D$4.$ A partial condenser takes vapor leaving the top of a distillation column and condenses a portion of it$.$ The vapor portion of mole fraction $y_D$ is removed as the distillate product. The liquid portion of mole fraction $x_0$ is returned to the column as reflux. The liquid and vapor leaving the partial condenser can be assumed to be in equilibrium. A distillation column with a partial condenser and a partial reboiler is separating $100\mathrm{.}0$kmo$\frac{l}{h}$ of saturated liquid feed that is $30\mathrm{.}0$mol$\%$ methanol and $70\mathrm{.}0$mol$\%$ water. Column pressure is $1\mathrm{.}0$atm. We desire a $99\mathrm{.}0\%$ recovery of the methanol in the vapor distillate and a $98\mathrm{.}0\%$ recovery of water in the bottoms. Equilibrium data are in Table $2-7($in Problem $2.$D$1),$ and other data are in Problem $3.$E$1.$

a$.$ Find $D,B,y_{D,M},$ and $x_{B,M}.$