How Many Nitrogen Molecules Collect on a Crystal Surface Per Second?

[Bandook]

From the kinetic theory of gases, the rate of the number of gas molecules bombarding the unit area of a surface (Z) is given by,
Z = P/(2mkT)^1/2

Consider a crystal inside a chamber containing nitrogen gas at pressure 10^-10 torr and at room temperature (300K).

Calculate the number of nitrogen molecules collected by unit area of the crystal per second. Assume that all colliding nitrogen molecules stick on the surface.

[1 torr = 1.33 x 10^-2 Ncm^-2, Avogadro number: 6.03 x 10²³ mol^-1]

 

[NateD]

Given:P = 10-10 torr = 10-12 Nm-2M = 28 gmol-1 (molar mass of nitrogen)T = 300KSolution:We have, Z = P/(2mkT)1/2Z = (10-12 Nm-2)/[(2 x 1.67 x 10-27 kg)(28 x 10-3 kgmol-1)(300K)]1/2= 7.5 x 1023 m-2s-1Therefore, the number of nitrogen molecules collected by unit area of the crystal per second = 7.5 x 1023 m-2s-1.