Hydrogen gas can be purified by allowing an initially impure mixture of gas to d

Question

Hydrogen gas can be purified by allowing an initially impure mixture of gas to diffuse through a thin sheet of metal. A hydrogen molecule is relatively small. Therefore, it tends to diffuse faster through the metal plate compared to the larger impurity molecules in the "unpure" gas. A purification process occurs at 700oC through a sheet of palladium metal with a cross sectional area of 1.93 m2 . The diffusivity of H2 in palladium at this temperature is 1.2x10-6 cm2/s The impure hydrogen is maintained at a high concentration and the purified hydrogen is maintained at a low concentration by pumping the excess purified gas to a separate storage tank in order to maintain a constant concentration gradient within the palladium plate. If 6 grams of Hydrogen is removed from the purified side of the metal every 1.9 hours, what is magnitude (absolute value) of the concentration gradient that drives this steady-state diffusion process, in g/cm4 ?

Explanation / Answer

Mass transferred = Diffusivity*Area* concentration gradient

1.9 hours = 1.9*60*60 sec = 6840 second

Area = 1.93 m2= 1.93*(100)2 cm2=19300cm2

Hence 1.9/(6840)= 1.2*10-6*19300* concentration gradient

0.000278= 0.02316* concentration gradient

Concentration gradient = 0.000278/0.02316=0.0119 gm/cm4

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