Thermodynamics Thermodynamic equilibrium

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. 

In the preceding derivation, the repulsion between overlapping double layers has been described by an increase in the osmotic pressure between the two planes. A closely related but more general concept of the disjoining pressure was introduced by Deijaguin [30]. This is defined as the difference between the thermodynamic equilibrium state pressure applied to surfaces separated by a film and the pressure in the bulk phase with which the film is equilibrated (see section VI-5). 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

The true thermodynamic equilibrium constant, Ksp, for the solubility of AglOa, therefore, is... 

Several features of equation 6.50 deserve mention. First, as the ionic strength approaches zero, the activity coefficient approaches a value of one. Thus, in a solution where the ionic strength is zero, an ion s activity and concentration are identical. We can take advantage of this fact to determine a reaction s thermodynamic equilibrium constant. The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolated... 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

In this experiment the equilibrium constant for the dissociation of bromocresol green is measured at several ionic strengths. Results are extrapolated to zero ionic strength to find the thermodynamic equilibrium constant. Equilibrium Constants for Calcium lodate Solubility and Iodic Acid Dissociation. In J. A. Bell, ed. Chemical Principles in Practice. Addison-Wesley Reading, MA, 1967. 

Gordus, A. A. Ghemical Equilibrium 1. The Thermodynamic Equilibrium Goncept, /. Chem. Educ. 1991, 68, 138-140. 

The amide formation reaction (highlighted by the circle) leads to the production of a hydrogen-bonded dimer (ZZ) of the reaction product Z with the template Z. The dimer is in thermodynamic equilibrium with free template in the reaction medium. 

Basic Thermodynamics. Equilibrium-phase behavior of mixtures is governed by the free energy of mixing and how this quantity, consisting of enthalpic... 

From a general point of view, the tautomeric studies can be divided into 12 areas (Figure 20) depending on the migrating entity (proton or other groups, alkyl, acyl, metals. ..), the physical state of the study (solid, solution or gas phase) and the thermodynamic (equilibrium constants) or the kinetic (isomerization rates) approach. 

Mass-Transfer Principles Dilute Systems When material is transferred from one phase to another across an interface that separates the two, the resistance to mass transfer in each phase causes a concentration gradient in each, as shown in Fig. 5-26 for a gas-hquid interface. The concentrations of the diffusing material in the two phases immediately adjacent to the interface generally are unequal, even if expressed in the same units, but usually are assumed to be related to each other by the laws of thermodynamic equihbrium. Thus, it is assumed that the thermodynamic equilibrium is reached at the gas-liquid interface almost immediately when a gas and a hquid are brought into contact. 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

Eroducts of reaction, the membrane reaclor can make conversion eyond thermodynamic equilibrium in the absence of separation. 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

The anticipated content of impurities in the refined metal may be calculated a priori by assuming thermodynamic equilibrium at both metal/gas interfaces, and using the relevant stabilities of tire gaseous iodides. Adequate thermodynamic data could provide the activities of the impurities widr that of zirconium close to unity, but tire calculation of tire impurity transport obviously requires a knowledge of activity coefficients in the original impure material, which are not sufficiently well known. 

It follows that the position of thermodynamic equilibrium will change along the reactor for those reactions in which a change of tire number of gaseous molecules occurs, and therefore that the degree of completion and heat production or absorption of the reaction will also vaty. This is why the external control of the independent container temperature and the particle size of the catalyst are important factors in reactor design. 

A number of metals, such as copper, cobalt and h on, form a number of oxide layers during oxidation in air. Providing that interfacial thermodynamic equilibrium exists at the boundaries between the various oxide layers, the relative thicknesses of the oxides will depend on die relative diffusion coefficients of the mobile species as well as the oxygen potential gradients across each oxide layer. The flux of ions and electrons is given by Einstein s mobility equation for each diffusing species in each layer... 

Constitutive relation An equation that relates the initial state to the final state of a material undergoing shock compression. This equation is a property of the material and distinguishes one material from another. In general it can be rate-dependent. It is combined with the jump conditions to yield the Hugoniot curve which is also material-dependent. The equation of state of a material is a constitutive equation for which the initial and final states are in thermodynamic equilibrium, and there are no rate-dependent variables. 

In the original announcement of the workshop the participants were told that everything was to be taken from methanol synthesis except the kinetics. Some may have interpreted this to mean that the known thermodynamic equilibrium information of the methanol synthesis is not valid when taken together with the kinetics. This was not intended, but... 

It is essential, however, to follow a r rous experimental protocol for such applications. To maintain the quantitadve character of NMR spectroscopy, the reped-tion rate of signal averaging experiments has to be at least five times the longest spin-latdce relaxadon dme present in the sample. This waiting period is necessary to ensure that the magnetizadon is probed in a reproducible state, corresponding to thermodynamic equilibrium. 

Local Thermodynamic Equilibrium (LTE). This LTE model is of historical importance only. The idea was that under ion bombardment a near-surface plasma is generated, in which the sputtered atoms are ionized [3.48]. The plasma should be under local equilibrium, so that the Saha-Eggert equation for determination of the ionization probability can be used. The important condition was the plasma temperature, and this could be determined from a knowledge of the concentration of one of the elements present. The theoretical background of the model is not applicable. The reason why it gives semi-quantitative results is that the exponential term of the Saha-Eggert equation also fits quantum-mechanical expressions. 

It is an inference naturally suggested by the general increase of entropy which accompanies the changes occurring in any isolated material system that when the entropy of the system has reached a maximum, the system will be in a state of equilibrium. Although this principle has by no means escaped the attention of physicists, its importance does not seem to have been duly appreciated. Little has been done to develop the principle as a foundation for the general theory of thermodynamic equilibrium (my italics). ... 

At the beginning of the century, nobody knew that a small proportion of atoms in a crystal are routinely missing, even less that this was not a mailer of accident but of thermodynamic equilibrium. The recognition in the 1920s that such vacancies had to exist in equilibrium was due to a school of statistical thermodynamicians such as the Russian Frenkel and the Germans Jost, Wagner and Schollky. That, moreover, as we know now, is only one kind of point defect an atom removed for whatever reason from its lattice site can be inserted into a small gap in the crystal structure, and then it becomes an interstitial . Moreover, in insulating crystals a point defect is apt to be associated with a local excess or deficiency of electrons. 

---