$100$kgmol$\frac{e}{h}r$ of a mixture containing $50$ mole percent A and $50$ mole percent B is to be fractionated to a distillate containing $90$ mole percent A and a residue containing $90$ mole percent $B$ using a total condenser and feed at its saturated liquid condition. The reflux ratio is $4\mathrm{.}5.$

For this assignment and the designated relative volatilities $()$ shown in the table below you need to perform the following tasks using the MC$-$Cabe Thile method:

$\backslash$table$[[$Task No$.,1,2,3,4,5,6,7,8],[(),1\mathrm{.}5,2\mathrm{.}0,2\mathrm{.}5,3\mathrm{.}0,3\mathrm{.}5,4\mathrm{.}0,4\mathrm{.}5,5]]$

a$)$ For the designated relative volatilities $(),$ find the theoretical stages required.

b$)$ For the designated relative volatilities $(),$ find the minimum stages required.

c$)$ For the designated relative volatilities $(),$ find the minimum reflux ratio required.

d$)$ For the designated relative volatilities $(),$ find the feed stage location.

The equilibrium relationship in terms of relative volatility is given by:

$y_A=\frac{x_A}{1+(-1)x_A}$

Summary of results

$\backslash$table$[[$Task No$.,1,2,3,4,5,6,7,8],[(),1\mathrm{.}5,2\mathrm{.}0,2\mathrm{.}5,3\mathrm{.}0,3\mathrm{.}5,4\mathrm{.}0,4\mathrm{.}5,5],[$No$.$ stages,,,,,,,,$],[N_{\text{m}\text{i}\text{n}},,,,,,,,],[R_{\text{m}\text{i}\text{n}},,,,,,,,],[\backslash$table$[[$Feed stage$],[$location$]],,,,,,,,]]$