Free energy, AG

The change in surface free energy, AG accompanying a small displacement of the liquid such that the change in area of solid covered,, is... 

To proceed fiirther, to evaluate the standard free energy AG , we need infonnation (experimental or theoretical) about the particular reaction. One source of infonnation is the equilibrium constant for a chemical reaction involving gases. Previous sections have shown how the chemical potential for a species in a gaseous mixture or in a dilute solution (and the corresponding activities) can be defined and measured. Thus, if one can detennine (by some kind of analysis)... 

The value of the standard free energy AG depends on the choice of reference state, as does the equilibrium constant. Thus it would be safer to write the equilibrium constant K for a gaseous reaction as... 

Similarly, changes must take place in the outer solvation shell diirmg electron transfer, all of which implies that the solvation shells themselves inliibit electron transfer. This inliibition by the surrounding solvent molecules in the iimer and outer solvation shells can be characterized by an activation free energy AG. ... 

The equilibrium constant at constant temperature is directly related to the maximum energy, called the free energy AG. which is obtainable from a reaction, the relationship being... 

Thermodynamics shows that equilibrium constants can be related to Gibbs free energies, AG, by Eq. (3). 

The free energy, AG associated with moving a charge, Q, under a potential, E, is given by... 

An electron transfer reaction may be separated into two half-reactions or redox couples so that the free energy, AG°, can be separated into AGa and AGg the free energies of reduction of the donor (D) and the acceptor (A), respectively, by... 

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

Chemical equilibrium for a reaction is associated with the change in Gibbs free energy (AG ) ealculated as follows ... 

TaUe 3.6. Conformational Free Energies (—AG°) for Substituent Groups ... 

Any reaction has associated with it changes in enthalpy (A//), entropy (A5), and free energy (AG). The principles of thermodynamics assure us that Aff, AS, and AG are... 

Steps 1 and 2 require thermodynamic data. Eigure 2-1 shows the equilibrium constants of some reactions as a function of temperature. The Appendix at the end of this chapter gives a tabulation of the standard change of free energy AG° at 298 K. 

Section 6.1 considered the noncovalent binding energies that stabilize a protein strnctnre. However, the folding of a protein depends ultimately on the difference in Gibbs free energy (AG) between the folded (F) and unfolded (U) states at some temperature T ... 

Ion Atomic Number Ionic Radius (nm) Hydration Free Energy, AG (kj/mol)... 

The differences in free energy, AG°, between 1,4-dihydro and 4,5-dihydro tautomers in CDCI3 solution for some dihydropyridazines were calculated and have been found to be 1.24 kcal/mol for 3,6-diphenyldihydropyridazine 39 (R = Ph) and only 0.73 kcal/mol for 3,6-di-tert-butyldihydropyridazine 39 (R = t-Bu) [85AHC(38)l,p.40]. 

Other thermodynamic functions described above in that the change in free energy AG is determined solely by the initial and final states of the system. The maximum work, or maximum available energy, defined in terms of the Gibbs free energy G, which is now called the free enthalpy, is... 

The relationship between the change in free energy AG and the equilibrium constant K is given by the vant Hofif isotherm... 

The equilibrium constant of a reaction can be related to the changes in Gibbs Free Energy (AG), enthalpy (AH) and entropy (AS) which occur during the reaction by the mathematical expressions ... 

For the electrochemical cell reaction, the reaction free energy AG is the utilizable electrical energy. The reaction enthalpy AH is the theoretical available energy, which is increased or reduced by an amount TAS. The product of the temperature and the entropy describes the amount of heat consumed or released reversibly during the reaction. With tabulated values for the enthalpy and the entropy it is possible to obtain AG. ... 

Using the reaction free energy AG, the cell voltage Aelectrons exchanged during an electrode reaction must be determined from the cell reaction. For the Daniell element (see example), two moles of electrons are released or received, respectively ... 

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 ... 

The reversible reaction heat of the cell is defined as the reaction entropy multiplied by the temperature [Eq. (15)]. For an electrochemical cell it is also called the Peltier effect and can be described as the difference between the reaction enthalpy AH and the reaction free energy AG. If the difference between the reaction free energy AG and the reaction enthalpy AH is below zero, the cell becomes warmer. On the other hand, for a difference larger than zero, it cools down. The reversible heat W of the electrochemical cell is therefore ... 

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