17.4 Electric Potential, Free Energy & Equilibrium

The product of the cell potential and the total charge is the maximum amount of energy available to do work, which is related to the change in free energy that occurs during the chemical process. Because the equilibrium constant K is related to ΔG, E°_cell and K are also related.

Changes in reaction conditions can have a tremendous effect on the course of a redox reaction. For example, under standard conditions, the reaction of Co(s)Co(s) with Ni2+(aq)Ni2+(aq) to form Ni(s)Ni(s) and Co2+(aq)Co2+(aq) occurs spontaneously, but if we reduce the concentration of Ni2+Ni2+ by a factor of 100, so that [Ni2+][Ni2+] is 0.01 M, then the reverse reaction occurs spontaneously instead. The relationship between voltage and concentration is one of the factors that must be understood to predict whether a reaction will be spontaneous.

Electrochemical cells convert chemical energy to electrical energy and vice versa. The total amount of energy produced by an electrochemical cell, and thus the amount of energy available to do electrical work, depends on both the cell potential and the total number of electrons that are transferred from the reductant to the oxidant during the course of a reaction. The resulting electric current is measured in coulombs (C), an SI unit that measures the number of electrons passing a given point in 1 s. A coulomb relates energy (in joules) to electrical potential (in volts). Electric current is measured in amperes (A); 1 A is defined as the flow of 1 C/s past a given point (1 C = 1 A·s):

In chemical reactions, however, we need to relate the coulomb to the charge on a mole of electrons. Multiplying the charge on the electron by Avogadro’s number gives us the charge on 1 mol of electrons, which is called the faraday (F), named after the English physicist and chemist Michael Faraday (1791–1867):

The total charge transferred from the reductant to the oxidant is therefore nF, where n is the number of moles of electrons.

The maximum amount of work that can be produced by an electrochemical cell (w_max) is equal to the product of the cell potential (E⁰ cell) and the total charge transferred during the reaction (nF):

Work is expressed as a negative number because work is being done by a system (an electrochemical cell with a positive potential) on its surroundings.

The change in free energy (ΔG) is also a measure of the maximum amount of work that can be performed during a chemical process (ΔG=wmax). Consequently, there must be a relationship between the potential of an electrochemical cell and ΔG; this relationship is as follows:

A spontaneous redox reaction is therefore characterized by a negative value of ΔG and a positive value of E⁰cell. When both reactants and products are in their standard states, the relationship between ΔG° and  E⁰cell is as follows:

A spontaneous redox reaction is characterized by a negative value of ΔG°, which corresponds to a positive value of E°_cell.

Reference: https://openstax.org/books/chemistry-2e/pages/17-4-potential-free-energy-and-equilibrium

Reference: https://www.youtube.com/watch?v=F1k8TJsVg_g

Reference: https://www.youtube.com/watch?v=ju61QlC5q9k

Potentials at Nonstandard Conditions: The Nernst Equation

Most of the redox processes that interest science and society do not occur under standard state conditions, and so the potentials of these systems under nonstandard conditions are a property worthy of attention. Having established the relationship between potential and free energy change in this section, the previously discussed relation between free energy change and reaction mixture composition can be used for this purpose.

Notice the reaction quotient, Q, appears in this equation, making the free energy change dependent upon the composition of the reaction mixture. Substituting the equation relating free energy change to cell potential yields the Nernst equation:

This equation describes how the potential of a redox system (such as a galvanic cell) varies from its standard state value, specifically, showing it to be a function of the number of electrons transferred, n the temperature, T, and the reaction mixture composition as reflected in Q. A convenient form of the Nernst equation for most work is one in which values for the fundamental constants (R and F) and a factor converting from natural to base-10 logarithms have been included.

SUMMARY AND KEY CONCEPTS

Potential is a thermodynamic quantity reflecting the intrinsic driving force of a redox process, and it is directly related to the free energy change and equilibrium constant for the process. For redox processes taking place in electrochemical cells, the maximum (electrical) work done by the system is easily computed from the cell potential and the reaction stoichiometry and is equal to the free energy change for the process. The equilibrium constant for a redox reaction is logarithmically related to the reaction’s cell potential, with larger (more positive) potentials indicating reactions with greater driving force that equilibrate when the reaction has proceeded far towards completion (large value of K). Finally, the potential of a redox process varies with the composition of the reaction mixture, being related to the reactions standard potential and the value of its reaction quotient, Q, as described by the Nernst equation.

KEY EQUATION;

Reference: https://courses.lumenlearning.com/chemistryformajors/chapter/the-nernst-equation/