Equilibrium constant discussed

Commonly, gas-liquid partitioning is expressed by the saturated liquid vapor pressure, pi, of the compound i. This important chemical property will be discussed in detail in Chapter 4. Briefly, pi is the pressure exerted by the compound s molecules in the gas phase above the pure liquid at equilibrium. Since this pressure generally involves only part of the total pressure, we often refer to it as a partial pressure due to the chemical of interest. In this case, when there is no more build up of vapor molecules in a closed system, we say that the gas phase is saturated with the compound. Note that because pa. is strongly temperature dependent, when comparing vapor pressures of different compounds to see the influence of chemical structure, we have to use pi values measured at the same temperature (which also holds for all other equilibrium constants discussed later see Section 3.4). 

Statistical thermodynamics is used to obtain the partition function for species strongly bound to the surface (i.e., chemisorbed species). This approach can be used to derive the Langmuir adsorption isotherm, and to estimate the associated equilibrium constant, discussed in Section 11.5.3. The situation in which the adsorbed species is more weakly bound, and moves freely across the surace is considered in Section 11.5.4. 

The above equation determines the relationship between the partial pressures of CO, C02 and 02 at equilibrium. The analysis given above is the basis of the concept of equilibrium constant discussed in the prior section. 

This chapter, after introducing the equilibrium constant, discusses briefly the rate of entropy production in chemical reactions and coupling aspects of multiple reactions. Enzyme kinetics is also summarized. 

All the equilibrium constants discussed earlier have been quoted in terms of concentrations. 

A chemical reaction is an irreversible process that produces entropy. The changes in thermodynamic potentials for chemical reactions yield the affinity A. All four potentials U, H, A, and G decrease as a chemical reaction proceeds. The rate of reaction, which is the change of the extent of the reaction with time, has the same sign as the affinity. The reaction system is in equilibrium state when the affinity is zero. This chapter, after introducing the equilibrium constant, discusses briefly the rate of entropy production in chemical reactions and coupling aspects of multiple reactions. Enzyme kinetics is also summarized. 

One important aspect needs to be emphasized and kept in mind when dealing with purine derivatives All of them show a pronounced tendency for selfassociation, which occurs via stacking of the purine rings [117,137,139,140]. Hence, experiments aimed at determining the properties of mOTiomeiic metal ion complexes of purine nucleosides or their phosphates should not be carried out in concentrations higher than 10 M. To be on the safe side, actually a maximum concentration of only 5 x 10 M is recommended (cf., e.g., [122,136]). The equilibrium constants discussed below were mostly obtained by potentiometric pH titrations and the corresponding experimental conditions adhere to the above request. 

Angyal and Angyal measured the pK of 2-aminothiazoles and 2-imino-4-thiazolines to obtain the protomeric equilibrium constants (Scheme l4) (74). The higher pK values of the imino derivative (9.65) compared with that of 2-aminothiazole (5.68) prove that the amino form is highly predominant, Xp = 2x 10" (72), The limitations of such a method of Kp determination are discussed by Elguero. Marzin and Katntzky in a review of protomeric equilibria in heterocycles (75). 

See the box entitled Enthalpy Free Energy and Equilibrium Constant accompanying this section for a discussion of these relationships... 

Finally, a consideration of equilibrium chemistry can only help us decide what reactions are favorable. Knowing that a reaction is favorable does not guarantee that the reaction will occur. How fast a reaction approaches its equilibrium position does not depend on the magnitude of the equilibrium constant. The rate of a chemical reaction is a kinetic, not a thermodynamic, phenomenon. Kinetic effects and their application in analytical chemistry are discussed in Chapter 13. 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

The text listed below provides more details on how the potentiometric titration data may be used to calculate equilibrium constants. This text provides a number of examples and includes a discussion of several computer programs that have been developed to model equilibrium reactions. 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

In a series of organic acids of similar type, not much tendency exists for one acid to be more reactive than another. For example, in the replacement of stearic acid in methyl stearate by acetic acid, the equilibrium constant is 1.0. However, acidolysis in formic acid is usually much faster than in acetic acid, due to higher acidity and better ionizing properties of the former (115). Branched-chain acids, and some aromatic acids, especially stericaHy hindered acids such as ortho-substituted benzoic acids, would be expected to be less active in replacing other acids. Mixtures of esters are obtained when acidolysis is carried out without forcing the replacement to completion by removing one of the products. The acidolysis equilibrium and mechanism are discussed in detail in Reference 115. 

The steric and electronic effects of substituents on the electrophilic attack at the nitrogen atom have been discussed in the general chapter on reactivity (Section 4.02.1.3). All the conclusions are valid for pyrazoles and indazoles. The effect on equilibrium constants will be discussed in detail in the sections dealing with values (Sections 4.04.2.1.3(iv) and (v)) and the kinetic effects on the rates of quaternization in the corresponding section (4.04.2.1.3(vii)). 

Estimation of fct for Reversible Reactions When the reaction is of the form A B, where B is a nonvolatile product and the equilibrium constant is defined by Cg = K Ca, the expressions for computing /cl become extremely complex. A good discussion of this situation is given in Mass Tran.sfer by Sherwood, Pigford, and Wilke (McGraw-Hill, New York, 1975, p. 317). Three limiting cases are hsted below ... 

It is always important to keep in mind the relative nature of substituent effects. Thus, the effect of the chlorine atoms in the case of trichloroacetic acid is primarily to stabilize the dissociated anion. The acid is more highly dissociated than in the unsubstituted case because there is a more favorable energy difference between the parent acid and the anion. It is the energy differences, not the absolute energies, that determine the equilibrium constant for ionization. As we will discuss more fully in Chapter 4, there are other mechanisms by which substituents affect the energy of reactants and products. The detailed understanding of substituent effects will require that we separate polar effects fiom these other factors. 

Since the domain explored will always be a very small part of the possible cases of tautomerism, it is essential to have general rules for families of compounds, substituents, and solvents. This chemical approach is maintained in this chapter, although the importance of the calculations is recognized. The following discussion begins with calculation of tautomeric equilibrium constants, followed by the combined use of theoretical calculations and experimental results (an increasingly expanding field) and ends with the calculations of the mechanisms of proton transfer between tautomers. 

In discussing the experimental data, we shall wish to make use of the equilibrium constants that are to be found in the literature. We must therefore inquire into the relation that the thermodynamic treatment bears to the treatment that has been given above. When the expression for any reaction, such as (66) for example, has been written down, the species that have been written on the left-hand side are called the reactants, and those on the right-hand side are called the products. The... 

The equation just written is generally applicable to any system. The equilibrium constant may be the K referred to in our discussion of gaseous equilibrium (Chapter 12), or any of the solution equilibrium constants (Rw Ra, Rj, K, . . . ) discussed in subsequent chapters. Notice that AG° is the standard free energy change (gases at 1 atm, species in solution at 1M). That is why, in the expression for K, gases enter as their partial pressures in atmospheres and ions or molecules in solution as their molarities. 

Only one equilibrium constant for gas-phase reactions (Chapter 12), the thermodynamic constant K, often referred to as Kp. This simplifies not only the treatment of gaseous equilibrium, but also the discussion of reaction spontaneity (Chapter 17) and electrochemistry (Chapter 18). 

This ease with which we can control and vary the concentrations of H+(aq) and OH (aq) would be only a curiosity but for one fact. The ions H+(aq) and OH (aq) take part in many important reactions that occur in aqueous solution. Thus, if H+(aq) is a reactant or a product in a reaction, the variation of the concentration of hydrogen ion by a factor of 1012 can have an enormous effect. At equilibrium such a change causes reaction to occur, altering the concentrations of all of the other reactants and products until the equilibrium law relation again equals the equilibrium constant. Furthermore, there are many reactions for which either the hydrogen ion or the hydroxide ion is a catalyst. An example was discussed in Chapter 8, the catalysis of the decomposition of formic acid by sulfuric acid. Formic acid is reasonably stable until the hydrogen ion concentration is raised, then the rate of the decomposition reaction becomes very rapid. 

We have seen that the value of an equilibrium constant tells us whether we can expect a high or low concentration of product at equilibrium. The constant also allows us to predict the spontaneous direction of reaction in a reaction mixture of any composition. In the following three sections, we see how to express the equilibrium constant in terms of molar concentrations of gases as well as partial pressures and how to predict the equilibrium composition of a reaction mixture, given the value of the equilibrium constant for the reaction. Such information is critical to the success of many industrial processes and is fundamental to the discussion of acids and bases in the following chapters. 

The equilibrium constant in Eq. 2 is defined in terms of activities, and the activities are interpreted in terms of the partial pressures or concentrations. Gases always appear in K as the numerical values of their partial pressures and solutes always appear as the numerical values of their molarities. Often, however, we want to discuss gas-phase equilibria in terms of molar concentrations (the amount of gas molecules in moles divided by the volume of the container, [I] = j/V), not partial pressures. To do so, we introduce the equilibrium constant Kt., which for reaction E is defined as... 

In this chapter, we see what acids and bases are and why they vary in strength. We shall use thermodynamics, particularly equilibrium constants, to discuss the strengths of acids and bases quantitatively and thereby develop our insight into their behavior. We then use our knowledge of equilibria involving acids and bases to examine systems in which more than one equilibrium is taking place simultaneously. 

Now we come to a very important point that will be the basis of much of the discussion in this chapter and the next. Because Kw is an equilibrium constant. the product of the concentrations ofHjO+ and OH ions is always equal to Kw. We can increase the concentration of H30+ ions by adding acid, and the concentration of OH ions will immediately respond by decreasing to preserve the value of Kk. Alternatively, we can increase the concentration of OH ions by adding base, and the concentration of H30 ions will decrease correspondingly. The autoprotolysis equilibrium links the concentrations of H30+ and OH" ions rather like a seesaw when one goes up, the other must go down (Fig. 10.10). 

The units of AG are joules (or kilojoules), with a value that depends not only on E, but also on the amount n (in moles) of electrons transferred in the reaction. Thus, in reaction A, n = 2 mol. As in the discussion of the relation between Gibbs free energy and equilibrium constants (Section 9.3), we shall sometimes need to use this relation in its molar form, with n interpreted as a pure number (its value with the unit mol struck out). Then we write... 

In discussing the elFect of structure on the stabilization of alkyl cations on the basis of the carbonylation-decarbonylation equilibrium constants, it is assumed that—to a first approximation—the stabilization of the alkyloxocarbonium ions does not depend on the structure of the alkyl group. The stabilization of the positive charge in the alkyloxocarbonium ion is mainly due to the resonance RC = 0 <-> RC = 0+, and the elFect of R on this stabilization is only of minor importance. It has been shown by Brouwer (1968a) that even in the case of (tertiary) alkylcarbonium ions, which would be much more sensitive to variation of R attached to the electron-deficient centre, the stabilization is practically independent of the structure of the alkyl groups. Another argument is found in the fact that the equilibrium concentrations of isomeric alkyloxocarbonium ions differ by at most a factor of 2-3 from each other (Section III). Therefore, the value of K provides a quantitative measure of the stabilization of an alkyl cation. In the case of R = t-adamantyl this equilibrium constant is 30 times larger than when R = t-butyl or t-pentyl, which means that the non-planar t-adamantyl ion is RT In 30= 2-1 kcal... 

For the determination of stabilizations of carbonium ions the equilibrium constants of carbonylation-decarbonylation have been used in previous Sections. For the ions discussed in this Seetion, however, the rate constants of decarbonylation are not known and, therefore, the rate constants of carbonylation will be used as a criterion for such stabilizations. This kinetic criterion is a useful indicator if there are no significant steric factors in the carbonylation step and if this step is indeed rate-determining in the overall process (Hogeveen and Gaasbeek, 1970). The following rate constants in Table 2 are of particular importance. 

Thermodynamic energy terms (and equilibrium constants) may differ for compounds containing different isotopic species of an element. This effect is described in theoretical detail by Urey (1947), and applications to geochemistry are discussed by Broecker and Oversby (1971) and Faure (1977). A good example is the case of the vapor/liquid equilibrium for water. The vapor pressure of a lighter isotopic species, H2 0, is higher relative to that of heavier species, (or HD O), and others. 

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