Consider the concentric tubular mass transfer device shown in the figure below. This device is designed to gradually introduce hydrogen (H₂) gas (species A) into a pure oxygen gas (O₂) inlet stream (species B) delivered to the shell side of the process. Pure H₂ gas enters the tube side of the process. Pure O₂ gas enters the shell side of the process. The tube wall material is only permeable only to H₂, and not to O₂. The system is designed so that the partial pressure of H₂ at the gas interface and the outer surface of the inner tube wall is equal to the total system pressure i.e. p_As = P or y_As = 1.0, down the entire length of the tube. In the present process, the Reynold’s number through the shell side is 10,000, the outer diameter of the inner tube is D_i = 1.5 cm, and the inner diameter of the outer tube is D_o = 2.5 cm. The tube length is L = 10 cm, and the process is carried out at constant 27 C and 1.0 atm total system pressure. For the purposes of this problem, you may assume the process is dilute with respect to H₂ in the O₂ gas stream. 

a. What is the velocity of gas on the shell side of the process?
b. What is the Schmidt number is for H₂ diluted in O₂ gas?
c. What is the convective mass transfer coefficient for H₂ in annular gas space for the H₂ + O₂ gas mixture on the shell side, k_c?

d. Develop a material balance model, in integrated final algebraic form, to predict the outlet mole fraction of H₂ from the shell side of the process, y_AL. At a minimum, your model must include the following terms: D_o, D_i, k_c, L, y_AL, y_As, y_Ao, v_∞.
e. At the conditions of the process, what is the outlet mole fraction of H₂ on the shell side, y_AL?

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100% O₂ YAo = 0 100% H₂ Shell side NA H₂ permeable tube wall T z = 0 cm YAs = 1.0 Tube side Re = 10,000 →VAL T z = 10 cm + D;=1.5 cm D₂ = 2.5 cm t