. Balance the following redox reaction under basic aqueous conditions. MnO4 (aq) + SO3²(aq) -> MnO2(s) + SO,²(aq)

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**Problem 35: Balancing a Redox Reaction under Basic Aqueous Conditions**

In this problem, we are tasked with balancing the following redox reaction that takes place in a basic aqueous environment:

\[ \text{MnO}_4^-(aq) + \text{SO}_3^{2-}(aq) \rightarrow \text{MnO}_2(s) + \text{SO}_4^{2-}(aq) \]

**Steps to Balance the Redox Reaction:**

1. **Identify the Half-Reactions:**
   - **Reduction Half-Reaction:** \(\text{MnO}_4^- \rightarrow \text{MnO}_2\)
   - **Oxidation Half-Reaction:** \(\text{SO}_3^{2-} \rightarrow \text{SO}_4^{2-}\)

2. **Balance Atoms Other than \(O\) and \(H\):**
   - Manganese is already balanced in the reduction half-reaction.
   - Sulfur is balanced in the oxidation half-reaction.

3. **Balance Oxygen Atoms by Adding \(H_2O\):**
   - For the reduction half-reaction: \(\text{MnO}_4^- \rightarrow \text{MnO}_2 + 2H_2O\)
   - For the oxidation half-reaction: \(\text{SO}_3^{2-} + H_2O \rightarrow \text{SO}_4^{2-}\)

4. **Balance Hydrogen Atoms by Adding \(OH^-\):**
   - Reduction Half-Reaction: Add \(4OH^-\) to the right side to balance hydrogen.
   - Oxidation Half-Reaction: Add \(2OH^-\) to the left side.

5. **Combine the Balanced Half-Reactions:**
   - Reduction: \(\text{MnO}_4^- + 2H_2O + 4OH^- \rightarrow \text{MnO}_2 + 4OH^-\)
   - Oxidation: \(\text{SO}_3^{2-} + H_2O + 2OH^- \rightarrow \text{SO}_4^{2-} + 2OH^-\)

6. **Balance Charges by Adding Electrons:**
   - Add electrons to balance the charges in each half-reaction, then multiply and combine the half-reactions
Transcribed Image Text:**Problem 35: Balancing a Redox Reaction under Basic Aqueous Conditions** In this problem, we are tasked with balancing the following redox reaction that takes place in a basic aqueous environment: \[ \text{MnO}_4^-(aq) + \text{SO}_3^{2-}(aq) \rightarrow \text{MnO}_2(s) + \text{SO}_4^{2-}(aq) \] **Steps to Balance the Redox Reaction:** 1. **Identify the Half-Reactions:** - **Reduction Half-Reaction:** \(\text{MnO}_4^- \rightarrow \text{MnO}_2\) - **Oxidation Half-Reaction:** \(\text{SO}_3^{2-} \rightarrow \text{SO}_4^{2-}\) 2. **Balance Atoms Other than \(O\) and \(H\):** - Manganese is already balanced in the reduction half-reaction. - Sulfur is balanced in the oxidation half-reaction. 3. **Balance Oxygen Atoms by Adding \(H_2O\):** - For the reduction half-reaction: \(\text{MnO}_4^- \rightarrow \text{MnO}_2 + 2H_2O\) - For the oxidation half-reaction: \(\text{SO}_3^{2-} + H_2O \rightarrow \text{SO}_4^{2-}\) 4. **Balance Hydrogen Atoms by Adding \(OH^-\):** - Reduction Half-Reaction: Add \(4OH^-\) to the right side to balance hydrogen. - Oxidation Half-Reaction: Add \(2OH^-\) to the left side. 5. **Combine the Balanced Half-Reactions:** - Reduction: \(\text{MnO}_4^- + 2H_2O + 4OH^- \rightarrow \text{MnO}_2 + 4OH^-\) - Oxidation: \(\text{SO}_3^{2-} + H_2O + 2OH^- \rightarrow \text{SO}_4^{2-} + 2OH^-\) 6. **Balance Charges by Adding Electrons:** - Add electrons to balance the charges in each half-reaction, then multiply and combine the half-reactions
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