Cell Potential, Electrical Work, and Free Energy

Schematic diagram for the galvanic cell based on the half-reactions 

Since Ag+ receives electrons and Fe2 + loses electrons in the cell reaction, the electrons flow from the compartment containing Fe2 + to the compartment containing Ag+. 

Oxidation occurs in the compartment containing Fe +. Hence this compartment functions as the anode. Reduction occurs in the compartment containing Ag+, so this compartment is the cathode. 

The electrode in the Ag/Ag+ compartment is silver metal and an inert conductor, such as platinum, must be used in the Fe2+/Fe3+ compartment. Appropriate counter ions are assumed to be present. The diagram for this cell is shown in Fig. 11.8. 

Cell Potential, Electrical Work, and Free Energy 

Cell Potential Electrical Work and Free Energy 

So far we have considered electrochemical cells in a very practical maimer without much theoretical background. The next step will be to explore the relationship between thermodynamics and electrochemistry. 

The work that can be accomplished when electrons are transferred through a wire depends on the push (the thermodynamic driving force) behind the electrons. This driving force (the emf) is defined in terms of a potential difference (in volts) between two points in the circuit. Recall that a volt represents a jonle of work per coulomb of charge transferred  

Thus 1 joule of work is produced or required (depending on the direction) when 1 conlomb of charge is transferred between two points in the circnit that differ by a potential of 1 volt. 

In this book work is viewed from the point of view of the system. Thus work flowing ont of the system is indicated by a minus sign. When a cell produces a current, the cell potential is positive, and the current can be used to 

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The equals sign is valid for a reversible i —> 0) conversion the greater than sign is valid for an irreversible conversion (finite i). Hence, an electrochemical cell delivers electric work equal to the free energy ehange only at infinitesimal current flow under these eonditions the cell potential is the OCV and the electric work delivered is the maximum ITei max = nPVoc = -AG (n is the number of moles of transferred electrons and Fthe Faraday constant). 

Relating the free energy change to electrical work and cell potential (701) ... 

Redox Potential and Free Energy. The concept of redox potential, derived from the above experimental setup, has been an invaluable aid in chemistry. The concept is intimately associated with the free energy of an oxidation-reduction reaction, because the reaction in a galvanic cell is reversible and electric energy is made available for useful work. Thus the redox potential becomes a direct measure of the free energy (cf. Chapt. V-2), except that it is expressed in different units. It must always be remembered, however, that the redox potential invariably refers to the reaction with gaseous hydrogen. That is the zero point of the redox scale. 

We now consider briefly the matter of electrode potentials. The familiar Nemst equation was at one time treated in terms of the solution pressure of the metal in the electrode, but it is better to consider directly the net chemical change accompanying the flow of 1 faraday (7 ), and to equate the electrical work to the free energy change. Thus, for the cell... 

An electrochemical cell generates a potential difference E. (The symbol E, commonly used in electrochemistry, refers to electromotive force, an archaic term for potential difference.) The electrical work done when n moles of electrons is passed by the cell can be found using Eq. (15-1), w = -nFE. It can be shown that the electrical work done by an electrochemical cell, at constant temperature and pressure, is equal to the change in Gibbs free energy of the cell components,... 

The amount of energy required to move a charge of F coulombs through a potential difference can be related to the free energy available to do useful work. The relation between the standard free-energy change of a reaction and the electrical potential of the corresponding half cell can be expressed as... 

Recall that free energy is related to the maximum possible amount of work that can he done hy the system. In the case of a galvanic cell, the work done is electrical work, so we can state the relationship between fi-ee energy and the cell potential as... 

For a given electrochemical reaction, the theoretical open-circuit voltage, the Nernst potential, is an important, if not the most important, parameter that affects and measures a fuel cell s performance. The Nernst potential is affected by the operating conditions of the SOFC, such as the temperature, pressure, and fuel composition, and is calculated from the maximum electrical work obtainable, the Gibbs free energy of the reaction (AG) ... 

The maximum amount of electrical work that can be done by an electrochemical cell is equal to the Gibb s free energy change (Chapter 15), AG (provided the temperature and pressure remain constant). The equation below gives the exact relationship between the Gibb s free energy and the cell potential ... 

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