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A protein is being separated on a chromatography column. The protein has been found to obey the Langmuir isotherm, with Stot= 300 µg/mL and Keq= 10 mL/mg. The concentration of the protein in the feed (3 liters) to the column is 2 mg/mL. The column flow rate is 2.0 liters/min. The column is 50 cm in diameter and 100 cm long. The void fraction of the chromatography bed is 0.35. Determine (a) the time for the protein shock front to exit the column, and (b) the time when the concentration of the protein in the diffuse wave is 0.01 mg/mL at the exit of the column.