The permeability of solids by gases is experimentally determined by steady-state diffusion measurements. The diffusing solute is introduced at one side of the membrane and removed from the other side...

The permeability of solids by gases is experimentally determined by steady-state diffusion measurements. The diffusing solute is introduced at one side of the membrane and removed from the other side as a gas. For a diatomic gas, A₂, which dissociates upon dissolving into a solid, Sievert’s law relates the concentration of A atoms in the surface layer of the membrane, cA₁, in equilibrium with the applied pressure, p₁, of the diatomic gas by the relation

This same equation also holds at the other surface of the membrane for the off-gas pressure, p₂. Sievert’s law is a variant of Henry’s law for gases that dissociate upon dissolving.

a. Prove that the rate of diffusion of a diatomic gas from a high-pressure reservoir, p₁, through a membrane of thickness z, into a low-pressure reservoir, p₂, is

where D_A2
is the diffusivity of A₂
through the membrane. When standard pressures are employed with a membrane of standard thickness, J_A2
is called the permeability of A₂.

b. A piece of laboratory equipment operating at 700C contains hydrogen gas at 8 atm that is separated from a continuously evacuated space by an 8 cm²
nickel disk, 2 mm thick. The solubility of hydrogen in nickel at 1 atm pressure and 700C is approximately 7.0 cm³/100 g of nickel. The diffusivity of hydrogen through nickel at 700C is
, and the density of nickel at 7008C is 9.0 g/cm³. Calculate the number of cubic centimeters of hydrogen per hour that diffuses through the nickel.