Given:

A stable isotope of xenon, $x{e}_{188},$ is frequently used as a tracer gas in respiratory experiments. Assume dry air containing mole percentages of $1\%$ Xe $($component $1),79\%N_2($component $2),$ and $20\%O_2($component $3).$ At $P=101\mathrm{.}3$kPa and $T=310K,$ the binary diffusion coefficients between these components in $c\frac{m^2}{s}$ are: $D_{12}=0\mathrm{.}133,D_{13}=0\mathrm{.}129,D_{23}=0\mathrm{.}219.$

Find:

Determine the multicomponent molar flux equations $(J)$ for all three components.

$($a$)$ Obtain the components of the $[$B$]$ matrix with oxygen as component, $I=3$

$($b$)$ When the mole fraction and thus the concentration gradients of the three components are similar $($i$.$e$.$ gradC$1$~~gradC$2$~~gradC$3),$ how do the coupled terms in the flux equations compare to the principle $($Fickian diffusion$)$ terms?

$($c$)$ How do the multicomponent diffusion coefficients of the principal terms compare to the binary coefficients of these gases with one another? Explain why this is the case.