In order to determine which statement is correct for the given balanced redox reaction, we need to analyze the changes in oxidation states of the elements involved in the reaction.
The balanced redox reaction is given as:
[tex]\[ Mn^{2+}(aq) + S_2O_3^{2-}(aq) + 2H_2O(l) \rightarrow MnO_2(s) + 4H^+(aq) + 2SO_4^{2-}(aq) \][/tex]
First, let's assign oxidation numbers to the relevant elements before and after the reaction.
1. Oxidation state of Manganese (Mn):
- Before the reaction: [tex]\( Mn^{2+} \)[/tex] has an oxidation state of +2.
- After the reaction: In [tex]\( MnO_2 \)[/tex], oxygen has an oxidation state of -2. Since there are 2 oxygens, the total oxidation state contributed by oxygen is -4. To balance this, manganese must have an oxidation state of +4.
Therefore, [tex]\( Mn \)[/tex] goes from +2 to +4, which means it is oxidized.
2. Oxidation state of Sulfur in [tex]\( S_2O_3^{2-} \)[/tex]:
- Before the reaction: In [tex]\( S_2O_3^{2-} \)[/tex], let's assign oxidation states. Oxygen has an oxidation state of -2. There are 3 oxygens contributing -6. The total charge of the ion is -2. Let the oxidation state of sulfur be x.
[tex]\[
2x - 6 = -2 \implies 2x = 4 \implies x = +2
\][/tex]
Therefore, each sulfur in [tex]\( S_2O_3^{2-} \)[/tex] has an oxidation state of +2.
- After the reaction: In [tex]\( SO_4^{2-} \)[/tex], oxygen has an oxidation state of -2. There are 4 oxygens contributing -8. The total charge of the ion is -2. Let the oxidation state of sulfur be y.
[tex]\[
y - 8 = -2 \implies y = +6
\][/tex]
Therefore, sulfur goes from +2 to +6, meaning it is oxidized.
Since oxidation state increases, [tex]\( Mn^{2+} \)[/tex] is losing electrons and is oxidized. The substance that is reduced (gains electrons) is considered an oxidizing agent.
Therefore, the correct statement is:
[tex]\[ \boxed{Mn^{2+}(aq) \text{ is the reducing agent and is oxidized.}} \][/tex]
