Cell Potential and Free Energy

Cell potential and Gibbs free energy both measure reaction spontaneity. The maximum electrical work performed by a galvanic cell equals the change in standard Gibbs free energy. This relationship is expressed as ΔG° = −nFE°cell, where n is moles of electrons transferred, F is Faraday's constant, and E°cell is standard cell potential. A negative ΔG° indicates a spontaneous reaction.

Faraday's constant (96,485 coulombs per mole) represents the electric charge in one mole of electrons. It converts moles of electrons transferred into total charge in coulombs. This conversion is essential for calculating maximum electrical work and free energy change in galvanic cells, linking electron transfer to measurable electrical quantities.

Standard cell potential and equilibrium constant are related through Gibbs free energy. Large equilibrium constants indicate reactions favor products, correlating with positive cell potentials and negative ΔG° values. The relationship is expressed as E°cell = (RT/nF) ln K, showing that higher cell potentials correspond to reactions proceeding toward completion.

A negative cell potential produces a positive Gibbs free energy change, which indicates the reaction is nonspontaneous under standard conditions. In a nickel-manganese redox reaction with E°cell = −0.93 volts, ΔG° equals +179 kilojoules, confirming the reaction will not proceed forward spontaneously without external energy input.

Maximum electrical work (wmax) is calculated as the product of total charge transferred and cell potential: wmax = −nFE°cell. In a zinc-copper galvanic cell with E°cell = 1.10 volts and n = 2 moles of electrons, the maximum work is −212 kilojoules. The negative sign indicates the cell performs work on the surroundings.

When E°cell = 0 and ΔG° = 0, the reaction is at equilibrium under standard conditions with an equilibrium constant of one. This means reactants and products are present in equal proportions, and no net reaction occurs. The system has reached a state where forward and reverse reactions proceed at equal rates.

In a galvanic cell, chemical energy from redox reactions drives electron transfer from the reducing agent to the oxidizing agent. This electron flow generates electrical energy measured as cell potential. The relationship between cell potential, free energy, and equilibrium constant demonstrates how thermodynamic principles govern this energy conversion process.