A new type of porous material serves as food packaging film, as shown in the figure below. The film rests on a nonporous metal plate. The packaging film is 0.20 cm thick (2.0 mm). The food contains liquid water, which exerts a vapor pressure of 0.030 atm at 25 C. At 25 C, the effective diffusion coefficient of water vapor in the porous film is 1.3 x 10^-4 cm2/s, and the molecular diffusion coefficient of water vapor in air is 0.26 cm²/s. You may assume that the total system pressure is constant at 1.0 atm, and initially, the gas space of the porous film contains air and no water vapor. How long will it take for the water vapor to achieve a partial pressure of 0.0150 atm at the back surface of the film (z = 0) at 25 C?

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Food (contains liquid water) Porous film (air + water vapor) Nonporous metal plate -z = L = 0.2 cm -z = 0