A gas is stored in a 3-m-outer-diameter spherical container made of 3-cm-thick plastic. Themolar concentration of the gas in the plastic is 0.001 kg/m3 at the inner surface and negligible at theouter surface. The diffusivity of the gas in the plastic is 5 x 10-10 m2/s. The gas is highly toxic so theplastic shell contains a catalyst to degrade the gas into a safe product. The rate of reaction of the drug islimited by the catalyst concentration so it is first order in the gas concentration with rate constant 10-8kg/(m3s).A. Start with a shell balance in spherical coordinates to determine the governing equation. Assume steadystate with zero order reaction.B. Solve the differential equation obtained from the shell balance with appropriate boundary conditions todetermine concentration profile.C. Use the solution for concentration profile to determine rate of diffusion into the air.D. Determine fractional reduction in gas diffusion in air due to incorporation of catalyst in the membrane
A gas is stored in a 3-m-outer-diameter spherical container made of 3-cm-thick plastic. The
molar concentration of the gas in the plastic is 0.001 kg/m3 at the inner surface and negligible at the
outer surface. The diffusivity of the gas in the plastic is 5 x 10-10 m2/s. The gas is highly toxic so the
plastic shell contains a catalyst to degrade the gas into a safe product. The rate of reaction of the drug is
limited by the catalyst concentration so it is first order in the gas concentration with rate constant 10-8
kg/(m3s).
A. Start with a shell balance in spherical coordinates to determine the governing equation. Assume steady
state with zero order reaction.
B. Solve the differential equation obtained from the shell balance with appropriate boundary conditions to
determine concentration profile.
C. Use the solution for concentration profile to determine rate of diffusion into the air.
D. Determine fractional reduction in gas diffusion in air due to incorporation of catalyst in the membrane
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