Chapter 14, Problem 14.34P

Consider a spherical organism of radius r₀ within which respiration occurs at a uniform volumetric rate of $N_A=-k_0$ . That is, oxygen (species A) consumption is governed by a zero-order, homogeneous chemical reaction.
(a) If a molar concentration of $C_A\left(r_0\right)=C_{A,0}$ is maintained at the surface of the organism, obtain an expression for the radial distribution of oxygen, $C_A\left(r\right)$ , 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 $r_0=0.10$ mm and a diffusion coefficient for oxygen transfer of $D_{AB}={10}^{-8}$ $m^2/s$ . If $C_{A,0}=5\times {10}^{-5}$ ${\text{kmol/m}}^{\text{3}}$ and $k_0=1.2\times {10}^{-4}$ ${\text{kmol/s•m}}^{\text{3}}$ , what is the molar concentration of at the center of the organism?