Consider the simplified process shown in the figure below, which is designed to treat a gas-phase mixture of trichloroethylene (TCE) in air by degrading the TCE within a porous catalyst layer of 0.50 cm thickness lining one side of a well-mixed chamber. The inlet composition of TCE is 5.0 mole%, but the treated gas exiting the process must contain no more than 2.0 mole% TCE. The process is carried out at 300 C and 1.0 atm total system pressure. At these conditions, the degradation of TCE within the porous catalyst layer is approximated as a homoge-homogeneous first-order reaction process with rate constant (k) of 1.5 s^–1.
The effective diffusion coefficient of TCE in air within the porous layer is 0.080 cm²/s. The gas mixing within the chamber is sufficiently high so that the gas space over the catalyst layer is well mixed and convective (boundary layer) resistances are minimized, resulting in c_Ao = cA_∞ = c_As.
a. What relationships best describe the boundary conditions for mass transfer in the system?
b. What is the mole fraction of TCE in the porous catalyst layer at z= L, the point where the porous catalyst layer is attached to its nonporous support surface?
c. If the process must be designed to remove 0.20 gmole TCE/s from the gas stream, what is the required external surface area (S) of the catalyst layer?

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2.0 mol% TCE in air Well-mixed gas phase C AO Porous catalyst layer degrades TCE (k = 1.5 s-¹) 5.0 mol % TCE (A) in air Nonporous barrier z = 0 Z=L= 0.5 cm