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# Velocity of nitrogen molecules

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At room temperature, what fraction of the nitrogen molecules in the air are moving at less than 300 m/s?

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#### Solution Preview

Please see the attached file.

SOLUTION

Basic theory

1) As per Maxwell speed distribution law :

a) The number of molecules per unit volume having speed v is given by :

f(v) = n (m/2Î kT)3/2exp( -mv2/2kT) where n = total number of molecules, m = mass of a molecule, k = Boltzmann constant, T = Absolute temp. ...............(1a)

Or f(v) = n (M/2Î RT)3/2exp( -Mv2/2RT) where n = total number of molecules, M = molecular mass of the gas, R = Universal gas constant, T = Absolute temp. ...(1b)

b) The fraction of molecules of a gas having speeds between v and v+dv is given by :

F(v) dv = 4Î  (m/2Î kT)3/2 v2 exp (-mv2/2kT) dv ............(2a)

Or F(v) dv = 4Î  (M/2Î RT)3/2 v2 ...

#### Solution Summary

Problem solved with application of Maxwell speed distribution law.

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