Answer Happy

Consider the biosensor device shown in the figure below. The biosensor is designed to measure the concentration of solute A in the well-mixed liquid phase. At the base of the device is an electrode of surface area 9.0 cm². The electrode is coated with an enzyme that catalyzes the reaction 2A → D. When solute A reacts to product D, product D is detected by the electrode, enabling for direct measurement of the flux of product D, which at steady state can be used to determine the concentration of A in the bulk liquid. The rate of reaction of A at the enzyme surface is rapid relative to the rate of diffusion of A down to the surface. Directly above the enzyme-coated electrode is a 1.2 cm thick (= L) gel layer that serves as a diffusion barrier for solute A and protects the enzyme. The gel layer is designed to make the flux of A down to the enzyme-coated surface diffusion limited. Above the gel layer is a well-mixed liquid containing a constant concentration of solute A, c'Ao. The solubility of solute A in the liquid differs from the solubility of A in the gel layer. Specifically, the equilibrium solubility of A in the liquid layer (c'a) is related to the solubility of A in the gel layer (CA) by c'a= K ca, with equilibrium partitioning constant K = 0.8 cm’ gel/cm’ liquid. The process is considered very dilute, and the total molar concentration of the gel layer is unknown. The concentration of product D in the well-mixed liquid is very small so that cpo 20. You would like to design the biosensor to have an easy to interpret relationship between the rate of formation of product D, W., and the corresponding concentration of solute A in the well-mixed liquid. Specifically, you decide to select a gel that will result in a production rate of D in mmol per minute equal to 10 x the concentration of A in the liquid in mol/cm². So, for example, a concentration of component A in the liquid of 2.25 mol/cm² would result in a production rate of component D of 22.5 mmol/min. What must the diffusion coefficient of A in the gel, Dae, be? C'AO z = 0 Ао Well-mixed liquid (C'Ao is constant) Gel layer Enzyme-coated electrode Surface area = 9.0 cm? CA z= L = 1.2 cm 2A →D