First, we need to calculate the number of moles of aluminum that reacted:
Molar mass of aluminum = 27 g/mol
Number of moles of aluminum = 0.84 g / 27 g/mol = 0.031 mol
According to the balanced chemical equation, 2 moles of aluminum react with 3 moles of chlorine gas to produce 2 moles of aluminum chloride. So, 0.031 moles of aluminum will react with:
0.031 mol Al x (3 mol Cl2 / 2 mol Al) = 0.0465 mol Cl2
Now, we can use the molar gas volume to calculate the volume of chlorine gas used:
Volume of Cl2 = (0.0465 mol Cl2) x (24 dm³/mol) = 1.116 dm³ or 1116 mL (rounded to 3 significant figures)
Therefore, the volume of chlorine gas used in the reaction is 1.116 dm³ or 1116 mL.