To balance the equation \( \text{Al} + \text{Cl}_2 \rightarrow \text{AlCl}_3 \), we need to make sure that the number of atoms of each element on the reactant side is equal to the number on the product side.
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On the left (reactants), we have:
- Aluminum (Al): 1 atom
- Chlorine (Cl): 2 atoms (from \( \text{Cl}_2 \))
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On the right (products), we have:
- Aluminum (Al): 1 atom
- Chlorine (Cl): 3 atoms (from \( \text{AlCl}_3 \))
To balance the chlorine, we can place a coefficient of 3 in front of \( \text{Al} \) in the reactants:
\[ 4 \text{Al} + 3 \text{Cl}_2 \rightarrow 2 \text{AlCl}_3 \]
Now, let's check the balance:
- Aluminum: 4 (from 4 Al) on the left and 2 (from 2 AlCl3) on the right.
- Chlorine: 6 (from 3 Cl2) on the left and 6 (from 2 AlCl3) on the right.
So the balanced equation is:
\[ 4 \text{Al} + 3 \text{Cl}_2 \rightarrow 2 \text{AlCl}_3 \]