Associated equilibrium potential

Even when a sample is not in equilibrium (and hence some process of adjustment toward equilibrium is running, such as diffusion of material from one point to another) for each component at a point, an associated equilibrium state can be identified. Then one can say that the component s behavior will be very much as if it had the chemical potential it would have if it were in the associated equilibrium state. For example, material will tend to migrate from a site where the associated equilibrium potential is high to a site where the associated equilibrium potential is lower this is a reliable... 

The idea that energy cannot simply appear out of nowhere seems to force us to believe that 5G and dG do differ by the stated amount. We form two quantities, jx = 5GJ5m and = 5GJ5m, and note that, if the entry and exit process were reversible, and would be chemical potentials as defined by Gibbs. That is to say, if crossing a boundary normal to z were an equilibrium process, the chemical potential associated with the process would be /ij, and if crossing a boundary normal to x were an equilibrium process, the potential associated with the process would be /r. Then for the real (nonequilibrium) processes that occur at the boundaries, if we identify associated equilibrium processes for them, we have to identify processes for which the potentials differ by — /x, there has to be a difference in the associated equilibrium potentials of this amount if they are to be useful in describing this kind of behavior. 

The train of thought is not restricted to principal planes of the stress state but applies to any plane. At some point in the material, for any direction through the point there is a normal-stress component hydrostatic pressure P" and an associated equilibrium potential p". The associated equilibrium potential is a direction-dependent scalar with an infinite number of magnitudes at a point, just like the normal-stress component of a stress state. The two quantities are linked by the factor Ij, the volume of one unit of component i (1 kg or 1 kg-mol or other unit) ... 

The simplest material that can change composition is a binary mixture of two atomic species an example would be a copper-tin alloy. Let a mixture of this type contain atomic species A and B then for the chemical potential of species A, dn fdC = RTfC, where is the mole fraction or number ratio of atoms of A to total number of atoms in a sample, n l(n -l- n ), and dfi /dP = the partial molar volume of species A. If stress is nonhydrostatic, the associated equilibrium potential of A for direction n follows a similar relation djx jda = V. ... 

Inspection of this equation allows us to see that as the equilibrium constant for the chemical step increases the associated equilibrium potential for the redox couple will become less negative, i.e. the species becomes easier to reduce leading to a positive shift in the voltammetric peak position. 

In the case of chromium in 1 N H2SO4 transpassivity occurs at about 1 1 V (below the potential for oxygen evolution, since the equilibrium potential in acid solutions at pH 0 is 1 23 V and oxygen evolution requires an appreciable overpotential) and is associated with oxidation of chromium to dichromate anions ... 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

When such a polyfunctional electrode is polarized, the net current, i, will be given by ii - 4. When the potential is made more negative, the rate of cathodic hydrogen evolution will increase (Fig. 13.2b, point B), and the rate of anodic metal dissolution will decrease (point B ). This effect is known as cathodic protection of the metal. At potentials more negative than the metaTs equilibrium potential, its dissolution ceases completely. When the potential is made more positive, the rate of anodic dissolution will increase (point D). However, at the same time the rate of cathodic hydrogen evolution will decrease (point D ), and the rate of spontaneous metal dissolution (the share of anodic dissolution not associated with the net current but with hydrogen evolution) will also decrease. This phenomenon is known as the difference effect. 

While the peaks associated with sulfate and pyrosulfate are essentially the same with and without vanadia, the equilibrium potentials in the melts are not. In the vanadia-free melts (Table 3) the equilibrium potentials are well-correlated with Eq. (53) [50] ... 

For simplicity we assume that the intermediate stays at the electrode surface, and does not diffuse to the bulk of the solution. Let (j>l0 and 0oo denote the standard equilibrium potentials of the two individual steps, and cred, Cint, cox the surface concentrations of the three species involved. If the two steps obey the Butler-Volmer equation the current densities j and j2 associated with the two steps are ... 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

REDOX HALF-REACTIONS. Electron transfer reactions involve oxidation (or loss of electrons) of one component and reduction (or gain of electrons) by a second component. Therefore, a complete redox reaction can be treated as the sum of two half-reactions such that the stoichiometry and electric charge is balanced across a chemical equilibrium. For each such half-reaction, there is an associated standard potential E°. The hydrogen ion-hydrogen gas couple is ... 

Table 5.1 summarizes the various constraint conditions and the associated thermodynamic potentials and second-law statements for direction of spontaneous change or condition of equilibrium. All of these statements are equivalent to Carnot s theorem ( dq/T < 0) or to Clausius inequality ([Pg.164]

Because of irreversibilities associated with electrode kinetics and concentration variations, the potential of an electrode is different from the equilibrium potential. This departure from equilibrium, known as the overpotential, can be measured with a reference electrode. So that significant overpotential at the reference electrode can be avoided, the reference electrode is usually connected to the working electrode through a high-impedance voltmeter. With this arrangement the reference electrode draws negligible current, and all of the overpotential can be attributed to the working electrode. 

Modeling EM solitary waves in a plasma is quite a challenging problem due to the intrinsic nonlinearity of these objects. Most of the theories have been developed for one-dimensional quasi-stationary EM energy distributions, which represent the asymptotic equilibrium states that are achieved by the radiation-plasma system after long interaction times. The analytical modeling of the phase of formation of an EM soliton, which we qualitatively described in the previous section, is still an open problem. What are usually called solitons are asymptotic quasi-stationary solutions of the Maxwell equations that is, the amplitude of the associated vector potential is either an harmonic function of time (for example, for linear polarization) or it is a constant (circular polarization). Let s briefly review the theory of one-dimensional RES. 

As shown by curve b in Figure 12.7, illumination at the open-circuit condition produces electron-hole pairs that are separated by the potential gradient associated with the interface. The concentration of holes increases at all positions within the semiconductor, and the concentration of electrons increases in the space-charge region, thus straightening the equilibrium potential variation. As the system approaches the short-circuit condition under illumination (curve c in Figure 12.7), the concentrations of electrons and holes tends toward the equilibrium distributions. 

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