A rectification column is fed $100$ kmol$/$h of a mixture of $50$ mol $\%$ benzene and$50$ mol $\%$ toluene at $101\mathrm{.}3$ kPa abs pressure. The feed is saturated vapor at the$$dew point. The distillate is to contain $90$ mol $\%$ benzene and the bottoms $10$mol$\%$ benzene. Average relative volatility of Benzene $$ Toluene is equal to $2\mathrm{.}5$

Calculate the $($i$)$ Minimum reflux ratio $($ii Minimum number of theoretical

plates at total reflux $($iii$)$ Theoretical number of trays at an operating reflux ratioof $1\mathrm{.}5$ times the minimum reflux ratio