In-depth Notes on Balancing Redox Reactions in Acidic Solutions

Redox Reactions Overview

• Involves oxidation (loss of electrons) and reduction (gain of electrons).

• Example: Ethanol (C₂H₆O) oxidized to acetic acid (C₂H₄O₂) with dichromate (Cr₂O₇²⁻) as oxidizing agent, producing chromium ions (Cr³⁺).

• Important historical application: First breathalyzers used this reaction due to color change indicating oxidation state of chromium.

Balancing Redox Reactions

• Method used: Half Reaction Method

• Split the overall reaction into oxidation and reduction half reactions.

• Oxidation Half Reaction:

  • C₂H₆O → C₂H₄O₂

• Reduction Half Reaction:

  • Cr₂O₇²⁻ → Cr³⁺

Steps to Balance Half Reactions

1. Separate the reaction:

   • Identify and separate oxidation and reduction half equations.

2. Balance atoms (except O & H):

   • Carbon atoms are balanced in oxidation half equation.

3. Balance O by adding H₂O:

   • Add 1 H₂O molecule to reactants in oxidation equation: - C₂H₆O + 1 H₂O → C₂H₄O₂

4. Balance H by adding H⁺:

   • Count H: 8 H in reactants (C₂H₆O) vs. 4 in products (C₂H₄O₂).

   • Add 4 H⁺ to balance hydrogen: - C₂H₆O + 1 H₂O → C₂H₄O₂ + 4 H⁺

5. Balance charge by adding electrons:

   • Adjust for charge: 0 in reactants, +4 in products.

   • Add 4 electrons to product side to balance charge.

     • C₂H₆O + 1 H₂O → C₂H₄O₂ + 4 H⁺ + 4 e⁻

   • Reduction Half Equation Steps:

6. Balance atoms except O & H:

   • 2 Cr on reactants, 1 Cr on products. Add coefficient 2 to Cr³⁺.

7. Balance O with H₂O:

   • 7 O in dichromate, add 7 H₂O to products. - Cr₂O₇²⁻ → 2 Cr³⁺ + 7 H₂O

8. Balance H with H⁺:

   • 14 H from 7 H₂O. Add 14 H⁺ to reactants. - Cr₂O₇²⁻ + 14 H⁺ → 2 Cr³⁺ + 7 H₂O

9. Balance charge with electrons:

   • Calculate total charge and add electrons to reactants. - Add 6 e⁻ to reactants:

     • Cr₂O₇²⁻ + 14 H⁺ + 6 e⁻ → 2 Cr³⁺ + 7 H₂O

Equalizing Electrons

• Multiply half equations to ensure equal electron transfer.

• Multiply oxidation half by 3 and reduction half by 2 to equalize, yielding:

1. Oxidation: - 3 C₂H₆O + 3 H₂O → 3 C₂H₄O₂ + 12 H⁺ + 12 e⁻

2. Reduction: - 2 Cr₂O₇²⁻ + 28 H⁺ + 12 e⁻ → 4 Cr³⁺ + 14 H₂O

Adding & Canceling Common Species

• Combine equations and cancel common species (H₂O, H⁺, and e⁻).

• Final balanced equation:

  • 3 C₂H₆O + 2 Cr₂O₇²⁻ + 16 H⁺ → 3 C₂H₄O₂ + 4 Cr³⁺ + 11 H₂O

Final Verification

• Check atom balance: Confirm equal number of atoms on both sides.

• Check charge balance:

  • Reactants: +16 (H⁺) + -2 (dichromate) = +12

  • Products: +4 * 3 (Cr³⁺) + 0 (H₂O) = +12

  • Both sides balance, confirming correct redox equation.