Please show step by step how to balance the following redox equation: Mn(NO3)2 + NaBiO3 + HNO3 → HMnO4 + Bi(NO3)3 + NaNO3 + H2O

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Chapter1: Chemical Foundations
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**Balancing Redox Reactions: A Step-by-Step Guide**

Please show step by step how to balance the following redox equation: 

\[ \text{Mn(NO}_3\text{)}_2 + \text{NaBiO}_3 + \text{HNO}_3 \rightarrow \text{HMnO}_4 + \text{Bi(NO}_3\text{)}_3 + \text{NaNO}_3 + \text{H}_2\text{O} \]

**Steps to Balance:**

1. **Assign Oxidation Numbers:**
   - Determine the oxidation states of each element in the reactants and products.

2. **Identify Oxidation and Reduction:**
   - Find which elements undergo changes in oxidation states. 

3. **Write Half-Reactions:**
   - Separate the oxidation and reduction processes into two half-reactions.

4. **Balance Atoms in Each Half-Reaction:**
   - Balance atoms other than O and H first, then balance oxygen using \(\text{H}_2\text{O}\) and hydrogen using \(\text{H}^+\).

5. **Balance Charges:**
   - Add electrons to balance the charges in each half-reaction.

6. **Equalize Electron Transfer:**
   - Multiply each half-reaction by the appropriate coefficients to equalize the number of electrons transferred.

7. **Combine Half-Reactions:**
   - Add the balanced half-reactions, canceling out electrons.

8. **Verify Mass and Charge Balance:**
   - Ensure all atoms and charges are balanced in the final equation.

This process will yield the balanced redox equation.
Transcribed Image Text:**Balancing Redox Reactions: A Step-by-Step Guide** Please show step by step how to balance the following redox equation: \[ \text{Mn(NO}_3\text{)}_2 + \text{NaBiO}_3 + \text{HNO}_3 \rightarrow \text{HMnO}_4 + \text{Bi(NO}_3\text{)}_3 + \text{NaNO}_3 + \text{H}_2\text{O} \] **Steps to Balance:** 1. **Assign Oxidation Numbers:** - Determine the oxidation states of each element in the reactants and products. 2. **Identify Oxidation and Reduction:** - Find which elements undergo changes in oxidation states. 3. **Write Half-Reactions:** - Separate the oxidation and reduction processes into two half-reactions. 4. **Balance Atoms in Each Half-Reaction:** - Balance atoms other than O and H first, then balance oxygen using \(\text{H}_2\text{O}\) and hydrogen using \(\text{H}^+\). 5. **Balance Charges:** - Add electrons to balance the charges in each half-reaction. 6. **Equalize Electron Transfer:** - Multiply each half-reaction by the appropriate coefficients to equalize the number of electrons transferred. 7. **Combine Half-Reactions:** - Add the balanced half-reactions, canceling out electrons. 8. **Verify Mass and Charge Balance:** - Ensure all atoms and charges are balanced in the final equation. This process will yield the balanced redox equation.
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