Which equation correctly relates ΔG°, n, F, and E°cell?

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

Answer: (D)

Relating Gibbs energy change to electrochemical cell potential: the standard Gibbs free energy change is given by ΔG° = - n F E°cell. Here, n is the number of electrons transferred in the balanced redox reaction, F is Faraday’s constant (about 96485 C/mol), and E°cell is the standard cell potential in volts. The negative sign shows that a positive E°cell (a spontaneous electrochemical cell under standard conditions) corresponds to a negative ΔG°, meaning the reaction can do electrical work.

Check units: F has units of C/mol and E°cell in volts (J/C). Multiplying gives J/mol, matching the units of ΔG°. If E°cell is positive, ΔG° is negative, signaling spontaneity; if E°cell is negative, ΔG° is positive, signaling non-spontaneity.

Why the other forms aren’t correct: dividing by nF would mis-scale the energy change and break the correct units; multiplying by F and dividing by n misses the required factor of n and still won’t give the proper sign structure; omitting the negative sign would imply a positive ΔG° when E°cell is positive, which contradicts the physical meaning of spontaneous electrochemical reactions.