AQUEOUS EQUILIBRIUM CONSTANTS

TABLE 7.4 Thermodynamic Data for Aqueous Equilibrium Constants... 

C. Aqueous Equilibrium Constants 1. Dissociation Constants for Acids at 25 °C... 

The solubilization of diverse solutes in micelles is most often examined in tenns of partitioning equilibria, where an equilibrium constant K defines the ratio of the mole fraction of solute in the micelle (X and the mole fraction of solute in the aqueous pseudophase. This ratio serves to define the free energy of solubilization -RT In K). 

In Chapter 2 the Diels-Alder reaction between substituted 3-phenyl-l-(2-pyridyl)-2-propene-l-ones (3.8a-g) and cyclopentadiene (3.9) was described. It was demonstrated that Lewis-acid catalysis of this reaction can lead to impressive accelerations, particularly in aqueous media. In this chapter the effects of ligands attached to the catalyst are described. Ligand effects on the kinetics of the Diels-Alder reaction can be separated into influences on the equilibrium constant for binding of the dienoplule to the catalyst (K ) as well as influences on the rate constant for reaction of the complex with cyclopentadiene (kc-ad (Scheme 3.5). Also the influence of ligands on the endo-exo selectivity are examined. Finally, and perhaps most interestingly, studies aimed at enantioselective catalysis are presented, resulting in the first example of enantioselective Lewis-acid catalysis of an organic transformation in water. 

The strength of a weak acid is measured by its acid dissociation constant, which IS the equilibrium constant for its ionization m aqueous solution... 

According to the Arrhenius definitions an acid ionizes m water to pro duce protons (H" ) and a base produces hydroxide ions (HO ) The strength of an acid is given by its equilibrium constant for ionization m aqueous solution... 

Table 8.9 Selected Equilibrium Constants in Aqueous Solution at Various...

Most reactions involve reactants and products that are dispersed in a solvent. If the amount of solvent is changed, either by diluting or concentrating the solution, the concentrations of ah reactants and products either decrease or increase. The effect of these changes in concentration is not as intuitively obvious as when the concentration of a single reactant or product is changed. As an example, let s consider how dilution affects the equilibrium position for the formation of the aqueous silver-amine complex (reaction 6.28). The equilibrium constant for this reaction is... 

In a simple liquid-liquid extraction the solute is partitioned between two immiscible phases. In most cases one of the phases is aqueous, and the other phase is an organic solvent such as diethyl ether or chloroform. Because the phases are immiscible, they form two layers, with the denser phase on the bottom. The solute is initially present in one phase, but after extraction it is present in both phases. The efficiency of a liquid-liquid extraction is determined by the equilibrium constant for the solute s partitioning between the two phases. Extraction efficiency is also influenced by any secondary reactions involving the solute. Examples of secondary reactions include acid-base and complexation equilibria. 

Aqueous solutions buffered to a pH of 5.2 and containing known total concentrations of Zn + are prepared. A solution containing ammonium pyrrolidinecarbodithioate (APCD) is added along with methyl isobutyl ketone (MIBK). The mixture is shaken briefly and then placed on a rotary shaker table for 30 min. At the end of the extraction period the aqueous and organic phases are separated and the concentration of zinc in the aqueous layer determined by atomic absorption. The concentration of zinc in the organic phase is determined by difference and the equilibrium constant for the extraction calculated. 

Scales for bases that are too weak to study in aqueous solution employ other solvents but are related to the equilibrium in aqueous solution. These equilibrium constants provide a measure of thermodynamic basicity, but we also need to have some concept of kinetic basicity. For the reactions in Scheme 5.4, for example, it is important to be able to make generalizations about the rates of competing reactions. 

The exceptions are formaldehyde, which is nearly completely hydrated in aqueous solution, and aldehydes and ketones with highly electronegative substituents, such as trichloroacetaldehyde and hexafluoroacetone. The data given in Table 8.1 illustrate that the equilibrium constant for hydration decreases with increasing alkyl substitution. 

Because of the unfavorable equilibrium constant in aqueous solution and the relatri e facility of the hydrolysis, acetals and ketals are rapidly converted back to aldehydes and ketones in acidic aqueous solution. 

The other C=N systems included in Scheme 8.2 are more stable to aqueous hydrolysis than are the imines. For many of these compounds, the equilibrium constants for formation are high, even in aqueous solution. The additional stability can be attributed to the participation of the atom adjacent to the nitrogen in delocalized bonding. This resonance interaction tends to increase electron density at the sp carbon and reduces its reactivity toward nucleophiles. 

The concentrations of the different intermediates are determined by the equilibrium constants. The observation of immonium ions [Eq. (5)] in strongly acidic solutions by ultraviolet and NMR spectroscopy also Indicates that these equilibria really exist (23,26). The equilibria in aqueous solutions are of synthetic interest and explain the convenient method for the preparation of 2-deuterated ketones and aldehydes by hydrolysis of enamines in heavy water (27). 

Customarily, because the term [HgO] is essentially constant in dilute aqueous solutions, it is incorporated into the equilibrium constant Alto give a new term, K, the acid dissociation constant (where K = [HgO]). Also, the term [HjO ] is often replaced by H, such that... 

The equilibrium constant at room temperature corresponds to pKi, = 4.74 and implies that a 1 molar aqueous solution of NH3 contains only 4.25 mmol 1 of NH4+ (or OH ). Such solutions do not contain the undissociated molecule NH4OH, though weakly bonded hydrates have been isolated at low temperature ... 

The ultraviolet spectrum of vitamin Be, or pyridoxine, measured in aqueous ethanol varies with the composition of the solvent indicating that this compound is in equilibrium with the zwitterion form 38. The equilibrium constant in pure water was obtained by extrapolation. Prior to this, equilibria which involved tautomers of type 39 had been suggested for vitamin Be, but see Section VI,A. In the case of pyridoxal, an additional equilibrium, 40 41, occurs (cf. Section VIII) other pyridoxal analogs have also been studied (Table II). 

Pyridine bases are well known as ligands in complexes of transition metals, and it might well be anticipated that the equilibrium constants for the formation of such complexes, which are likely to be closely related to the base strength, would follow the Hammett equation. Surprisingly, only very few quantitative studies of such equilibria seem to have been reported, and these only for very short series of compounds. Thus, Murmann and Basolo have reported the formation constants, in aqueous solution at 25°, of the silver(I) complexes... 

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 ... 

Flo. 33. Extrapolation to zero ionic strength of the equilibrium constant of acetic acid in aqueous solution at 25°C. 

Table 10. Equilibrium Constants for Proton Transfers in Aqueous Solution...

If any equilibrium constants show this linearity, this behavior is most likely to be found among proton transfers of type (118) and type (120). The expressions for log K given in Table 11 show this linearity they represent, within the experimental error, the accurate data obtained by measurements on three proton transfers in aqueous solution. All three are of the type (120). 

In the dilute aqueous solution normally used for measuring acidity, the concentration of water, H20], remains nearly constant at approximately 55.4 M at 25 °C. We can therefore rewrite the equilibrium expression using a new quantity called the acidity constant, Ka. The acidity constant for any acid HA is simply the equilibrium constant for the acid dissociation multiplied by the molar concentration of pure water. 

In this and succeeding chapters, a wide variety of different types of equilibria will be covered. They may involve gases, pure liquids or solids, and species in aqueous solution. It will always be true that in the expression for the equilibrium constant—... 

Using the equilibrium constants in Table 13.2, rank the following 0.1 Af aqueous solutions in order of increasing Xj,... 

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