(Solved): Consider a binary, multi-stage distillation column operating with a reflux ratio of 2.5 . The feed ...

Consider a binary, multi-stage distillation column operating with a reflux ratio of 2.5 . The feed molar flowrate is $200\mathrm{kmol}{\mathrm{s}}^{-1}$ and the distillate molar flowrate is $40\mathrm{kmol}\mathrm{s}$. The ratio of the flowrates of liquid and vapour in the section of the column below the feed is, ${}^{L_S}=2.0$. a) It is known that the operating lines for the sections of the column above and below the feed intersect at $(x=0.25,y=0.35)$. Calculate the mole fraction of the more volatile component in: i) the bottom product streams. ii) the feed streams. b) An alternative multi-stage distillation column for the same separation has a feed with identical molar flowrate, composition, and quality to those stated above or calculated previously. The distillate molar flowrate and reflux ratio are also unchanged. For this alternative distillation column, the intersection of operating lines is instead at $(x=0.255,y=0.405)$. Explain in around 100-150 words what must be the difference between the alternative multi-stage columns, and which one would be expected to achieve a greater recovery of the more volatile component in the distillate. You may wish to use a sketch as part of your explanation.