Question $1$

A fractionating column is required to distill a liquid containing $25\%$ benzene and $75\%$ toluene by mass to give a product of $90\%$ benzene. A reflux ratio of $3\mathrm{.}5$ is to be used and the feed will enter at its boiling point.

$\backslash$table$[[\backslash$table$[[$Mole fraction of$],[$benzene in liquid$]],0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}9],[\backslash$table$[[$Mole fraction of$],[$benzene in$],[$vapour$]],0\mathrm{.}20,0\mathrm{.}38,0\mathrm{.}51,0\mathrm{.}63,0\mathrm{.}71,0\mathrm{.}78,0\mathrm{.}85,0\mathrm{.}91,0\mathrm{.}96],[,,,,,,,,,]]$

a$.$ Calculate by the Lewis$-$Sorel method the composition of the liquid and vapor in the third plate. $(10)$

b$.$ Estimate the number of plates required for this distillation operation, using the McCabeThiele method. $(14)$

c$.$ How many plates are in the rectifying section?

$(2)$

d$.$ How many plates are the stripping section? $(2)$

e$.$ Given $60\%$ efficiency, what are the actual number of plates for the column?

$(2)$