A distillation column is separating \(150 \mathrm{kmol} / \mathrm{h}\) of a saturated liquid mixture that is \(30 \mathrm{~mol} \%\) methanol and \(70 \mathrm{~mol} \%\) water. The column operates at 1.0 \(\mathrm{atm}\) pressure. Reflux ratio is 2.0 , and reflux is returned as a saturated liquid. We desire a \(97 \%\) recovery of methanol in the distillate and a methanol distillate mole fraction of 0.990 .

Find distillate flow rate \(\mathrm{D}\), bottoms flow rate \(\mathrm{B}\), methanol mole fraction in the bottoms \(\mathrm{x}_{\mathrm{M}, \mathrm{bot}}\), and the fractional recovery of water in the bottoms.