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

Answer:

The answer is "$\bold{ 259.2 \times 10^{11} }$".

Explanation:

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

$M= -DAt \frac{\Delta C}{ \Delta x}$

$D =1.0 \times 10^{8} \ \ \ \frac{m^2}{s} \\\\ A = 0.20 \ m^2\\\\t = 1\ \ h = 3600 \ \ sec$

calculating the value of $\Delta C:$

$\Delta C =C_A -C_B$

  $= 2.4 - 0.6 \\\\ = 1.8 \ \ \frac{kg}{m^3}$

calculating the value of $\Delta X:$

$\Delta x = x_{A} -x_{B}$

     $= 0 - (5\ mm) \\\\ = - 5 \ \ mm\\\\= - 5 \times 10^{-3} \ m$

$M = -(1.0 \times 10^{8} \times 0.20 \times 3600 \times (\frac{1.8}{-5 \times 10^{-3}}))$

    $= -(1.0 \times 10^{8} \times 720 \times (\frac{1.8}{-5 \times 10^{-3}})) \\\\= -(1.0 \times 10^{8} \times \frac{ 1296}{-5 \times 10^{-3}})) \\\\= (1.0 \times 10^{8} \times 259.2 \times 10^3)) \\\\= 259.2 \times 10^{11}$