Consider a ternary system $($components $1,2,$ and $3)$ where a binary liquid mixture of volatile

components $1$ and $2$ is evaporating $($at $z=0)$ through stagnant component $3($gas$)$ in a vertical tube.

A sweep gas at the top of the tube $(z=L)$ maintains essentially pure component $3$ at the top of the

tube.

a$.$ Use the Maxwell$-$Stefan equations to determine the pseudo steady state gas phase mole

fraction profiles for components $1$ and $3,$ i$.$e$.,y_1[z]$ and $y_3[z],$ in the tube. These profiles will

be a function of the molar fluxes, $N_{iz}.$ Your profiles should have the forms of:

$y_3[z]=e^{-A(L-z)}$ and $y_1[z]=\frac{D}{A-B}{e}^{-A(L-z)}-(\frac{C}{B}+\frac{D}{A-B})e^{-B(L-z)}+\frac{C}{B}$

Where $A,B,C,$ and $D$ are functions $($that you should define$)$ of the total molar

concentration, the molar fluxes, and the binary diffusion coefficients.

b$.$ Calculate $N_{1z}$ and $N_{2z}$ for $L=0\mathrm{.}1,1,$ and $10cm.$

What happens to the fluxes as $L$ increases. Why?

c$.$ Plot $y_1[z],y_2[z],$ and $y_3[z]$ on a single plot from $z=0$ to $z=10cm.$

Use: $c{D}_{12}=1\mathrm{.}8{10}^{-4}molc{m}^{-1}se{c}^{-1}$

$c{D}_{13}=3\mathrm{.}6{10}^{-4}molc{m}^{-1}se{c}^{-1}$

$c{D}_{23}=2\mathrm{.}7{10}^{-5}molc{m}^{-1}se{c}^{-1}$

$y_1[z=0]=0\mathrm{.}2$

$y_2[z=0]=0\mathrm{.}4$