Living cells immobilized within an agarose gel require glucose to survive. An important aspect of the biochemical system design is the effective diffusion coefficient of glucose into the agarose gel itself, which you may consider as a homogeneous material that is mostly liquid water. Consider the experiment shown in the figure below, where a slab of the agarose gel of 1.0 cm thickness is placed within a well- mixed aqueous solution of glucose maintained at a concentration of 50 mmole/L(1.0 mole = 1000 mmole), which is relatively dilute. The solubility of the glucose in water is equal to the solubility of glucose in the gel. A syringe mounted in the center of the gel carefully excises a tiny sample of the gel for glucose analysis. Initially, there is no glucose in the gel. However, after 42 hours, the measured concentration of glucose in the gel at the sampling point is 48.5 mole/m³. Based on this measurement, what is the effective diffusion coefficient of glucose into the gel?

Transcribed Image Text:

Agarose Gel (no cells) (1.0 cm thick) Glucose (50 mmole/L) Glucose (50 mmole/L) Sampling syringe (center of gel)