To balance the given chemical equation using the half-reaction method, follow these steps:
1. Identify the two half-reactions:
- Oxidation half-reaction: [tex]\( 2 Br^{-} \longrightarrow Br_{2} + 2e^{-} \)[/tex]
- Reduction half-reaction: [tex]\( Cl_{2} + 2e^{-} \longrightarrow 2 Cl^{-} \)[/tex]
2. Combine the half-reactions:
Add the two half-reactions together, ensuring that the electrons [tex]\( (e^{-}) \)[/tex] cancel each other out.
[tex]\[
\begin{array}{rcl}
2 Br^{-} & \longrightarrow & Br_{2} + 2e^{-} \\
Cl_{2} + 2e^{-} & \longrightarrow & 2 Cl^{-}
\end{array}
\][/tex]
Now, we sum the two half-reactions:
[tex]\[
2 Br^{-} + Cl_{2} + 2e^{-} \longrightarrow Br_{2} + 2e^{-} + 2 Cl^{-}
\][/tex]
3. Cancel the electrons:
The [tex]\(2e^{-}\)[/tex] on each side cancels out, leaving us with:
[tex]\[
2 Br^{-} + Cl_{2} \longrightarrow Br_{2} + 2 Cl^{-}
\][/tex]
The final, balanced equation is:
[tex]\[
Cl_{2} + 2 Br^{-} \longrightarrow Br_{2} + 2 Cl^{-}
\][/tex]
Therefore, the correct answer is:
[tex]\[
Cl_{2} + 2 Br^{-} \longrightarrow Br_{2} + 2 Cl^{-}
\][/tex]
