Question

Hydrogen gas is allowed to permeate through a thin plastic membrane that is 109 microns thick. Concentrations of 0.025 moles /m3 and 0.0025moles/m3 are maintained on the high and low pressure sides of the membrane, respectively. If the diffusivity of hydrogen gas molecules in the plastic is 4.1×10−8 m2/s, how many moles of hydrogen gas pass through a 4.0 square meter area of the plastic membrane every hour? Hint: Compare to the previous question and note that the plastic membrane may have changed thickness and also chemical identity may have also changed. A change in the latter would also likely change the diffusion coefficient (make sure you understand why). Here we are computing a flow rate of hydrogen gas, rather than a flux of hydrogen gas. Recall that a flow rate is equal to a flux multiplied by an area of interest, and its units are generally count / time. In this case specifically, the flow rate units will be mol / hour. In other scenarios, the units could be gram / hour, atom / hour, molecule / hour, etc.

Answer 1

To find the flow rate of hydrogen gas through a plastic membrane, use Fick's first law to calculate the flux, and then multiply by the membrane area and the time in seconds. Convert the final value to moles per hour.

Step-by-step explanation:

The problem is a classic example of steady-state diffusion through a membrane, as described by Fick's first law of diffusion. To calculate the number of moles of hydrogen passing through the membrane, we first calculate the flux (J), then multiply by the area and the time to get the flow rate. Flux (J) is given by the equation:

J = -D (dC/dx)

Where J is the flux, D is the diffusivity of hydrogen in the plastic membrane, dC is the concentration difference across the membrane, and dx is the thickness of the membrane. Substituting the given values, we get:

J = -4.1×10⁻⁸ m²/s × (0.025 mol/m³ - 0.0025 mol/m³) / (109×10⁻⁶ m)

After calculating the flux, the flow rate (Q) can be found by multiplying the flux by the area (A) and converting the units from seconds to hours:

Q = J × A × time

Using A = 4.0 m² and time = 3600 s (1 hour), we can find the total moles of hydrogen passing through the membrane per hour.