In the given redox reaction:
[tex]\[ Mg\ (s) + Fe^{2+}\ (aq) \longrightarrow Mg^{2+}\ (aq) + Fe\ (s) \][/tex]
we need to identify the half-reaction that describes the reduction process.
Step-by-Step Solution:
1. Identify the Oxidation States:
- Magnesium (Mg) starts as a solid with an oxidation state of [tex]\(0\)[/tex] and becomes [tex]\(Mg^{2+}\ (aq)\)[/tex], which means it loses 2 electrons ([tex]\(e^-)\)[/tex]. Hence, it is oxidized.
- Iron ([tex]\(Fe^{2+}\)[/tex]) in aqueous state starts with an oxidation state of [tex]\(+2\)[/tex] and becomes solid iron (Fe) with an oxidation state of [tex]\(0\)[/tex], which means it gains 2 electrons. Hence, it is reduced.
2. Write the Reduction Half-Reaction:
- The reduction process involves gaining electrons. Here, iron is being reduced from a [tex]\(+2\)[/tex] state to [tex]\(0\)[/tex].
- The balanced half-reaction for the reduction process can be written as:
[tex]\[ Fe^{2+}\ (aq) + 2e^- \longrightarrow Fe\ (s) \][/tex]
Among the given options, the correct half-reaction describing the reduction process is:
[tex]\[ Fe^{2+}\ (aq) + 2e^- \longrightarrow Fe\ (s) \][/tex]
Thus, the correct equation is:
[tex]\[ Fe^{2+}\ (aq) + 2e^- \longrightarrow Fe\ (s) \][/tex]
This matches the answer option:
[tex]\[ Fe^{2+}\ (aq) + 2e^- \longrightarrow Fe\ (s) \][/tex]
