=1.41xx10^(-23) cm^(3)`
To calculate the empty space in 1 mole of `O_(2)` molecules, let us first calculate the volume occupied by 1 mole of molecules, i.e., `(6.0 22xx10^(23))xx(1.41xx10^(-23)cm^(23)) ` molecules, This will be
`=(6.022xx10^(23))xx(1.41xx10^(-23)cm^(3))=8.49" cm"^(3)`.
But volume occupied by 1 mole of molecules at S.T.P.`=22400" cm"^(3)`
`:. " "` Empty space=22400-8.49`" cm"^(3)=22391.51" cm"^(3)`
`:. ` % age of empty space `=(22391.51)/(22400)xx100=99.9%`