A distillation column is a process unit in which a feed mixture is separated by multiple partial vaporizations and condensations to form two or more product streams. The overhead product stream is rich in the most volatile components of the feed mixture (the ones that vaporize most readily), and the bottom product stream is rich in the least volatile components. The following flowchart shows a distillation column with two feed streams and three product streams:

(a) How many independent material balances may be written for this system?

(b) How many of the unknown flow rates and/or mole fractions must be specified before the others may be calculated? Also; remember what you know about the component mole fractions of a mixture?for example the relationship between x₂ and y₂. Briefly explain your answer.

(c) Suppose values are given for m and x2. Give a series of equations, each involving only a single unknown, for the remaining variables. Circle the variable for which you would solve. (Once a variable has been calculated in one of these equations. it may appear in subsequent equations without being counted as an unknown.)

m(kg/h) 0.03 kg 8/kg 0.97 kg C/kg 5300 kg/h x(kg A/kg) y(kg B/kg) m3(kg A/h) 1200 kg/h 0.70 kg A/kg Y4(kg B/kg) (kg C/kg) ms(kg/h) 0.60 kg 8/kg 0.40 kg C/kg