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...

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.