18.5
Cell Potential and Free Energy
Thermodynamics of a Redox Reaction
Thermodynamics is the branch of physics dealing with the relationship between heat and other forms of energy. In an…
The standard cell potential indicates a redox reaction’s spontaneity, so does the change in standard Gibbs free energy for a reaction. As both terms are a measure of reaction spontaneity, are they related to each other?
In a zinc-copper galvanic cell, the cell potential of 1.10 volts causes an electron flow, which is the maximum electrical work done by the cell. wmax is measured in joules and is expressed as the product of the total charge transferred in coulombs and the cell potential in volts.
The total charge, q, depends on n, the number of moles of electrons transferred during the reaction. In the zinc-copper galvanic cell, 2 moles of electrons are transferred from zinc to copper, so n = 2. To get the total charge, N is multiplied by Faraday’s constant, which is the magnitude of electric charge present in 1 mole of electrons: 96,485 coulombs.
Thus, the maximum electrical work performed by the zinc-copper galvanic cell is determined from the moles of electrons, Faraday’s constant, and the cell potential.
Here, all the energy for the electrical work is supplied by the cell itself, resulting in the system performing work on the surroundings which is denoted by a negative sign.
Recall that Gibbs free energy is associated with a reaction’s energy available to perform work. Under standard-state conditions, the change in Gibbs free energy is a measure of the highest amount of work generated in a reaction.
Thus, the maximum work can be substituted with ΔG, allowing the free energy change of an electrochemical reaction to be determined.
For the zinc-copper reaction, ΔG is −212 kilojoules, indicating that it is spontaneous. In comparison, a nickel-manganese redox reaction with a standard cell potential of −0.93 volts yields a value of +179 kilojoules, indicating that it is nonspontaneous.
The standard free energy change is also related to the equilibrium constant, K. A large equilibrium constant indicates that the reaction lies to the product side correlating with a negative ΔG value, and vice versa.
Given their relation to ΔG, the standard cell potential and equilibrium constant are also related. This relationship is derived by solving this equation for the cell potential and substituting ΔG with the gas constant, temperature, and the natural log of K.
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Q1: How is cell potential related to Gibbs 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.
Q2: What is Faraday's constant and why is it important in electrochemistry?
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.
Q3: How does the equilibrium constant relate to standard cell potential?
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.
Q4: Why does a negative cell potential indicate a nonspontaneous reaction?
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.
Q5: How is maximum electrical work calculated in a galvanic cell?
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.
Q6: What does a zero cell potential and free energy indicate about a reaction?
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.
Q7: How does chemical energy convert to electrical energy in electrochemical cells?
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.