Free energy electrochemical reaction

The assumptions, equations and several applications of a recently formulated theory of electron transfer reactions of solvated electrons are outlined. The relationship of the reorganization terms to those of ordinary electron exchange and electrochemical reactions is described, together with the role played by an effective standard free energy of reaction. Applications include prediction of conditions under which chemiluminescence might be found and description of conditions under which reactions might not be diffusion-controlled. 

The success of these reactions depends on the nucleophihc-ity of the anions used. Numerous accounts have discussed the basicity and the nucleophilicity of metal carbonyl anions and their influence on reactivity. Electrochemical studies (see Section 9.3) are particularly helpful in predicting the feasibility of reactions. The driving force for these reactions is often attributed to the precipitation of the insoluble salt. In spite of this, the free energies of reaction can be close to zero. In some cases, the metal-metal bond is cleaved by salts or an... 

The thermodynamics of the redox couple in Eq. (a) can be described by an electrochemical free energy of reaction, AG° ... 

Three main changes need to be made to ary of the homogeneous equations to make them appropriate for heterogeneous, i.e. electrochemical, electron transfer or photo-induced electron transfer (Chidsey, 1991 Marcus, 1996 Royea et al., 1997). First, because the reaction involves movement of an electron across a charged interface, the potential drop across which changes with the electrode potential U, the free energy of reaction is a function of U. For the reduction (cathodic) reaction Ox + e Rd we may write... 

A simple and accurate method of comparing the scales of energies and electrode potentials follows from Reference 22 and lies in the calculation of the work function of a metal, which is in the electrolyte solution at the reference-electrode potential. This is illustrated in Fig. 2, which shows a metal in equilibrium with an ox/red couple in the solution (so that their electrochemical potential levels coincide Fredox = Fmet)- The change in the free energy of reaction (16) is the sum of the energies of stages c and d of the cycle shown in Fig. 1, that is the quantity Fredox (which coincides, as was already noted, with Fq for = Cred)-... 

F is the Faraday constant (96,485 CVmol), n the charge number, and Erev Qie reversible potential or equilibrium potential of the cell reaction. By convention, the work supplied by a system is negative, which explains the negative sign of equation (2.35). For a given electrochemical redox reaction (2.1), the free energy of reaction is equal to ... 

The sum of these values yields the free energy of reaction for the standard hydrogen electrode. By definition, E° and therefore AG° are zero thus the electrochemical potential of the electrons (equal to the Fermi energy) is equal to ... 

The Gibbs free energy expresses the maximum work of an electrochemical cell operating at constant temperature and pressure. The Gibbs free energy of reaction AG is evaluated for the reaction as written and is given by the general formula... 

A simplified representation of the energetic situation where a stable intermediate may form is depicted in Fig. 3.12. In both cases, the reaction A B exhibits the same overall standard free energy of reaction. However, if a stable intermediate (1) forms, the second step of the reaction 1 B is endergonic and therefore thermodynamically unfavorable. As a result, the reaction stops at I and the electrochemical data are correlated with the transition of A 1 rather than A B. Such processes can occur, if there is an element in the reaction mixture, which forms very stable compounds with one of the elements of the electrode material so that, at least gradually, A —> B becomes less and less available and the system degrades or alters its properties. The capacity may fade, if reaction A 1 is electrochemically not reversible. 

These studies have shown that single molecules can be trapped and detected electrochem-ically at electrodes and single reaction events of reactants generated at electrodes can be observed. These have involved soluble species and UMEs or nanoparticles. It should also be possible to observe single molecules adsorbed on a surface, e.g., self-assembled mono-layers (SAMs), if a suitable amplification process can be developed. Such studies would be of use in determining free energies and reaction kinetics with tiny samples. They would also represent the ultimate sensitivity for electroanalytical detection. 

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. ... 

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 Gibbs free energy for the reaction is related to the equilibrium cell potential ( 0) (Equation 6.4). For the reaction between hydrogen and oxygen to produce water, n, the number of electrons per molecule participating in the electrochemical reaction is 2 and AG has a value of —37.2 kJ mol giving Eq a value of 1.23 V... 

Electrochemically, a spontaneous reaction generates a positive cell potential, Scell Thermodynamically, a spontaneous reaction has a negative change in free energy, AG. Thus, a reaction that has a negative change in free... 

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