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#### 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  N= 28 u

The molar mass of N= 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.