Question

Problem: When alpha-iron is subjected to an atmosphere of hydrogen gas, the concentration of hydrogen in the iron, CH (in weight percent), is a function of hydrogen pressure, PH2 (in Mpa), and asbsolute temperature (T) according to Ch= 1.34 x 10-2 sqrt(PH) exp(- (27.2KJ/mol) /RT) Consider a thin iron membrane with the thickness and temperature listed below. Calculate the flux in (kg/(m²-s)) through this membrane if the hydrogen pressure on one side of the membrane is 0.17 MPa, and on the other side it is 6.1MPa, utilizing the densities provided by your examination booklet. Assume the values for Do is 4.9x107m²/s and Qs is 13.4KJ/mol. --Given Values-- Membrane Thickness (mm) = 4.4 Temperature in Celsius = 315 Part A: What is the concentration of hydrogen at the low-pressure (or B) side in wt%? Write your answer in Engineering Notation. Your Answer = Part B: What is the concentration of hydrogen at the low-pressure (or A) side in wt%? Write your answer in Engineering Notation. Your Answer = Part C: What is the concentration of hydrogen at the B face in kilograms of H per cubic meter (Density for Hydrogen is 7.87 g/cm)? Write your answer in Engineering Notation.

Answer 1

(1) The hydrogen ang CHCB) = 1.34 x162 x152 JP He exp 27.2 KJ/mol RT where, R=gos constant = 8.314 J/mol- T= absolute Temperature = 315+273 - 588K PH2 = pressure at low pressure si de = 0.17 Mpa. CHCB) (1-34x164) (JoJa mpa).exe [ 27.2 KJ/mol (8.314 5/mo1).(1886) 2:118X105 wt% CH(B) Ary (2) The hydrogen concentrcution at Resh pressure síce (CH) CA(A) = 1.34 X15² JP Ha exp. 272 KJ/mol RT > PHg = pressure at high pressure side= Gimpa. CHCA) = (1.34 x162) (Jessmpa). exp 27-2810 J/mol (8.314 5/mo) (588K) (HCA)= 1.268x154 % Volume of Iron at low pressure aide (VB): - 100 VB Pfe. where, Ire= density of Iron = 7.87 g/cm? 100g 2) VB 7-879/cm3 = 12.7 cm (109) = 1.97X165 m2

(3) The concentration of hydrogen at low pressure dicle in kg of hydrogen hydrogen per cubic meter of alley (CH (B)). CACIB) CHCB) VB 2.18x69 1.27x105 m² 1.667X163 kg I mi? Clu(3) Any concentration of hydrogen at high presseux side (c'Aca)) CMCA) CHCA) VA 1.268x10 1. 27x185 mi 9.984x18 Kalma CHCA) -Ary б) The concentration gradient Cen). AC с нео) - салу زخ Ax Ara Thecleness of membeane = 4.4 mm - 4.4x15m AC ) (1•667x X10 AX 63 kg/mp) - (9.984 xió? Kelma) 4.4 xiom | . AC De j = -1.89 Kelmy Ang (6) The diffusion coefficient (D) :- D = Doexp(-es) Where Do =) Temperature independent expre-exponential 4.9x107 mols. Qd5 Activation encegy for cliffusion = 13,400 J/mol.

D= (4.9ximºys) exp [- 13,466 T/mo) (8.314 J/molk)(588K [ད། D = 3.16 X168 m/s Ang (A) The Diffusion flux for steady stult cliffusion (J) = do de 9 J=-(3.16x109 m2/8) (-1.89 kg /my) J = 5.9724 X108 Kelimis Ars: Therefore, the diffusion flux through the membrane is : 15.972x168 kg / m²