Solvent equilibrium constant

Various thermodynamic properties of 178 have been studied. Lucken early recognized that the radical associates to a dimeric form in solid salts and certain solutions. This association has been the object of recent scrutiny. Optical spectra of 178 free, in ion-paired form with perchlorate, and in a dimeric form associated with two perchlorate ions have been recognized. The exact nature of the forms present in a solution depends upon the solvent equilibrium constants and activation parameters for the association were determined. 

Figure 8-7. Correlation between equilibrium constant for esterification and solubility of water in the solvent. Equilibrium constant was defined as [Ester]/([Alcohol].[Acid]), for reactions at fixed water activity (close to 1). Solvents are bb, butyl benzoate be, bromoethane bk, dibutyl ketone bp, dibutyl phthalate bz, benzene ca, 1,1,1-trichloroethane cf, chloroform ct, carbon tetrachloride cy, trichloroethylene ee, ethyl ether ek, diethyl ketone ep, diethyl phthalate hd, hexadecane hx, hexane me, methylene chloride mk, methyl iso-butyl ketone nm, nitromethane oc, /so-octane pe, iso-propyl ether tl, toluene. Valivety et al...

Equilibrium constants for protein-small molecule association usually are easily measured with good accuracy it is normal for standard free energies to be known to within 0.5 kcal/mol. Standard conditions define temperature, pressure and unit concentration of each of the three reacting species. It is to be expected that the standard free energy difference depends on temperature, pressure and solvent composition AA°a also depends on an arbitrary choice of standard unit concentrations. 

An interesting ring-chain tautomerism between 2-azidothiazole (328) and thiazolotetrazole (328a) has been reported (597, 618, 619), the 328 structure predominating (Scheme 190). The solvent polarity and basicity influences this equilibrium constant significantly (1592). 

Even though water is a reactant (a Brpnsted base) its concentration does not appear m the expression for because it is the solvent The convention for equilibrium constant expressions is to omit concentration terms for pure solids liquids and solvents... 

The equilibrium constant for a reaction in which an acid donates a proton to the solvent (Vi). 

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. 

The mean chemical shifts of A- unsubstituted pyrazoles have been used to determine the tautomeric equilibrium constant, but the method often leads to erroneous conclusions (76AHC(Sl)l) unless the equilibrium has been slowed down sufficiently to observe the signals of individual tautomers (Section 4.04.1.5.1). When acetone is used as solvent it is necessary to bear in mind the possibility (depending on the acidity of the pyrazole and the temperature) of observing the signals of the 1 1 adduct (55) whose formation is thermodynamically favoured by lowering the solution temperature (79MI40407). A similar phenomenon is observed when SO2 is used as solvent. 

When R = H, in all the known examples, the 3-substituted tautomer (129a) predominates, with the possible exception of 3(5)-methylpyrazole (R = Me, R = H) in which the 5-methyl tautomer slightly predominates in HMPT solution at -17 °C (54%) (77JOC659) (Section 4.04.1.3.4). For the general case when R = or a dependence of the form logjRTT = <2 Za.s cTi + b Xa.s (Tr, with a>0,b <0 and a> b, has been proposed for solutions in dipolar aprotic solvents (790MR( 12)587). The equation predicts that the 5-trimethylsilyl tautomer is more stable than the 3-trimethylsilylpyrazole, since experimental work has to be done to understand the influence of the substituents on the equilibrium constant which is solvent dependent (78T2259). There is no problem with indazole since the IH tautomer is always the more stable (83H(20)1713). 

The magnitude of the anomeric effect depends on the nature of the substituent and decreases with increasing dielectric constant of the medium. The effect of the substituent can be seen by comparing the related 2-chloro- and 2-methoxy-substituted tetrahydropy-rans in entries 2 apd 3. The 2-chloro compound exhibits a significantly greater preference for the axial orientation than the 2-methoxy compound. Entry 3 also provides data relative to the effect of solvent polarity it is observed that the equilibrium constant is larger in carbon tetrachloride (e = 2.2) than in acetonitrile (e = 37.5). 

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. 

Some further uses of kinetics, less sweeping in their scope than the preceding applications, are for the testing of rate theories the measurement of equilibrium constants the analysis of solutions, including mixtures of solutes and the measurement of solvent properties that depend upon rates. Some of these applications are treated later in the book. 

Alkali metal alkoxides, r-butyl acetate neat, 45°, 30 min, 98% yield of r-butyl ester from methyl benzoate. The rate constant for the reaction increases with increasing ionic radius of the metal and with decreasing polarity of the solvent. Equilibrium for the reaction is achieved in <10 sec. Other examples eire presented. " ... 

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). 

The equilibrium between neutral a and zwitterionic b forms in the case of nicotinic 6 and isonicotinic 7 acids has been studied by Halle in mixtures of DMSO and water (from 0 to 100%) (Scheme 4). The position of the equilibrium is very sensitive to the composition of the solvent and for more than 80% of DMSO, the a form essentially dominates the equilibrium in solution (96CJC613). An analysis of their data shows a perfect linear relationship (r = 1) between the In Kt of the two acids and moderate linear relationships between In Kt and the percentage of DMSO. Johnston has studied the equilibrium 2-hydroxypyridine/2-pyridone in supercritical fluids (propane at 393 K and 1,1-difluoroethane at 403 K) (89JPC4297). The equilibrium constant Kt (pyridone/hydroxypyridine) increases four-fold for a pressure increase of 40 bar in 1,1-difluoroethane. 

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. 

Different Types of Proton Transfers. Molecular Ions. The Electrostatic Energy. The ZwiUertons of Amino Acids. Aviopro-tolysis of the Solvent. The Dissociation Constant of a Weak Acid. Variation of the Equilibrium Constant with Temperature. Proton Transfers of Class I. Proton Transfers of Classes II, III, and IV. The Temperature at Which In Kx Passes through Its Maximum. Comparison between Theory and Experiment. A Chart of Occupied and Vacant Proton Levels. 

In summary, the concentrations of solids and the concentrations of solvent (usually water) can be and usually are incorporated in the equilibrium constant, so they do not appear in the equilibrium law relation. 

Equilibrium constants for complex formation (A") have been measured for many donor-acceptor pairs. Donor-acceptor interaction can lead to formation of highly colored charge-transfer complexes and the appearance of new absorption bands in the UV-visible spectrum may be observed. More often spectroscopic evidence for complex formation takes the font) of small chemical shift differences in NMR spectra or shifts in the positions of the UV absorption maxima. In analyzing these systems it is important to take into account that some solvents might also interact with donor or acceptor monomers. 

Some data for the equilibrium constant XXno and the rate constant k2 for the aniline 7V-nitrosation step (Scheme 3-27) are presented in Table 3-1. For comparison purposes the table also includes data on diazotization with N203. The rate constant k2 for the nitrosation step (Scheme 3-27) with NOC1 and NOBr is close to the limits given by the diffusion velocity of particles in a solvent. As postulated by... 

The lack of a substrate isotope effect suggests very extensive internal return and is readily explained in terms of the fact that conversion of the hydrocarbon to the anion would require very little structural reorganisation. Since koba = k 1k 2/(kLl+k 2) and k 2 is deduced as > k2, then kobs = Kk 2, the product of the equilibrium constant and the rate of diffusion away of a solvent molecule, neither of the steps having an appreciable isotope effect. If the diffusion rates are the same for reactions of each compound then the derived logarithms of partial rate factors (above) become pAT differences between benzene and fluorobenzene hydrogens in methanol. However, since the logarithms of the partial rate factors were similar to those obtained with lithium cyclohexylamide, a Bronsted cor-... 

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