Thermodynamic equilibrium half-cell

Cathodic protection is the process whereby the corrosion rate of a metal is decreased or stopped by decreasing the potential of the metal from Ecorr to some lower value and in the limit to E M, the thermodynamic equilibrium half-cell potential. At this potential, iox M = ired X[ = i() xi- and net transfer of metal ions to the solution no longer occurs. This is the criterion for complete cathodic protection (i.e., E = E m). 

The sensing mechanism was studied in detail by Hotzel and Weppner from a thermodynamic point of view. Under open circuit conditions, the equilibrium half cell electrochemical reaction at the reference electrode is... 

We have seen in Section 26.2.1 that thermodynamics (i.e., equilibrium half-cell potentials) can be used to determine which of two half-cell reactions proceeds spontaneously in the anodic or cathodic direction when the two reactions occur on the same piece of metal or on two metal samples that are in electrical contact with one another. The half-cell reaction with the higher equilibrium potential will always be at the cathode. Thus, under standard conditions any metal dissolution (corrosion) reaction with an E° less than 0.0 V vs. SHE will be driven by proton reduction while metal dissolntion reactions with an E° less than -e1.23 V vs. SHE will be driven by dissolved... 

Figures 4.3(a) and (b) are sections in the zx-plane showing the distribution of potential (( )) in the solution as cross sections of imaginary surfaces in the solution of equal potential (isopotentials) and the distribution of current as current channels with cross sections defined by traces of the surfaces. ..(n - l),n, (n + 1)... perpendicular to the isopotentials. These traces are located such that each current channel carries the same total current. Figure 4.3(a) applies to an environment of higher resistivity (e.g., water with specific resistivity of 1000 ohm-cm) and Fig. 4.3(b) to an environment of lower resistivity (e.g., salt brine, 50ohm-cm). The figures are representative of anodic and cathodic reactions, which, if uncoupled, would have equilibrium half-cell potentials of E M = -1000 mV and E x = 0 mV and would, therefore, produce a thermodynamic driving force of Ecell = E x - E M = +1000 mV. This positive Ecell indicates that corrosion will occur when the reactions are coupled. For the example of Fig. 4.3(a), the high solution resistivity allows the potential E"m at the anode to approach its equilibrium value (E M = -1000 mV) and, therefore, allows the potential in the solution at the anode interface, < )s a, to approach +1000 mV (recall that (j)s = -E"M). The first isopotential above the anode, 900 mV, approaches this value. The solution isopotentials are observed to decrease progressively and approach 0 mV at the cathode reaction site.

Fig. 22.6. Redox potentials (mV) of various half-cell reactions during mixing of fluid from a subsea hydrothermal vent with seawater, as a function of the temperature of the mixture. Since the model is calculated assuming 02(aq) and H2(aq) remain in equilibrium, the potential for electron acceptance by dioxygen is the same as that for donation by dihydrogen. Dotted line shows currently recognized upper temperature limit (121 °C) for microbial life in hydrothermal systems. A redox reaction is favored thermodynamically when the redox potential for the electron-donating half-cell reaction falls below that of the accepting half-reaction.

One in which the half-cell reactions are reversed by reversing the current flow such a cell is said to be in thermodynamic equilibrium. 

Transport in cells. Up until now, all of the cells that we have studied have been simple to describe mathematically because no charge was transferred between the two half cells. A state of frustrated equilibrium exists, thus allowing for straightforward thermodynamic analyses to be performed since all internal compositions in the cell remain static. Such cells are said to be cells without transport. 

In this present chapter, we will be looking at a slightly more complicated situation, i.e. one in which the contents of two redox half cells are not separated but are allowed to mix. Because mixing occurs, redox chemistry can occur, i.e. electron-transfer reactions are not forbidden. Any electrochemical equilibrium attained is thus a genuine thermodynamic equilibrium and is not frustrated . 

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... 

Factors Involved in Galvanic Corrosion. Emf series and practical nobility of metals and metalloids. The emf. series is a list of half-cell potentials proportional to the free energy changes of the corresponding reversible half-cell reactions for standard state of unit activity with respect to the standard hydrogen electrode (SHE). This is also known as Nernst scale of solution potentials since it allows to classification of the metals in order of nobility according to the value of the equilibrium potential of their reaction of dissolution in the standard state (1 g ion/1). This thermodynamic nobility can differ from practical nobility due to the formation of a passive layer and electrochemical kinetics. 

Reversible cell. One in which the half-cell reactions are reversed by reversing the current flow such a cell is said to be in thermodynamic equilibrium. Standard Hydrogen Electrode SHE). This consists of a platinum electrode coated with platinum black to catalyse the electrode reaction and over the... 

F is the Faraday constant, K is the equilibrium constant of the reaction, R is the gas constant, and T is the thermodynamic temperature. However, E jj is not the standard potential of the electrode reaction (or sometimes called half-cell reaction), which is tabulated in the tables mentioned. It is the standard potential of the reaction in a chemical cell which is equal to the standard potential of an electrode reaction (abbreviated as standard electrode potential), E when the reaction involves the oxidation of molecular hydrogen to solvated protons... 

We saw earlier that one can predict the thermodynamic open circuit (zero current) potential of an electrochemical cell by combining two half-cell reactions, one for the anode and the second for the cathode. The half-cell reaction with the lower (i.e., more negative) equilibrium potential will proceed spontaneously in the anodic direction, where the electrode acts as an electron sink for the anodic de-electronation (oxidation) reaction and the higher equilibrium potential reaction will occur spontaneously at the cathode, where the electrode acts as an electron source for the electronation (reduction) reaction. A cell with spontaneous reactions at the anode and cathode is called a self-... 

The above reduction reaction occurs at the surface of the cathode and is defined as a half-cell reaction. At thermodynamic equilibrium, the Nernst equation is applicable and can be expressed as ... 

There is, for example, an extensive databank of thermodynamic data, including half-cell enthalpies and entropies of reduction, that has been built up from investigations that use small mediators to carry electrons between protein and electrode. In these potentiometric studies, one measures the equilibrium concentrations of components in oxidized and reduced states at various values of the electrode potential. There are a number of variations on this theme. For example, a determination may also be carried out without using an electrode, by equilibrating the couple of interest with a titrant whose reduction potential is known accurately. Most importantly, it is necessary that the component of interest (or the titrant) exhibits some difference, in a readily measurable property, between oxidized and reduced forms. Light adsorption is the most convenient parameter since it may be monitored conveniently in situ. An excellent method, which has now gained wide... 

The Nemst equation describes the reversible electrode or equilibrium potential, .(iox. associated with the thermodynamic tendency for an electrochemical half-cell reaction to occur spontaneously. At potentials more positive than the equilibrium potential associated with a particular electrochemical half-cell reaction, oxidation proceeds spontaneously, while at potentials more negative, reduction occurs. The forms of the Nemst equation for the oxidation reactions given in Eqs 2 and 7 are, respectively,... 

The thermodynamic potentials of a system in the initial state A and final state B do not depend on the way the system is transferred from A to B, provided that the transfer proceeds through a series of equilibrium states (reversibility). In particular, the quantities appearing in Eq. (1.3) remain the same if we produce water from H2 and O2 either in hypothetical reversible direct combustion (1.4), or in the half-cell reactions (1.1) and (1.2)2. 

Also known as the standard hydrogen electrode (SHE), it is a redox reference electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. The potential of the NHE is defined as zero and based oti equilibrium of the following redox half-cell reaction, typically on a Pt surface 2H+(aq) + 2e H2(g). The activities of both the reduced form and the oxidized form are maintained at unity. That implies that the pressure of hydrogen gas is 1 atm and the concentration of hydrogen ions in the solution is 1 M. 

Appendix A Common Mathematical Operations in Chemistry A-1 Appendix B Standard Thermodynamic Values for Selected Substances A-5 Appendix C Equilibrium Constants for Selected Substances A-8 Appendix D Standard Electrode (Half-Cell) Potentials A-14 Appendix E Answers to Selected Problems A-15 Glossary G-1 Credits C-1 Index 1-1... 

The main objective of this chapter is to introduce students to one of the most important subjects of the book, equilibrium electrochemistry, which is mainly based on equilibrium thermodynamics. Equilibrium electrochemistry is usually the first and required step in analyzing any electrochemical system. How to estimate the equilibrium potential of a half-reaction and the electric potential difference of an electrochemical cell are described in this chapter. One of the most fundamental equations of electrochemical science and engineering, the Nemst equation, is introduced and anployed for composing the potential-pH (Pourbaix) diagrams. Temperature dependence of the electrode potential and the cell potential difference is also described. 

The half-cell potentials hsted in Table 17.1 are thermodynamic parameters that relate to systems at equilibrium. For example, for the discussions pertaining to Figures 17.2 and 17.3, it was tacitly assumed that there was no current flow through the external circuit. Real corroding systems are not at equilibrium there is a flow of electrons from anode to cathode (corresponding to the short-circuiting of the electrochemical cells in Figures 17.2 and 17.3), which means that the half-cell potential parameters (Table 17.1) cannot be applied. 

The half-cell potentials in the standard emf series are thermodynamic parameters that are valid only at equilibrium corroding systems are not in equilibrium. Furthermore, the magnitudes of these potentials provide no indication as to the rates at which corrosion reactions occur. 

Weaver calculated the open circuit potentials of these and other possible reactions that might occur under open circuit conditions, finding agreement between measured potentials and the potentials calculated from thermodynamic tables (Weaver et al, 1979). Hemmes and Cassir (2004) recalculated the cell open circuit potentials. They determined the equilibrium concentrations and electrode potentials in a system comprised of carbon, carbonate, CO2, CO, O ", and electrons, using the phase rule modified for electrochemical systems by Coleman and White (1996). Hemmes expressed the half-cell potentials of the anode reactions (3) and (4) referenced to an idealized cathode reaction (unit oxygen and CO2 partial pressures) ... 

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

Potentiometric measurements are based on the Nernst equation, which was developed from thermodynamic relationships and is therefore valid only under equilibrium (read thermodynamic) conditions. As mentioned above, the Nernst equation relates potential to the concentration of electroactive species. For electroanalytical purposes, it is most appropriate to consider the redox process that occurs at a single electrode, although two electrodes are always essential for an electrochemical cell. However, by considering each electrode individually, the two-electrode processes are easily combined to obtain the entire cell process. Half reactions of electrode processes should be written in a consistent manner. Here, they are always written as reduction processes, with the oxidised species, O, reduced by n electrons to give a reduced species, R ... 

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