Question

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 m^2 at 500°C. Assume a diffusion coefficient of 1.0 x 10^8 m^2 /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 1

The answer is "
`\bold{ 259.2 * 10^(11) }`".

Step-by-step explanation:

The amount of kilograms, which travel in a thick sheet of hydrogen:

`M= -DAt (\Delta C)/( \Delta x) \\\\`

`D =1.0 * 10^(8) \ \ \ (m^2)/(s) \\\\ A = 0.20 \ m^2\\\\t = 1\ \ h = 3600 \ \ sec \\\\`

calculating the value of
`\Delta C:`

`\Delta C =C_A -C_B`

`= 2.4 - 0.6 \\\\ = 1.8 \ \ (kg)/(m^3)`

calculating the value of
`\Delta X:`

`\Delta x = x_(A) -x_(B)`

`= 0 - (5\ mm) \\\\ = - 5 \ \ mm\\\\= - 5 * 10^(-3) \ m`

`M = -(1.0 * 10^(8) * 0.20 * 3600 * ((1.8)/(-5 * 10^(-3)))) \\\\`

`= -(1.0 * 10^(8) * 720 * ((1.8)/(-5 * 10^(-3)))) \\\\= -(1.0 * 10^(8) * ( 1296)/(-5 * 10^(-3)))) \\\\= (1.0 * 10^(8) * 259.2 * 10^3)) \\\\= 259.2 * 10^(11) \\\\`