Free energy calculating from electrode potentials

Calculating the Free-Energy Change from Electrode Potentials... 

Calculating the free-energy change from electrode potentials Given standard electrode potentials, calculate the standard free-energy change for an oxidation-reduction reaction. (EXAMPLE 20.9)... 

While in previous ab initio smdies the reconstructed surface was mostly simulated as Au(lll), Feng et al. [2005] have recently performed periodic density functional theory (DFT) calculations on a realistic system in which they used a (5 x 1) unit cell and added an additional atom to the first surface layer. In their calculations, the electrode potential was included by charging the slab and placing a reference electrode (with the counter charge) in the middle of the vacuum region. From the surface free energy curves, which were evaluated on the basis of experimentally measured capacities, they concluded that there is no necessity for specific ion adsorption [Bohnen and Kolb, 1998] and that the positive surface charge alone would be sufficient to lift the reconstmction. 

It is sometimes desirable to calculate the electrode potential of a half-reaction derived from a combination of two or more other half-reactions. We may combine two half-reactions by addition if we regard the free-energy change, or its negative nFE°, as being additive. But, since the faraday is common to all such additions, the summation is simplified if we regard the quantity nE° or the volt-electrons as additive, rather than the joules. 

The interfacial free energy y(T, a, o e. Oac. A) depends only on temperature, the activities, and the difference between the electrostatic potentials of electrode and electrolyte, A, which, apart from a, are aU well-defined and experimentally accessible quantities. Therefore, the accurate calculation of y depends on the accuracy of evaluating or the corresponding activity coefficient/.. 

Fig.1 Calculated free energy diagram for hydrogen evolution at a potential U = 0 V relative to the standard hydrogen electrode at pH = 0. The free energy of H+ + e is by definition the same as that of j - i at standard conditions. The free energy of H atoms bound to different catalysts is then found by calculating the free energy with respect to molecular hydrogen including zero-point energies and entropy terms (reprinted from Ref 83 with permission).

The electrochemical redox potential of several possible decomposition reactions at pH = 0 (relative to the potential of the saturated calomel electrode), which have been estimated from thermodynamic parameters (6,17-21), are shown schematically in Figure A. The band levels are shown for open-circuit conditions. The standard electrode potentials were calculated from the free energies of formation, which are summarized below in Table III. 

The free energies in (18) are illustrated in Fig. 10. It can be seen that GA is that part of AG ° available for driving the actual reaction. The importance of this relation is that it allows AGXX Y to be calculated from the properties of the X and Y systems. In thermodynamics, from a list of n standard electrode potentials for half cells, one can calculate j (m — 1) different equilibrium constants. Equation (18) allows one to do the same for the %n(n— 1) rate constants for the cross reactions, providing that the thermodynamics and the free energies of activation for the symmetrical reactions are known. Using the... 

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... 

The electrochemical series tabulates standard electrode potentials. Some sources call the electrochemical series oxi-dation/reduction potentials, electromotive series, and so on. The reference state of electrochemical series is the hydrogen evolution reaction, or H+/H2 reaction. Its standard electrode potential has been universally assigned as 0 V. This electrode is the standard hydrogen electrode (SHE) against which all others are compared. For example, the standard electrode potential of the Fe/Fe2+ reaction is —0.440 V and that of Cu/Cu2+ reaction is +0.337 V. The standard electrode potentials are calculated from Gibbs free energy values by Eq. (8) that is applicable only in the above-mentioned standard state. 

Numerous applications of standard electrode potentials have been made in various aspects of electrochemistry and analytical chemistry, as well as in thermodynamics. Some of these applications will be considered here, and others will be mentioned later. Just as standard potentials which cannot be determined directly can be calculated from equilibrium constant and free energy data, so the procedure can be reversed and electrode potentials used for the evaluation, for example, of equilibrium constants which do not permit of direct experimental study. Some of the results are of analjrtical interest, as may be shown by the following illustration. Stannous salts have been employed for the reduction of ferric ions to ferrous ions in acid solution, and it is of interest to know how far this process goes toward completion. Although the solutions undoubtedly contain complex ions, particularly those involving tin, the reaction may be represented, approximately, by... 

Calculate the standard Gibbs free energy change, AG , in J/mol at 25°C for the following reaction from standard electrode potentials. 

Standard aqueous electrode potentials for reactions involving carbon have been calculated from the free energy of formation of carbon-containing compounds at different pH and temperature[3-6]. These data, displayed as potential-pH equilibrium diagrams, determine the domains of relative predominance of carbon as such or under a dissolved carbon-containing species such as methanol, aldehyde, acetic acid, carbonate, bicarbonate, or gaseous species such as methane, carbon dioxide, and carbon monoxide. 

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