Gaseous hydrogen at 150 psia and 80°F is stored in a small, spherical, steel pressure vessel having an inside diameter of 4 in. and a wall thickness of 0.125 in. At these conditions, the solubility of hydrogen in steel is 0.094 lbmol/ft3 and the diffusivity of hydrogen in steel is 3.0 x 10–9 cm2/s. If the inner surface of the vessel remains saturated at the existing hydrogen pressure and the hydrogen partial pressure at the outer surface is assumed to be zero, estimate:
(a) The initial rate of mass transfer of hydrogen through the metal wall
(b) The initial rate of pressure decrease inside the vessel
(c) The time in hours for the pressure to decrease to 50 psia, assuming the temperature stays constant at 80°F