Q13.10 Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at and temperature . Take the radius of a nitrogen molecule to be roughly . Compare the collision time with the time the
molecule moves freely between two successive collisions (Molecular mass of ).
Pressure, P = 2atm
Temperature, T = 17 oC
The radius of the Nitrogen molecule ,
The molecular mass of N2 = 28 u
The molar mass of N2 = 28 g
From ideal gas equation
The above tells us about the number of moles per unit volume, the number of molecules per unit volume would be given as
The mean free path is given as
The root mean square velocity vrms is given as
The time between collisions T is given as
Collision time T' is equal average time taken by a molecule to travel a distance equal to its diameter
The ratio of the average time between collisions to the collision time is
Thus we can see time between collisions is much larger than the collision time.