Give the expression for the Gibbs free energy change for an electrochemical cell in terms of E°cell and nF.

• A. ΔG° = -n F E°cell
• B. ΔG° = n F E°cell
• C. ΔG° = -E°cell / (n F)
• D. ΔG° = F E°cell / n

Answer: (A)

The key idea is that the thermodynamic driving force of an electrochemical reaction is linked to the standard cell potential. For a reaction that transfers n electrons, the standard Gibbs free energy change is ΔG° = - n F E°cell. Here F is Faraday’s constant (about 96485 C/mol), so nF is the total charge per mole of reaction, and multiplying by E°cell (in volts, J/C) gives energy per mole (J/mol). The minus sign reflects that a positive standard cell potential corresponds to a spontaneous process with ΔG° negative, meaning energy is released as electrical work. If E°cell is negative, ΔG° is positive, indicating non-spontaneity under standard conditions. The other forms either mix up the units or change the sign, so they don’t correctly represent the energy—potential times charge, with the proper sign.