An equimolal mixture of A and B with a relative volatility of 2.3 is to be separated into a distillate product with 98.5 percent A. a bottoms product with 2 percent A. and an intermediate liquid product that is 80 percent A and has 40 percent of the A fed. 

(a) Derive the equation for the operating line in the middle section of the column, and sketch the three operating lines on a McCabe-Thiele diagram. 

(b) Calculate the amounts of each product per 100 moles of feed, and determine the minimum reflux rate if the feed is liquid at the boiling point. 

(c) How much greater is the minimum reflux rate because of the withdrawal of the side-stream product?