To determine which species is reduced in the reaction
[tex]\[Fe + AgNO_3 \rightarrow Fe(NO_3)_3 + Ag,\][/tex]
we need to identify the changes in oxidation states of the elements involved and see which species gains electrons (is reduced) and which loses electrons (is oxidized).
1. Identify Oxidation States of Reactants and Products:
- For Iron (Fe) in the reactant, its oxidation state is [tex]\(0\)[/tex] (pure element).
- For Silver Nitrate ([tex]\(AgNO_3\)[/tex]):
- The nitrate ion ([tex]\(NO_3^-\)[/tex]) generally has no change in oxidation state during the reaction. [tex]\(NO_3^-\)[/tex] remains as [tex]\(NO_3^-\)[/tex].
- Silver in [tex]\(AgNO_3\)[/tex] has an oxidation state of [tex]\(+1\)[/tex] ([tex]\(Ag^+\)[/tex]).
On the product side:
- For Iron Nitrate ([tex]\(Fe(NO_3)_3\)[/tex]):
- Iron forms [tex]\(Fe^{3+}\)[/tex], an ion with an oxidation state of +3.
- For Silver (Ag), the oxidation state changes to [tex]\(0\)[/tex] (pure element).
2. Determine Oxidation and Reduction:
- Fe changes from an oxidation state of [tex]\(0\)[/tex] to [tex]\(+3\)[/tex]. This means Fe is losing electrons and is thus oxidized.
[tex]\[Fe \rightarrow Fe^{3+} + 3e^-\][/tex]
- Ag changes from an oxidation state of [tex]\(+1\)[/tex] to [tex]\(0\)[/tex]. This means [tex]\(Ag^+\)[/tex] is gaining electrons and is thus reduced.
[tex]\[Ag^+ + e^- \rightarrow Ag\][/tex]
3. Conclusion:
By examining the species involved and their changes in oxidation states, we can determine that the species being reduced (gaining electrons) is the silver ion [tex]\(Ag^+\)[/tex].
Therefore, the species that is reduced in the reaction is:
[tex]\[ \boxed{Ag^+} \][/tex]
Hence, the correct answer is:
[tex]\[ C. \, Ag^+ \][/tex]
