In the thermodynamic relation ΔG° = -n F E°cell, what does n represent?

• A. The number of electrons transferred in the cell reaction
• B. The number of protons transferred
• C. The number of moles of reactants
• D. The temperature coefficient

Answer: (A)

The n in this relation is the number of electrons transferred in the balanced cell reaction. In a redox process, electrons move from the oxidation half-reaction to the reduction half-reaction, and the total amount of charge moved per mole of reaction is n moles of electrons. The equation ΔG° = -n F E°cell links the thermodynamic driving force to the electrical work, with F (Faraday constant) converting moles of electrons to coulombs and E°cell (the standard cell potential) giving the work per coulomb. The negative sign reflects that a positive cell potential corresponds to a decrease in Gibbs free energy (spontaneity).

For example, in a Zn–Cu cell, zinc loses 2 electrons while Cu2+ gains 2 electrons, so n = 2. If another reaction involved transferring 3 electrons, n would be 3. This n is not the number of protons, nor the moles of reactants, nor a temperature coefficient.