Ethanol$-$water mixture is to be distilled at $1$atm using a batch distillation column, which has $8$

trays plus a reboiler. System is operated under total reflux to reach equilibrium. Afterwards,

samples are taken from the reboiler and the distillate within $30$ minutes time interval, starting from

time $0.$ Pycnometer was calibrated as $10\mathrm{.}540mL$ and the experimental data are tabulated below.

$($a$)(20$ pts$)$ Derive the governing equation for the operating line in an enriching section in a

distillation column.

$($b$)$ pts $)$ Determine theoretical number of trays and overall tray efficiency at the end of the

operation if reflux ratio is $5.$ Use necessary tables provided on the next page. Draw the stages on

the equilibrium data provided.