A$10.$ Use the vapor$-$liquid equilibrium data at $1\mathrm{.}0$atm for methanol$-$water $($Table $2-7$ in Problem $2.$D$1)$ for the following:

a$.$ If the methanol vapor mole fraction is $0\mathrm{.}60,$ what is the methanol liquid mole fraction?

b$.$ Is there an azeotrope in the methanol$-$water system at a pressure of $1\mathrm{.}0$atm $?$

c$.$ If water liquid mole fraction is $0\mathrm{.}35,$ what is the water vapor mole fraction?

d$.$ What are the $K$ value of methanol and of water at a methanol mole fraction in the liquid of $0\mathrm{.}20?$

e$.$ What is the relative volatility $M-W$ at a methanol mole fraction in the liquid of $0\mathrm{.}20?$

$\backslash$table$[[$Methanol Liquid,Methanol Vapor,Temp., $C,],[0,0,100,],[2\mathrm{.}0,13\mathrm{.}4,96\mathrm{.}4,],[4\mathrm{.}0,23\mathrm{.}0,93\mathrm{.}5,],[6\mathrm{.}0,30\mathrm{.}4,91\mathrm{.}2,],[8\mathrm{.}0,36\mathrm{.}5,89\mathrm{.}3,],[10\mathrm{.}0,41\mathrm{.}8,87\mathrm{.}7,],[15\mathrm{.}0,51\mathrm{.}7,84\mathrm{.}4,],[20\mathrm{.}0,57\mathrm{.}9,81\mathrm{.}7,],[30\mathrm{.}0,66\mathrm{.}5,78\mathrm{.}0,],[40\mathrm{.}0,72\mathrm{.}9,75\mathrm{.}3,],[50\mathrm{.}0,77\mathrm{.}9,73\mathrm{.}1,],[60\mathrm{.}0,82\mathrm{.}5,71\mathrm{.}2,],[70\mathrm{.}0,87\mathrm{.}0,69\mathrm{.}3,],[80\mathrm{.}0,91\mathrm{.}5,67\mathrm{.}6,],[90\mathrm{.}0,95\mathrm{.}8,66\mathrm{.}0,],[95\mathrm{.}0,97\mathrm{.}9,65\mathrm{.}0,\backslash$table$[[$TABLE $2-7.$ Vapor$-$liquid equilibrium data$],[$for methanol water $)=(1$atm