Consider a spherical carbon particle of initial radius R$0$ surrounded by an atmosphere of oxygen. A very rapid heterogeneous reaction $(2C+O_{2}2CO)$ takes place on the surface of the carbon particle. Show that the time the particle takes to disappear completely is $t=\frac{1}{48ln2}\frac{R_0^2{}_C}{c{D}_{O_2*CO}},$ where ${}_C$ is the density of carbon.