Kinetic Theory

Question : 10

Total: 14

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17°C. Take the radius of a nitrogen molecule to be roughly 1.0 Å. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of N2=28.0u).

Solution:

Here, Pressure of nitrogen = 2 atm
=2×1.013×105Nm−2 =2.026×105Nm−2
Temperature of nitrogen =17°C=17+273=290K
Molecular diameter d =2×1=2Å=2×10–10m
Molecular mass of nitrogen =28g=28×10–3kg
Mean free path = ?
Collision frequency f=?
Mean free path λ=

√2πd2P

1.38×10−23×290

1.414×3.14(2×10−10)2×2.026×105

1.38×29×10−7

1.414×3.14×4×2.026

=1.11×10−7m
rms velocity of nitrogen vrms=√

3RT

=√

3×8.31×290

28×10−3

=508.24m∕s
Collision frequency =

vrms

508.24

1.11×10−7

=4.58×109

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