To determine which half-reaction describes the reduction process taking place, we first need to understand what reduction means in the context of a redox (reduction-oxidation) reaction. Reduction refers to the gain of electrons by a species.
Given the redox reaction:
[tex]\[ Mg (s) + Fe^{2+} (aq) \longrightarrow Mg^{2+} (aq) + Fe (s) \][/tex]
We break it down into oxidation and reduction half-reactions:
1. Oxidation: Magnesium metal [tex]\( (Mg) \)[/tex] is oxidized as it loses electrons:
[tex]\[ Mg (s) \longrightarrow Mg^{2+} (aq) + 2e^{-} \][/tex]
2. Reduction: Iron(II) ions [tex]\( (Fe^{2+}) \)[/tex] are reduced as they gain electrons:
[tex]\[ Fe^{2+} (aq) + 2e^{-} \longrightarrow Fe (s) \][/tex]
Now we will examine each provided option to determine which one correctly represents the reduction half-reaction:
1. [tex]\( Fe^{2+} (aq) + 2e^{-} \longrightarrow Fe (s) \)[/tex]
- This equation shows iron(II) ions gaining 2 electrons to form solid iron, a reduction process.
2. [tex]\( Mg (s) \longrightarrow Mg^{2+} (aq) + 2e^{-} \)[/tex]
- This equation shows magnesium losing 2 electrons, indicating oxidation, not reduction.
3. [tex]\( Fe^{2+} (aq) \longrightarrow Fe (s) + 2e^{-} \)[/tex]
- This equation incorrectly shows iron(II) ions losing electrons to form solid iron, which is not a reduction half-reaction.
4. [tex]\( Mg (s) + 2e^{-} \longrightarrow Mg^{2+} (aq) \)[/tex]
- This equation incorrectly shows magnesium gaining electrons to form magnesium ions, contrary to the actual process which is oxidation.
Considering the correct reduction half-reaction:
[tex]\[ Fe^{2+} (aq) + 2e^{-} \longrightarrow Fe (s) \][/tex]
Therefore, the correct half-reaction that describes the reduction taking place is:
[tex]\[ \boxed{Fe^{2+} (aq) + 2e^{-} \longrightarrow Fe (s)} \][/tex]
