Equilibrium in aqueous solutions

Gibbs-Duhem Equation and the Phase Rule at Chemical Equilibrium 

Chemical Thermodynamic Tables Including Biochemical Species 

In this chapter we will find that when isomers are in chemical equilibrium, it is convenient to treat isomer groups like species in order to reduce the number of terms in the fundamental equation. We will also discuss the effect of ionic strength and temperature on equilibrium constants and thermodynamic properties of species. More introductory material on the thermodynamics of chemical reactions is provided in Silbey and Alberty (2001). 

When a chemical reaction occurs in a system, the changes in the amounts n, of species are not independent because of the stoichiometry of the reaction that occurs. A single chemical reaction can be represented by the reaction equation 

When a single chemical reaction occurs in a closed system, the differential of the Gibbs energy (see equation 2.5-5) is given by 

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Atlas of Electrochemical Equilibrium in Aqueous Solutions, 2nd ed., Marcel Pourbaix, National Association of Corrosion Engineers, Houston, Tex. 

There are many related examples which are now known as the general Dimroth rearrangement. For example, 3-ethylamino-l,2-benzisothiazole (419) is in equilibrium in aqueous solution with the 2-ethyl-3-imino isomer (420) <72AHCf 14)43). Dimroth rearrangements are known in the 1,2,4-thiadiazole series (421- 422), and in the 1,3,4-thiadiazole series as products of reactions of halogeno-l,3,4-thiadiazoles see Section 4.02.3.9.1 <68AHC(9)165). For a similar example in the 1,2,3,4-thiatriazole series, see Section 4.02.3.1.9. 

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. 

On the basis of these empirical observations and your own knowledge of steric effects in six-mem-bered rings, predict the preferred form (a- or (3-pyranose) at equilibrium in aqueous solution for each of the following ... 

CI2O is very soluble in water, a saturated solution at —9.4°C containing 143.6 g CI2O per 100 g H2O in fact the gas is the anhydride of hypochlorous acid, with which it is in equilibrium in aqueous solutions ... 

Acetamido-2-deoxy-D-galactopyranose (—), and 2-Acetamido-2-deoxy-D-mannopyranose ( ) at Anomeric Equilibrium in Aqueous Solution (redrawn from Ref. 28), and 2-Acetamido-2-deoxy-D-glucopyranose (- -) at Anomeric Equilibrium in Aqueous Solution. (Redrawn from Ref. 29.)... 

Reactions in aqueous solution behave in a similar way to those in the gas phase. As the concentration of products increases, the products react to regenerate reactants, and eventually the reaction reaches equilibrium. Example treats an equilibrium in aqueous solution. 

Figure 4 Heterocycles for which the tautomeric equilibrium in aqueous solution has been studied using free energy calculations including explicit solvent. Tautomerism occurs by exchanging a proton between the labeled atoms.

If a sugar has two carbonyl groups, each can form pyranose or furanose rings bicyclic forms sometimes result. An example is D-t/irao-3,4-hexodiu-lose42 because this compound is symmetrical, and pyranoses are not possible, only two forms are present at equilibrium. In aqueous solution, and also in dimethyl sulfoxide, 72% of the a,a- and 28% of the / ,/ -difuranose were found at 27°. The a,/ form, which would have two transfused five-mem-bered rings, was not observed. In dimethyl sulfoxide, there is also a small proportion of the monocyclic furanose form present. 

Eh-pH diagrams are sometimes used to predict or describe the major dissolved species and precipitates that should exist at equilibrium in aqueous solutions, including groundwaters, surface waters, laboratory solutions, and porewaters from soils, sediments, or rocks. However, as previously described, many natural aqueous systems are not at equilibrium and they often contain metastable species that are not predicted by Eh-pH diagrams. Metastable species refer to compounds, other substances, or ions that are present under redox, pH, pressure, temperature, or other conditions where chemical equilibrium indicates that they should be unstable and absent. Many metastable species (such as As(III) in oxygenated seawater) result from biological activity. 

In summary, while the nonionic surfactant dimethyldo-decylamine oxide forms only spherical micelles even in 0.20 M NaCl (see above and ref. 498), micelles of dimethyloleylamine oxide are subject to a sphere-rod equilibrium in aqueous solutions of NaCl as dilute as 10 4 M and even in water alone (ref. 500). Thus, Imae and Ikeda (ref. 479) conclude the rodlike micelles are stabilized more, as compared with the spherical micelles, when the hydrocarbon chain of the surfactant molecule is longer. This conclusion is, therefore, consistent with the earlier-mentioned belief of these authors that the rodlike micelles are more stable when the polar head group of the surfactant molecule is smaller and the chain length of its hydrocarbon part is longer (ref. 473). Since the surfactants referred to all behave as nonionics, these findings of rodlike micelle production have direct relevance to the formation of artificial gas microbubbles (see Section 10.3) with either the earlier-mentioned surfactant mixture Filmix 3 (see Chapter 9 and Section 10.4) or another, related surfactant preparation (see Section 10.4). 

The thermodynamic and kinetic characteristics of an intramolecular transimination reaction observed in solutions containing pyridoxal-5-phosphate and ethylenediamine have been investigated (75JA6530). The open-chain structure Schiff bases and the cyclic tautomers such as 54 are in equilibrium in aqueous solution over the pH range 7.5-14, but these equilibria are rather complex owing to the different states of the ionization (protonation) in both tautomers. The ring-chain equilibrium constant (the sum of all cyclic tautomers versus all open-chain tautomers) varies by less than a factor of 4 over the pH range 7-14. At pH 14, KT = 1.2 at pH 10,... 

Table 1.3 Composition of some aldoses at equilibrium in aqueous solution...

These compounds provide a rich variety of structural types and features. The two terpenoids possess the typical branched carbon skeletons of isoprenoids both compounds have diastereotopic methylene and methyl groups. Lactose is a /3-1,4-linked disaccharide of galactose and glucose glucose is the reducing residue, which at equilibrium in aqueous solution shows both anomers. The tetra-peptide, VGSE, contains four different amino... 

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