Hydrogen gas is purified by causing it to diffusion through

Hydrogen gas is purified by causing it to diffusion through a thin sheet (diaphragm) of palladium (Pd). Having a much smaller atom size than other gases in air, hydrogen diffuses much faster by an interstitial mechanism.

If the diffusion coefficient of hydrogen in palladium is 1.0x10^-8 m²/s, how many kilograms of hydrogen will pass per hour through a 4.0 mm thick sheet of palladium having an area of 0.10 m² at 600°C? Assume that the concentrations of hydrogen at the high-pressure and low-pressure sides of the palladium sheet are 2.0 and 0.5 kg of hydrogen per cubic meter of palladium and that the source and sink are very large volumes.

Solution

According to fick\'s law

mass of hydrogen that passes =   J * A * ( Co - Cf) * 3600 / t

                                              = 10^-8 * 0.1 * (2 - 0.5) * 3600 / 0.004

                                              = 0.00135 kg   in an hour