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Cell Potential and Free Energy

Electrochemical cells convert chemical energy into electrical energy. The relationship between cell potential and free energy helps us predict the spontaneity of redox reactions.

Cell Potential (Ecell)​

  • Definition: The voltage difference between two electrodes in a galvanic cell
  • Standard Electrode Potential (E⁰): Measured under standard conditions (1 M, 1 atm, 25°C)
  • Calculation for a Cell:
    • Ecell = E⁰(cathode) − E⁰(anode)
  • Significance:
    • Ecell > 0 → Spontaneous reaction
    • Ecell < 0 → Non-spontaneous reaction

Gibbs Free Energy and Cell Potential​

  • ΔG is related to Ecell:
    • ΔG = −nFEcell
      • n = moles of electrons transferred
      • F = Faraday constant (96,485 C/mol e⁻)
  • Spontaneity:
    • ΔG < 0 → reaction is spontaneous
    • ΔG > 0 → reaction is non-spontaneous

Nernst Equation​

  • Accounts for non-standard conditions:
    • E = E⁰ − (0.0592/n) log Q
      • Q = reaction quotient
  • Allows calculation of cell potential at any concentration

Key Points​

  • The more positive the Ecell, the more spontaneous the reaction.
  • ΔG provides a quantitative measure of energy available to do work.
  • Ecell and ΔG are directly related through the number of electrons transferred.

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