A distillation column with a total condenser and a partial reboiler is separating $200$ kmo$\frac{l}{h}$ of a feed that is $40$mol$\%n-$pentane and $60$mol$\%n-$hexane. The feed is a twophase mixture that is $20\%$ liquid. Column pressure is $1\mathrm{.}5$ bar, and reflux is returned as a saturated liquid. The external reflux ratio is $\frac{L}{D}=3.$ The mol fraction of $n-$pentane in the distillate stream is $0\mathrm{.}97.$ The column has a vapor side stream located above the feed stage, and the $n-$pentane mol fraction in the side stream is $0\mathrm{.}80.$ The fractional recovery of $n-$hexane in the bottoms is $0\mathrm{.}90,$ and the bottoms flow rate is $B=130$kmo$\frac{l}{h}.$ Find distillate flow rate $D,$ side stream flow rate $S,$ and the mole fraction of $n-$pentane in the $S=58\mathrm{.}8\frac{\text{k}\text{m}\text{o}\text{l}}{hc}$ and $D=11,2\frac{\text{k}\text{m}\text{o}\text{l}}{hr}$

$$ explain and show all work please and write clearly answer pervious answers are wrong so don't use them or I will give you a thumbs down and report you if its wrong