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.

Answer

`99.26`

Explanation

As Oxygen molecule is spherical , therefore , volume of one molecule = `4/3 pi r^(3)`
`= 4/3 xx 22/7 (150 xx 10^(-10)cm)^(3) = 1.41 xx 10^(-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., `6.022 xx 10^(23)` molecules . This will be
`= ( 6.022 xx 10^(23)) xx (1.41 xx 10^(-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 xx 100 = 99.6 % `