Question

In the early 1990s, fusion involving hydrogen dissolved in palladium at room temperature, or cold fusion, was proposed as a new source of energy. This process relies on the diffusion of H2 into palladium. The diffusion of hydrogen gas through a 0.005-cm-thick piece of palladium foil with a cross section of 0.780 cm2 is measured. On one side of the foil, a volume of gas maintained at 298 K and 1 atm is applied, while a vacuum is applied to the other side of the foil. After 24 h, the volume of hydrogen has decreased by 14.2 cm3 . What is the diffusion coefficient of hydrogen gas in palladium?

Answer 1

By maintaining constant hydrogen pressure to each side of the sheet then a steady state will be reached with a linear concentration profile in the Palladium sheet

Whereby the concentration gradient wil be

we can get The diffusion coefficient by Fick 's first law

To clear the diffusion coefficient we need to know the flow , which upon reaching steady state we can get just as the number of moles that have passed from one side to the other divided by time. The number of moles that have passed from left to right we can get by lower volume that has occurred since the pressure on that side remains constant

=[[ (760mmHg) * (14.2x10^-6m)]/[(8.3145J K⁻¹ mol⁻¹)*(298K)]]/(24h*3600s)

dn/dt= [0.011*2477.57]/86400s

dn/dt = 5.14x10^-11 mols^-1

Then the diffusion coefficient will be