A distillation column is used to separate benzene and toluene by distillation. The relative volatility for this system is approximately 2.5 with benzene the more volatile component. a) To find the height equivalent to a theoretical plate a packed column is operated at total reflux. The distillate and bottoms compositions are measured to be 0.9 and 0.05 respectively in mole fraction of benzene. Determine the number of equilibrium stages in this column using both the Fenske equation and the McCabe-Thiele method (an equilibrium diagram with =2.5 is included on the next page).  b) If the height of the column is 5 feet, what is the HETP for the column in part a)?  c) Under normal operation, the two-thirds of the feed vaporizes as it enters the column and the feed contains 40 mole% benzene. Plot the q-line.  d) If the distillate composition is 70 mole% benzene, and the reflux ratio (from total condenser) is equal to 2, plot the top operating line and determine optimal location for the feed from part c) (in feet from the top of the column).