We are interested in measuring the effective diffusion coefficient of blue dextran dye into an…

We are interested in measuring the
effective diffusion coefficient of blue dextran dye into an agarose gel. An
aqueous, well-mixed solution containing 1.0 g/L of the dye rests over the rigid
gel of 2.0 cm thickness, as shown below. The solubilities of the dye in both
water and the gel are the same; that is, the concentration of the dye on the
water side of the water–gel interface is equal to the concentration of dye on
the gel side of the water–gel interface. There is no dye initially in the gel.
After 24 h, a tiny section of the gel 2 mm from the surface is very carefully
excised with a
»

We are interested in measuring the
effective diffusion coefficient of blue dextran dye into an agarose gel. An
aqueous, well-mixed solution containing 1.0 g/L of the dye rests over the rigid
gel of 2.0 cm thickness, as shown below. The solubilities of the dye in both
water and the gel are the same; that is, the concentration of the dye on the
water side of the water–gel interface is equal to the concentration of dye on
the gel side of the water–gel interface. There is no dye initially in the gel.
After 24 h, a tiny section of the gel 2 mm from the surface is very carefully
excised with a syringe needle, and the concentration of

the dye within the gel, as measured by a
spectrophotometer is 0.203 g dye/L. An aqueous ‘‘gel’’ is generally considered
a water-hydrated polymer, where solute molecules diffuse through the hydrated
regions.

a. What is the effective diffusion
coefficient of blue dextran dye into the gel based on the experimental
measurements?

b. State at least three assumptions you had
to make to arrive at your answer in part (a).

c. If the system temperature is increased
from 20 to 40C and the
experiment is repeated exactly as described above, what would you expect the
new measured diffusion coefficient to be? The viscosity of water is  at 20C and  at 40C.

»

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