Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

5.3 Transport processes in gases 111
I The general transport equation: We consider the net flux of Γ through an area
at = 0 that is transported by gas molecules coming from an area above at = 0 +
and from below from an area above at = 0 − (where isthemeanfreepathlength).
Denoting the respective transport quantity per molecule as Γ, these partial fluxes are
given by the number of gas kinetic collisions hitting on ( = 0 ) times the Γ carried
by each gas molecule (number density ):
• Using the gas kinetic wall collision frequency wall = 1 (Eq. 5.92), we obtain
4
Γ + = 1 µ Γ
µΓ
4 × × 0 + (5.102)
and
• Net effect:
Γ − = 1 4 × × µΓ 0 −
µ Γ
(5.103)
Γ = Γ + − Γ − = 1 µ Γ
2 × × (5.104)
• Net flux (with − sign to account for the fact that the flux is directed along the
downhill gradient of Γ):
−→ Γ = Γ
µ Γ
= −1 2
with given by (see the derivation of wall above)
=
µ 8
(5.105)
12
(5.106)
and, for only one type of gas molecules A (i.e., A - A collisons),
= 1 √
2
1
2 ×
(5.107)
• If also varies along (diffusion), Eq. 5.105 may be recast by defining the overall
transport quantity Γ 0 from the transport quantity per molecule Γ as
Γ 0 = Γ (5.108)
into the form
−→ Γ = − 1 2 Ã
!
Γ 0
(5.109)
In the following, ³ we shall apply Eqs. 5.105 or 5.109 to determine the self-diffusion coefficient
Γ =1 Γ 0 =
´, the heat conductivity ¡ Γ = ¢ ,andtheviscosity ¡ ¢
Γ =
of gases.