Step 1: Balancing the Aluminum and Iodine Reaction
First, we need to balance the chemical equation for the reaction between aluminum (Al) and iodine (\(\mathrm{I}_2\)) to form aluminum iodide (\(\mathrm{AlI}_3\)).
The unbalanced equation is:
\[
\mathrm{Al} + \mathrm{I}_2 \rightarrow \mathrm{AlI}_3
\]
To balance the equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation.
Aluminum (Al): There is 1 Al atom on both sides.
Iodine (I): There are 2 I atoms on the left and 3 I atoms on the right.
To balance the iodine atoms, we need to find the least common multiple of 2 and 3, which is 6. Therefore, we need 2 \(\mathrm{AlI}_3\) molecules on the right side and 3 \(\mathrm{I}_2\) molecules on the left side.
The balanced equation is:
\[
2\mathrm{Al} + 3\mathrm{I}_2 \rightarrow 2\mathrm{AlI}_3
\]
Step 2: Balancing the Hydrogen and Bromine Reaction
Next, we need to balance the chemical equation for the reaction between hydrogen (\(\mathrm{H}_2\)) and bromine (\(\mathrm{Br}_2\)) to form hydrogen bromide (\(\mathrm{HBr}\)).
The unbalanced equation is:
\[
\mathrm{H}_2 + \mathrm{Br}_2 \rightarrow \mathrm{HBr}
\]
To balance the equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation.
Hydrogen (H): There are 2 H atoms on the left and 1 H atom on the right.
Bromine (Br): There are 2 Br atoms on the left and 1 Br atom on the right.
To balance the hydrogen and bromine atoms, we need 2 \(\mathrm{HBr}\) molecules on the right side.
The balanced equation is:
\[
\mathrm{H}_2 + \mathrm{Br}_2 \rightarrow 2\mathrm{HBr}
\]