$26\mathrm{.}27$ A $20-$cm$-$long, cylindrical graphite $($pure carbon$)$ rod is inserted into an oxidizing atmosphere at $1145K$ and $1\mathrm{.}013{10}^{5}Pa$ pressure. The oxidizing process is limited by the diffusion of oxygen counterflow to the carbon monoxide that is fomed on the cylindrical surface. Under the conditions of the combustion process, the diffusivity of oxygen in the gas mixture may be assumed to be $1\mathrm{.}0{10}^{-5}\frac{m^2}{s}.$

a$.$ Determine the moles of $CO$ that are produced at the surface of the rod per second at the time when the diameter of the rod is $1\mathrm{.}0cm$ and the oxygen concentration that is $1\mathrm{.}0cm$ radial distance from the rod is $40$mol$\%.$ Assume a steadystate process.

b$.$ What would be the composition of oxygen $1\mathrm{.}0cm$ from the center of the rod.