Equilibrium constants from experimentation

Westall, J. "FITEQL. A Computer Program for Determination of Chemical Equilibrium constants from Experimental Data,"... 

A. L. Herbelin and J. Westall, A computer program for determination of chemical equilibrium constants from experimental data. Raport 96-01, Oregon State University, Cornvalis, OR, 1996. 

Heller-Kallai, L. 2002. Clay catalysis in reactions of organic matter. In Organo-clay complexes and interactions, ed. S. Yariv, H. Cross, 567-613. New York Marcel Dekker. Herbelin, A. L., and J. C. Westall. 1996. FITEQL3.2, A Program for the Determination of Chemical Equilibrium Constants from Experimental Data. Corvallis Oregon State University. 

Herbelin, A. L., and J. C. Westall. 1996. FITEQL3.2, A Program for the Determination of Chemical Equilibrium Constants from Experimental Data. Corvallis, Oregon Oregon State University. 

This equation has three parameters ks is a limiting retention factor for solvated analyte, k s is a limiting retention factor for desolvated analyte, and K is a desolvation parameter [151], The description of the experimental results with function (4-39) is shown in Figure 4-50. Expression (4-39) in principle allows for the calculation of the solvation equilibrium constant from experimental chromatographic data. 

Calculate equilibrium constants from experimental measurements of partial and total pressures (Section 14.5, Problems 21-26). 

WestaU, J. C., 1982, FITEQL A program for the determination of chemical equilibrium constants from experimental data Oregon State University Technical Report 82-02, 61 p. 

A. Herbelin and J. Westall, EITEQL A Computer Program for Determination of Chemical Equilibrium Constants from Experimental Data, Version 4.0. Technical Report. Department of Chemistry, Oregon State University, OR, USA (1999). 

I calculate equilibrium constants from experimental data. 

Finding Equilibrium Constants from Experimental Concentration Examples 14.5, 14.6 For Practice 14.5, 14.6... 

Combining eqns [45] and [46], we can get the relationship that allows determination of the ratio of products of cross- and homopropagation equilibrium constants from experimentally determined contribution of various dyads (previously derived by O Driscoir" for systems of infinitely large An) ... 

From plots of the distribution ratio against the variables of the system— [M], pH, [HA] , [B], etc.—an indication of the species involved in the solvent extraction process can be obtained from a comparison with the extraction curves presented in this chapter see Fig. 4.3. Sometimes this may not be sufficient, and some additional methods are required for identifying the species in solvent extraction. These and a summary of various methods for calculating equilibrium constants from the experimental data, using graphical as well as numerical techniques is discussed in the following sections. Calculation of equilibrium constants from solvent extraction is described in several monographs [60-64]. 

Experimentally, we are free to choose either K or Kc to report the equilibrium constant of a reaction. However, it is important to remember that calculations of an equilibrium constant from thermodynamic tables of data (standard free energies of formation, for instance), give K when we use Eq. 10. Because, in some cases, we need to know Kc after we have calculated K from thermodynamic data, we need to be able to convert between these two constants. 

For the value K the equilibrium constants from equation (29a), i.e. K — kijk-i should be used, but this value is experimentally inaccessible. If the experimentally determined value Kn — [RCH(OH2]/[RCHO] is used, the calculated value of the rate constant equals I0 likik jk2 instead of k. ... 

Discussions of results of rate studies permeate thisbookbecause kinetics investigations are the single most important group of techniques in mechanistic determinations. However, kinetics results have to be derived from measurements which are the outcome of experiments. Chapter 3 on conventional kinetics methods includes techniques which are generally applicable, and also current procedures for extracting rate constants (and, in some cases, equilibrium constants) from raw experimental data. 

Considering the literature review above, it is necessary to develop a comprehensive view that may apply to any system, whatever the luminescent probe is, each system being considered as one specific case of a more general theory. In this section, we first discuss the general scheme of (photo)chemical equations needed to describe a TRES experiment as well as a simplified scheme without photophysical reactions. The theoretical conditions to derive equilibrium constants from TRES data are discussed for the R(III), U(VI), and Cm(III) cases and are related to the experimental data presented above. 

In some cases, the reaction rates are very fast and a pseudoequilibrium approach is used to model the system (4.30). This approach consists of assuming that the concentration of species is always close to the equilibrium conditions and hence, they can be calculated using equilibrium constants from the values of other species present in the reaction system. This approach is especially important for the modeling processes in which the reaction rates are fast and when the kinetic rates are ill-defined (because of a large number of species or a lack of experimental data that makes difficult the kinetic analysis)... 

Table 18 gives an example for the calculation of an equilibrium constant from the free energy. Due to the relatively big error for the determination of the free energy, it is not advisable to perform such conversions unless unavoidable. Direct experimental determination of equilibrium constants is often more reliable. 

In calculating the equilibrium constants from imperfect experimental data, it is often convenient to assume successive approximate values to find the best fit to... 

Ascorbic acid is known to inhibit the nitrosation of secondary amines. A computer model has been developed to predict the amount of nitrosamine formed under conditions that are experimentally inaccessible. The computer-calculated rates for N-nitrosomorpholine formation using rate and equilibrium constants from the literature agree well with experimental values in the absence of and presence of ascorbic acid under anaerobic conditions. In the aerobic system the inhibitory efficiency of ascorbic acid is lower, and the nature of the interactions among the various components of the mixtures is less well understood. The use of ascorbic acid for inhibition of N-nitroso compound formation both in vitro and in vivo is briefly reviewed. 

Equation (10.58) shows how the chemical constants, which determine the value of J, enter into the equilibrium constant. An experimental determination of J for a given reaction can therefore be compared with the value deduced from the various chemical constants as calculated on the basis of statistical mechanics (Tables 10.3 and 10.4). In practice, when using decadic logarithms, it is more convenient to use the integration constant... 

The fact that reactions go to the equilibrium position was discovered empirically, and the equilibrium constant was first defined empirically. All the aforementioned applications can be accomplished with empirically determined equilibrium constants. Nonetheless, the empirical approach leaves unanswered several important fundamental questions Why should the equilibrium state exist Why does the equilibrium constant take its particular mathematical form These and related questions are answered by recognizing that the chemical equilibrium position is the thermodynamic equilibrium state of the reaction mixture. Once we have made that connection, thermodynamics explains the existence and the mathematical form of the equilibrium constant. Thermodynamics also gives procedures for calculating the value of the equilibrium constant from the thermochemical properties of the pure reactants and products, as well as procedures for predicting its dependence on experimental conditions. 

In Section 14.3 we showed how to evaluate K from calorimetric data on the pnre reactants and products. Occasionally, these thermodynamic data may not be available for a specific reaction, or a quick estimate of the value of K may suffice. In these cases we can evaluate the equilibrium constant from measurements made directly on the reaction mixture. If we can measure the equilibrium partial pressures of all the reactants and products, we can calculate the equilibrium constant by writing the eqnilibrinm expression and substituting the experimental values (in atmospheres) into it. In many cases it is not practical to measnre directly the equilibrium partial pressure of each separate reactant and prodnct. Nonetheless, the equilibrium constant can usually be derived from other available data, although the determination is less direct. We illustrate the method in the following two examples. 

The expression for the equilibrium constant from the experimentally determined values can be written in the following form ... 

Figure 14.1-3 is an overs imp I i float ion. In practice, mass transfer and dispersion effects smooth out the shock wave into an S-shaped curve. Eq nation (14.1-3) with Unite differences does give a good prediction of where the center of the S-shaped curve win be, When equilibrium theory predicts a shock wave, a consmet pettem is observed and constant pattern solutions can be used.1 Except at the two comets, (he diffuse wave is often a good fit to the experimental data. This allows the calculation of nonlinear equilibrium constants from diffuse waves.1... 

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