A saturated-liquid feed stream containing 40 mol% n-hexane (H) and 60 mol% n-octane is fed to a plate column. A reflux ratio L/D equal to 0.5 is maintained at the top of the column. An overhead product of 0.95 mole fraction H is required, and the column bottoms is to be 0.05 mole fraction H. A cooling coil submerged in the liquid of the second plate from the top removes sufficient heat to condense 50 mol% of the vapor rising from the third plate down from the top.

(a) Derive the equations needed to locate the operating line.

(b) Locate the operating lines and determine the required number of theoretical plates if the optimal feed plate location is used.