To balance a redox equation using the half-reaction method, you need to individually balance the oxidation and reduction half-reactions and then combine them in such a way that the electrons lost in oxidation equal the electrons gained in reduction. Here's a step-by-step guide to balancing the given half-reactions:
1. Write down the two half-reactions:
Oxidation half-reaction:
[tex]\[
2 Br^{-} \longrightarrow Br_2 + 2 e^{-}
\][/tex]
Reduction half-reaction:
[tex]\[
Cl_2 + 2 e^{-} \longrightarrow 2 Cl^{-}
\][/tex]
2. Multiply each half-reaction by appropriate coefficients to ensure the number of electrons lost equals the number of electrons gained.
Both half-reactions already have 2 electrons involved, so no further multiplication is necessary.
3. Add the two half-reactions together:
Simply combine the two balanced half-reactions. Since the number of electrons lost and gained is equal, they cancel each other out:
[tex]\[
2 Br^{-} + Cl_2 \longrightarrow Br_2 + 2 Cl^{-}
\][/tex]
4. Verify that the equation is balanced for both mass and charge:
- Atoms:
- Bromine (Br): [tex]\(2\)[/tex] atoms on both sides.
- Chlorine (Cl): [tex]\(2\)[/tex] atoms on both sides.
- Charge Balance:
- Left side: [tex]\(2 \text{(from }2 Br^- \text{)}\)[/tex]
- Right side: [tex]\(2 \text{(from }2 Cl^- \text{)}\)[/tex]
Both sides have a net charge of [tex]\(-2\)[/tex], so the charge is balanced.
Therefore, the balanced equation is:
[tex]\[
Cl_2 + 2 Br^{-} \longrightarrow Br_2 + 2 Cl^{-}
\][/tex]
The correct final balanced equation is:
[tex]\[ Cl_2 + 2 Br^{-} \longrightarrow Br_2 + 2 Cl^{-} \][/tex]
