$1.$ The feed to a series of distillation columns is $100$ kmol$/$h with $80$ mole$\%$ ethanol and

$20$ mole$\%$ benzene. The azeotrope is at $85$ mole$\%$ ethanol at high pressure and at

$70$ mole$\%$ at low pressure. Ethanol is more volatile at mole fractions below the azeotrope. The azeotropes are low boilers. The low pressure column is first.

a$.$ Sketch the Txy diagram.

b$.$ Draw this series of distillation columns and give the flowrates and compositions $($in terms of ethanol mole fraction$)$ of all streams.

c$.$ For what range of feed ethanol mole fractions will a series with the low pressure column first work? For high pressure column first?

d$.$ Redo parts a and b if the azeotropes are high boilers and ethanol is more volatile above the azeotrope instead.

Please draw out the diagram and the columns don't type them and show all the calculations used to get to an answer, thank you!