$5-14.$ A three$-$tray column is used to concentrate a binary mixture of ethanol and

water. Liquid feed, at a rate of $1,500kg-$mole $\frac{?}{hr}$ and composition of $13$ mole

percent ethanol, is fed to the top tray.

Instead of using a reboiler in the bottom of the column, "live steam" $($pure

water vapor$)$ is fed in at a rate of $1,000kg-$mole$/hr$ below the first tray.

The liquid leaving the column from tray $1$ has a composition of $2$ mole percent

ethanol. Assume equimolal overflow and theoretical trays.

$($a$)$ What is the composition of the vapor leaving the top of the column?

$($b$)$ Assuming a simple VLE relationship $(y=Kx),$ what is the $K-$value in this

system?