Free reaction energy

Figure A3.8.1 A schematic diagram of the PMF along the reaction coordinate for an isomerizing solute in the gas phase (frill curve) and in solution (broken curve). Note the modification of the barrier height, the well positions, and the reaction free energy due to the interaction with the solvent.

Much of chemistry occurs in the condensed phase solution phase ET reactions have been a major focus for theory and experiment for the last 50 years. Experiments, and quantitative theories, have probed how reaction-free energy, solvent polarity, donor-acceptor distance, bridging stmctures, solvent relaxation, and vibronic coupling influence ET kinetics. Important connections have also been drawn between optical charge transfer transitions and thennal ET. 

Figure C3.2.10.(a) Dependence of electron transfer rate upon reaction free energy for ET between biphenyl radical anions and various organic acceptors. Experiments were perfonned with the donors and acceptors frozen into...

Chemical changes are not irreversible unless tliere is some fonn of dissipation in tire system. That is, tire reaction free energy must be dispersed to a number of degrees of freedom distinct from tire reaction coordinate. Models tliat include... 

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 temperature coefficient of the reaction free energy follows, through thermodynamic relationships [7], by partial differentiation of Eq. (15) ... 

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 ... 

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)]. 

The calculation of the reaction free energy is possible with Eq. (34) and the determination of the reaction entropy AS follows from Eq. (33). 

The pressure dependence of the reaction free energy is equivalent to the volume change resulting from one formula conversion ... 

The extent of these reactions will be determined by the reaction free energy and concentration for each of the impurities in the molten anode/electrolyte salt system. Americium can be used as an example of a very electropositive impurity ... 

Exercise 3.7. Consider the system introduced in Exercise 3.6. Calculate both the free energy of moving from e1 to e2 [AG( A)] and the reaction free energy Ag(Ae). 

FIGURE 3.10. (a) Showing the relationship between the activation free energy Ag and the reaction free energy AG0 for the X + CH3Y- XCH3 + Y system. (6) The dependence of the "linear correlation coefficient 8 = d bg /d AG0 on AG0. 

Exchange integrals, 16,27 Exchange reactions, free energy diagram for, 89... 

The thermodynamic function used as the criterion of spontaneity for a chemical reaction is the Gibbs free energy of reaction, AG (which is commonly referred to as the reaction free energy ). This quantity is defined as the difference in molar Gibbs free energies, Gm, of the products and the reactants ... 

FIGURE 35.3 Free-energy functions for reactant (AE) and product Ag (AE) of an electron transfer reaction as calculated using umbrella sampling within a simple dipolar diatomic solvent. AG° is the reaction free energy. Solid lines are polynomial fittings to the simulated points. Dashed lines are parabolic extrapolations from the minimum of the curves. (From King and Warshel, 1990, with permission from the American Institute of Physics.)... 

Equation (3.3) gives the potential dependence of the reaction free energy of Reaction (3.2). Since this reaction equilibrium defines the standard hydrogen electrode potential, we now have a direct fink between quite simple DFT calculations and the electrode potential. In a similar way, we can now calculate potential-dependent reaction free energies for other reactions, such as O - - H" " + e OH or OH - -+ e HzO. 

Table 14-1. Calculated reaction free energies and barrier heights (kcal/mol) for uncatalyzed model and catalyzed transesterification reactions in solution and in the hairpin ribozyme3...

Values are estimated from references [152] and [153], which combine experimental and computational values for the reaction free energies and activation energies of relevant reactions in solution. 

The configurational model was used for the calculation of the elementary act in the reactions of solvated electrons21 and in the electrochemical generation of solvated electrons.22 The results for the activation free energy of the process of electrochemical generation of solvated electrons as a function of the reaction free energy... 

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