Thermodynamic equilibrium condition

If an appreciable current flows between the electrode and the solution, thus disturbing the reversible thermodynamic equilibrium conditions, the electrode is said to be polarized and the system is then operating under irreversible conditions. 

The formation of the combination of defects may be described as a chemical reaction and thermodynamic equilibrium conditions may be applied. The chemical notations of Kroger-Vink, Schottky, and defect structure elements (DSEs) are used [3, 11]. The chemical reactions have to balance the chemical species, lattice sites, and charges. An unoccupied lattice site is considered to be a chemical species (V) it is quite common that specific crystal structures are only found in the presence of a certain number of vacancies [12]. The Kroger-Vink notation makes use of the chemical element followed by the lattice site of this element as subscript and the charge relative to the ideal undisturbed lattice as superscript. An example is the formation of interstitial metal M ions and metal M ion vacancies, e.g., in silver halides ... 

As can be seen, conditions in a flowing reactor, even the simplest such as a tube, may be far from the thermodynamic equilibrium conditions predicted by the equilibrium computer programs. However, in the diffusion controlled range, it is possible to use as the driving force for diffusion, the difference between an assumed equi-... 

Introducing the thermodynamical equilibrium condition into Eq. (5) produces the relation ... 

The effect of the medium (solvent) on the dissolved substance can best be expressed thermodynamically. Consider a solution of a given substance (subscript i) in solvent s and in another solvent r taken as a reference. Water (w) is usually used as a reference solvent. The two solutions are brought to equilibrium (saturated solutions are in equilibrium when each is in equilibrium with the same solid phase—the crystals of the dissolved substance solutions in completely immiscible solvents are simply brought into contact and distribution equilibrium is established). The thermodynamic equilibrium condition is expressed in terms of equality of the chemical potentials of the dissolved substance in both solutions, jU,(w) = jU/(j), whence... 

Stabilization of Ru based oxides by valve metal oxides has not been studied in such detail using photoelectron spectroscopy. The most common compositions, however, with relatively high valve metal content, are not in favor of formation of a solid solution. Studies of the phase formation in Ru/Ti mixed oxides has shown [49] that homogeneous solutions are formed for compositions with Ru < 2% or Ru > 98% (see Section 3.1.1). Therefore electrodes with other compositions are better described as physical mixtures and the electrochemical behaviour is most likely that of a linear superposition of the single components. It has to be considered, however, that the investigations performed by Triggs [49] concern thermodynamic equilibrium conditions. If, by means of the preparation procedure, thermodynamic equilibrium is... 

The first question to ask about the formation of interstellar molecules is where the formation occurs. There are two possibilities the molecules are formed within the clouds themselves or they are formed elsewhere. As an alternative to local formation, one possibility is that the molecules are synthesized in the expanding envelopes of old stars, previously referred to as circumstellar clouds. Both molecules and dust particles are known to form in such objects, and molecular development is especially efficient in those objects that are carbon-rich (elemental C > elemental O) such as the well-studied source IRC+10216.12 Chemical models of carbon-rich envelopes show that acetylene is produced under high-temperature thermodynamic equilibrium conditions and that as the material cools and flows out of the star, a chemistry somewhat akin to an acetylene discharge takes place, perhaps even forming molecules as complex as PAHs.13,14 As to the contribution of such chemistry to the interstellar medium, however, all but the very large species will be photodissociated rapidly by the radiation field present in interstellar space once the molecules are blown out of the protective cocoon of the stellar envelope in which they are formed. Consequently, the material flowing out into space will consist mainly of atoms, dust particles, and possibly PAHs that are relatively immune to radiation because of their size and stability. It is therefore necessary for the observed interstellar molecules to be produced locally. 

Relations (9.3.12) and (9.3.13) are intuitively clear and can be easily obtained using thermodynamic equilibrium conditions for L and H in the three states of occupancy. 

The second part of Eqn. (4.136) is true if the attempt frequency v° (Eqn. (4.131)) is independent of the composition. This kinetic steady state condition is obviously equivalent to the thermodynamic equilibrium condition. 

Of the elements considered in this study (see Table II), nickel, palladium, antimony, and lead are particularly sensitive to the presence of reduced sulfur species (S2, HS") in the groundwater. For each of these radionuclides, if sulfur speciates under thermodynamic equilibrium conditions, solid sulfide phases will control their solubility at low Eh values. The implication of this fact is illustrated in Figure 1 by a bold, dashed line that corresponds to the solubility of nickel in the reference groundwater and a patterned zone representing the total range... 

Multilayer adsorption models have been used by Asada [147,148] to account for the zero-order desorption kinetics. The two layers are equilibrated. Desorption goes from the rarefied phase only. This model has been generalized [148] for an arbitrary number of layers. The filling of the upper layer was studied with allowance for the three neighboring molecules being located in the lower one. The desorption frequency factor (CM) was regarded as being independent of the layer number. The theory has been correlated with experiment for the Xe/CO/W system [149]. Analysis of the two-layer model has been continued in Ref. [150], to see how the ratios of the adspecies flows from the rarefied phases of the first and the second layers vary if the frequency factors for the adspecies of the individual layers differ from one another. In the thermodynamic equilibrium conditions these flows were found to be the same at different ratios of the above factors. 

The relationship between the growth rate and 4 1 can be explained easily if it is considered that the faces with highest dhki also show the highest concentration of chemical and/or electrostatic bonds within the plane of the face and the minimal density of bonds in the direction perpendicular to the plane of the face. When oxides and halides are considered, the previous rule can also be formulated in the following way Faces exposing ions with the lowest coordinative unsaturation are the most stable and least reactive and hence determine the final morphology of the microcrystals under thermodynamic equilibrium conditions. 

There is a saturation value of the concentration of non-aggregated amphiphile at which phase separation occurs. The nonaggregated amphiphile and aggregates in solution are in this case in thermodynamic equilibrium with a bulk amphiphilar phase. The corresponding thermodynamic equilibrium condition introduces an upper limit, n,Sx> fur . The equilibrium condition leads to... 

A metal CMP process involves an electrochemical alteration of the metal surface and a mechanical removal of the modified film. More specifically, an oxidizer reacts with the metal surface to raise the oxidation state of the material, which may result in either the dissolution of the metal or the formation of a surface film that is more porous and can be removed more easily by the mechanical component of the process. The oxidizer, therefore, is one of the most important components of the CMP slurry. Electrochemical properties of the oxidizer and the metal involved can offer insights in terms of reaction tendency and products. For example, relative redox potentials and chemical composition of the modified surface film under thermodynamically equilibrium condition can be illustrated by a relevant Pourbaix diagram [1]. Because a CMP process rarely reaches a thermodynamically equilibrium state, many kinetic factors control the relative rates of the surface film formation and its removal. It is important to find the right balance between the formation of a modified film with the right property and the removal of such a film at the appropriate rate. 

In practice, when current flows in the system, thermodynamic equilibrium conditions no longer exist at the interfaces. The response of the PEVD system is also related to the... 

In these studies, thermodynamic equilibrium conditions were assumed. Constant pH monitoring was used as an estimator of the equilibration times involved, since a stable pH is an overall indicator of the Internal chemical stability of pH dependent processes. In order to allow the assumptions of atmospheric O2 and CO2 partial pressures, water scrubbed compressed air was pumped into the reaction vessels under constant temperature and constant vigorous mixing conditions. The air was introduced by fritted glass bubblers which had been teflon coated while air flowed through them in order to minimize the glass-solution interface. 

If the forward and reverse X coefficients of a step are much larger than all others, that step is at quasi-equilibrium (see Section 4.2). The participants in that step then are present at all times in concentrations related to one another by the thermodynamic equilibrium condition, and so can be lumped into one pseudo-component. Since the number of denominator terms in the rate equation equals the square of the number of the cycle members, this reduces the amount of algebra considerably. 

Due to the large number of components, natural waters are rather complex systems. The relative concentrations of many components, as well as the pH and Eh, are controlled by chemical equilibria. However, there are also components, in particular colloids and microorganisms, for which thermodynamic equilibrium conditions are not applicable. The complexity of the chemistry in natural waters and the non-applicability of thermodynamics are the main reasons for the fact that calculations are very difficult and problematic. The same holds for laboratory experiments with model waters results obtained with a special kind of water are, in general, not applicable for other natural waters of different origin. 

The symbols u and v here play the role of proton order parameters. Then the thermodynamic equilibrium conditions 0H/Snmf = 0 and dF/dnmf = 0 are... 

For reversible phase transitions in thermodynamic equilibrium conditions, the relation between Gibb s free energy G, internal energy U, temperature T,... 

Under the thermodynamic equilibrium condition the free energy G of a closed system can be expressed as... 

The way in which the separation of the terms of the right hand side of the entropy equation into the divergence of a flux and a source term has been achieved may at first sight seem to be to some extent arbitrary The two groups of terms must, however, satisfy a number of requirements which determine this separation uniquely First, one such requirement is that the entropy source term totai must be zero if the thermodynamic equilibrium conditions are satisfied within the system. Another requirement the source term must satisfy is that it should be invariant under a Galilean transformation (e.g., [147]), since the notations of reversible and irreversible behavior must be invariant under such a transformation. The terms included in the source term satisfy this requirement [32]. 

By measuring the spectral distribution of the upwelling infrared radiation emitted by the Earth and its atmosphere, spaceborne sensors can provide information on the vertical temperature profile and on the atmospheric abundance of radiatively active trace gases. When local thermodynamic equilibrium conditions apply, the radiance received by a detector with spectral response function y> over frequency interval Av and viewing vertically downwards is given by (see Eq. 4.69a)... 

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