Equilibrium constants, in polarography

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

In addition to the information that can be obtained from DC polarography as indicated above, polarography can also be used to study solution equilibria of coordination compounds. Thus from measurements of the shift of E1/2 with solution environment, such as pH or concentration of complexing agent, it is possible to ascertain both the stoichiometry and values of the equilibrium constants of the species formed. For example, cis-[Run(bipy)2(H20)2]2+ was found1 to undergo... 

Cyclic voltammetric methods, or other related techniques such as differential pulse polarography and AC voltammetry,3 provided a convenient method for the estimation of equilibrium constants for disproportionation or its converse, comproportionation. In this respect, the experimentally measured quantity of interest in a cyclic voltammetric experiment is E>A, the potential mid-way between the cathodic and anodic peak potentials. For a one-electron process, E,A is related to the thermodynamic standard potential Ea by equation (4).13 In practice, ,/2 = E° is usually a good approximation. 

Most of the work on the boric acid-diol reaction during the last twenty years has been done to determine the coordination number of the diol (number of diol molecules) in the complex and to evaluate the equilibrium constant (often called a stability constant) for a number of diol-boric acid reactions. Several techniques have been used to study these questions, including polarimetry (7), optical rotatory dispersion (8), polarography (9), conductivity (3), vapor pressure osmometry (10), and electrochemistry (II, 12, 13). The most frequently studied system has been the electrochemical (pH) titration of boric acid or borax solutions with various diols. 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

Polarography offers some possibilities for the study of reaction kinetics and mechanisms of homogeneous organic reactions. The main advantages are a rather simple and easily accessible experimental technique, the possibility to work in dilute solutions and limited requirements on the amount of substances studied. The main limitation is that some of the components of the reaction mixture must be polarographically active. But this limitation is not so restrictive as it would appear, because most substances that can be studied spectro photometrically are electro-active as well. For rapid reactions polarography seems to be most useful for a range of second-order rate constants between about 10 -10 sec M, whereas for faster reaetions the specific properties of the electrode, in particular its electrical field and adsorption, can play a role. A certain limitation is that for most systems the equilibrium constant has to be known from independent measurements. 

In the equilibrium reaction of trimethyl phosphite with benzylideneacetophe-nones to produce 1,2-oxaphospholes 110 the second-order rate constants for the formation of 110 have been determined using a polarography method, and the rate constants for the decomposition reaction were calculated from the equilibrium constants,... 

Feroci, Fini, Badiello, and Breccia [97FER/FIN] studied the complex formation between and SeO by classical polarography in 0.15 M NaN03. They found no evidence for an interaction, see Appendix A. The review estimates from an assumed accuracy of the polarographic measurement of 2 mV, the equilibrium constant of the reaction ... 

The complex formation in the Th(TV)-nitrite system was investigated using conductometry, spectrophotometry and polarography in methanol. The composition and equilibrium constants for ternary complexes Th(0Me)2(N02), Th(0Me)2(N02)2 and Th(0Me)2(N02)3 were determined. These data are not relevant for estimates of nitrite complexes in aqueous solution. 

The measurement of formal potentials allows the determination of the Gibbs free energy of amalgamation (cf Eq. 1.2.27), acidity constants (pATa values) (cf. Eq. 1.2.32), stability constants of complexes (cf. Eq. 1.2.34), solubility constants, and all other equilibrium constants, provided that there is a definite relationship between the activity of the reactants and the activity of the electrochemical active species, and provided that the electrochemical system is reversible. Today, the most frequently applied technique is cyclic voltammetry. The equations derived for the half-wave potentials in dc polarography can also be used when the mid-peak potentials derived from cyclic voltammograms are used instead. Provided that the mechanism of the electrode system is clear and the same as used for the derivation of the equations in dc polarography, and provided that the electfode kinetics is not fully different in differential pulse or square-wave voltammetry, the latter methods can also be used to measure the formal potentials. However, extreme care is advisable to first establish these prerequisites, as otherwise erroneous results will be obtained. 

Application of DPP to the mechanism The electroreduction of the system Cd(II)-EDTA, already extensively studied [14, 124] by DC and AC polarography, has been chosen as an example of the elucidation of the electrode mechanism by the DPP technique [120]. Rate constants kp and and the equilibrium constant estimated by this method can hence be compared with literature data. In buffered solu-... 

Equilibrium constants for various acid-base reactions were determined based on inflection points of plots of absorbances at selected wavelengths on pH or acidity function, by potentiometry and from changes in shapes of Ei/2-pH plots in polarography or Ep-pH plots in differential pulse polaro-graphy (Table 1). 

The complexation of Pu(IV) with carbonate ions is investigated by solubility measurements of 238Pu02 in neutral to alkaline solutions containing sodium carbonate and bicarbonate. The total concentration of carbonate ions and pH are varied at the constant ionic strength (I = 1.0), in which the initial pH values are adjusted by altering the ratio of carbonate to bicarbonate ions. The oxidation state of dissolved species in equilibrium solutions are determined by absorption spectrophotometry and differential pulse polarography. The most stable oxidation state of Pu in carbonate solutions is found to be Pu(IV), which is present as hydroxocarbonate or carbonate species. The formation constants of these complexes are calculated on the basis of solubility data which are determined to be a function of two variable parameters the carbonate concentration and pH. The hydrolysis reactions of Pu(IV) in the present experimental system assessed by using the literature data are taken into account for calculation of the carbonate complexation. 

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