Calculate the average volume available to a molecule in a sample of nitrogen gas at STP. What is the average distance between neighbouring molecules if nitrogen molecules are spherical in nature ?

Explanation

`6.023 xx10^(23)` molecules of `N_(2)` occupy `22400 cm^(3)`
`therefore` one molecules of `N_(2)` occupies `=(22400)/(6.023xx10^(23))cm^(3)`
or volume of one molecule of `N_(2)=3.72xx10^(-20) cm^(3)`
Also, the average distance between two molecules =2r
and `(4)/(3) pi r^(3)=3.72xx10^(-20)`
`therefore r^(3) =(3.72xx10^(-20)xx3xx7)/(4xx22)`
`therefore r=20.7xx10^(-8) cm`
Thus, average distance `=2xx20.7xx10^(-8)`
`=41.4xx10^(-8) cm`