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Balancing Redox Reactions Using the Half-Reaction Method with Oxidation Numbers

The half-reaction method effectively balances redox reactions by separating the oxidation and reduction processes, balancing each half-reaction individually, then combining them to achieve an overall balanced equation. This method is especially useful for aqueous solutions in acidic or basic media, where hydrogen or hydroxide ions are present.

What is the Half-Reaction Method?

This method splits a redox equation into two half-reactions—one for oxidation and one for reduction. Each half-reaction is balanced separately for atoms and charges. Electrons are explicitly included to ensure charge conservation. Once balanced, the half-reactions combine, cancelling out electrons to form a balanced overall equation.

Step-by-Step Illustration: Oxidation of Fe2+ by Dichromate in Acidic Solution

1. Write unbalanced ionic equation: \(\ce{Fe^{2+} (aq) + Cr_2O_7^{2-} (aq) -> Fe^{3+} (aq) + Cr^{3+} (aq)}\)
2. Separate into half-reactions and assign oxidation numbers: Oxidation: \(\ce{Fe^{2+} -> Fe^{3+}}\) Reduction: \(\ce{Cr_2O_7^{2-} -> Cr^{3+}}\) (Cr changes from +6 to +3)
3. Balance atoms except H and O: \(\ce{Cr_2O_7^{2-} -> 2 Cr^{3+}}\)
4. Balance oxygen by adding water: \(\ce{Cr_2O_7^{2-} -> 2 Cr^{3+} + 7 H_2O}\)
5. Balance hydrogen by adding H+ (acidic medium): \(\ce{14 H^+ + Cr_2O_7^{2-} -> 2 Cr^{3+} + 7 H_2O}\)
6. Balance charges by adding electrons: Oxidation: \(\ce{Fe^{2+} -> Fe^{3+} + e^-}\) Reduction: \(\ce{6 e^- + 14 H^+ + Cr_2O_7^{2-} -> 2 Cr^{3+} + 7 H_2O}\)
7. Equalize electrons by multiplying: Multiply oxidation half-reaction by 6: \(\ce{6 Fe^{2+} -> 6 Fe^{3+} + 6 e^-}\)
8. Add half-reactions and cancel electrons: \[ \begin{aligned} 6 \ce{Fe^{2+}} &\to 6 \ce{Fe^{3+}} + 6 \ce{e^-} \\ 6 \ce{e^-} + 14 \ce{H^+} + \ce{Cr_2O_7^{2-}} &\to 2 \ce{Cr^{3+}} + 7 \ce{H_2O} \\ \hline 14 \ce{H^+} + 6 \ce{Fe^{2+}} + \ce{Cr_2O_7^{2-}} &\to 6 \ce{Fe^{3+}} + 2 \ce{Cr^{3+}} + 7 \ce{H_2O} \end{aligned} \]
9. Check final balance: Atoms of H, Fe, Cr, and O are equal on both sides. Charges add up to +24 each side. The equation is correctly balanced.

Why Use the Half-Reaction Method?

• Separates oxidation and reduction processes clearly.
• Includes electrons explicitly to balance charge.
• Handles reactions in acidic or basic aqueous solutions well.
• Ensures conservation of mass and charge.

Summary of Key Steps

• Write unbalanced ionic equation.
• Split into oxidation and reduction half-reactions with oxidation states.
• Balance atoms except H and O.
• Balance oxygen with water molecules.
• Balance hydrogen with H+ or OH-, depending on medium.
• Add electrons to balance charge in each half-reaction.
• Multiply to equalize electrons lost and gained.
• Combine half-reactions and cancel electrons.
• Verify atom and charge balance.

What is the main advantage of using the half-reaction method for balancing redox reactions?

The half-reaction method treats oxidation and reduction separately. It works well in aqueous solutions, especially in acidic or basic media where H⁺ or OH⁻ ions are present.

How does the half-reaction method ensure electron balance in redox equations?

Electrons are added to each half-reaction to balance charge. Then, the half-reactions are multiplied so the electrons lost in oxidation equal those gained in reduction. Finally, electrons cancel out when combined.

Why are hydrogen ions (H⁺) added during the balancing process in acidic solutions?

When balancing oxygen atoms by adding water, hydrogen atoms appear. H⁺ ions are added in acidic media to balance these hydrogens, keeping atom and charge balance correct.

Can the half-reaction method be applied in basic solutions, and how does it differ?

Yes. Instead of adding H⁺ ions, hydroxide ions (OH⁻) are added to balance hydrogens in basic media. The rest of the steps are similar to the acidic case.

How do you confirm that a redox equation is fully balanced after using the half-reaction method?

Check that the number of atoms for each element is equal on both sides, and verify that the total charge is the same on reactants and products. This confirms proper balancing.