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)
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)
posted by Dr. B at 8:50 AM
6 Comments:
why can't we use yf/y0=sqrt(2*pi*N); since we know yf/y0=1/1.8 and q in the material balance is the concentration of the substance in the solid phase, right?
a :
You can and should use: yf/y0=sqrt(2*pi*N)
to determine N. yF/y0 = 1/0.018.
I do not understand what you mean about q. It is the concentration in/on the solid adsorbent. But I am not entirely sure what material balance you are talking about.
Part (c)
Please plot y/y0 as a function of V not t.
Part (a)
This is the tricky part of this problem.
Use this: V0 = F t0 = Vbed [ epsilon + (1-epsilon) K ]
Where did this come from ?
If there were no packing in the bed,
I hope you can see that V0 = F t0 = Vbed
If we had inert packing in the bed, then: V0 = F t0 = Vbed * epsilon
But with solid packing that can adsorb some of the solute, the column behaves as if it had an EFFECTIVE volume of:
Vbed [ epsilon + (1-epsilon) K ]
where Vbed * epsilon is the volume of the liquid
and Vbed (1-epsilon) is the volume of the solids
and Vbed (1-epsilon) K is the EFFECTIVE volume of the solids that is accessible to adsorbed proteins.
As a result: V0 = F t0 = Vbed [ epsilon + (1-epsilon) K ]
I do not see that Fto=Vbed. I can follow most of the logic in your explain except for the fact that it seems like you are talking about the solute distribution in the part about Vbed and epsilon but started out with simply talking about plain volume in V0 = Ft0. How did you transition from total volume collected to adding a K for solute distribution? If the volumes were multiplied all by a y it would make more sense.
karen:
Because there was no packing in the bed at first and no absorption when I first added a solid phase, there was no need to consider adsorption or y. The concentration was everwhere the same so the mean residence time of the fluid is the same as the residence time of the solute.
Maybe it would be easier to discuss this further in person. It is important, but it really is going into a bit greater depth than I intended.
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