Oxygen is consumed by living cells at a rate that is often independent of \(\mathrm{O}_{2}\) concentration. As a model for a living cell, consider a steady state \(\mathrm{O}_{2}\) diffusion in a sphere of \(r_{o}\) with a zeroth order reaction, \(k_{o}\), of \(\mathrm{O}_{2}\). The \(\mathrm{O}_{2}\) concentration at \(r=r_{o}\) is maintained at \(C_{o}\).

a. Determine the concentration profile, \(C(r)\).

b. What is the flux of oxygen into the cell?

c. How much oxygen exists in the cell at any one time?