Equilibria experimental data

Figure 10,4 Applications of the local lattice distortion model to mineral-hydrothermal solution equilibria. Experimental data from liyama (1972) for Ba/K and Sr/K, Volfinger (1970) for Li/K, and Roux (1971b) for Rb/Na. Reprinted from liyama (1974), Bullettin de la Societee Francaise de Mineralogie et Cristallographie, 97, 143-151, with permission from Masson S.A., Paris, France.

As with multicomponent vapor-liquid and liquid-liquid equilibria, experimental data for multicomponent gas-solid adsorbent equilibria are scarce and less accurate than the corresponding data for pure gases. 

A significant advantage of the Wilson equation is that it can be used to calculate the equilibrium compositions for multicomponent systems using only the Wilson coefficients obtained for the binary pairs that comprise the multicomponent mixture. The Wilson coefficients for several hundred binary systems are given in the DECHEMA vapour-liquid data collection, DECHEMA (1977), and by Hirata (1975). Hirata gives methods for calculating the Wilson coefficients from vapour liquid equilibrium experimental data. 

Figure 9,13 Relationship between activity of H2O in gaseous phase and molar amount of H2O in melt at equilibrium. Experimental data from Burnham and Davis (1974) ( ) Fraser (1975b) ( ) Kurkjian and Russel (1958) ( ). Reprinted from B. J. Wood and D. G. Fraser, Elementary Thermodynamics for Geologists, 1976, by permission of Oxford University Press.

A recent paper by Liapis et al. (46) suggested that the Langmuir model could provide a satisfactory correlation of the equilibrium experimental data of the adsorption of lysozyme onto its antibody immobilized on nonporous silica particles. 

Henry s constant, 4 High-pressure phase equilibrium experimental data, 259-352 experimental methods, 5... 

Vapor-liquid equilibrium experimental data, 21-60 experimental methods, 2 Volume... 

By fitting the above adsorption isotherm equation with equilibrium experimental data, the parameters n and q can be obtained hence the energy distribution F(z) is obtained, from which one could readily determine the micropore size distribution from eq. (4.4-27). 

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. 

The method for studying intennediate exchange in NMR is to obtain an excellent equilibrium spectmm of tlie system as a fiinction of temperature. Then the theoretical apparatus developed above can be used to simulate and to fit the experimental data, in order to obtain the rate data. 

The vapor-liquid equilibrium of the binary mixture is well fitted by Van Laar s equations (228). It was determined from 100 to 760 mm Hg. and the experimental data was correlated by the Antoine equation (289, 290), with P in mm Hg and t in °C ... 

The term heat of adsorption has been defined in a number of different ways. Unfortunately, the initial and final states of the adsorption system and the conditions under which the exchange of heat takes place have not always been adequately defined. As in all applications of thermodynamics, it is essential that the experimental data refer to a system which has reached equilibrium. 

In addition to thermodynamically based predictions of Hquid—Hquid equihbria, a great deal of experimental data is to be found in the research hterature (26). A Hquid—Hquid equilibrium data bank is also available (27). 

Essential for synthesis considerations is the abiUty to determine the amount of ammonia present ia an equiUbrium mixture at various temperatures and pressures. ReHable data on equiUbrium mixtures for pressures ranging from 1,000 to 101,000 kPa (10 —1000 atm) were developed early on (6—8) and resulted ia the determination of the reaction equiUbrium constant (9). Experimental data iadicates that is dependent not only on temperature and pressure, but also upon the ratio of hydrogen and nitrogen present. Table 3 fists values for the ammonia equilibrium concentration calculated for a feed usiag a 3 1 hydrogen to nitrogen ratio and either 0 or 10% iaerts (10). 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

When liquid-phase resistance is important, particular care should be taken in employing any given set of experimental data to ensure that the equilibrium data used conform with those employed by the original author in calculating values of fci or Hi. Extrapolation to widely different couceutratiou ranges or operating conditions should... 

As discussed in Sec. 4, the icomplex function of temperature, pressure, and equilibrium vapor- and hquid-phase compositions. However, for mixtures of compounds of similar molecular structure and size, the K value depends mainly on temperature and pressure. For example, several major graphical ilight-hydrocarbon systems. The easiest to use are the DePriester charts [Chem. Eng. Prog. Symp. Ser 7, 49, 1 (1953)], which cover 12 hydrocarbons (methane, ethylene, ethane, propylene, propane, isobutane, isobutylene, /i-butane, isopentane, /1-pentane, /i-hexane, and /i-heptane). These charts are a simplification of the Kellogg charts [Liquid-Vapor Equilibiia in Mixtures of Light Hydrocarbons, MWK Equilibnum Con.stants, Polyco Data, (1950)] and include additional experimental data. The Kellogg charts, and hence the DePriester charts, are based primarily on the Benedict-Webb-Rubin equation of state [Chem. Eng. Prog., 47,419 (1951) 47, 449 (1951)], which can represent both the liquid and the vapor phases and can predict K values quite accurately when the equation constants are available for the components in question. 

Various Langmiiir-Hinshelwood mechanisms were assumed. GO and GO2 were assumed to adsorb on one kind of active site, si, and H2 and H2O on another kind, s2. The H2 adsorbed with dissociation and all participants were assumed to be in adsorptive equilibrium. Some 48 possible controlling mechanisms were examined, each with 7 empirical constants. Variance analysis of the experimental data reduced the number to three possibilities. The rate equations of the three reactions are stated for the mechanisms finally adopted, with the constants correlated by the Arrhenius equation. 

This type of correlation applies to almost any siibstrate involved in cellular energy metabolism and is supported by experimental data and energetic considerations. However, it is based on assumptions true at or near the steady-state equilibrium conditions and may not be valid... 

The quantitative computations were conducted using equilibrium thenuodynamic model. The proposed model for thermochemical processes divides layer of the sample into contacting and non-contacting zones with the material of the atomizer. The correlation of all initial components in thermodynamic system has been validated. Principles of results comparison with numerous experimental data to confirm the correctness of proposed mechanism have been validated as well. 

Both kinetic and equilibrium experimental methods are used to characterize and compare adsorption of aqueous pollutants in active carbons. In the simplest kinetic method, the uptake of a pollutant from a static, isothermal solution is measured as a function of time. This approach may also yield equilibrium adsorption data, i.e., amounts adsorbed for different solution concentrations in the limit t —> qo. A more practical kinetic method is a continuous flow reactor, as illustrated in Fig. 5. 

When two or more substituents are present on a cyclohexane ring, the interactions between the substituents must be included in the analysis. The dimethylcyclohexanes provide an example in which a straightforward interpretation is in complete agreement with the experimental data. For 1,2-, 1,3-, and 1,4-dimethylcyclohexane, the free-energy change of the equilibrium for the cis trans isomerization is given below. ... 

This review is structured as follows. In the next section we present the theory for adsorbates that remain in quasi-equilibrium throughout the desorption process, in which case a few macroscopic variables, namely the partial coverages 0, and their rate equations are needed. We introduce the lattice gas model and discuss results ranging from non-interacting adsorbates to systems with multiple interactions, treated essentially exactly with the transfer matrix method, in Sec. II. Examples of the accuracy possible in the modehng of experimental data using this theory, from our own work, are presented for such diverse systems as multilayers of alkali metals on metals, competitive desorption of tellurium from tungsten, and dissociative... 

For the equihbrium properties and for the kinetics under quasi-equilibrium conditions for the adsorbate, the transfer matrix technique is a convenient and accurate method to obtain not only the chemical potentials, as a function of coverage and temperature, but all other thermodynamic information, e.g., multiparticle correlators. We emphasize the economy of the computational effort required for the application of the technique. In particular, because it is based on an analytic method it does not suffer from the limitations of time and accuracy inherent in statistical methods such as Monte Carlo simulations. The task of variation of Hamiltonian parameters in the process of fitting a set of experimental data (thermodynamic and... 

There is very little experimental data available for H2", apart from the dissociation energy and equilibrium bond distance. 

Thus, estimates of tautomeric equilibrium constants are available without any experimental data except the necessary a- and p-values. 

The predominance in the gas phase of the CH tautomers in the case of several pyrazolinones including one 3-aminopyrazolin-5-one was demonstrated by PES [88JCS(P2)641] this result is consistent with previous findings (76AHCS1, p. 325). The same technique was applied to the study of the amino/imino equilibrium in 9-amino and 9-(methylamino)acridines [91MI(61)166] although both tautomers have similar stabilities, the experimental data are in better agreement with the amino tautomer. 

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