Equilibrium, dynamic

The direction of a chemical reaction or a phase transformation can be determined from the equilibrium thermodynamic properties of the phases involved. Note, though, that the speed of any transformation is not accessible from thermodynamics. Thermodynamics clearly states that diamond will transform into graphite at room temperature, but the rate of the reaction is insignificant. This chapter is concerned mainly with the kinetics of reactions, the speed at which they occur. Marrying this aspect with thermodynamics lies outside the scope of this chapter, but some introductory notes are given in Section S3.2. 

Dynamic equilibrium is an important and powerful concept in many areas of science. It is useful when discussing matters as diverse as the population of plants or animals in a region, the ozone layer in the 

While equilibrium indicates a stable state, it is crucial to understand that equilibrium does not necessarily imply a completely static and unchanging state. We will often encounter the concept of dynamic equilibrium in our discussions of kinetics. In a dynamic equilibrium, backward and forward kinetic processes of equal but opposite rates occur. For example, a glass of water can be in dynamic equilibrium with 100% relative humidity air above it. In such a situation, the overall level of water in the 

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Fluctuations of observables from their average values, unless the observables are constants of motion, are especially important, since they are related to the response fiinctions of the system. For example, the constant volume specific heat of a fluid is a response function related to the fluctuations in the energy of a system at constant N, V and T, where A is the number of particles in a volume V at temperature T. Similarly, fluctuations in the number density (p = N/V) of an open system at constant p, V and T, where p is the chemical potential, are related to the isothemial compressibility iCp which is another response fiinction. Temperature-dependent fluctuations characterize the dynamic equilibrium of themiodynamic systems, in contrast to the equilibrium of purely mechanical bodies in which fluctuations are absent. 

Hoover W G 1985 Canonical dynamics equilibrium phase-space distributions Phys. Rev. A 31 1695-7... 

The acronym LASER (Light Amplification via tire Stimulated Emission of Radiation) defines the process of amplification. For all intents and purjDoses tliis metliod was elegantly outlined by Einstein in 1917 [H] wherein he derived a treatment of the dynamic equilibrium of a material in a electromagnetic field absorbing and emitting photons. Key here is tire insight tliat, in addition to absorjDtion and spontaneous emission processes, in an excited system one can stimulate tire emission of a photon by interaction witli tire electromagnetic field. It is tliis stimulated emission process which lays tire conceptual foundation of tire laser. 

Hoover W G 1985. Canonical Dynamics Equilibrium Phase-space Distributions. Physical Revic A31 1695-1697. 

The Clapeyron equation expresses the dynamic equilibrium existing between the vapor and the condensed phase of a pure substance ... 

The BET treatment is based on a kinetic model of the adsorption process put forward more than sixty years ago by Langmuir, in which the surface of the solid was regarded as an array of adsorption sites. A state of dynamic equilibrium was postulated in which the rate at which molecules arriving from the gas phrase and condensing on to bare sites is equal to the rate at which molecules evaporate from occupied sites. 

Biosynthesis of Protein. The dynamic equilibrium of body protein was confirmed by animal experiments using A/-labeled amino acids in 1939 (104). The human body is maintained by a continuous equilibrium between the biosynthesis of proteins and their degradative metabolism where the nitrogen lost as urea (about 85% of total excreted nitrogen) and other nitrogen compounds is about 12 g/d under ordinary conditions. The details of protein biosynthesis in living cells have been described (2,6) (see also Proteins). 

In accordance with observations in halodinitrobenzene derivatives, fluoropyrazines are by far the most reactive of the halopyrazines. Fluoropyrazine undergoes facile reaction with sodium azide to give azidopyrazine (27), which exists in dynamic equilibrium with tetrazolo[l,5-a]pyrazine (28) (66JHC435). 

Wet-bulb temperature is the dynamic equilibrium temperature attained by a water surface when the rate of heat transfer to the surface by convection equals the rate of mass transfer away from the surface. At equilibrium, if neghgible change in the dry-bulb temperature is assumed, a heat balance on the surface is... 

Tti e wet-bulb temperature is established by a dynamic equilibrium between heat and mass transfer when liquid evaporates from a small mass, such as the wet bulb of a thermometer, into a veiy large mass of gas such that the latter undergoes no temperature or humidity change. It is expressed by the relationship... 

When the heat for evaporation in the constant-rate period is supplied by a hot gas, a dynamic equilibrium establishes the rate of heat transfer to the material and the rate of vapor removal from the surface ... 

Stratospheric ozone is in a dynamic equilibrium with a balance between the chemical processes of formation and destruchon. The primary components in this balance are ultraviolet (UV) solar radiation, oxygen molecules (O2), and oxygen atoms (O) and may be represented by the following reactions ... 

This description of the dynamics of solute equilibrium is oversimplified, but is sufficiently accurate for the reader to understand the basic principles of solute distribution between two phases. For a more detailed explanation of dynamic equilibrium between immiscible phases the reader is referred to the kinetic theory of gases and liquids. 

Coefficient A and exponent a must be evaluated experimentally. Experiments have shown that A and a are themselves functions of the Reynolds number. Equation 47 shows that the resistance force increases with increasing velocity. If the force field (e.g., gravity) has the same potential at all points, a dynamic equilibrium between forces P and R develops shortly after the particle motion begins. As described earlier, at some distance from its start the particle falls at a constant velocity. If the acting force depends on the particle location in space, in a... 

The perfluoroalkylsilver complexes exist in a dynamic equilibrium in solution with solvated silver ion and anionic perfluoroalkylsilver complexes such as Ag[CF(CF5) r [277] The triflnoromethylated silver complex, Ag(CF3)4 , is prepared via reaction of bis(trifIuoromethyl)cadmium with silver nitrate in acetoni trile [278]... 

Additional evidence that a dynamic equilibrium exists between an enamine, N-hemiacetal, and aminal has been presented by Marchese (41). It should be noted that no acid catalysts were used in the reactions of aldehydes and amines discussed thus far. The piperidino enamine of 2-ethylhexanal (0.125 mole), morpholine (0.375 mole), and p-toluene-sulfonic acid (1.25 x 10 mole) diluted with benzene to 500 ml were refluxed for 5 hr. At the end of this time the enamine mixture was analyzed by vapor-phase chromatography, which revealed that exchange of the amino residue had occurred in a ratio of eight morpholine to one piperidine. Marchese proposed a scheme [Eqs. (4), (5) and (6)] to account for these... 

Vapor pressure is an important property of liquids, and to a much lesser extent, of solids. If a liquid is allowed to evaporate in a confined space, tlie pressure of Uie vapor phase increases as Uie amount of vapor increases. If Uiere is sufficient liquid present, Uie pressure in Uie vapor space eventually comes to equal exacUy Uie pressure exerted by the liquid at its own surface. At Uiis point, a dynamic equilibrium exists in wliich vaporization and condensation take place at equal rates and Uie pressure in Uie vapor space remains constant. The pressure exerted at equilibrium is called Uie vapor pressure of the liquid. Solids, like liquids, also exert a vapor pressure. EvaporaUon of solids (sublimaUon) is noUccable only for Uie few solids characterized by appreciable vapor pressures. 

It is clear that pure" anhydrous sulfuric acid, far from being a single substance in the bulk liquid phase, comprises a dynamic equilibrium involving at least seven well-defined species. The... 

O to give H-SOj rather than HO-S02 (C, symmetry). However, recent O nmr studies appear to provide evidence for the existence in solution of a dynamic equilibrium between the two i.somers H-SOl - HO-S02 ... 

Similar considerations apply to nitrogen-containing heterocycles carrying acidic groups, for example 2-hydroxypteridine, but the situation is further complicated by lactam-lactim tautomerism in the neutral species. Thus, hydroxypteridines exist predominantly as lactams, such as 6, in dynamic equilibrium with small amounts of lactims, such as 7. There is, in consequence, a decrease in the aromatic... 

Because of the dynamic equilibrium between neutral species and their anions, the rate constants for reactions 2 and 3 and those for reactions 4 and 5 cannot be evaluated separately. The relation between and the above constants is... 

W.G. Hoover, Canonical dynamics Equilibrium phase-space distributions,... 

For simplicity a cell consisting of two identical electrodes of silver immersed in silver nitrate solution will be considered first (Fig. 1.20a), i.e. Agi/AgNOj/Ag,. On open circuit each electrode will be at equilibrium, and the rate of transfer of silver ions from the metal lattice to the solution and from the solution to the metal lattice will be equal, i.e. the electrodes will be in a state of dynamic equilibrium. The rate of charge transfer, which may be regarded as either the rate of transfer of silver cations (positive charge) in one direction, or the transfer of electrons (negative charge) in the opposite direction, in an electrochemical reaction is the current I, so that for the equilibrium at electrode I... 

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