Q$5.$ Fractional Distillation Tower $(29$ pts$)$

Fractional distillation tower is one of the most common unit operations of chemical engineering

which is used to separate large quantities of liquids such as water and ethanol mixture. A

simple fractional distillation tower generates two product streams $($which are called top and

bottom$)$ from a fresh feed.

Suppose you are working as an engineer in a distillation unit. This unit consists of two

distillation towers. A liquid mixture of $60\%$ ethanol, $5\%$ dissolved $MgC{l}_2$ salt and $35\%$ water is

continuously fed into the first distillation tomer. The tomer separates the mixture into two

product streams which have equal mass flow rates. The top stream contains $90\%$ ethanol by

mass and no $MgC{l}_2.$ The bottom stream is purged.

The top stream is then fed into the second distillation tower. This tower generates two streams

as well. The top stream consists of pure ethand, and the bottom stream contains $50\%$ water

by mass. The bottom stream is purged again, and the top stream is stored in an ethanol tank.

Your job as a chemical engineer is to check if this distillation unit works at steady state, and to

perform relevant calculations. To accomplish your job suppose you measure the mass of the

pure ethanol accumulated in the ethanol tank. Your collected data is given below.

a$)(9$ pts$)$ Draw the block diagram and label the knowns and unknowns.

b$)(10$ pts$)$ Verify that the distillation unit works at steady state $($Hint: Consider the given

table$).$

c$)(10$ pts$)$ Calculate the molar flowrate of $MgC{l}_2$ that exits the unit in molesh and the

mass flowrate of the fresh feed in $k\frac{g}{h}.(MgC{l}_2=95\mathrm{.}21\frac{g}{m}ol)$