To solve this problem using the half-reaction method, we need to follow these steps:
1. Determine the half-reactions:
- Oxidation half-reaction (loss of electrons):
[tex]\[
2 Br^{-} \longrightarrow Br_{2} + 2 e^{-}
\][/tex]
- Reduction half-reaction (gain of electrons):
[tex]\[
Cl_{2} + 2 e^{-} \longrightarrow 2 Cl^{-}
\][/tex]
2. Balance the electrons in each half-reaction:
- In the given half-reactions, you can see that both have 2 electrons involved, so they are already balanced in terms of electron transfer.
3. Combine the half-reactions:
- The electrons lost in the oxidation half-reaction should equal the electrons gained in the reduction half-reaction. Hence, when combining, the electrons cancel each other out.
[tex]\[
Cl_{2} + 2 e^{-} + 2 Br^{-} \longrightarrow Br_{2} + 2 Cl^{-} + 2 e^{-}
\][/tex]
- Simplify by canceling the electrons on both sides:
[tex]\[
Cl_{2} + 2 Br^{-} \longrightarrow Br_{2} + 2 Cl^{-}
\][/tex]
This final equation is balanced with respect to both mass and charge.
The correct balanced equation is:
[tex]\[
Cl_{2} + 2 Br^{-} \longrightarrow Br_{2} + 2 Cl^{-}
\][/tex]
Therefore, the student should write the final balanced equation as:
[tex]\[
Cl_{2} + 2 Br^{-} \longrightarrow Br_{2} + 2 Cl^{-}
\][/tex]
