### How many liters of solution can be theoretically purified

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Problem 1: Packed beds with adsorbent material are frequently used in pharmaceuti- cal industry for affinity chromatography based purification. The proteins to be separated are labeled with molecular tags that interact with the surface of the adsorbent packing and cause the proteins to stick to the adsorbent. Your company has designed a new adsorbent. In theoretical modeling, the capacity of adsorption is predicted to be 2.1 ?mol protein/m2adsorbent. The material density of this solid adsorbent is 1.9 g/mL.

For some bench top studies, you ordered 3 million spherical pellets of the adsorbent with a particle diameter of 1.5 mm to pack in a 10 L column. Instead of spherical pellets, the manufacturing company delivered cylindrically shaped particles with a length of 1.5 mm and diameter of 1.5 mm.

(i). Due to the error in delivery, what is the percentage change that will occur in the following when the column is filled with the cylindrical versus the spherical particles

the void fraction of the column. Void fraction is defined in the end of chapter problem 3.10 moles of protein that can be immobilized on the adsorbent based on the laboratory rate of adsorption

the bulk density of the packed column in kg solid/L of column.

(ii). If a solution containing 3 ?mol of protein/L is to be purified, how many liters of the solution can be theoretically purified with the column filled with spherical particles versus a column filled with cylindrical pellets.

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