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. A purification process occurs at 700oC through a sheet of palladium with a cross sectional area of 2.16 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 3 grams of Hydrogen is removed from the purified side of the metal every 9.9 hours, what is magnitude (absolute value) of the concentration gradient that drives this steady-state diffusion process, in g/cm4?

Explanation / Answer

Answer:

For steady state condition, we follow : J= -D*dc/dx -------------- equation 1

Where , D= Diffusivity, J=  number of atoms pass through a unit area in unit time. and dc/dx= concentration gradient

As given in the question, D= 1.2x10-6 cm2/s and area = 2.16 m2= 21600cm2

Now, J = 21600cm2 * 3gm * 9.9 hours( 35640 seconds)= 2309472000 cm2/s

Now, put values in equation 1, we get:

2309472000= -1.2x10-6 * dc/dx

Hence, dc/dx= 2309472000 / 1.2x10-6

dc/dx = 1924560000 * 10 6gm/ cm4

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