Calculation of equilibrium constant: from

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. 

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. 

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]. 

Calculation of equilibrium constant from emf of a cell The equilibrium constant of a chemical reaction can be calculated from the standard free-energy change by the equation... 

Calculation of equilibrium constant from electrode potentials of the halfreactions The two half-reactions involved in the chemical reaction (12-37) are... 

Calculation of Equilibrium Constants from Entropies and Heats of Formation. 

Activation entropies are useful because they can give information on the structure of a transition state (as stated above, a more confined transition state is signalled by a negative activation entropy), but the ab initio calculation of rate constants [104] from activation free energies is not as straightforward as the calculation of equilibrium constants from reaction free energies. The crudest way to calculate a rate constant is to use the Arrhenius equation [96c,105]... 

We shall not deal with the third law of thermodynamics at this point. The principal utility of the third law to the chemist is that it permits the calculation of equilibrium constants from calorimetric data (thermal data) exclusively. 

A converse exists to the calculation of equilibrium constants from the halfreduction potentials It is the possibility to obtain the unknown redox potentials of some couples. In order to achieve it, a redox equilibrium between two couples is investigated. The equilibrium constant is determined, if the standard redox potential of one of both couples is already known. The value of the other (unknown) is immediately deduced. This strategy is, of course, of great importance in physical and analytical chemistries. It is in this way that the standard potentials of slow electrochemical systems (see electrochemistry), in particular, those of organic redox couples, have been determined. 

Examples through illustrate the two main types of equilibrium calculations as they apply to solutions of acids and bases. Notice that the techniques are the same as those introduced in Chapter 16 and applied to weak acids in Examples and. We can calculate values of equilibrium constants from a knowledge of concentrations at equilibrium (Examples and), and we can calculate equilibrium concentrations from a knowledge of equilibrium constants and initial concentrations (Examples, and ). 

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 ... 

For t vo systems in chemical equilibrium we can calculate the equilibrium constant from the ratio of partition functions by requiring the chemical potentials of the t vo systems to be equal. 

The concentration of M = I(T3 molar. Suppose we want to reduce the concentration of M to 10 5. When we calculate the equilibrium constant from the first example and then calculate the required concentration ofLatM= 1(T5 molar we find the following rule of thumb if an excess ofL is needed, keep [L] the same and lower fM] only ... 

The standard entropy and enthalpy changes for each of the 312 steps of the reaction sequence (AS and A// ) can now be calculated from the thermodynamic properties of the gaseous and surface species, followed by calculation of equilibrium constants ( eq) f°r each step ... 

This equation permits the calculation of equilibrium constants for polymerization-depolymerization from copolymer composition data extrapolated to zero Mi feed. The agreement between equilibrium constants calculated in this manner from free radical copolymerizations and those obtained from anionic homopolymerizations is shown in Table II, and again emphasizes the thermodynamic character of this work. 

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 many calculations the hydrogen ion concentration is more accessible than the activity. For example, the electroneutrality condition is written in terms of concentrations rather than activities. Also, from stoichiometric considerations, the concentrations of solution components are often directly available. Therefore, the hydrogen ion concentration is most readily calculated from equilibrium constants written in terms of concentration. When a comparison of hydrogen ion concentrations with measured pH values is required (in calculation of equilibrium constants, for example), an estimate of the hydrogen ion activity coeflScient can be made by application of the Debye-Huckel theory if necessary, an estimate of liquid-junction potentials also can be made. Alternatively, the glass electrode can be calibrated with solutions of known hydrogen ion concentration and constant ionic strength. " ... 

We may calculate the equilibrium constant from available data on the standard free energy of formation. The National Bureau of Standards gives the following... 

In this chapter we shall consider the application of tabulated values of affinities, heats and entropies of reaction to the calculation of equilibrium constants. As we have pointed out already it is much more convenient to consider standard affinities of reaction than equilibrium constants. This is because standard affinities can be added and subtracted in just the same way as stoichiometric equations, so that the standard affinity of a reaction not included in the table is easily calculated. This means, as we shall see, that the only reactions which need to be included are those relating to the formation of compounds from their elements. 

When processes are conducted at constant T and P, the criteria for spontaneity and for equilibrium are stated more conveniently in terms of another state function called the Gibbs free energy (denoted by G), which is derived from S. Because chemical reactions are usually conducted at constant T and constant P, their thermodynamic description is based on AG rather than AS. This chapter concludes by restating the criteria for spontaneity of chemical reactions in terms of AG. Chapter 14 shows how to identify the equilibrium state of a reaction, and calculate the equilibrium constant from AG. 

The equilibrium constants Kf are not measurable and we must resort to statistical thermodynamics to estimate these values theoretically. The partition function (Q) is a quantity with no simple physical significance but it may be substituted for concentrations in the calculation of equilibrium constants (Eqns. 4 and 5) [5], (It is assumed that there is no isotopic substitution in B.) Partition functions may be expressed as the product of contributions to the total energy from translational, rotational and vibrational motion (Eqn. 6). 

KAR/KUL] Karlsson, R., Kullberg, L., A computer method for simultaneous calculation of equilibrium constants and enthalpy changes from calorimetric data, Chem. Scr., 9, (1976), 54-57. Cited on pages 368, 377. 

It is obvious from the introduction that the authors were not aware of the current literature at the time, a fact that might explain both their neglect of polynuclear complexes and the far from adequate calculation method used to calculate the equilibrium constants from the experimental Uq, v5. pH data. The reported equihbrium constants are not reliable because of an erroneous chemical model, the neglect of polynuclear species that are totally dominating the speciation under the experimental conditions used. 

The third law of thermodynamics, like the first and second laws, is a postulate based on a large number of experiments. In this chapter we present the formulation of the third law and discuss the causes of a number of apparent deviations from this law. The foundations of the third law are firmly rooted in molecular theory, and the apparent deviations from this law can be easily explained using statistical mechanical considerations. The third law of thermodynamics is used primarily for the determination of entropy constants which, combined with thermochemical data, permit the calculation of equilibrium constants. 

First, calculate the standard emf of the cell from the standard reduction potentials in Table 19.1 of the text. Then, calculate the equilibrium constant from the standard emf using Equation (19.5) of the text. 

Obviously, conditional equilibrium constants, as well as concentration constants, are no universal constants as their values strongly depend on the total composition of the solution. But they are very convenient for calculation of equilibrium directly from analytical data of the dissociated ions content. 

Equations such as equation (4.13) or (4.15) make it possible to calculate chemical equilibrium constants from the chemical potentials of the pure components which again can be obtained from data on pure component enthalpies and entropies... 

The isotherms InK vs. 1/e (298.15K) are presented in Figure 9.8. These dependencies (right lines 1,2,4,5) are required for calculation of equilibrium constants of the heteromolecular association process free from specific solvation effect. It can be seen from Figure 9.8 that the values InK, regardless of solvent nature, lie on the same line 3, which describes the change of equilibrium constants of the process [9.84] in the universal solution CCl4-heptylchloride. 

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