Question

Consider a solid spherical medium B with area P and density ρ. The sphere is subjected on both sides to different concentrations C, of species A to which it is permeable. The boundary surfaces at inner radius r1 to outer radius r2 are located within the solid adjacent to the interfaces, and the mole fractions of A at those surfaces are maintained at and respectively at all times. If DAB is the binary diffusivity of A through B, show through the basis that the molar fraction of species A through the sphere at can be expressed as; Ndiff,A, Sphere=4pier1r2CDab(Ya,1-Ya,2/r2-r1) and in terms of the concentration of A at the interfaces as: Ndiff,A,sphere=4pier1r2CDab(Ca,1-Ca,2/r2-r1) (b) Given inner and outer diameter of surfaces of B to be 4.68m and 4.80m respectively; moles per volume of A at the inner surface of B is 0.087 kmol/m3 and the same is negligible at the outer surface. Assuming there is no diffusion in medium B and the total molar concentration is constant, determine the mass flow rate of A by diffusion through medium B.

Answer 1

using equation of continuity we can use appropriate assumptions to find molar rate equation

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