To determine the overall equation for the given chemical reaction, we need to analyze the provided half-reactions and combine them systematically.
The half-reactions given are:
[tex]\[ \text{Zn} \longrightarrow \text{Zn}^{2+} + 2e^- \][/tex]
[tex]\[ \text{Cu}^{2+} + 2e^- \longrightarrow \text{Cu} \][/tex]
### Step-by-Step Solution:
1. Identify Oxidation and Reduction Half-Reactions:
- The first half-reaction, [tex]\( \text{Zn} \longrightarrow \text{Zn}^{2+} + 2e^- \)[/tex], is the oxidation reaction because zinc is losing electrons.
- The second half-reaction, [tex]\( \text{Cu}^{2+} + 2e^- \longrightarrow \text{Cu} \)[/tex], is the reduction reaction because copper ions are gaining electrons.
2. Balance the Electrons:
- The number of electrons lost in the oxidation half-reaction (2 electrons) is equal to the number of electrons gained in the reduction half-reaction (2 electrons). Therefore, both half-reactions can be directly added together without any additional adjustments for balancing electrons.
3. Combine the Half-Reactions:
- When the half-reactions are added together, electrons cancel out since the number of electrons lost and gained is equal.
- Combining these half-reactions, we get:
[tex]\[ \text{Zn} + \text{Cu}^{2+} \longrightarrow \text{Zn}^{2+} + \text{Cu} \][/tex]
4. Write the Overall Equation:
- The overall chemical equation includes the reactants from both half-reactions on the left side and the products on the right side.
[tex]\[ \text{Zn} (s) + \text{Cu}^{2+} (aq) \longrightarrow \text{Zn}^{2+} (aq) + \text{Cu} (s) \][/tex]
### Conclusion:
The overall equation for this reaction is:
[tex]\[ \text{Zn} (s) + \text{Cu}^{2+} (aq) \longrightarrow \text{Zn}^{2+} (aq) + \text{Cu} (s) \][/tex]
So, the first option is the correct overall equation for the chemical reaction.
