Proteins can be extracted without denaturation into solutions of isooctane containing the detergent Aerosol OT. The proteins are solubilized within inverted micelles of detergent. Because the amount solubilized is a strong function of pH, the proteins can be extracted into the organic at one pH, often near the isoelectric point, and then later stripped at a different pH. You are studying an aqueous solution containing 0.2 vol\% protein, for which at the isoelectric point, x=2.9y where x is the protein concentration in the organic phase and y is the equilibrium concentration in the aqueous phase. You have 6.8 liters of this solution and 3.8 liters of organic solution. (a) What are the raffinate concentration and fraction extracted if you contact the two solutions in one stage? (b) What are they if you contact the solutions in three countercurrent stages? (c) What are they if you use a 2.0m column in which the HTU (based on the aqueous concentration) is 0.85m