$4\mathrm{.}10.-$ A stream of $223$ kmol$/$h composed of $44\%$ cyclohexanone, $23\%$ cyclohexanol and $33\%$ phenol must be fractionated into a distillate product containing $99\%$ of the cyclohexanone fed and into a bottom product containing $99\%$ of the cyclohexanol fed. A column with a total condenser and a partial reboiler will be used.

a$)$ Select the key components of the process and make a first estimate, through external material balances, of the distribution and concentration of each component in the distillate and bottom streams.

b$)$ Calculate the minimum number of theoretical stages using the Fenske equation. Consider a bubble temperature of $100$C in the condenser. Consider a pressure drop across the tower of $50$ kPa; That is$,$ the pressure in the reboiler will be $50$ kPa higher than that in the distillate.

c$)$ For the minimum number of stages above, estimate a new distribution of components in the distillate and bottoms streams. Compare it with the one obtained in section $($a$).$

d$)$ Calculate the minimum reflux ratio using Underwood's equations. Consider the feed at its bubble temperature $($saturated liquid$).$

e$)$ Using the above results, use the Gilliland correlation to estimate the theoretical number of stages required when the reflux ratio is $1\mathrm{.}5$ times the minimum. Obtain the optimal location of the feeding stage. "Please could you tell me how to obtain rehevridos temperature?