Apparent equilibrium: definition

Chemically bound water is most reasonably defined as including that present in interlayer spaces, or more firmly bound, but not that present in pores larger than interlayer spaces. As will be seen in Chapter 8, the distinction between interlayer space and micropores is not sharp water adsorbed on surfaces of pores further blurs the definition. From the experimental standpoint, the determination is complicated by the fact that the amount of water retained at a given RH depends on the previous drying history of the sample and on the rate at which water is removed. An approximate estimate is obtained by equilibrating a sample, not previously dried below saturation, with an atmosphere of 11% RH (F12,F13,F14). Saturated aqueous LiCl HjO gives the required RH (partial pressure of water vapour = 2,7 torr at 25°C). To achieve apparent equilibrium in a reasonable time (several days), the sample must be crushed and the system evacuated the salt solution should be stirred, at least intermittently. Young and Hansen (Y5) found the composition of the C-S-H in C3S paste thus... 

This apparently peculiar definition arises from the transition from electrostatic units to SI units). The debye can also be defined as the dipole moment of two charges e separated by 0.2082 A. If 8 is the fraction of a unit charge on each atom in a diatomic molecule (q = e8) and R is the equilibrium bond length, then... 

Here Xa, Ya are strictly equilibrium mole fractions for component A in the adsorbed phase and adsorbate (fluid) phase, respectively as are Xb, Fb for component B. For equilibrium-based adsorptive separation process, the adsorbent selectivity is the same as the separation factor as defined in Eq. (1). Apparently, this definition is not applicable to other processes based on kinetic and steric effects. In a kinetically controlled adsorption process, the adsorbent selectivity depends on both equilibrium and kinetic effects. A simplified definition for adsorbent separation factor is given by Ruthven et al. ... 

Combining Equations 18.1-18.4 and using the definitions of the partition coefficients, the apparent equilibrium constant biphasic fo " the biphasic system can be expressed as... 

A theoretical analysis of charge distribution within supercomplexes (or clusters in which the movement of diffusible carriers is restricted) has been developed by Lavergne et al [4]. This theory predicts the evolution of the redox state of the carriers under continuous illumination or flash excitation for any cluster stoichiometry. The predictive power of this treatment is illustrated by the analysis of the light-induced oxidation of primary and secondary donors in isolated centers of Rhodopseudomonas viridis (Fig. 3). In this case, it is definitely established that the secondary donors (cytochromes) are irreversibly bound to the reaction center. In the absence of mediators, no electron exchange is expected to occur between photocenters. In the presence of 200yM ascorbate, only two of the four cytochromes (cyt 556 and cyt 559) are in their reduced state prior to the illumination. As expected, the apparent equilibrium constant between P and the cytochromes measured during the course of illumination is much lower than that computed from the value of the redox potentials (K = 50 for cyt 559 and K 1500 for cyt 556). The fit between the experimental data and the theoretical simulation (dashed lines) is excellent and clearly demonstrates that the measurement of electron transfer reactions under weak illumination is a powerful tool to characterize the degree of structuration of a photosynthetic electron transfer chain. 

By definition, electrode II at which oxidation is the predominant reaction is the anode, whereas electrode I at which reduction is the predominant reaction is the cathode. It is apparent that the removal of electrons from Ag will result in the potential of its interface becoming more positive, whilst the concomitant supply of electrons to the interface of Ag, will make its potential become more negative than the equilibrium potential ... 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

With the assumptions, just given, division of (7a) and (7b) leads to a simple definition (8) of an apparent constant for the dissociation of TS-cat into TS and catalyst. Obviously, KTS is a woW-equilibrium constant, since... 

Fig. 4.18 shows the result of Cd2+ adsorption on illite in presence of Ca2+ (Comans, 1987). The data are fitted by Freundlich isotherms after an equilibration time of 54 days. It was shown in the experiments leading to these isotherms that adsorption approaches equilibrium faster than desorption. Comans has also used 109Cd to assess the isotope exchange he showed that at equilibrium (7-8 weeks equilibration time) the isotopic exchangeabilities are approximately 100 % i.e., all adsorbed Cd2+ is apparently in kinetic equilibrium with the solution. The available data do not allow a definite conclusion on the specific sorption mechanism. 

Each of these dissociation reactions also specifies a definite equilibrium concentration of each product at a given temperature consequently, the reactions are written as equilibrium reactions. In the calculation of the heat of reaction of low-temperature combustion experiments the products could be specified from the chemical stoichiometry but with dissociation, the specification of the product concentrations becomes much more complex and the s in the flame temperature equation [Eq. (1.11)] are as unknown as the flame temperature itself. In order to solve the equation for the n s and T2, it is apparent that one needs more than mass balance equations. The necessary equations are found in the equilibrium relationships that exist among the product composition in the equilibrium system. 

The p/<, of a base is actually that of its conjugate acid. As the numeric value of the dissociation constant increases (i.e., pKa decreases), the acid strength increases. Conversely, as the acid dissociation constant of a base (that of its conjugate acid) increases, the strength of the base decreases. For a more accurate definition of dissociation constants, each concentration term must be replaced by thermodynamic activity. In dilute solutions, concentration of each species is taken to be equal to activity. Activity-based dissociation constants are true equilibrium constants and depend only on temperature. Dissociation constants measured by spectroscopy are concentration dissociation constants." Most piCa values in the pharmaceutical literature are measured by ignoring activity effects and therefore are actually concentration dissociation constants or apparent dissociation constants. It is customary to report dissociation constant values at 25°C. 

This has been studied much less frequently and appears to be a rather more complex reaction. The first results obtained, for the butyl-lithium, styrene reaction in benzene have already been described. In a similar way the addition of butyllithium to 1,1-diphenylethylene shows identical kinetic behaviour in benzene (26). Even the proton extraction reaction with fluorene shows the typical one-sixth order in butyllithium (27). It appears therefore that in benzene solution at least, lithium alkyls react via a small equilibrium concentration of unassociated alkyl. This will of course not be true for reactions with polar molecules for reasons which will be apparent later. No definite information can be obtained on the dissociation process. It is possible that the hexamer dissociates completely on removal of one molecule or that a whole series of penta-mers, tetramers etc. exist in equilibrium. As long as equilibrium is maintained, the hexamer is the major species present and only monomeric butyllithium is reactive, the reaction order will be one-sixth. A plausible... 

If there is no constant influx of fluid of a certain composition, decomposition of magnetite ceases. The limiting case is a dry system closed to CO2. By analogy with systems closed to water, in such a system with constant pressure P — Pf = const) the fluid phase disappears entirely, and the Mgt + Sid + Hem association (system Fe-C-O) becomes bivariant and can exist stably below the P-T curve (see Fig. 77) in the stability field of the Sid -1- Hem (+ fluid) association. From these considerations the Mgt -I- Sid + Hem association cannot be used to judge the low-temperature limit of mineral formation the upper limit is fixed quite definitely inasmuch as removal of CO2 begins at P P and the reaction proceeds irreversibly to the right. The extensive occurrence of magnetite in oxide-carbonate iron-formations of low-rank metamorphism apparently indicates the absence of equilibrium or even a deficiency of COj and special dry conditions. 

The reaction temperature profile is of particular importance because the reaction rate responds vigorously to temperature changes. Figure 82 plots lines of constant reaction rate illustrating its dependence on temperature and ammonia concentration in the reacting synthesis gas. The line for zero reaction rate corresponds to the temperature-concentration dependence of the chemical equilibrium. From Figure 82 it is apparent that there is a definite temperature at which the rate of reaction reaches a maximum for any given ammonia concentration. Curve (a) represents the temperature-concentration locus of maximum reaction rates. To maintain maximum reaction rate, the temperature must decrease as ammonia concentration increases. 

Tautomerism.—While therefore these three cyanogen compounds do not exist in isomeric forms as do the alkyl cyanogen compounds yet we cannot assign one definite formula to each compound because the evidence goes to show that sometimes one formula and sometimes the other is the true representation of the constitution. The two forms probably exist together in equilibrium the conditions of which are different for each of the compounds so that though they are very similar in character their apparent constitution is different. Thus we have another inter-... 

When solid ammonium chloride is heated in vacuo or in an atmosphere of an inert gas, a definite equilibrium pressure is reached at each temperature, in apparent contradiction with... 

The design of the experiment is not well suited for an equilibrium analysis, but definitely showed that Ag2Se03(cr) is dissolved by an excess of SeOj. No equilibrium constants were derived in the paper from these data. The review calculated ((A.22), 298.15 K) from the data at the lowest total selenite concentration and pH < 6. The protonation constants from the first series were used in the calculation. The result was log Ai, ((A.22), 298.15 K) = - (15.20 + 0.15). Hence there is a significant difference between the values of the solubility product determined by the two techniques, which cannot be accounted for and apparently not observed by the authors. 

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