Free energy and cell voltage

Voltaic cells can only be created when each half-cell contains a reaction that occurs spontaneously. Because of this, cell voltage and free energy can be related (using Equation 18.3). 

To obtain a quantitative relation between cell voltage and concentration, it is convenient to start with the general expression for the free energy change discussed in Chapter 17 ... 

The relation between reaction free energy, temperature, cell voltage, and reversible heat in a galvanic cell is reflected by the Gibbs-Helmholtz equation [Eq. (31)]. 

Determine the spontaneity (feasibility) of the following reactions by determining the standard cell voltage and the standard free-energy change AG for the following cell reactions ... 

Cell Voltage and Its Components. The minimum voltage required for electrolysis to begin for a given set of cell conditions, such as an operational temperature of 95°C, is the sum of the cathodic and anodic reversible potentials and is known as the thermodynamic decomposition voltage, E°. E° is related to the standard free energy change, AG°C, for the overall chemical reaction,... 

Recall from Chapters 12 and 13 that the standard state of a substance means a pressure of 1 atm and a specified temperature. In addition, the standard state of a solute is that for which its concentration in ideal solution is 1 M. The standard free energy change AG° for a reaction in which all reactants and products are in their standard states can be calculated from a table of standard free energies of formation AG° of the substances taking part in the reaction (see Appendix D). For reactions that can be carried out in electrochemical cells, the standard free energy change AG° is related to a standard cell voltage A ° by... 

Equations (18.15) allow calculation of the free energy of reaction of cell reactions to be calculated from measured cell voltages, and the use of the SHE reference and the lUPAC conventions then allows calculation of individual ionic Iree energies. If cell voltages are measured over a range of temperatures, the entropy and enthalpy of the cell reaction and individual ions can also be calculated. Thus... 

Let s say that this reaction reaches equilibrium with an external measuring system (constraint), giving cell voltage . If operated under standard conditions, it would give cell voltage °, and the corresponding free energies of reaction are... 

Table 1.7. Change in Gibbs free energy, reversible cell voltage, and efficiency limit (HHV basis) of hydrogen fuel cell reaction at different temperatures [26]. (From Larminie J, Dicks A. Fuel cell systems explained. 32003 John Wiley Sons Limited. Reproduced with permission.)...

When the e.m.f. of a cell is measured by balancing it against an external voltage, so that no current flows, the maximum e.m.f. is obtained since the cell is at equilibrium. The maximum work obtainable from the cell is then nFE J, where n is the number of electrons transferred, F is the Faraday unit and E is the maximum cell e.m.f. We saw in Chapter 3 that the maximum amount of work obtainable from a reaction is given by the free energy change, i.e. - AG. Hence... 

This reaction has a positive free energy of 422.2 kj (100.9 kcal) at 25°C and hence energy has to be suppHed in the form of d-c electricity to drive the reaction in a net forward direction. The amount of electrical energy required for the reaction depends on electrolytic cell parameters such as current density, voltage, anode and cathode material, and the cell design. 

One of the most important characteristics of a cell is its voltage, which is a measure of reaction spontaneity. Cell voltages depend on the nature of the half-reactions occurring at the electrodes (Section 18.2) and on the concentrations of species involved (Section 18.4). From the voltage measured at standard concentrations, it is possible to calculate the standard free energy change and the equilibrium constant (Section 18.3) of the reaction involved. 

As pointed out previously, the value of the standard cell voltage, E°, is a measure of the spontaneity of a cell reaction. In Chapter 17, we showed that the standard free energy change, AG°, is a general criterion for reaction spontaneity. As you might suppose, these two quantities have a simple relation to one another and to the equilibrium constant, K, for the cell reaction. 

As a result of the combination of Eqs. (20) and (21), the reaction free energy, AG, and the equilibrium cell voltage, A< 00, under standard conditions are related to the sum of the chemical potentials //,. of the substances involved ... 

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