9.8 Cell Potential and Free Energy

Linking ΔG° and E°cell

The relationship ΔG° = −nFE°cell connects thermodynamics to electrochemistry. Here, n is moles of electrons transferred, F is Faraday's constant (96,485 C/mol), and E°cell is the standard cell potential. A positive E°cell gives a negative ΔG°, meaning the reaction is spontaneous — consistent with a galvanic cell producing usable work.

Sign relationships matter

Spontaneous redox reactions have E°cell > 0 and ΔG° < 0. Nonspontaneous reactions (like electrolysis) have E°cell < 0 and ΔG° > 0, requiring external energy input to proceed. Since F and n are always positive, ΔG° and E°cell always have opposite signs.

Connecting to equilibrium

ΔG° also relates to the equilibrium constant K via ΔG° = −RT ln K. Combining this with ΔG° = −nFE°cell shows that a large positive E°cell corresponds to a large K, meaning the reaction strongly favors products at equilibrium. This ties together cell potential, free energy, and equilibrium position.

Key terms

ΔG° = −nFE°cell

Equation relating standard free energy change to standard cell potential; n = moles of electrons, F = Faraday's constant.

Faraday's constant (F)

96,485 C/mol of electrons; converts moles of electrons to charge.

Sign relationship: E°cell and ΔG°

They always have opposite signs — positive E°cell gives negative ΔG° (spontaneous), and vice versa.

Spontaneous redox reaction

E°cell > 0 and ΔG° < 0; occurs in galvanic (voltaic) cells.

Connection between ΔG°, E°cell, and K

ΔG° = −nFE°cell = −RT ln K; larger E°cell means larger K, favoring products at equilibrium.

Try an AP-style question

What is E°cell for a Zn–Cu galvanic cell?

1. −1.10 V
2. −0.42 V
3. +1.10 V
4. +0.42 V