Q$1)$

$1000$kmo$\frac{l}{h}r$ of a feed containing $30\%$moln$-$hexane and $70\%n-$octane is to be distilled in a column consisting of a partial re$-$boiler, one equilibrium $($theoretical$)$ plate, and a partial condenser, all operating at $1$atm. Thus, hexane is the light key and octane is the heavy key. The feed is at the bubble point and a reflux ratio $2$ is returned from the partial condenser to the column. Assuming the relative volatility is equal to $5,$ the vapour distillate contains $80\%$mol hexane and the vapour distillate is in equilibrium with the reflux $($i$.$e$.y{D}_D=x_R),$ apply McCabe$-$Thiele method to calculate the bottom composition and the rate of distillate produced $($ kmo$\frac{l}{h}r)$ for the following two cases:

i$-$ The feed is entered to the re$-$boiler

ii$-$ The feed is introduced on plate no$\mathrm{.}1,$ and only three plates are used in the column including the partial re$-$boiler.