Which equation correctly relates ΔG° and E°cell under standard conditions?

• 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 standard Gibbs free energy change and standard cell potential are directly linked: ΔG° is proportional to the product of the number of electrons transferred, Faraday’s constant, and the standard cell potential, with a minus sign. Specifically, ΔG° = - n F E°cell. Here n is how many electrons are exchanged in the balanced redox reaction, and F is Faraday’s constant (about 96485 C/mol e−). The negative sign matters: a positive E°cell means the reaction can do work spontaneously, which corresponds to a negative ΔG°, i.e., energy is released. The units work out to joules per mole because F is C/mol and E°cell is volts (J/C). If you drop the minus sign or misplace the factors, you’d get the wrong sign or inconsistent units, which is why the correct relation is ΔG° = - n F E°cell.