Water is added to a sample of $5.76\ \text{g}$ of the carbide $\text{Al}_4\text{C}_3$ ($143.96\ \text{g/mol}$), which contains the methanide ion. What volume of the hydrocarbon gas that bubbles off is formed at $273\ \text{K}$ and $1\ \text{atm}$? Take $22.4\ \text{L/mol}$.