Equilibrium Constants from Data

A third calculation of a" gives 0.029874, which is substantially the same as the result of the second approximation hence, it can be used in Equation (20.27). As with the iterative procedure for calculating equilibrium constants from data on cell potentials, the iterative procedure for conductance data can be programmed for a computer. 

Determine equilibrium constants from data and use the equilibrium equations in calculations... 

Measurement of n experimental values of fi at different [L] will give n equations in n unknowns, the K values. Thus, equation (8-6) provides a starting point for determination of equilibrium constants from data. 

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 Gibbs free energies of formation, for instance) and Eq. 8 give K, not Kc. In some cases, we need to know Kc after we have calculated K from thermodynamic data, and so we need to be able to convert between these two constants. 

One of the most useful applications of standard potentials is in the calculation of equilibrium constants from electrochemical data. The techniques that we develop here can be applied to any kind of reaction, including neutralization and precipitation reactions as well as redox reactions, provided that they can be expressed as the difference of two reduction half-reactions. 

HOWTO CALCULATE EQUILIBRIUM CONSTANTS FROM ELECTROCHEMICAL DATA... 

The procedure for calculating an equilibrium constant from electrochemical data is as follows. 

To calculate the equilibrium composition of a mixture at a given temperature, we first need to calculate the equilibrium constant from thermodynamic data valid under the standard conditions of 298 K and 1 bar, as in Tab. 2.2. Differentiating Eq. (22) and using AG° = A - TAS° we obtain the Van t Hoff equation ... 

Oxidation potentials lead to a value of 7.9 x 10 for the equilibrium constant. Kinetic data for the reaction (from 0 to 55.6 °C) in acid perchlorate solutions (over the range 0.047-1.0 M) have been obtained spectrophotometrically by following the disappearance of V(V) (which absorbs strongly between 305 and 350 m/i) as a function of time. The second-order nature of the rate law... 

Gampp, H., Maeder, M., Meyer, C. J., Zuberbtihler, A. D. Calculation of equilibrium constants from multiwavelength spectroscopic data. 1. Mathematical considerations. Talanta 1985, 32, 95-101. 

H. Gampp, M. Maeder, C.J. Meyer and A.D. Zuberbuhler, Calculation of equilibrium constants from multiwavelength spectroscopic data. Ill Model-free analysis of spectrophotometric and ESR titrations. Talanta, 32 (1985) 1133-1139. 

Alcock, R. M. Hartley, F. R. Rogers, D. E., A damped non-linear least-squares computer program (dalsfek) for the evaluation of equilibrium constants from spectrophotometric and potentiometric data, J. Chem. Soc. Dalton Trans. 115-123 (1978). 

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

A test calculation, using the data from the Atlantic Ocean where [L]j = 4 nM and log Apj.L = 19.3 and the equilibrium constants from Table 5.5, yields a solubility [Fe(in)]jQ(gj = 5.2 nM, close to a threefold increase This estimate is substantially higher... 

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]. 

TOOLBOX 12.2 How to calculate equilibrium constants from electrochemical data... 

The solubility of a substance will change on the formation of a complexwith a second substance. The extent of solubility alteration directly relates to the binding afL nity of the two compounds. Therefore, it is possible to evaluate equilibrium constants from solubility data (Higuchi and Connors, 1965). 

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. 

TRES appears to be a sensitive tool to follow lanthanide and actinide complexation in solution, because most of the spectroscopic parameters are influenced by complexation. It has been shown that caution should be paid to the type of photochemical processes occurring in solution in order to correctly analyse the data. Taking account this important point, TRES is an interesting technique for the determination of equilibrium constants. From a more fundamental viewpoint, one may wonder why inorganic ligands lead to regime A with U(VI) and to regime C with Cm(III). 

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. 

Calculation of equilibrium conversions is based on the fundamental equations of chemical-reaction equilibrium, which in application require data for the standard Gibbs energy of reaction. The basic equations are developed in Secs. 15.1 through 15.4. These provide the relationship between the standard Gibbs energy change of reaction and the equilibrium constant. Evaluation of the equilibrium constant from thermodynamic data is considered in Sec. 15.5. Application of this information to the calculation of equilibrium conversions for single reactions is taken up in Sec. 15.7. In Sec. 15.8, the phase role is reconsidered finally, multireaction equilibrium is treated in Sec. I5.9.t... 

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)... 

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

Calculate equilibrium constants. From the data, the equilibrium constants for the two reactions, respectively, may be determined as follows (see Section 4) ... 

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. 

---