A cylindrical graphite rod (pure solid carbon, density 2.25 g/cm³) of length 25 cm and initial diameter of 2.0 cm is inserted into a flowing air stream at 1100 K and 2.0 atm total system pressure. The flowing gas creates a stagnant gas boundary layer 5.0 mm thick around the external surface of the rod. At this high temperature, the solid carbon oxidizes to carbon dioxide, CO₂, gas according to the reaction C(s) + O₂(g) 2 → CO₂(g). This surface oxidation reaction is limited by the molecular diffusion of O₂ through the stagnant gas film surrounding the surface of the rod, so that the O₂ concentration at the graphite surface is effectively zero. Outside of the gas film, the bulk composition of the gas stream represents that of air.

 a. Estimate the initial rate of CO₂ production from the rod, assuming that the surface reaction is diffusion-limited.

b. How long will it take for the graphite rod to completely disappear?