Step 1: Analyzing the reaction.
The balanced chemical equation shows that 2 moles of Al react with 6 moles of HCl to produce 3 moles of H$_2$. Therefore, the moles of H$_2$ produced per mole of HCl reacted are:
\[
\frac{3}{6} = \frac{1}{2} \text{ mole of H}_2 \text{ per mole of HCl}.
\]
Step 2: Volume of H$_2$ gas produced.
Using the molar volume of an ideal gas (22.4 L at 1 atm and 273 K), the volume of H$_2$ gas produced per mole of HCl reacted will be:
\[
\text{Volume of H}_2 = \frac{1}{2} \times 22.4 = 11.2 \, \text{L}.
\]
Step 3: Conclusion.
Thus, the correct answer is (2), as 11.2 L of H$_2$ gas are produced per mole of HCl reacted at 1 atm and 273 K.