Question

Compute the number of kilo- grams of hydrogen that pass per hour through a 6-mm-thick sheet of palladium having an area of 0.25 m^2 at 600°C. Assume a diffusion coefficient of 1.7 x 10^8 m^2/s, that the 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.

Answer 1

The number of kilo- grams of hydrogen that pass per hour through this sheet of palladium is
`4.1 * 10^(-3) (kg)/(h)`

Step-by-step explanation:

Given

x1 = 0 mm

x2 = 6 mm = 6 *
`10^(-3)` m

c1 = 2 kg/
`m^(3)`

c2 = 0.4 kg/
`m^(3)`

T = 600 °C

Area = 0.25
`m^(2)`

D = 1.7 *
`10^(8) m^(2)/s`

First equation

J = - D
`(c1 - c2)/(x1 - x2)`

Second equation

J =
`(M)/(A*t)`

To find the J (flux) use the First equation

J = - 1.7 *
`10^(8) m^(2)/s` *
`(2 kg/m^(3) - 0.4 kg/m^(3))/(0 - 6 * 10^(-3) ) = 4.53 * 10^(-6) (kg)/(m^(2)s )`

To find M use the Second equation

`4.53 * 10^(-6) (kg)/(m^(2)s)` =
`(M)/(0.25 m^(2) * 3600s/h)`

M =
`4.1 * 10^(-3) (kg)/(h)`