A porous ceramic sphere of radius R1 is kept saturated with a pure component liq
ID: 2076017 • Letter: A
Question
A porous ceramic sphere of radius R1 is kept saturated with a pure component liquid A. the vapor pressure of A is 50 torr. This sphere is surrounded by a concentric solid spherical surface of radius R2. Species A reacts at the surface r=R2 according to A>B. Species B is deposited as a solid film by this reaction, which is first order. Assume that the system is in a steady state and derive an expression for the partial pressure of species A at the reacting surface r=R2. Assume that the space between the two spheres is isothermal and at a uniform pressure of 1 atm. 1. (10 pt) A porous ceramic sphere of radius Riis kept saturated with a pure component liquid A. The vapor pressure of A is 50 torr. This sphere is surrounded by a concentric solid spherical surface of radius R2. Species A reacts at the surface r R2 according to A B (s). Species Bis deposited as a solid film by this reaction, which is first-order. Assume that system is in a steady state, and derive an expression for the partial pressure of species A at the reacting surface r R2. Assume that the space between the two sphere is isothermal and at a uniform pressure of one atmosphere.Explanation / Answer
Let us consider a sphere of radium R1 is placed in a concentric spherical shell of R2. The partial pressure of liquid A is at the surface of the sphere is kept constant P’As
The spherical shell contain a film of liquid B, DAB, the diffusivity of A is constant
The partial pressure of A at the boundary of the spherical shell is uniform at P’AB (P’As < P’Ar). This boundary act as sink for A. Since the diffusion in steady state. The material between the surface of the sphere and boundary of the shell is not act as a sink
Equation for steady state diffusion from the surface of the sphere is expressed as
4R12 NAR2 =4R22 NAR2 = (-4R22 DAB PAB / RT ( P-P’A)) *(dPA/dr)*((R1-R2)/R1R2)
NAR is radial flux at R
PAB is the partial pressure.
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