Lecture Notes: Standard Cell Potential (E°)

Key Concepts

• Standard Cell Potential (E°): Refers to the potential energy related to the cell reaction measured in volts (Joules per coulomb).
• Property of E°: E° remains unchanged when a chemical reaction is multiplied by a factor (e.g., 2 or 3).
• Delta G (ΔG): Refers to the change in Gibbs free energy in kilojoules per mole.

Example Reaction

• Lithium Reaction:
  • Reaction: Li → Li⁺ + e⁻
  • ΔG: 289.5 kJ/mol (exothermic)
  • E°: 3 volts

Doubling the Reaction

• When the reaction is doubled:
  • 2Li → 2Li⁺ + 2e⁻
  • ΔG doubles, but E° remains the same (3 volts).

Explanation

• Reason for Unchanged E°:
  • E° is potential energy (energy per electron).
  • Units: Joules per coulomb (Volt).
  • Energy per electron is consistent even if the total energy doubles.

Mathematical Derivation

• Nernst Equation:

  • ΔG = -nFE°
  • To find E°: E° = -ΔG/nF
  • ΔG in joules: ΔG = -289,500 J/mol.
  • Faraday constant (F): 96485 C/mol.
  • For 1 electron (n=1), E° = 3 volts.

• Doubling Reaction:

  • ΔG = 579,000 J/mol (2×-289,500 J/mol)
  • Electrons (n=2).
  • This maintains E° at 3 volts as doubling ΔG and n cancels out.

Reaction Reversal and Multiplication

• Flipping Chemical Reaction:
  • Original: Li → Li⁺ + e⁻
  • Flipped: 2Li⁺ + 2e⁻ → 2Li
  • Changes sign of ΔG: Now +579 kJ/mol.
  • Changes sign of E°: Becomes -3 volts due to reversal.

Important Points

• Multiplying reaction does not change E° since energy per electron is unchanged.
• Reversing the reaction changes the sign of E° due to the switch in reactants/products.

Conclusion

• E° remains constant with reaction scaling, but not when flipped.
• Mathematical understanding via Nernst Equation explains these phenomena.