A distillation column with a total condenser and a partial reboiler is separating \(200 \mathrm{kmol} / \mathrm{h}\) of a feed that is \(40 \mathrm{~mol} \% \mathrm{n}\)-pentane and \(60 \mathrm{~mol} \%\) n-hexane. The feed is a two-phase mixture that is \(20 \%\) liquid. Column pressure is \(1.5 \mathrm{bar}\), and reflux is returned as a saturated liquid. The external reflux ratio is \(\mathrm{L} / \mathrm{D}=3\). The mol fraction of \(\mathrm{n}\)-pentane in the distillate stream is 0.97 . The column has a vapor side stream located above the feed stage, and the n-pentane mol fraction in the side stream is 0.80 . The fractional recovery of \(\mathrm{n}\)-hexane in the bottoms is 0.90 , and the bottoms flow rate is \(\mathrm{B}\) \(=130 \mathrm{kmol} / \mathrm{h}\). Find distillate flow rate \(\mathrm{D}\), side stream flow rate \(\mathrm{S}\), and the mole fraction of n-pentane in the bottoms, \(\mathrm{x}_{\text {pent }}\) bot .