Consider a model of respiration in a spherical organism of radius $r_o$ for which oxygen consumption is governed by a first$-$order reaction

of the form $N_A^{}=-k_1{C}_A.$ If a molar concentration of $C_A(r_o)=C_{A,o}$ is maintained at the surface of the organism, obtain an

expression for the radial distribution of oxygen, $C_A(r),$ within the organism. Hint: To simplify solution of the species diffusion equation,

invoke the transformation $y-=r{C}_A.$ Additionally, obtain an expression for the rate of oxygen consumption within the organism.

For an organism of radius $r_o=0\mathrm{.}125mm$ and a diffusion coefficient for oxygen transfer of $D_{AB}={10}^{-8}\frac{m^2}{s},$ if $C_{A,o}=5{10}^{-5}$

kmo$\frac{l}{m^3}$ and $k_1=20s^{-1},$ what is the molar concentration of $O_2$ at the center of the organism, in kmo$\frac{l}{m^3}?$ What is the rate of oxygen

consumption by the organism, in kmo$\frac{l}{s}?$

$C_A(r0)=,$dots,kmo$\frac{l}{m^3}$

$R^{}=,-,$kmo$\frac{l}{s}$