This question is incomplete, the complete question is;
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 5-mm-thick sheet of palladium having an area of 0.20 m² at 500C.
Assume a diffusion coefficient of 1.0 × 10⁻⁸ m²/s, that the concentrations at the high- and low-pressure sides of the plate are 2.4 and 0.6 kg of hydrogen per cubic meter of palladium, and that steady-state conditions have been attained
Answer:
the number of kilograms of hydrogen that pass per hour through is 2.592 × 10⁻³ kg
Explanation:
Given the data in the question;
thickness of sheet t = 5 mm
Area A = 0.20 m²
Temperature T = 500°C
diffusion coefficient ∝ = 1.0 × 10⁻⁸ m²/s
concentration high pressure side C[tex]_A[/tex] = 2.4
concentration low pressure side C[tex]_B[/tex] = 0.6 kg
from the question, we calculate the concentration gradient
dc/dx = (C[tex]_A[/tex] - C[tex]_B[/tex])/dt
so we substitute
dc/dx = (2.4 - 0.6) / ( - 5 × 10⁻³ )
dc/dx = -360
now, mass of hydrogen per hour that diffuse through a pd sheet
M = -∝AT(dc/dx)
where time t is 1 hour ( 3600 sec )
we substitute
M = -(1.0 × 10⁻⁸) × 0.20 × 3600 (-360)
M = 0.002592
M = 2.592 × 10⁻³ kg per one hour
Therefore, the number of kilograms of hydrogen that pass per hour through is 2.592 × 10⁻³ kg
