Example: Transition$-$Region Diffusion of

$He$ and $N_2$

A gas mixture at a total pressure of $0\mathrm{.}10$atm abs and $298K.$ is composed of

$N_2($A$)$ and $He(B).$ The mixture is diffusing through an open capillary $0\mathrm{.}010$

$m$ long having a diameter of $5{10}^{-6}m.$ The mole fraction of $N_2$ at one end is

$x_{A_1}=0\mathrm{.}8$ and at the other end is $x_{A_2}=0\mathrm{.}2.$ The molecular diffusivity $D_{AB}$ is

$6\mathrm{.}98{10}^{-5}\frac{m^2}{s}$ at $1$aim. which is an average value by several investigators.

$($a$)$ Calculate the flux NA at steady slate.

$($b$)$ Use the approximate equations for this case.

Solution: The given values are $T=273+25=298K,$vec$(r)=5\frac{{10}^{-6}}{2}=$

$2\mathrm{.}5{10}^{-6}m,L=0\mathrm{.}01m,P=0\mathrm{.}1(1\mathrm{.}01325{10}^5)=1\mathrm{.}013{10}^{4}Pa,$

$x_{A1}=0\mathrm{.}8,x_{A2}=0\mathrm{.}2,D_{AB}=6\mathrm{.}98{10}^{-5}\frac{m^2}{s}$ at $1$atm. Other values needed

$are{M}_A=28\mathrm{.}02k\frac{g}{k}$gmol,$M_B=4\mathrm{.}003.$