A $200mo\frac{l}{h}$ liquid mixture containing $35$mol$\%$ benzene and $65$mol$\%$ toluene will be evaporated by $40\%$ under $101\mathrm{.}32$kPa pressure. This process is carried out in a single$-$stage system and the steam and liquid are kept in contact with each other until evaporation is completed.

Calculate the volatile matter compositions of the vapor and liquid leaving the separator as a result of this process. $(30$ points$)$

Equilibrium data for the Benzene$-$Toluene system

$\backslash$table$[[\backslash$table$[[$Mole fraction of benzene$],[$in liquid$]],0\mathrm{.}00,0\mathrm{.}13,0\mathrm{.}26,0\mathrm{.}30,0\mathrm{.}41,0\mathrm{.}58,0\mathrm{.}78,1\mathrm{.}00],[\backslash$table$[[$Mole fraction of benzene$],[$in vapor$]],0\mathrm{.}00,0\mathrm{.}26,0\mathrm{.}46,0\mathrm{.}71,0\mathrm{.}63,0\mathrm{.}78,0\mathrm{.}90,1\mathrm{.}00]]$