We are interested in the diffusion of CO₂gas out of a randomly porous adsorbent material slab of 2.0 cm thickness, as shown in the figure below. Initially, the gas space inside the porous material contains 10% mole CO₂(A) and 90 mole% air (B). The process is maintained at 25^oC and total system pressure of 1.0 atm. At these conditions, the binary molecular diffusion coefficient of CO₂in air is 0.161 cm²/s, but the effective diffusion coefficient of CO₂within the porous medium is only 0.0 10 cm²/s. Fresh air containing no CO₂blows over the surface of the slab so that the convective mass-transfer coefficient for CO₂transfer (k_c) is 0.0025 cm/s. How long will it take for the CO₂concentration of the gas space inside the porous material to be reduced to only 2.0 mole% CO₂at a depth of 1.6 cm from the exposed surface of the slab?

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CAO Air flow (no CO2) CAS Boundary layer Exposed surface Porous L = 2.0 cm 1.6 cm slab YAO = 0.10 (CO2) Inert surface