A pressure vessel contains a large volume of CO2 gas at 10 atm pressure. A membrane composed of a poly(ether ketone) polymer with thickness 100 microns and net effective area of 100 cm2 covers a small perforated port in the container. The solubility of CO2 at 10 atm is 6.97 x 10-4 moles/cm3 at 35 ∘C. The diffusivity of CO2 in the polymer is known to be 2.29 x 10-8 cm2/s at this temperature. How long will it take for 0.001 moles of CO2 to leak from the container at steady-state? Assume that the amount of carbon dioxide in the surroundings is insignificant. Express your answer in hours.

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a) 1.74

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Anyone know b)?

b) 0.551

To find the time it takes for 0.001 moles of CO2 to leak from the container at steady-state, we can use Fick's Law of Diffusion. Fick's Law states that the rate of diffusion is proportional to the concentration gradient and the diffusion coefficient, and inversely proportional to the thickness of the membrane.

First, let's calculate the concentration difference across the membrane. We know the solubility of CO2 at 10 atm is 6.97 x 10^-4 moles/cm^3. Since we want to find the time it takes for 0.001 moles to leak, we have:

Concentration difference = (0.001 moles) / (100 cm^2 * 0.0001 cm) = 0.1 moles/cm^3

Next, we can calculate the diffusion rate using Fick's Law. The diffusion rate is given by:

Diffusion rate = (Diffusion coefficient) * (Concentration difference) / (Membrane thickness)

Plugging in the values we know:

Diffusion rate = (2.29 x 10^-8 cm^2/s) * (0.1 moles/cm^3) / (100 microns * 0.0001 cm/micron) = 2.29 x 10^-5 moles/(cm^2 s)

Now, we can find the time it takes for 0.001 moles to leak using the formula:

Time = (Amount of CO2) / (Diffusion rate)

Plugging in the values:

Time = (0.001 moles) / (2.29 x 10^-5 moles/(cm^2 s)) = 43.63 seconds

Finally, we need to convert the time from seconds to hours:

Time = 43.63 seconds * (1 minute / 60 seconds) * (1 hour / 60 minutes) = 0.0121 hours

Therefore, it will take approximately 0.0121 hours for 0.001 moles of CO2 to leak from the container at steady-state.