A cell mono layer used in a tissue engineering scaffold adheres onto the top surface of a silicone rubber (polymer) sheet of 0.10 cm thickness, as shown in the figure below. The rectangular sheet is 5.0 cm by 10.0 cm. The underside of the silicone polymer layer is in contact with pure O₂gas. The O₂gas dissolves into the polymer and diffuses through the polymer to the adhered cells to deliver oxygen to them. The solubility of dissolved O₂in the silicone polymer is defined by a linear relationship p_A= C'_A/S, where p_Ais the partial pressure of O₂gas (atm), S is the solubility constant of O₂dissolved in the silicone polymer (S = 3.15 × 10^-3mmole O₂/cm³· atm at 25ºC), and C'_Ais the concentration of O₂dissolved in the silicone rubber (mmole O₂/cm³). The process is isothermal at 25^oC. The molecular diffusion coefficient of O₂in silicone rubber is 1 × 10^-7cm²/s at 25^oC. It is assumed that (1) the cells are oxygen-starved, and so any O₂that reaches the cell layer is immediately consumed and that (2) the cells consume O₂by a zero-order process that is not dependent on dissolved O₂concentration. It is determined that the sustainable O₂consumption rate of the cell mono layer is fixed at 1.42 × 10^€“5O₂mmole O₂/min (0.0142 μmole O₂/min). What the required O₂partial pressure (p_A) required to for the diffusion process to enable this O₂consumption rate?

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Liquid medium Cell monolayer (consumes O2) | = 0.10 cm Silicone polymer NA 100% O2 gas