Mass Transfer: November 2006

HW 9 - SP1 - Gel Permeation Chromatography of Urease - 3 pts

We plan a large scale purification of urease using a packed column of polyacrylamide beads. We obtain the following data.
Volume Eluted (L) , Concentration (arbitrary units)
174 L , 0.0063
190 L , 0.0152 (peak)

The bed volume is 20 L. Determine V0, sigma and the yield at 190 L and at 200 L

HW 9 - SP2 - Affinity Chromatography to Purify an Antibody - 5 pts

We need to purify an antibody which is to used as an affinity adsorbent in the production of a synthetic vaccine. The feed contains 1.63 g antibody and 0.45 g of a protein of similar molecular weight. We use gel permeation chromatography to obtain the following results.
Time(h), Antibody Concentration y1, Impurity Concentration y2
6.42 , 82 , ~ 0
7.00 , 63 , 0.14
7.60 , 28 , 43 (peak)

a.) Use these reults to plot the antibody and impurity yields as functions of time on the same graph.
b.) Plot the purity as a fuction of time.

HW 9 - SP3 - Discrete Stage Analysis of a Chromatographic Column - 5 pts

Ten grams of bovine serum albumin (BSA) is eluted from an 80 L Sephadex column which has a void fraction of 0.40. The concentration in the column peaks after 470 L have been eluted. The maximum concentration, y0, is 1.8% of the concentration in the sample that was injected.

a.) Estimate the equilibrium constant for binding the albumin to Sephadex
b.) Estimate the number of stages in the column
c.) Plot the elution chromatograph for this process. (y/y0 as a function of time)

HW 9 - SP4 - Kinetic Analysis of a Chromatographic Column - 6 pts

Racemic amino acids can be separated using l-proline attached with silanes to the surface of silica gel. In one set of experiments, aspartame isomers gave the following results.

d-aspartame: t0 = 62 min , σt0 = 3 min
l-aspartame: t0 = 71 min , σt0 = 6 min

These results were obtained with a 25 cm column, 0.41 cm in diameter, filled with 45 μm silica gel spheres. The void fraction of the bed was 0.62. The flow in the column was 2.0 mL/min. Find the apparent rate constants for this separation. Compare these rate constants with those predicted from the following mass transfer correlation.

mass transfer correlation

where: d = packing particle diameter, v = superficial solvent velocity, ν = solution kinematic viscosity, D = diffusion coefficient of the solute (7.0 x 10^-6 cm2/s).

HW 9 - SP5 - Scaling Up a Chromatographic Separation of Fumarase - 5 pts

Ten grams of the enzyme fumerase are being purified in an ion exchange chromatography column. At a superficial velocity of 30 cm/h, the peak exits the column in 93 min and the standard deviation of the peak is σt0 = 12 min.

a.) How long must we purify to obtain a 90% yield ?
b.) If we increase the flow to 60 cm/h, how long must we run to obtain the same 90% yield if the process is controlled by diffusion within the packing particles ?
c.) How long must we wait if the process is controlled by external mass transfer ?
d.) How long must we wait if Taylor Dispersion controls the rate of the process ?
e.) How long must we wait if the column actually contains equilibrium stages ?

HW 9 - SP6 - Approximate Analysis of an Elution Chromatograph - 6 pts

Three proteins, A, B and C, are eluted through a pilot plant chromatographic column. The outlet concentration as a function of time was determined using an ultraviolet spectrophotometer. The results appear in the graph shown below.

a.) Estimate y0, t0 and σt0 for each species.
b.) Determine the yield and purity of species B in a fraction collected between t = 30 min and t = 40 min.
c.) What is the concentration of species B in this fraction ?
Elution Chromatograph

HW 9 - SP7 - Electrophoresis of BSA and Human Hemoglobin - 5 pts

A sample of bovine serum albumin (BSA) in solution was placed in a small electrophoretic cell. A laser anemometer measured its velocity as -1.4 x 10-3 cm/sec under the influence of an electric field of 10 V/cm. This experiment was repeated with a sample of human hemoglobin in solution and a velocity of -7.7 x 10-4 cm/sec was observed. Both samples were at 20oC.

a.) How much time is required to separate a mixture of BSA and human hemoglobin by gel electrophoresis ? An electric field of 4 V/cm is used and the initial band width of the mixture is 3 mm. Neglect diffusion. Assume the electrophoretic mobility of the proteins is unaffected by the presence of the gel.

b.) A Rayleigh light scattering experiment yields the diffusion coefficients of macromolecules. This experiment at 20oC yields the following results.

Do20,w (cm2/sec)
Bovine Serum Albumin
6.15 x 10-7
Human Hemoglobin
6.90 x 10-7

What is the charge number, z, of a molecule of BSA ? Human hemoglobin ?

Data: R = 8.314 g-cm2 / sec2-mole-K and F = 96487 coul/equiv

HW 8 - SP1 - Filtration of a Beer Containing Protease - 4 pts

A suspension of Bacillus subtilis has been fermented to produce the enzyme protease. In order to separate the biomass, we added 1.3 times the biomass of a Celatom filter aid, yielding a beer containing 3.6 wt% solids with a viscosity of 6.6 cP. With a Buchner funnel 5 cm in diameter attached to an aspirator, we have found that we can filter 100 mL of this beer in 24 minutes with a pressure drop of 14.7 psi. However, previous studies with this type of beer have had a compressible cake with s = 2/3.

We now need to filter 3000 L of this beer in a plate-and-frame filter press. The press has 15 frames, each with an area of 3520 cm2 on each side. The resistance of the filter medium is much smaller than the resistance of the filter cake.

a.) How long will take to filter the beer at 50 psig ?
b.) How long will it take at 25 psig ?