Dynamic equilibrium defined

In Figure 6.7 is shown the sequence of regimes that can be met from irreversible in the forward direction to irreversible in the backward direction in going through the quasireversible regime around r. 2 = 1. The dynamic equilibrium, defined by the equality between forward and backward flows, is reached exactly for - 1-... 

There is no need of a reference effort because the dynamic equilibrium defined by the equality of forward and backward flows corresponds also in a conductive dipole to the equality between polar efforts. 

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. 

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... 

Whenever we see the symbol it means that the species on both sides of the symbol are in dynamic equilibrium with each other. Although products (water molecules in the gas phase) are being formed from reactants (water molecules in the liquid phase), the products are changing back into reactants at a matching rate. With this picture in mind, we can now define the vapor pressure of a liquid (or a... 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

B is transforming back to A. The result, after a time, is a dynamic equilibrium condition in which the total numbers of A and B remain fairly constant even though the individual ingredients are constantly switching from one form to the other. The equilibrium constant eq for this situation is defined as... 

Given that, under the defined conditions, there is no interfacial kinetic barrier to transfer from phase 2 to phase 1, the concentrations immediately adjacent to each side of the interface may be considered to be in dynamic equilibrium throughout the course of a chronoamperometric measurement. For high values of Kg the target species in phase 2 is in considerable excess, so that the concentration in phase 1 at the target interface is maintained at a value close to the initial bulk value, with minimal depletion of Red in phase 2. Under these conditions, the response of the tip (Fig. 11, case (a)] is in agreement with that predicted for other SECM diffusion-controlled processes with no interfacial kinetic barrier, such as induced dissolution [12,14—16] and positive feedback [42,43]. A feature of this response is that the current rapidly attains a steady state, the value of which increases... 

Most chemical reactions do not progress completely from reactants to products. Instead, the net reaction stops in the forward direction when equilibrium is established. Analysis of the contents of the reaction vessel would show a constant concentration of monomers and polymer once equilibrium is reached. This situation is actually a dynamic equilibrium, where the monomers are forming polymers at the same rate as the polymers depolymerize to monomer. Therefore, at equilibrium, the net concentrations of any one species remains constant. The amount of monomer converted into polymer will be defined by the equilibrium constant, K. This constant is the ratio of the concentration of the products to the reactants, with each concentration raised to the stoichiometric coefficients in the balanced equation. For Eq. 3.5 ... 

Histone acetylation is a reversible amidation reaction involving defined e-amino groups of lysine residues (see Fig. 6) at the N-terminal tails of core histones. The highly dynamic equilibrium between the acetylated and non-acetylated states of lysine is maintained by two enzymatic groups, referred to as histone acetyltransferases (HATs) and histone deacetylases (HDACs). 

Recall that the concept of Fermi quasilevels, suggested by Shockley (1950), can be introduced as follows. Under steady state photogeneration of charge carriers, a dynamic equilibrium arises in a semiconductor between generation and recombination of electron-hole pairs. As a result, certain steady state (but not equilibrium ) concentration values nj and p are established. The quasiequilibrium concentrations ng and pg are defined by the relations ng = n0 + A and Po = Po + Ap> and since photogeneration of carriers occurs in pairs, we have An = Ap = A. Let the following inequalities be satisfied ... 

A wide range of monomers, including styrene, can be polymerised in this way. Cu(I)/ligand is a commonly used metal complex which can act as a catalyst. These metal complexes must have the ability to be oxidised to a higher oxidation state. In the case of copper, the oxidised form of the metal is Cu(II), the deactivator of the process. The dynamic equilibrium of this method is responsible for the well-defined behaviour of these kinds of polymerisations. This equilibrium can, in its turn, be controlled by the ratio of concentrations of both the metal-complex forms. In this chapter, preliminary research results are described concerning the voltammetric determi-... 

The spin density matrix Pj(t) which describes the properties of any spin system of a molecule A, is defined as follows. We assume that the density matrices Pj(0), j = 1, 2,..., S, which describe the individual components of the dynamic equilibrium at any arbitrary time zero, are known explicitly, and that at any time t such that t > t > 0 the pj(t ) matrices are already defined. Our reasoning is applied to a pulse-type NMR experiment, and we therefore construct the equation of motion in a static magnetic field. The p,(t) matrix is the weighted average over the states involved, according to equation (5). The state of a molecule A, formed at the moment t and persisting as such until t, is given by the solution of equation (35) with the super-Hamiltonian H° ... 

Chemical equilibria A chemical reaction often exists in a state of dynamic equilibrium. The equilibrium constant (K) defines the ratio of the concentrations of substrates and products at equilibrium. Enzymes do not alter the equilibrium position, but do accelerate the attainment of the equilibrium position by speeding up the forward and reverse reactions. 

It should be pointed out at this juncture that strict thermodynamics treatment of the film-covered surfaces is not possible [18]. The reason is difficulty in delineation of the system. The interface, typically of the order of a 1 -2 nm thick monolayer, contains a certain amount of bound water, which is in dynamic equilibrium with the bulk water in the subphase. In a strict thermodynamic treatment, such an interface must be accounted as an open system in equilibrium with the subphase components, principally water. On the other hand, a useful conceptual framework is to regard the interface as a 2-dimensional (2D) object such as a 2D gas or 2D solution [ 19,20]. Thus, the surface pressure 77 is treated as either a 2D gas pressure or a 2D osmotic pressure. With such a perspective, an analog of either p- V isotherm of a gas or the osmotic pressure-concentration isotherm, 77-c, of a solution is adopted. It is commonly referred to as the surface pressure-area isotherm, 77-A, where A is defined as an average area per molecule on the interface, under the provision that all molecules reside in the interface without desorption into the subphase or vaporization into the air. A more direct analog of 77- c of a bulk solution is 77 - r where r is the mass per unit area, hence is the reciprocal of A, the area per unit mass. The nature of the collapsed state depends on the solubility of the surfactant. For truly insoluble films, the film collapses by forming multilayers in the upper phase. A broad illustrative sketch of a 77-r plot is given in Fig. 1. 

The kind of attachment of the metal coordinating groups to the cavitand is an important structure-defining parameter. Hong et al. studied the self-assembly of a cavitand 15 functionalized with pyridyl groups via flexible ether linkages (Fig. 5) [48, 49]. Due to the conformational freedom of the connection, intramolecular coordination of the metal (Pt2+ and Pd2+) centers is observed in competition with intermolecular complexation leading to the supramolecular capsules 16a-b. While the capsules 16a b and the half-capsules 17a-b are in dynamic equilibrium in nitromethane, the dimeric capsule is formed exclusively in chloroform/methanol mixtures. 

The most defined relation appears to be that between the volume and stability of a foam formed by gas barbotage through a foaming solution [93]. In this case the rate of foaming wF is determined by the difference between the rate of gas supply wc, accounting for the liquid volume wl transformed into a foam per unit time and the volumetric rate of foam collapse wcou. After a certain time a dynamic equilibrium is achieved for foams of low stability, i.e. wF = wcoU. 

The Vapor Pressure of Liquids. Vapor pressure is defined as the pressure exerted by a vapor in equilibrium with its liquid. Consider a closed, evacuated container which has been partially filled with a liquid. The molecules of the liquid are in constant motion but not all the molecules move with the same velocity and there will be some which possess a relatively high kinetic energy. If one of these fast moving molecules reaches the liquid surface, it may possess sufficient energy to overcome the attractive forces in the liquid and pass into tiie vapor space above. As the number of molecules in the vapor phase increases the rate of return to the liquid phase also increases and eventually a condition of dynamic equilibrium is attained when the number of molecules leaving the liquid is equal to the number returning. The molecules in the vapor phase obviously exert a pressure on the containing vessel and this pressure is known as the vapor pressure. 

A second way of defining the distribution constant results from considering a single solute molecule. Under the conditions of dynamic equilibrium, this single molecule spends some of its time in each phase. The time spent in the stationary phase relative to the time spent in the mobile phase is also given by the distribution constant. This definition forms the basis of the chromatography theory. 

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