Assignment#$1-$final part $(5pts)$

Q$)$ A mixture of $30\%$ benzene, $25\%$ toluene, and $45\%$ ethyl benzene is to be separated by distillation at atmospheric pressure, with $98\%$ of the benzene and only $1\%$ of the toluene in the distillate $($all in mole $\%).$ Given that ${}_{\text{b}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}=2\mathrm{.}25,{}_{\text{t}\text{o}\text{l}\text{u}\text{e}\text{n}\text{e}}=1\mathrm{.}00,{}_{\text{e}\text{t}\text{h}\text{y}\text{l}\text{b}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}=1\mathrm{.}23.$ Based on the feed rate of $100$ kmo$\frac{l}{h}.$

a$)$ Calculate the minimum number of ideal plates and the approximate compositions of the products

b$)$ Estimate the concentration of ethyl benzene in the distillate.

c$)$ Calculate minimum reflux ratio of all possible cases.

d$)$ Estimate the total number of equilibrium states and the optimal feed stage if the actual reflux ratio is set at $1\mathrm{.}8.$