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
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
posted by Dr. B at 8:54 AM
10 Comments:
All the formulas I gave you in class for Gaussian peaks were written in terms of t and t0. But since t = Vbed/V where V is the volume eluted through the column, t/t0 = V/V0. So, for this problem, the first step is to rewrite the eqn for a Gaussian peak in terms of the volume eluted at time t (which is V) and the volume eluted at the max of the peak V0 (at t0). I hope this helps.
Do we have to use the error function to calculate the yield? Moreover, what is t' in this problem?
V=174L, and Vo=peak=190L, right? So when you do V/Vo and then subtract one from it in the yield equation, it will give you a negative number, but the erf() cant do a negative number. Is something wrong here?
Anon:
Yes, you do need to use the error function to evaluate the yield. The function, "ERF" in Excel will do the trick for you.
In this problem, the fractions begin at time zero, so t' = 0.
spastic:
Yes, V=174L, and Vo=peak=190L.
Erf(infinity) = 1
Erf(0) = 0
Erf(-x) = - Erf(x)
That should make everything work for you ! I am sorry I did not put this in the hints.
Dr. Phil, 8:24:
Yes, rewrite the Gaussian peak eqn in terms of V and V0 and solve for either sigma or sigma*V0 (the dimensional form of the standard deviation). I used 190 L to determine V) (easy) and then used {174L, 0.0063) to solve for sigma or sigma*t0.
No, the yield is from t' to t or in this case from 0 to t0, so the yield is not zero. V'/V0 = 0, not 1.
Dr. Phil 8:51:
You use 174 L to determine sigma or sigma*t0. Then, use sigma or sigma*t0 to calculate the yield at 200 L. You should be able to state the yield at 190L without doing any calculations.
I wonder if erf(0) supposed to be = 0.5 instead of 0 as you posted earlier?
OK, here is the issue that has confused several people.
t' = 0 in the lab, but in the equations for the Gaussian peak and the Yield, t' = -infinity.
This may help on some other problems as well.
Va:
Nope, erf(0) = 0. But erf(-infinity) = -erf(infinity) = -1
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