Question

Please calculate the steady state flux of atomic hydrogen, and then calculate the time for dissipation.

Problem 1 (2 marks) Estimate the steady-state flux of atomic hydrogen at 25 °C through a steel vessel of wall thickness 4 mm given that its inside surface is kept saturated with hydrogen at a concentration of 4.2 moles m ; the outside surface is exposed to the atmosphere. The diffusivity of hydrogen in a-iron is D. = 0.1 mm ?s?, Q = 13.4 kJ mol?. If the vessel contains 20 moles of hydrogen, estimate the hours taken to dissipate all of the hydrogen given that the vessel has a surface area of 2m². Comment on why it is possible to store hydrogen gas in iron cylinders for much longer periods. How does dissolved hydrogen affect the mechanical properties of a-iron?

Answer 1

We will use Fick's law of diffusivity for the question. All the numerical values have been aptly taken care of, along with dimensions. All the parts have been answered. Hope it helps.

Tick's first low, J = - Dac ax where I is the flex (moles m2 sec 2) Diffusivity of hydrogen and-irong D= Do e a where Do is constant o is activation energy Ris gas constant Tis temperature. is concentration x is thickness of wall Given that concentration of hydrogen within the vessel in contact with air can be taken O, - la = 4,2-0 =4.2moles in 3 Do= 0,1 mm² sec ² = 0,1x10 meseca &= 13,4 kJ mol = 134 Go Innol I R = 8,314 I mot kl T225°C = 298K ac = 4,2 moles m 4.2 moles in? 2x 4mm 4x103 m O/RT . Steady state flux, J = Do é ac P 6-13400 2 4.2 er 8,314x298J 4X203

= 1.05x16"exp (-5,4085) = 1.05x154x44783 x 103 = 4.7810 7 moles m? see a Moles through 1 m² in 1 see = 4,7X10 moles i. Moles through m 2 in 1 sec = 4.78107x2. moles Moles through 2 m² in 1 h (3600 sec) = 4,7x107x2X 3600 molos = 3,38 4 x 10s moles through 2m² - 2 Time taken to dissipate zo moles O moles 3,384X103 moles het - 5910 hr 1 omin It is possible to store hydrogengas in iron cylinders for very long time because hydrogenegas is essentially fly , which has negligible solubility in iron. Dissolved hydrogen embrittles &-iron (called hydrogen embrittlement) . It does so by reducing the energy required to generate new surfaces, thus making any fracture easier to occur.