Problem 5.8 The purification of hydrogen gas by diffusion through a palladium sh

Question

Problem 5.8 The purification of hydrogen gas by diffusion through a palladium sheet was discussed in Section 5.3. Compute the number of kilograms of hydrogen that pass per hour through a 6-mm thick sheet of palladium having an area of 0.25 m2 at 600°C. Assume a diffusion coefficient of 1.7 × 10–8 m2/s, that the respective concentrations at the high- and low-pressure sides of the plate are 2.0 and 0.4 kg of hydrogen per cubic meter of palladium, and that steady-state conditions have been attained.

Explanation / Answer

For mass:

M = -DAT*dC/dx

where M is the mass of hydrogen and its respective diffusion coefficeidn Da

dx = Xa-xb

so..

dx = (0- 6*10^-3) = -6*10^-3 m (direciton gradient)

dC = Ca-Cb

so

dC = 2-0.5 = 1.6 kg/m3

so

D = 1.7*10^-8 m2/s

for A = 3600 s so...

M = -DA*dC/dx

M = -17*10^-)(0.25)(3600=(1-6)/(-6*10^-3)

M = 0.00408 kg

M = 4.08*10^-3 kg

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