Equilibrium constants, values

The bond lengths appearing on the right-hand side of Eq. (46) are assumed to take their equilibrium (constant) values. 

Four anthocyanin species exist in equilibrium under acidic conditions at 25°C/ according to the scheme in Figure 4.3.3. The equilibrium constant values determine the major species and therefore the color of the solution. If the deprotonation equilibrium constant, K, is higher than the hydration constant, Kj, the equilibrium is displaced toward the colored quinonoidal base (A), and if Kj, > the equilibrium shifts toward the hemiacetalic or pseudobase form (B) that is in equilibrium with the chalcone species (C), both colorless." - Therefore, the structure of an anthocyanin is strongly dependent on the solution pH, and as a consequence so is its color stability, which is highly related to the deprotonation and hydration equilibrium reaction constant values (K and Kj,). 

The structure complexity also interferes with the equilibria in acidic medium, as shown in Figure 4.3.3. The deprotonation equilibrium constant value (KJ of zebrinin was higher than the hydration constant (Kj,), leading to the formation of a greater amount of colored quinonoidal with no formation of the colorless species, pseudobase or chalcone. ... 

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. 

EXAMPLE 19.18. Repeat the last example, but with an equilibrium constant value of 0.100. 

Esterification is a homogeneous equilibrium reaction when all the species are liquids. The equilibrium constant value is commonly determined by following the concentration of acid with time by titration of solution aliquots with NaOH. As a homogeneous equilibrium, the concentrations of the liquids are not set to 1, but can be determined as M= moles/L of solution, assuming the liquids are ideal. 

Table IV summarizes the final reported compositions of the solids and aqueous solutions (8) with calculated equilibrium constants. Values of log K(x) fr°m companion runs at constant composition differ by no more than 0.003 log K units.

Single-temperature equilibrium constant values may also yield quantitative information about reaction enthalpies, provided that the entropy term can be estimated. Take, for example, reaction 14.32, which involves hydrogen transfer between two substituted phenols (ArOH and Ar OH see examples in figure 14.4). Note that Kc = Km in this case. 

To obtain satisfactory results, several conditions must be fulfilled. The chemical reaction involved must be stoichiometric, no side reactions may occur or at least should be reproducible and quantitatively describable (such as the reaction of protons with ligands in chelatometric titrations) and the main reaction should have a high equilibrium constant value. The ISE should respond only to the titration system and the response should be fast and reproducible. 

Table 4. Dimensionless self- and inter-association equilibrium constants values determined from miscible polymer blends scaled to a common reference volume (100 cm /mol) [83]...

Because the Meisenheimer adducts are usually characterized by intense UV-visible absorption bands, the equilibrium constants for their formation (K) can be determined spectrophotometrically by standard methods, whether complete conversion to the adduct can be attained39 or not,60 depending on the equilibrium constant value (K 5 10). 

Linear correlations are observed between both log k, and log kr and the molar fraction of DMSO in DMSO-MeOH mixed solvents. As a consequence, the log K too is linearly correlated with the DMSO content. These correlations can be useful for predicting rate and equilibrium constant values in methanol by extrapolation whenever such values are too low for measurement in this solvent. 

Selected values of Ksp for various ionic compounds at 25°C are listed in Table 16.2, and additional values can be found in Appendix C. Like all equilibrium constants, values of Ksp depend on temperature (Section 13.9). 

Solids and Liquids Pure solids or liquids comprise a different phase from where reactions in aqueous media occur. Furthermore, the concentration of pure solids and liquids is a constant value (or very nearly so), and these constant values for concentration are included with the equilibrium constant value. Water sometimes appears as a reactant or product in reactions occurring in aqueous media. Because the concentration of water is so much greater than the concentrations of any of the reacting species, the concentration of water is also essentially constant. Therefore, the concentrations of solids, liquids, and water (as a solvent) do not appear explicitly in the equilibrium constant expression. 

For a reversible reaction AbB + C, the presence of chemical equilibrium imposes a further constraint on the operating region, as illustrated in Fig. 6.14, where the effect of the equilibrium constant value on the operating parameter region for a conversion of 90 % is shown. 

All of the above reactions and accompanying equilibrium constants may also be written for the complexes derived from trans-DDP. We shall be comparing the equilibrium-constant values for aquation and deprotonation of the cis- and /ran.v-complcxcs. 

Applicability of the first approach suggested by Keiko and Zarod-nyuk is based on the unity of thermodynamics and kinetics which explain differently the same physical regularities. As was said above this unity was brilliantly revealed by Boltzmann in his "kinetic" and "thermodynamic" explanations of the second law. In our case, setting, for example, a constraint on the equilibrium constant value of an individual reaction S VjXj = 0 within complex chemical process and writing this constraint intone of the possible forms ... 

The equilibrium constant values are in good agreement with the literature values with the exception of yttrium. 

PI] = 6 mM, based on the equilibrium constant value Keq = 7.5 x 105M. Assuming that all rate constants remain the same as for the physiological example, these concentrations yield Ai = 0.0333sec-1 and 2.2 = 0.0585 sec-1. In this case, setting pdS)) = 1, Equation (5.32) yields a = 1.31. The functions pvj+d) and fj(/) for the equilibrium case are plotted as dashed lines in Figure 5.7. 

What is the relationship between the equilibrium constant values for the two equations in each of the following sets ... 

Selected values of Kg and K are presented in Table 19.2. Although the reactions are equilibria and can be written with either set of species on the left, the equilibrium constant values in such tables represent the equations with the molecular acid or base on the left and the ions on the right. 

Using these data, estimate the equilibrium constant value at 25°C for the following reaction ... 

The overall reaction and equilibrium constant value for a hydrogen-oxygen fuel cell at 298 K is... 

In glycine, the carboxylic acid group has = 4.3 X 10- 1 and the amino group has Kb = 6.0 X 10 5. Use these equilibrium constant values to calculate the equilibrium constants for the following. 

Measurements of Tj have been made (269,270) to probe the structure of the second coordination sphere around Cr(acac)3. Acetone, chloroform, and methylene chloride were chosen as second sphere ligands. The shortening of their Tj values is found to be independent of solute concentration, and the value measured is determined by the diffusional correlation time of the solute molecule. No detectable second coordination sphere therefore exists in these solvents. However, methanol forms a discrete second sphere, and above a certain concentration the measured Ty values vary linearly with solute concentration. The observed Tj values are compatible with a model having a coordination number of 8, a Cr-CH3 separation of 700 pm, and an equilibrium constant for displacing solvent (CHCI3) of ca. 10. This equilibrium constant value is consistent with values previously... 

Table 10 reports some equilibrium constant values for hydrogen bond formation between 81 and some hydrogen bond acceptors. 

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