The average collision cross section sigma_c for molecules in a nitrogen gas arou

Question

The average collision cross section sigma_c for molecules in a nitrogen gas around 0 degree C is about 0.43 nm^2. (a) If the N_2 molecules were represented as spheres of radius R, what radius would this cross section correspond to? (b) Estimate the mean free path lambda_mfp for the molecules in nitrogen at 0 degree C and 1 atm. (c) Estimate the mean free flight time between the collisions t f = lambda/upsilon_rms in nitrogen at the above conditions. As air is dominated by nitrogen and the relevant characteristics of oxygen are not very different, your estimates should be relevant for air too. (d) Determine the corresponding diffusivity D for nitrogen. The traditional unit for diffusivity is cm^2/s. The measured value is 0.155 cm^2/s. (e) Estimate the heat conductivity K for nitrogen. Around 0 degree C the rotational degrees of freedom in the molecules are fully active. The measured conductivity, both for nitrogen and air, is about 24mW/(m degree K). (f) Finally estimate the viscosity eta for nitrogen in Pa middot s. The measured viscosity value, both for nitrogen and air around 0 degree C, is 1.7 times 10^-5 Pa middot s.

Explanation / Answer

(a)

c=(2R)2=0.43 nm2=0.43*10-9 m2

R=5.85*10-6 m=5.85 µm

(b)

=RT/1.41*NAc*P=(8.314*273.15)/(1.41*0.43*10-9*6.022*1023*101325)=6.13*10-17 m

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