A continuous distillation unit receives a saturated liquid tertiary mixture at a flow rate of 450kmolhrr1. The feed contains 40 mole \% A, 35 mole \% B and 25 mole %C. Through the distillation process, a distillate that has at least 92 mole \% A and no more than 6 mole %B, and a bottom product that has 6 mole %A are to be acquired. The distillation column operates at a reflux ratio of 2.8. A partial reboiler and a total condenser are used. It is known that the relative volatility of component A to C,AC, is 2.4 and AB is 2.0 over the working temperature and pressure range. A. Determine the flow rate of the distillate and bottom products. B. Calculate the mole fractions of all components in both the distillate and the bottom product stream. C. Use Fenske's method and determine the minimum number of plates. D. Apply Lewis-Matheson method to find the compositions of the liquid stream on the first tray from the bottom of the column. And show your derivation of the operating line equations and the vapour liquid equilibrium relations you use. Comment on the possible assumptions needed for the use of this method