The Hall process is an important method by which pure aluminum is prepared from its oxide (alumina, $\mathrm{Al}_{2} \mathrm{O}_{3}$ ) by indirect reaction with graphite (carbon). Balance the following equation, which is a simplified representation of this process.
$$\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{C}(s) \rightarrow \mathrm{Al}(s)+\mathrm{CO}_{2}(g)$$