Question $(1)$

$(5$marks$)$

Use the given equilibrium data of methanol $(MeOH)$ and water for solving the simple batch distillation problem with the following description: A single equilibrium stage batch still pot is used to separate MeOH from water. The feed with a total amount of $50$ moles contains $80\%$MeOH and is charged into the still pot operated at $1$atm. The mole fraction of MeOH left on the pot after the distillation has ended is $65\%.$ Calculate the following:

$(1)$ The amount of residue on the still pot after the distillation has ended. $(3$marks$)$

$(2)$ The total amount of distillate collected. $(1$ mark$)$

$(3)$ The distillate mole fraction. $(1$ mark$)$

VLE equilibrium Data

$\backslash$table$[[\backslash$table$[[$Methanol$-$liquid$],[$mole fraction$]],0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}65,0\mathrm{.}7,0\mathrm{.}75,0\mathrm{.}8,0\mathrm{.}9],[\backslash$table$[[$Methanol$-$vapour$],[$mole fraction$]],0\mathrm{.}78,0\mathrm{.}825,0\mathrm{.}845,0\mathrm{.}871,0\mathrm{.}895,0\mathrm{.}915,0\mathrm{.}958]]$