A platinum catalytic reactor in an automobile is used to convert carbon monoxide to carbon dioxide in an oxidation reaction of the form \(2 \mathrm{CO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2}\). Species transfer between the catalytic surface and the exhaust gases may be assumed to occur by diffusion in a film of thickness \(L=8 \mathrm{~mm}\). Consider an exhaust gas that has a pressure of \(1.2 \mathrm{bar}\), a temperature of \(500^{\circ} \mathrm{C}\), and a \(\mathrm{CO}\) mole fraction of 0.001 . If the reaction rate constant of the catalyst is \(k_{1}^{\prime \prime}=0.005 \mathrm{~m} / \mathrm{s}\) and the diffusion coefficient of \(\mathrm{CO}\) in the mixture is \(10^{-4} \mathrm{~m}^{2} / \mathrm{s}\), what is the molar concentration of \(\mathrm{CO}\) at the catalytic surface? What is the rate of removal of \(\mathrm{CO}\) per unit area of the catalyst? What is the removal rate if \(k_{1}^{\prime \prime}\) is adjusted to render the process diffusion limited?