# The permeability of solids by gases is experimentally determined by steady-state diffusion…

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
»

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 DA2 is the diffusivity of
A2 through the membrane. When standard pressures are employed with a
membrane of standard thickness, JA2 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.

»

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