The balanced equation is 2AlBr₃ + 3Cl₂ ⟶ 2AlCl₃ + 3Br₂
Step 1. Start with the most complicated-looking formula (AlBr₃?) and balance its atoms.
Al: Already balanced — 1 atom each side.
Br: We have 3 Br on the left-hand side and 2 Br on the right. the lowest common multiple of 3 and 2 is 6. Put a 2 in front of AlBr₃ and a 3 in front of Br₂.
2AlBr₃ + Cl₂ ⟶ AlCl₃ + 3Br₂
Step 3: Balance Al
We now need 2Al on the right to balance the 2 Al on the left. Put a 2 in front of AlCl₃.
2AlBr₃ + Cl₂ ⟶ 2AlCl₃ + 3Br₂
Step 4. Balance Cl.
We have 6 Cl on the right, so we need 6 Cl on the left. Put a 3 in front of Cl₂.
2AlBr₃ + 3Cl₂ ⟶ 2AlCl₃ + 3Br₂
The balanced equation is
2AlBr₃ + 3Cl₂ ⟶ 2AlCl₃ + 3Br₂