Oxide equilibrium constant

Several types of reactions are commonly used in analytical procedures, either in preparing samples for analysis or during the analysis itself. The most important of these are precipitation reactions, acid-base reactions, complexation reactions, and oxidation-reduction reactions. In this section we review these reactions and their equilibrium constant expressions. 

Unlike the reactions that we have already considered, the equilibrium position of a redox reaction is rarely expressed by an equilibrium constant. Since redox reactions involve the transfer of electrons from a reducing agent to an oxidizing agent, it is convenient to consider the thermodynamics of the reaction in terms of the electron. 

In a redox reaction, one of the reactants is oxidized while another reactant is reduced. Equilibrium constants are rarely used when characterizing redox reactions. Instead, we use the electrochemical potential, positive values of which indicate a favorable reaction. The Nernst equation relates this potential to the concentrations of reactants and products. 

Preparation and chemistry of chromium compounds can be found ia several standard reference books and advanced texts (7,11,12,14). Standard reduction potentials for select chromium species are given ia Table 2 whereas Table 3 is a summary of hydrolysis, complex formation, or other equilibrium constants for oxidation states II, III, and VI. 

In the case of tire direct oxidation, the oxygen partial pressure must be greater than that at the Pb/PbO equilibrium, while in the process involving sodium-based salts, the oxygen pressure is less than this. The two equilibrium constants for the refining reactions... 

Several additional points should be made. First, although oxygen esters usually have lower group-transfer potentials than thiol esters, the O—acyl bonds in acylcarnitines have high group-transfer potentials, and the transesterification reactions mediated by the acyl transferases have equilibrium constants close to 1. Second, note that eukaryotic cells maintain separate pools of CoA in the mitochondria and in the cytosol. The cytosolic pool is utilized principally in fatty acid biosynthesis (Chapter 25), and the mitochondrial pool is important in the oxidation of fatty acids and pyruvate, as well as some amino acids. 

Molecular orbital calculations have been used to estimate equilibrium constants, although up to the present these attempts have not met with much success. Using calculations of this type, 2- and 4-hydroxypyridine 1-oxide were predicted to be more stable than 1-hydroxypyrid-2- and -4-one by ca. 20 kcal/mole, which corresponds to a ratio of ca. 10 between the forms. It was later shown experimentally that, at least in the series of 4-substituted compounds, there is very little energy difference between the forms and that the ratio between them is about unity. Molecular orbital calculations for... 

The standard electrode potentials , or the standard chemical potentials /X , may be used to calculate the free energy decrease —AG and the equilibrium constant /T of a corrosion reaction (see Appendix 20.2). Any corrosion reaction in aqueous solution must involve oxidation of the metal and reduction of a species in solution (an electron acceptor) with consequent electron transfer between the two reactants. Thus the corrosion of zinc ( In +zzn = —0-76 V) in a reducing acid of pH = 4 (a = 10 ) may be represented by the reaction ... 

This reaction shows that the hydrated oxide SiCV-xHjO is acidic, since it reacts with a base-As we mentioned earlier, phosphorus can be found in four different oxidation states. The hydroxides of the +1, +3, and +5 states of phosphorus are hypophosphorous acid, H3P02, phosphorous acid, H3P03, and phosphoric acid, H3P04. Their structures are shown in Figure 20-4. As suggested by their names, these compounds are distinctly acidic, and are of moderate strength. The equilibrium constant for the first ionization of each acid is approximately 10-2 hypophosphorous acid ... 

Sulfur in the +4 oxidation state also forms an oxyacid, sulfurous acid (HjSOj). This compound is not as strong an acid as H2S04. The equilibrium constant for the reaction... 

It is now possible to calculate the equilibrium constants of oxidation-reduction reactions, and thus to determine whether such reactions can find application in quantitative analysis. Consider first the simple reaction ... 

It is evident that the abrupt change of the potential in the neighbourhood of the equivalence point is dependent upon the standard potentials of the two oxidation-reduction systems that are involved, and therefore upon the equilibrium constant of the reaction it is independent of the concentrations unless these are extremely small. The change in redox potential for a number of typical oxidation-reduction systems is exhibited graphically in Fig. 10.15. For the MnO, Mn2+ system and others which are dependent upon the pH of the... 

Where the parenthesis refer to the chemical activities of the reactants and K is the equilibrium constant for the previous equation. Similar considerations apply to the oxidation of less electropositive impurities from the anode when a current is passed through the cell. Thus, for the case of iron impurity in the anode, the reaction... 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

The composition of sodium polysulfide solutions saturated with sulfur of zero oxidation number (S°) has also been studied at 25 and 80 °C (solutions in contact with elemental sulfur) [76]. In this case the ratio 8° 8 per polysulfide ion increases with increasing alkahnity. The maximum average number of sulfur atoms per polysulfide molecule was obtained as 5.4 at 25 °C and 6.0 at 80 °C and pH values of >12. Equilibrium constants for reactions as in Eqs. (26) and (27) have been derived assuming various models with differing numbers of polysulfide ions present. 

The magnitude of this equilibrium constant indicates that the redox reaction goes essentially to completion. This reflects the fact that bromine is a potent oxidizing agent and copper is relatively easy to oxidize. 

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... 

Fig. 2. Relationship between the logarithms of the rate coefficients (Atj. 2) and the logarithms of the equilibrium constants (Jfi.i) for the oxidation of various substituted Fe(II)-phenanthroline complexes by Mn(III) in 1 A/ and 3 Af HCIO4 at 25.0 °C. (From Diebler and Sutin, by courtesy of The American Chemical Society.)...

The authors believe that a similar mechanism to the above operates for the dichromate-ion dependent path, but that the equilibrium constant K is much smaller. This oxidation presents two novel features, namely the lack of an acidity dependence of the rate and the participation of a term involving dichromatic ion. 

The reduction of iodine by ferrocyanide is simple second-order with Aij (25 °C) = (1.3 + 0.3)x 10 l.mole sec This is the reverse of the oxidation of iodide by ferricyanide (p. 409), but the ratio k(forward)/k(back) does not agree well with the equilibrium constant determined potentiometrically. Addition of 1 strongly retards the reduction and 13 was discounted as a reactant, the mechanism suggested being... 

This scheme shows that cyanide sourced from smoking or otherwise (see 6.3.7) may determine the metabolism of chrysotherapeutic agents. [Au(CN)2] anions bind to serum albumin predominantly by the formation of adducts without the displacement of cyanide [94]. The ions bind tightly to albumin independent of the oxidative state of Cys-34. The equilibrium constant values for [Au(CN)2] binding to serum albumin are similar to values for other gold complexes that bind to albumin. This indicates that albumin can act as a carrier for transporting [Au(CN)2] in the bloodstream. 

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