What is the complete written solution to this problem for all parts.

Please do not use chatgpt or any form of AI$.$

Problem Statement: The feed to a depropaniser column operating at $15$atm contains $6\%$ ethane, $41\%$ propane, $28\%$ i$-$butane, $23\%n-$butane and $2\%n-$pentane. The distillate which leaves the partial condenser as vapour has $98\%$ of the propane from the feed whereas $98\%$ of the of the i$-$butane is recovered in the saturated liquid bottoms product. The partial condenser may be assumed to operate at equilibrium and the reflux ratio is $1\mathrm{.}5R_{\text{m}\text{i}\text{n}}.$ The bottoms product exits the reboiler as a saturated liquid. You may assume negligible pressure drop throughout the tower.

i$.$ the boiling point of the feed

ii$.$ the composition of the distillate and bottoms streams

iii. the condenser outlet temperature

iv$.$ the reboiler outlet temperature

v$.$ the temperature on tray $1$

vi$.$ the minimum number of stages

vii. the minimum reflux ratio

viii. the number of stages required in the distillation tower

ix$.$ the feed tray

$x$ the condenser duty

xi$.$ the reboiler duty

Note: You will need to find your own equilibrium and enthalpy data. Remember to include the reference. Use a constant relative volatility across the tower for each component. Determine the value of the relative volatility at the average tower temperature i$.$e$.$ the average of the temperatures in the condenser and reboiler.