How is the standard free energy change ΔG° related to E°cell?

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

Answer: (B)

The standard free energy change is tied to the standard cell potential because the cell potential represents the driving force for electron transfer, scaled to charge. For a reaction that transfers n electrons, the electrical work available per mole is n F E°cell, where F is Faraday’s constant (about 96485 C/mol) and E°cell is in volts (J/C). Thermodynamics says ΔG° = -w_rev, and the reversible electrical work is w_rev = n F E°cell, so the sign carries as ΔG° = - n F E°cell. This means a positive E°cell gives a negative ΔG°, i.e., a spontaneous reaction under standard conditions; a negative E°cell gives a positive ΔG°, i.e., nonspontaneous.