A spherical particle made of pure carbon is burned in pure oxygen at $800^{\circ}\mathrm{C}$ and a pressure of 1 atm, as schematically shown in Fig. 9. At this high temperature, the reaction at the particle surface, i.e. $\mathrm{C} + \mathrm{O}_2 \rightarrow \mathrm{CO}_2$ , is much faster than the diffusional transport of oxygen to the surface and carbon dioxide away from the surface. Hence, the burning of the particle is said to be diffusion controlled.

In the following we consider the diffusion of carbon dioxide away from the surface as the rate controlling step. Initially, the particle diameter is $2\mathrm{cm}$ . At the particle surface the partial pressure of $\mathrm{CO}_{2}$ is $1.013\times 10^{5}\mathrm{Pa}$ ( $= 1$ atm) while far away from the particle the partial pressure is zero. The temperature is constant at $800^{\circ}\mathrm{C}$ .