Equilibrium constants water

However, in dilute solution [H O] is virtually conslant ([H,0] = 55.5 since 1 litre of water contains 1000/18 mol of H O) and taking this into the above expression for the equilibrium constant we obtain a second constant... 

Hydrogen sulphide is slightly soluble in water, giving an approximately 0.1 M solution under 1 atmosphere pressure it can be removed from the solution by boiling. The solution is weakly acidic and dissolves in alkalis to give sulphides and hydrogensulphides. The equilibrium constants... 

Conformational free energy simulations are being widely used in modeling of complex molecular systems [1]. Recent examples of applications include study of torsions in n-butane [2] and peptide sidechains [3, 4], as well as aggregation of methane [5] and a helix bundle protein in water [6]. Calculating free energy differences between molecular states is valuable because they are observable thermodynamic quantities, related to equilibrium constants and... 

Table 2.6. Equilibrium constants from complexation of 2.4a, 2.4b, and 2.4d to different metal ions (Kj) and second-order rate constants for the Diels-Alder reaction of these complexes with 2 (%cd) in water at 2.00 M ionic strength and 25°C. ...

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. 

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... 

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... 

The carbon-metal bonds of organolithium and organomagnesium compounds have appreciable carbamomc character Carbanions rank among the strongest bases that we 11 see m this text Their conjugate acids are hydrocarbons—very weak acids indeed The equilibrium constants for ionization of hydrocarbons are much smaller than the s for water and alcohols thus hydrocarbons have much larger pA s... 

The equilibrium constant for this reaction is called water s dissociation constant, K, ... 

A dye used in the coloration of materials, such as fibers, must be present as the monomer if it is to adsorb to the material s surface. This experiment describes how spectrophotometry can be used to determine the equilibrium constant between a monomer and a dimer for the dye pinacyanol iodide in water. 

Sta.bilizers. Cyanuric acid is used to stabilize available chlorine derived from chlorine gas, hypochlorites or chloroisocyanurates against decomposition by sunlight. Cyanuric acid and its chlorinated derivatives form a complex ionic and hydrolytic equilibrium system consisting of ten isocyanurate species. The 12 isocyanurate equilibrium constants have been determined by potentiometric and spectrophotometric techniques (30). Other measurements of two of the equilibrium constants important in swimming-pool water report significantly different and/or less precise results than the above study (41—43). A critical review of these measurements is given in Reference 44. 

Equilibrium Constants. The reaction between an organic acid and an alcohol to produce an ester and water is expressed ia equation 4 ... 

For most simple carbonyl compounds, the equilibrium constant for addition of water to the carbonyl group is unfavorable ... 

Althoi h the equilibrium constant for hydration is unfavorable, the equilibrium between an aldehyde or ketone and its hydrate is established rapidly and can be detected by isotopic exchange, using water labeled with 0, for example ... 

The equilibrium constants for addition of alcohols to carbonyl compounds to give hemiacetals or hemiketals show the same response to structural features as the hydration reaction. Equilibrium constants for addition of metiianoHb acetaldehyde in both water and chloroform solution are near 0.8 A/ . The comparable value for addition of water is about 0.02 The overall equilibrium constant for formation of the dimethyl acetal of... 

Taking known values for the molar refractivities of water and methanol, and again assuming a range of values for the equilibrium constant (k) and the refractive index (ni) of the methanol/water associate, the actual values that fit the equation for these... 

It is seen that the three values for the equilibrium constant (k) range from 0.00443 to 0.00565 with an average value of 0.00504. The two values for the densities of the methanol/water associate are in reasonable agreement and have a magnitude that would be expected for the hydrogen bonded associate. 

Using the average value for the equilibrium constant, the distribution concentration of the different components of a methanol water mixture were calculated for initial methanol concentrations ranging from zero to 100%v/v. The curves they obtained are shown in Figure 28. The molar refractivities of 11.88 is also in accordance with that expected since the molar refractivity s of water and methanol are 3.72 and 8.28 respectively. The refractive index of the associate of 1.3502 is, as would be expected, higher than that of either water or methanol. 

Figure 29. Graph of the Logarithm of the Water/Methanol Association Equilibrium Constant against the Reciprocal of the Absolute Temperature...

For cases when the concentration of water remains almost constant with respect to the other species, one can define the following reaction equilibrium constants for Eqs. (8.15) and (8.16), respectively ... 

Since the concentration of water remains approximately constant, one can define the following two reaction equilibrium constants... 

The vapor-solid equilibrium constant is determined experimentally and is defined as the ratio of the mol fraction of the hydrocarbon component in gas on a water-free basis to the mol fraction of the hydrocarbon component in the solid on a water-free basis. That is ... 

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). 

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. 

When the added water has a molarity n, let a fraction g of positive ions be alcoholic ions, while the fraction (1 — g) is in the form of (HjO)+ ions, On extrapolating to infinite dilution, the equilibrium constant of the reaction (43) may be written... 

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. 

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