Consider a homogeneous spherical bacterium with a radius of 10 cm. A substance A diffuses into the bacteria and a first-order reaction takes place there. In the steady state, ignoring the term convective transfer; a) Derive the differential equation that gives the change in substance A concentration .

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Consider a homogeneous spherical bacterium with a radius of 10 cm. A substance A diffuses into the bacteria and a first-order reaction takes place there. In the steady state, ignoring the term convective transfer;

a) Derive the differential equation that gives the change in substance A concentration .

b) Solve the differential equation you found in part (a) using the boundary conditions given below.

(Reaction rate constant, k=0.8 s-1 and diffusion coefficient, D=0.2 cm2/s)

Boundary Conditions;

SK1: r = 0.01 cm CA = 0 mol/cm3

SK2: r = 1 cm CA= 10 mol/cm3

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