Equilibria, characterization

J Sjoblom, R Lindberg, SE Friberg. Microemulsions-phase equilibria characterization, structures, applications and chemical reactions, Adv Colloid Interf Sci 65 125-287, 1996. 

Fig. 6. The four possible redox states of a system comprising two centers. Redox equilibria characterized by the potentials involved in Eqs (Al) and (A2) are indicated...

Similar to aqueous solutions studies on lanthanide complex formation in non-aqueous solutions involve complex equilibria characterized by equilibrium constants and stability constants which have been discussed in detail in Chapter 3. To recall, we define the equilibrium constants and stability constants as follows ... 

Equilibria characterizing hydrogen ion transfer reactions are among the simpler types of models. In this chapter we demonstrate the use of numerical and graphical methods and mass law equilibria in order to establish the equilibrium composition. We try to go from the simple to the more complex. Many examples are given and the equilibrium compositions are graphically displayed. Dealing with dilute solutions, we will initially often set concentrations = ac-... 

Characterization of porous activated carbon and its derivatives has been a subject of great interest for many decades. Various tools for equilibria characterization are available in the literature, and they can be broadly classified into two groups One is based on classical approaches while the other has firm foundation on molecular interaction calculations. Scientists constantly develop new tools or refine existing methods to better characterize porous carbons as the structure has significant effects on equilibria as well as kinetics. 

At equilibrium, a certain amount of KCl must pass from one phase into the other in order that the equilibrium characterized for the K and Cl ions (termed diffusible ions) by (2.2.2) may be established, i.e. 

Having looked at an example of micellar catalysis, let us next consider how such results are analyzed quantitatively. By analogy with Reaction (E), we visualize the micelle M and the substrate A entering a solubilization equilibrium characterized by an equilibrium constant K ... 

Recall that for first-order kinetics a plot of In (fraction unreacted) versus time has a slope — k. Also note that the reaction reaches an equilibrium characterized by an absorbance 0.115 the data must be corrected for this. For both the anionic and cationic micelles, qualitatively sketch, emphasizing the charge state, the micelle, the solubilized substrate, and the approaching OH" reactant. Indicate how these pictures are consistent with the experimental rate constants. 

Takahashi, M., Altschmied, L. and Hillen, W. (1986) Kinetic and equilibrium characterization of the Tet repressor-tetracycline complex by fluorescence measurements. Evidence for divalent metal ion requirement and energy transfer. J. Mol. Biol., 187, 341-348. 

Rogers GA, Kornreich WD, Hand K, Parsons SM (1993) Kinetic and equilibrium characterization of vesamicol receptor-ligand complexes with picomolar dissociation constants. Mol Pharmacol 44 633-641. 

The work appearing in the surroundings is given by this equation only when certain characteristics of the reversible process are realized. The first requirement is that th i rstem be no more than infinitesimally displaced from a state of internal equilibrium characterized by uniformity of temperature and pressure. The system then always has an identifiable set of properties, including pressure P. The second requirement is that the system be no more than infinitesimally displaced from mechanical equilibrium with its surroundings. In this event, the internal pressure P is never more than minutely out of balance with the external force, and we may make the substitution F = PA that transforms Eq. (1.1) into Eq. (1.2). Processes for which these requirements are met are said to be mechanically reversible. For such processes, Eq. (1.3) correctly yields the work appearing in the surroundings ... 

This equation, which gives the transformed integral molar enthalpy of adsorption for the adsorption equilibrium characterized by the variables T and t (or n), must not be confused with Equation (2.68), which gives the differential enthalpy of adsorption. Indeed, by combining Equations (2.31), (2.44), (2.56) and (2.63) we obtain the... 

If it is assumed that at equilibrium, characterized by the pressure p, the fractions of bare and covered surface, 80 and 0 remain constant, we can equate the rate of condensation on the bare surface to the rate of evaporation from the first layer ... 

Claudius JS, Neau SH. Kinetic and equilibrium characterization of interactions between glycopeptide antibiotics and sodium carb-oxymethyl starch. Int J Pharm 1996 144 71—79. 

Equilibrium models are widely used in assessments of trace metal bioavailability, toxicity, and transport through the environment. Properly applied, equilibrium models are powerful tools in such assessments. Due to a variety of factors, however, equilibrium modeling often falls short of its full potential. One problem, of special importance in equilibrium characterizations, is simplistic modeling. The use of simplistic chemical models is particularly important because it affects not only the modeling of complex natural systems, but also modeling of relatively simple chemical media used to generate primary thermodynamic data. 

Le Chatelier s principle assures us that if external pressure is applied to a solution, the chemical equilibrium, characterized by the equilibrium constant K, will change in the direction that reduces the solution volume, which depends on AK , so that... 

The dissolution in water of a slightly soluble ionic compound reaches an equilibrium characterized by a solubility-product constant, Kgp, that is much less than 1. Addition of a common ion lowers such a compound s solubility. Lowering the pH (adding HsO" ) increases the solubility if the anion of the ionic compound is that of a weak acid. 

In some solvents, such as K+- OR-DMSO, it can be shown that the internal return equilibrium characterized by k /k is fast relative to the dissociation process characterized by k2- In this process, the base returns the proton to the carbanion faster than the proton donor exchanges with other molecules from solution. If internal return is important under a given set of conditions, how might that affect the correlation between observed kinetic and thermodynamic acidity How can the occurrence of internal return be detected experimentally ... 

The sessile drop method is similar to the pendant drop one [Sakai, 1965]. The same scheme is used, but in this case the droplet is resting on a plane surface immersed in the second component (see Figure 4.8) — Vj is calculated from analysis of the drop shape at equilibrium (characterized by the relative magnitude of the shape parameters, X and Z, dehned in Figure 4.8), knowing the densities of the polymeric huids at the temperature of measurement. 

Vasicek O (1977) An Equilibrium Characterization of the Term Structure. Journal of Financial Economics 5 177-188. 

Vasicek, O. An equilibrium characterization of the term structure. Journal of Financial... 

As any ring-opening polymerization, the polymerization of lactams is characterized by competition between the intermolecular reaction resulting in a linear polyamide and the intramolecular reaction of cyclization. Thus, if thermodynamically feasible, as indicated by a negative value of the free-energy change of polymerization AGp, the conversion of lactam to the linear polyamide can be realized if an appropriate reaction path exists for a reasonable rate in a polymer-monomer equilibrium characterized by a preponderance of linear macromolecules. The corresponding equilibrium monomer concentration [M]g is related to the standard enthalpy and entropy ASp of polymerization and to... 

From thermodynamic point of view, it is not possible to decide whether we have and ne or Mad the interface. If the equilibrium characterized by Eq. (51) is considered as a reality, only two from the three reaction partners can be considered as independent components of the (thermodynamic) system. Depending on... 

These observations suggest that ionic hydration under these conditions might be described well by an adsorption model, and that idea can be tested directly using simulation data [51]. An adsorption model has been used to determine the local density of CF3H about a nonelectrolyte. [62] If one defines a local solvent density pi c by the average simulated density over the first solvent shell, then for an adsorption equilibrium, characterized by constant K, between the bulk density p and the first shell leads to the relation... 

In an open system with a gas phase moving parallel to the surface of the shallow water pool formed, the attainment of an equilibrium characterized by the I2 partition coefficient R applies only for a boundary layer that is limited by the flow characteristics, and not for the whole moving gas phase. This means, then, that there is a greatly reduced transport of I2 from the liquid to the gas phase, as compared to the assumption of an instantaneous attainment of equilibrium for the entire gas phase. It can be theoretically derived that the fraction of I2 released (X) in time t is given by... 

If, in their use conditions, polymers are subjected to a residual molecular mobility (Ji motions in glassy polymers, a motions in the rubbery amorphous phase of semi-crystalline polymers), they will undergo a molecular reorganization towards the thermodynamic equilibrium, characterized by ... 

Most Basic Characteristics. Tend toward thermodynamic equilibrium characterized by maximum entropy [it is stationary with time, stationary in the sense of death (i.e., nothing happens)]. 

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