A $0.216\,\text{g}$ portion of aluminium carbide is allowed to react with an excess of water, forming methane gas. No other carbon-containing product is produced in this reaction. The methane gas is then burned completely in $\text{O}_2$, giving only $\text{H}_2\text{O}$ and $\text{CO}_2$. The volume of $\text{CO}_2$ generated at room temperature and pressure is $108\,\text{cm}^3$. What is the formula of aluminium carbide?
- A$\text{Al}_2\text{C}_3$
- B$\text{Al}_3\text{C}_2$
- C$\text{Al}_3\text{C}_4$
- D$\text{Al}_4\text{C}_3$