A distillation column with a partial condenser and a partial reboiler operating at $1\mathrm{.}0$atm is separating $200$kmo$\frac{l}{h}$ of a feed that is $60$mol$\%$ acetone and $40$mol$\%$ ethanol. The feed is a subcooled liquid, and $12$ moles of the feed condense one mole of vapor in the column. The feed is fed to the fourth stage below the partial condenser. The bottoms mole fraction is $x_B=0\mathrm{.}08$ acetone and the distillate is $y_D=0\mathrm{.}80$ mole fraction acetone. The boilup rate $\frac{?}{\text{b}\text{a}\text{r}}(V)=944\mathrm{.}82$kmo$\frac{l}{h}.$ Assume CMO is valid. VLE data are in Problem $4.$D$7.$

a$.$ Determine B and D$.$

b$.$ Calculate $q=\frac{\frac{?}{\text{b}\text{a}\text{r}}(L)-L}{F}$ and the slope of the feed line. Then, plot the feed line.

c$.$ Determine $\frac{?}{\text{b}\text{a}\text{r}}(L),L,$ and V$.$

d$.$ Plot the operating lines.

e$.$ Step off stages from the top down and determine the number of stages needed.

$\backslash$table$[[x_A,0,0\mathrm{.}1,0\mathrm{.}15,0\mathrm{.}2,0\mathrm{.}25,0\mathrm{.}3,0\mathrm{.}35,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}9,1],[y_A,0,0\mathrm{.}262,0\mathrm{.}348,0\mathrm{.}417,0\mathrm{.}478,0\mathrm{.}524,0\mathrm{.}566,0\mathrm{.}605,0\mathrm{.}674,0\mathrm{.}739,0\mathrm{.}802,0\mathrm{.}865,0\mathrm{.}929,1],[TC,78\mathrm{.}3,-,-,-,67\mathrm{.}3,65\mathrm{.}9,-,63\mathrm{.}6,-,60\mathrm{.}4,59\mathrm{.}1,58,57,56\mathrm{.}1]]$