Gibbs energy change relationship with

An electrical potential difference between the electrodes of an electrochemical cell (called the cell potential) causes a flow of electrons in the circuit that connects those electrodes and therefore produces electrical work. If the cell operates under reversible conditions and at constant composition, the work produced reaches a maximum value and, at constant temperature and pressure, can be identified with the Gibbs energy change of the net chemical process that occurs at the electrodes [180,316]. This is only achieved when the cell potential is balanced by the potential of an external source, so that the net current is zero. The value of this potential is known as the zero-current cell potential or the electromotive force (emf) of the cell, and it is represented by E. The relationship between E and the reaction Gibbs energy is given by... 

Practically in every general chemistry textbook, one can find a table presenting the Standard (Reduction) Potentials in aqueous solution at 25 °C, sometimes in two parts, indicating the reaction condition acidic solution and basic solution. In most cases, there is another table titled Standard Chemical Thermodynamic Properties (or Selected Thermodynamic Values). The former table is referred to in a chapter devoted to Electrochemistry (or Oxidation - Reduction Reactions), while a reference to the latter one can be found in a chapter dealing with Chemical Thermodynamics (or Chemical Equilibria). It is seldom indicated that the two types of tables contain redundant information since the standard potential values of a cell reaction ( n) can be calculated from the standard molar free (Gibbs) energy change (AG" for the same reaction with a simple relationship... 

Cmp and Dmp are specific constants related to the dimensions of the macromolecule, while the coefficient Amp is inversely dependent on protein size. A similar relationship can be derived for the stationary phase component of the change in the Gibbs free energy due to electrostatic effects (AG >sp><), although the precise relationship between salt concentration in the mobile phase and activity coefficient of the protein when bound to the sorbent may take a more complex form. The electrostatic free-energy change associated with the chromatographic retention process then can be expressed as... 

Although the Bronsted relation was first discussed with respect to proton transfer reactions, it has been found to apply to other types of reactions including electron and atom transfer reactions. Equation (7.11.1) implies that there is also a linear relationship between the Gibbs activation energy for the reaction and the standard Gibbs energy change for the associated equilibrium. Thus, one may also write... 

As an example of the relationship between the sign of a Gibbs-energy change and the question of whether a process is spontaneous or not, we may consider the vaporization of water at 100° C, the normal boiling point. Suppose first that we have liquid water at 100° C in equilibrium with water vapor, which will be at 1 atm... 

The standard potential of a cell reaction (E n) values can be calculated from the standard molar free (Gibbs) energy change (AG" ") for the same reaction with a simple relationship ... 

By starting with the relationship between standard Gibbs energy change and the equilibrium constant, the van t Hoff equation—relating the equilibrium constant and temperature—can be written (equation 13.25). With this equation, tabulated data at 25 °C can be used to determine equilibrium constants not just at 25 °C but at other temperatures as well. 

The Van t Hoff isotherm establishes the relationship between the standard free energy change and the equilibrium constant. It is of interest to know how the equilibrium constant of a reaction varies with temperature. The Varft Hoff isochore allows one to calculate the effect of temperature on the equilibrium constant. It can be readily obtained by combining the Gibbs-Helmholtz equation with the Varft Hoffisotherm. The relationship that is obtained is... 

The Gibbs-Helmholtz equation (Eq. (3.25) below) can be conveniently used to calculate the enthalpy if the rate of change of Gibbs energy with temperature is known. AS is obtained from Eq. (3.24a) by differentiating it with respect to temperature, so dAG/dT = AS. Substituting back into Eq. (3.24a) gives the relationship... 

This chapter is devoted to the important relationship between electrode potentials and the changes in Gibbs energy (AO ) for half-reactions and overall reactions. In discussions of the properties of ions in aqueous solution it is frequently more convenient to represent changes in Gibbs energy, quoted with units of k.I mol-1, in terms of electrode potentials, quoted with units of volts (V). The electrochemical series is introduced. The properties of the hydrated electron are described. 

The standard electrode potential E° of a redox reaction is a measure of the potential that would be developed if both reductants and oxidants were in their standard states at equal concentrations and with unit activities. The units of E° are volts and ° can be calculated from the Gibbs free energy change (AG ) of the redox reaction from the relationships... 

Calculate AG° and Kfor each independent reaction. This may be done as in the relevant examples earlier in this section, with determination of AG° as a function of temperature. An easier route, however, is to use the standard Gibbs free-energy change of formation A Gy for each compound at the temperature of interest in the relationship... 

Relationship between the Gibbs free energy G and the temperature T for two polymorphs for (a) an enantiotropic system and (b) a monotropic system in which the system is cooled from point X [9]. The arrows indicate the direction of change. (Reproduced with permission of the copyright owner, Elsevier, Amsterdam,... 

---