AP® Chemistry · Unit 9 · Topic 9.9
Cell Potential and Free Energy
Cell potential and free energy describe the same spontaneity from two angles: delta G = -nFE converts a voltage, per electron transferred, into an energy change in joules.
A galvanic cell's voltage measures how hard the electrons are being pushed from one electrode to the other. The bigger that push, the more the reaction wants to happen, so a larger positive E lines up with a more negative delta G, a more favored reaction. The equation delta G = -nFE is what makes that link exact: n is the moles of electrons transferred (from the balanced half-reactions), F is Faraday's constant, 96485 coulombs per mole of electrons, and E is the cell potential in volts. Multiply volts by coulombs and you get joules, so nFE already has units of energy — the minus sign just makes a positive E (favorable cell) give a negative delta G (spontaneous reaction).
The easiest trap is treating E itself as an energy. It isn't. Cell potential is intensive: a AA battery and a car battery built from the same chemistry have the same voltage even though the car battery can push far more charge. Delta G is extensive — it scales with how many moles of electrons actually move, which is exactly the job n does in the equation. That's why you cannot compare delta G values from two different reactions just by comparing their voltages; you need n too.
This equation is the bridge between the electrochemistry of this unit and the equilibrium ideas from earlier: delta G is also tied to the equilibrium constant through delta G = -RT ln K, so setting the two expressions for delta G equal connects E directly to K. A cell with a large positive standard potential corresponds to a reaction that favors products heavily at equilibrium, large K, tying voltage, free energy, and equilibrium into one consistent story.
Key terms
- Cell potential (E)
- The voltage of an electrochemical cell, an intensive measure of the driving force per electron transferred.
- Faraday's constant (F)
- The charge per mole of electrons, 96485 coulombs per mole.
- Delta G
- The Gibbs free energy change, an extensive quantity that predicts spontaneity and scales with moles reacted.
- Intensive property
- A property, like voltage, that does not depend on the amount of substance present.
- Extensive property
- A property, like delta G, that scales directly with the amount of substance reacting.
Watch it explained
- How it worksHow does delta G equals minus nFE convert volts into kilojoules per mole?
- Worked exampleFind delta G for a cell with a potential of 1.10 V transferring 2 moles of electrons.
- Common mistakeWhy isn't the cell potential an amount of energy the way delta G is?
- Ties togetherHow does cell potential connect to the equilibrium constant of the underlying reaction?
Check yourself
End of topic.