To identify the reduction half-reaction for the given chemical reaction, we need to understand the concepts of oxidation and reduction. In a redox reaction, oxidation involves the loss of electrons, while reduction involves the gain of electrons. A reduction half-reaction shows the species that is gaining electrons.
The given full reaction is:
[tex]\[ \text{Mg (s)} + \text{ZnCl}_2 (\text{aq}) \rightarrow \text{MgCl}_2 (\text{aq}) + \text{Zn (s)} \][/tex]
We need to determine the species that undergoes reduction.
1. Oxidation States Assignment:
- Magnesium (Mg) in its elemental form (s) has an oxidation state of 0.
- Zinc (Zn) in \(\text{ZnCl}_2\) is in the +2 oxidation state.
- Chlorine (Cl) in \(\text{ZnCl}_2\) and \(\text{MgCl}_2\) is in the -1 oxidation state.
- Magnesium (Mg) in \(\text{MgCl}_2\) is in the +2 oxidation state.
- Zinc (Zn) in its elemental form (s) has an oxidation state of 0.
2. Determine the Species Being Reduced:
- Magnesium (Mg) starts in the 0 oxidation state and ends up in the +2 oxidation state. Hence, magnesium is oxidized (it loses electrons).
- Zinc (Zn) starts in the +2 oxidation state in \(\text{ZnCl}_2\) and ends up in the 0 oxidation state. Hence, zinc is reduced (it gains electrons).
3. Write the Reduction Half-Reaction:
Since zinc is gaining electrons, the reduction half-reaction involves the conversion of zinc ions (\( \text{Zn}^{2+} \)) to elemental zinc (Zn).
Therefore, the reduction half-reaction is:
[tex]\[ \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn (s)} \][/tex]
From the given options:
- A. \( \text{Zn (s)} \rightarrow \text{Zn}^{2+} + 2e^- \) (This is an oxidation reaction)
- B. \( \text{Mg (s)} \rightarrow \text{Mg}^{2+} + 2e^- \) (This is an oxidation reaction)
- C. \( \text{Mg}^{2+} + 2e^- \rightarrow \text{Mg (s)} \) (This is a reduction reaction but not relevant to this problem)
- D. \( \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn (s)} \) (This is the correct reduction reaction)
Thus, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
Which corresponds to option D: [tex]\( \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn (s)} \)[/tex].
