$13\mathrm{.}1$ Assuming the validity of Raoult's law, do the following calculations for the benzene$(1)/$toluene$(2)$ system:

$($a$)$ Given $x_1=0\mathrm{.}33$ and $T=100C,$ find $y_1$ and $P.$

$($b$)$ Given $y_1=0\mathrm{.}33$ and $T=100C,$ find $x_1$ and $P.$

$13\mathrm{.}10.$ Problems

$517$

$($c$)$ Given $x_1=0\mathrm{.}33$ and $P=120$kPa, find $y_1$ and $T.$

$($d$)$ Given $y_1=0\mathrm{.}33$ and $P=120$kPa, find $x_1$ and $T.$

$($e$)$ Given $T=105C$ and $P=120$kPa, find $x_1$ and $y_1.$

$($f$)$ For part $($e$),$ if the overall mole fraction of benzene is $z_1=0\mathrm{.}33,$ what molar fraction of the two$-$phase system is vapor?

$($g$)$ Why is Raoult's law likely to be an excellent VLE model for this system at the stated $($or computed$)$ conditions?