A distillation system with a still pot plus a column with one equilibrium stage is used to batch distill $1\mathrm{.}0$kmol of a $57\mathrm{.}0$ mol$\%$ methanol and $43\mathrm{.}0$ mol$\%$ water feed. A total condenser is used. The final bottoms concentration is $15\mathrm{.}0$ mol$\%$ methanol. Pressure is $101\mathrm{.}3$kPa. Reflux is a saturated liquid, and $\frac{L_0}{D}=1\mathrm{.}85.$ The equilibrium curve is in Fig. $1.$ Find $W_{\text{f}\text{i}\text{n}\text{a}\text{l}\text{,}}{D}_{\text{t}\text{o}\text{t}\text{a}\text{l}\text{,}}$ and $x_{D,\text{a}\text{v}\text{g}\text{.}}.$

Fig. $1$ y vs$.$ x diagram for methanol$-$water at $101\mathrm{.}3$kPa.

$$ part B

$4\mathrm{.}0$ kmoles of a feed that is $0\mathrm{.}60$ mole fraction acetone and $0\mathrm{.}40$ mole fraction ethanol is batch distilled in a system with a still pot $($an equilibrium contact$),$ a column that acts as one equilibrium stage $($total two equilibrium contacts$),$ a total condenser, and reflux to the column. $p=1\mathrm{.}0$atm, the reflux ratio is $\frac{L_0}{D}=1\mathrm{.}0,$CMO is valid, and $x_w,$ fin $=0\mathrm{.}20.$ The equilibrium curve is in Fig. $2.$ Find $W_{\text{f}\text{i}\text{n}\text{a}\text{l}\text{,}}{D}_{\text{t}\text{o}\text{t}\text{a}\text{l}},$ and $x_{D,\text{a}\text{v}\text{g}}.$

Fig. $2$ y vs$.x$ diagram for ethanol$-$water at $1$ atm.