A hydrogen storage tank maintains a constant internal concen

A hydrogen storage tank maintains a constant internal concentration of hydrogen of 400moles/m³. Assume D= 2x10^-8 m²/s for hydrogen in iron. If the tank wall has a thickness of 0.8 cm and a surface area of 1.5 m², how much hydrogen would leak through the tank walls through diffusion in one day? Assume there is no hydrogen in the surroundings and steady-state diffusion.

Solution

Hydrogen diffuses through the storage tank.The tank wall is considered to be a flat plate:
N_a/A = -D (C_a2-C_a1)/ (x₂-x₁)

= 2*10^-8*(400-0) / (0.8*10^{-2) =} 10 * 10^-4 MOL/sm²

m_{a =} 2 * 10 * 10^-4 gm/sm^{2 (}Molar mass of hydrogen is 2 gm/mol)

For surface area = 1.5 m²

m_a\'=1.5*m_a = 3*10^-3 gm/m²

For a day hydrogen leak:

M_{a =} m_a\' * 24 *60*60 =259.2 gm