Thermodynamics electrical potential

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

The overall pattern of behaviour of titanium in aqueous environments is perhaps best understood by consideration of the electrochemical characteristics of the metal/oxide and oxide-electrolyte system. The thermodynamic stability of oxides is dependent upon the electrical potential between the metal and the solution and the pH (see Section 1.4). The Ti/HjO system has been considered by Pourbaix". The thermodynamic stability of an... 

Figure 42. Scheme comparing expected potential-independent charge-transfer rates from Marcus-Gerischer theory of interfacia) electron transfer (left) with possible mechanisms for explaining the experimental observation of potential-dependent electron-transfer rates (right) a potential-dependent concentration of surface states, or a charge-transfer rate that depends on the thermodynamic force (electric potential difference) in the interface. 

Electrochemical cells can be constructed using an almost limitless combination of electrodes and solutions, and each combination generates a specific potential. Keeping track of the electrical potentials of all cells under all possible situations would be extremely tedious without a set of standard reference conditions. By definition, the standard electrical potential is the potential developed by a cell In which all chemical species are present under standard thermodynamic conditions. Recall that standard conditions for thermodynamic properties include concentrations of 1 M for solutes in solution and pressures of 1 bar for gases. Chemists use the same standard conditions for electrochemical properties. As in thermodynamics, standard conditions are designated with a superscript °. A standard electrical potential is designated E °. 

The system of distinctions and terminology of the thermodynamic and electric potentials introduced by Lange is still very useful and recommended for describing all electrified phases and interphases. Therefore these potentials can be assigned to metal/solution (M/s), as well as the liquid/liquid boundaries created at the interfaces of two immiscible electrolyte solutions water (w) and an organic solvent (s). 

The extensive variable Q associated with the electrical potential + in Eqs. (15), (17), and (21) is the thermodynamic surface excess charge density, which is defined by... 

The portion AQ = AH - AG = TAS of AH is transformed into heat. Ideal theoretical efficiencies % determined by the types and amounts of reactants and by the operating temperature. Fuel cells have an efficiency advantage over combustion engines because the latter are subdued to the Carnot limitation. High thermodynamic efficiencies are possible for typical fuel cell reactions (e.g., e,h = 0.83 (at 25°C) for H2 + I/2O2 -> H20(i)). The electrical potential difference between anode and cathode, = -AG/W(f, which is also called the electromotive force or open-circuit voltage, drives electrons through the external... 

Osmotic Work. It is characteristic of living cells that they maintain nonequilibrium values of the concentrations of certain solutes on opposite sides of membranes, particularly ions such as Na and K. It is this nonequHibrium distribution of ions that probably is responsible for the electrical potentials developed by living organisms. Again, although thermodynamic data do not lead to deductions about molecular mechanisms, they provide limiting values with which any mechanism must be consistent. We shall discuss the thermodynamic aspects of osmotic work in detail when we have developed the methods requited to deal with solutions. 

In 1848 du Bois-Reymond [21] suggested that the surfaces of biological formations have a property similar to the electrode of a galvanic cell and that this is the source of bioelectric phenomena observed in damaged tissues. The properties of biological membranes could not, however, be explained before at least the basic electrochemistry of simple models was formulated. The thermodynamic relationships for membrane equilibria were derived by Gibbs in 1875 [29], but because the theory of electrolyte solutions was formulated first by Arrhenius as late as 1887, Gibbs does not mention either ions or electric potentials. 

Warburg on the other hand used the theory of the concentration cell to relate the thermodynamic potential fx, of the mercurous salt, measured in ergs per grm. equivalent with V, the excess of the electric potential of the mercury over that of the dilute acid con-. taining the salt, expressed in volts thus ... 

According to Gibbs, any constituent of a system in equilibrium must have the same thermo-dynamic potential in all the phases of which it is a component. Hence, when equilibrium has been established across an interface between a metal and an electrolyte containing its ions, the thermo-d3mamic potential f Me iona of the metallic ions must be the same in both. In general the thermodynamic potential of a constituent which is electrically neutral may be said to depend only on its concentration G and its environment, but if it is an ion the electrical potential of the ]... 

If when a metal comes into contact with an electrolyte, e.g. mercury in contact with dilute sulphuric acid containing mercurous sulphate it is not at the electrical potential necessary for equilibrium the thermodynamic potential of the metallic ions in the two phases will differ and consequently some of them will pass across the boundary or compensating adjustment of the surface will take place. 

Several important energy-related applications, including hydrogen production, fuel cells, and CO2 reduction, have thrust electrocatalysis into the forefront of catalysis research recently. Electrocatalysis involves several physiochemical environmental dfects, which poses substantial challenges for the theoreticians. First, there is the electric potential which can aifect the thermodynamics of the system and the kinetics of the electron transfer reactions. The electrolyte, which is usually aqueous, contains water and ions that can interact directly with a surface and charged/polar adsorbates, and indirectly with the charge in the electrode to form the electrochemical double layer, which sets up an electric field at the interface that further affects interfacial reactivity. 

One approach to accounting for the potential and solution effects is to treat them separately (the additive approach). The thermodynamics due to an electric potential is described by the Nernst equation, which is, to the first order of approximation,... 

One may think that AG" " and A values in the tables cited are determined by calorimetry and electrochemical measurements, respectively. It is not so the way of tabulations mentioned serves practical purposes only. Several thermodynamic quantities (AG , A// , A5 etc.) have been determined electrochemically, especially when these measurements were easier or were more reliable. On the other hand, A values displayed in the tables mentioned have been determined mostly by calorimetric measurements since in many cases - owing to kinetic reasons, too slow or too violent reactions - it has been impossible to collect these data by using the measurement of the electric potential difference of a cell at suitable conditions. Quotation marks have been used in writing thermodynamic , as A is per se also a thermodynamic quantity. 

Passage of 1.0 mol of electrons (one faraday, 96,485 A s) will produce 1.0 mol of oxidation or reduction—in this case, 1.0 mol of Cl- converted to 0.5 mol of Cl2, and 1.0 mol of water reduced to 1.0 mol of OH- plus 0.5 mol of H2. Thermodynamically, the electrical potential required to do this is given by the difference in standard electrode potentials (Chapter 15 and Appendix D) for the anode and cathode processes, but there is also an additional voltage or overpotential that originates in kinetic barriers within these multistep gas-evolving electrode processes. The overpotential can be minimized by catalyzing the electrode reactions in the case of chlorine evolution, this can be done by coating the anode with ruthenium dioxide. 

A gradient of electrical potential constitutes the classic (external) force field for ionic solids. Let us study the effect of this electric field on the interface morphology and stability. The thermodynamic driving force in ionic crystals is Vi/,(= +... 

We now see that mitochondria contain a variety of molecules—cytochromes, flavins, ubiquinone, and iron-sulfur proteins—all of which can act as electron carriers. To discuss how these carriers cooperate to transport electrons from reduced substrates to 02, it is useful to have a measure of each molecule s tendency to release or accept electrons. The standard redox potential, E°, provides such a measure. Redox potentials are thermodynamic properties that depend on the differences in free energy between the oxidized and reduced forms of a molecule. Like the electric potentials that govern electron flow from one pole of a battery to another, E° values are specified in volts. Because electron-transfer reactions frequently involve protons also, an additional symbol is used to indicate that an E° value applies to a particular pH thus, E° refers to an E° at pH 7. 

If the solute carries a net charge, there is an additional thermodynamic effect of moving the charge across any difference in electric potential that exists between the solutions on the two sides of the membrane. The free energy change then is... 

Active transport of a solute against a concentration gradient also can be driven by a flow of an ion down its concentration gradient. Table 17.6 lists some of the active-transport systems that operate in this way. In some cases, the ion moves across the membrane in the opposite direction to the primary substrate (antiport) in others, the two species move in the same direction (symport). Many eukaryotic cells take up neutral amino acids by coupling this uptake to the inward movement of Na+ (see fig. 17.26c). As we discussed previously, Na+ influx is downhill thermodynamically because the Na+-K+ pump keeps the intracellular concentration of Na+ lower than the extracellular concentration and sets up a favorable electric potential difference across the membrane. Another example is the /3-galactosidc transport system of E. coli, which couples uptake of lactose to the inward flow of protons (see fig. 17.26Proton influx is downhill because electron-transfer reactions (or,... 

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