Please provide the full solution and do not skip steps. Everything is Provided i

Question

Please provide the full solution and do not skip steps. Everything is Provided in the question. A "biofilm" (component B) coats the surface of non-porous inert sphere. The diameter of the nonporous inert core is 4.0 mm, and the overall diameter of the spherical biofilm particle is 8.0 mm. The spherical biofilm particle is suspended within water containing a known, constant, dilute concentration of solute A (CA). Within the biofilm, a known, constant, dilute concentration of solute A (CAm). Within the biofilm, a homogeneous, first-order reaction A-D takes place. a) Define the system, the source and sink for mass transfer of rectant A. Consider that the process is dilute with respect to species A and D. velop the differential material balance for the process in terms of concentration b) De profile cA. State all boundary conditions necessary to completely specify this differential equation.

Explanation / Answer

(a) The system includes the spherical biofilm particle and dilute solution of A.

The souce of reactant A is the dilute solution of A.

The sink is the spherical biofilm particle.

(b) A ------> D

k1 is the reaction constant

Rate = k1CA

The material balance for a constant-volume reactor gives:

dCA / dt = - k1CA

We denote the initial concentration of A as CA0

CA(t) = CA0, t = 0

The solution to the differential equation with this boundary condition is:

CA = CA0e-kt

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