Estimate the mean free path for a water molecule in water vapour at 373 K. Given diameter of water molecule `= 2 Å` and number density of water molecule (at NTP) `= 2.7 xx 10^(25) m^(-3)`. Compare it with interatomic distance for water `= 40 Å`.

Explanation

The d for water vapour is same as that of air. The number density is inversely proportional to absolute temperature.
so `n= 2.7 xx 10^(25) xx (273)/(373)= 2 xx 10^(25)cm^(-3)`
Note that the mean free path is 100 times the interatomic distance `~ 40 Å = 4 xx 10^(-9)`m calculated earlier. It is this large value of mean free path that leads to the typical gaseous behaviour. Gases can not be confined without a container. Using, the kinetic theory of gases, the bulk measurable properties like viscosity, heat conductivity and diffusion can be related to the microscopic parameters like molecular size. It is through such relations that the molecular sizes were first estimated.