Consider a spherical organism of radius ro within which respiration occurs at a uniform volumetric rate of N_A = –k₀. That is, oxygen (species A) consumption is governed by a zero-order, homogeneous chemical reaction.

(a) If a molar concentration of C_A (r₀) = C_{A, 0} is maintained at the surface of the organism, obtain an expression for the radial distribution of oxygen, C_A(r), within the organism. From your solution, can you discern any limits on applicability of the result?

(b) Obtain an expression for the rate of oxygen consumption within the organism.

(c) Consider an organism of radius ro = 0.10 mm and a diffusion coefficient for oxygen transfer of D_AB = 10^-8 m²/s. If C_A,0 = 5 x 10^-5k mol/m³ and k₀ = 1.2 x 10^-4k mol/s ∙ m³, what is the molar concentration of O₂ at the center of the organism?