# Estimation of the Number of Theoretical Plates for Ion Exchange Chromatography of a Protein…

Estimation of the Number of Theoretical Plates for Ion Exchange Chromatography of a Protein Following a Langmuir Isotherm A20cm long ion exchange column is loaded with a protein solution at a concentration of 3 mg/ml and is eluted isocratically at a superficial velocity of 30cm/h. The void fraction is 0.3. The protein has a Keq (Langmuir isotherm) of 1.0 ml/mg, and the columns resin is saturated with the protein at a resin-phase concentration of 10 mg/ml. If the protein peak has a standard deviation of 4.0 min, estimate the number of theoretical plates in the column. 7.16

Estimation of the Number of Theoretical Plates for Ion Exchange Chromatography of a Protein Following a Langmuir Isotherm A20cm long ion exchange column is loaded with a protein solution at a concentration of 3 mg/ml and is eluted isocratically at a superficial velocity of 30cm/h. The void fraction is 0.3. The protein has a Keq (Langmuir isotherm) of 1.0 ml/mg, and the columns resin is saturated with the protein at a resin-phase concentration of 10 mg/ml. If the protein peak has a standard deviation of 4.0 min, estimate the number of theoretical plates in the column. 7.16 Chromatographic Separation of a Protein A protein is being separated on a chromatography column. The protein has been found to obey the Langmuir isotherm, with Stot=300 g/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 50cm in diameter and 100cm 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. 7.17 Chromatography of an Antibiotic with a Freundlich Isotherm The antibiotic cephalosporin C is being purified on a chromatography column packed with XAD-2 adsorbent beads. Adsorption experiments have shown that the equilibrium can be described by the following Freundlich isotherm: q = 1 99 c 0.746 for q and c in units of mg/ml. For an injection concentration of 0.5 mg/ml and elution superficial velocity of 30cm/h, determine the time for the shock wave front to exit a column that is 50cm long and has a void fraction of 0.37 (Data from N.F. Kirkby, N.K. H.Slater, K.H. Weisenberger, F.Addo-Yobo, and D.Doulia, An HPLC technique for parameter estimation for reversed-phase chromatography:Acase study on cephalosporin C, Chem. Eng. Sci., vol 41, p.2005, 1986).

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