Thermodynamic Aspects of Solubility

To describe the phenomena that occur during the solubility process, the relationship between the solubility equilibrium constant and the free enthalpy variation can be defined first  

As for other reactions, K q, and thus solubility, increases as the AG becomes increasingly negative. Free enthalpy variation is related to the variation in both enthalpy and entropy  

During the dissolution process, two opposite processes occur— release of ions from the crystal lattice (endothermic process) and hydration of the liberated ions (exothermic process). 

The hydration process is an exothermic one. In the case of cations, the enthalpy of hydration is dependent on the size and charge of metal ions. The smaller and higher charged a metal ion is, the more energy is released at its hydration. In Table 3.12, the enthalpies of hydration of some metal ions are presented. The enthalpy of hydration AijH was used in QSAR studies for the analysis of metal ion toxicity (Enache et al. 1999 Enache et al. 2003). 

FIGURE 3.14 Born-Haber cycle for the dissolution process of a salt. 

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Thermodynamic Aspects of Solubility At equilibrium in a saturated solution, the chemical potential, or partial molal free energy, of the solute must be the same in the solution as in the solid phase. If we consider two different saturated solutions, there-fore, both in equilibrium with the same solid phase, the chemical potential of the solute must be the same in both. The chemical potential ( ) and activity (c) are related by the equation p — po — RT In o, where Po is the chemical potential of the substance in the standard state. Hence, if the same standard state is chosen for all the solutions considered, the activity of the solute must be the same in all. 

These are but a few examples of the roles that solubility plays in technology, in physical chemistry, and in colloid science. Solubility is one of the truly basic thermodynamic parameters of any system, and so it is of pervasive importance. Some of the thermodynamic aspects of solubility will now be considered. 

One last concept must be considered with respect to the thermodynamic aspects of solubility—the condition of equilibrium in mixtures that contain two or more phases. What specific conditions must be met for a particular mixture to be regarded as being in thermodynamic equilibrium A particularly important requirement is that the chemical potential of each component must be the same in all the phases that are present. Numerous boundary conditions apply to this requirement, which have been discussed elsewhere [34]. By introducing the concepts of field and density thermodynamic variables, Griffiths and Wheeler were able to restate the condition of equilibrium for heterogeneous mixtures in a particularly simple, rigorous, and elegant form [35,36]. 

With these concepts in hand, we may now briefly consider some thermodynamic aspects of solubility. Suppose (as above) one starts with pure solute (say, sodium chloride crystals) and pure solvent (water) and adds the salt crystals to the water at constant temperature. Just at the point when they are brought together, a nonequilibrium state exists, because salt has a finite solubility in water but has not yet dissolved. The concentration profile at this time is the step-function described in Fig. 1. The process of dissolving salt in water has a negative free energy, and thus occurs irreversibly until the liquid is saturated. As the concentration of salt in the liquid phase increases, so does its chemical potential, as seen from Eq. (4), and so the driving force for dissolution (the difference between the chemical potential at any given time and the equilibrium chemical potential) steadily decreases. Finally, a concentration is reached at which the chemical potential of sodium... 

For a vary thorough discusson of enthalpy, entropy, and the solubility of ionic compounds, see Johnson. D. A. Some Thermodynamic Aspects of Inorganic Chemistry Cambridge University London. 1968. Chafrter 5. 

The point of this discussion has been to consider some of the thermodynamic aspects of the process that occurs when a solute is dispersed in a solvent to form a solution. Our observations tell us that like dissolves like. However, the dissolution process is so complex that predicting whether a particular solute will dissolve in a given solvent is risky. Solubility is difficult to explain and even more difficult to predict, especially when water is the solvent. The only way to be certain about the compatibility of a given solute and solvent is to do the experiment. 

D. A. Johnson (1982) Some Thermodynamic Aspects of Inorganic Chemistry, 2nd edn, Cambridge University Press, Cambridge - Contains a useful discussion of the solubility of ionic salts in aqueous solution. 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

Indeed, in the world of tomorrow we can expect new aspects of polymer solids to extend the conventional and successful structure ideas of this century. These, of course, were the recognition as molecular identities of the chains of repeating chemical monomers. The circumstances of those entities have resulted in interesting concepts of solubilities, viscosity, and other mechanics, and especially thermodynamic limitations m mutual solubility or comparability of polymer mixtures. But we have known for decades that even homogeneous regular chain polymers such as Carothers polyesters and polyamides formed solids with manifold imperfections and irregularities, such as order-disorder crystal configurations.(22,23)... 

The design of crystallization processes for the manufacture of Active Pharmaceutical Ingredients is a significant technical challenge to Process Research and Development groups throughout the Pharmaceutical and related industries. It requires an understanding of both the thermodynamic and kinetic aspects of crystallization, to ensure that the physical properties of the product will consistently meet specification. Failure to address these issues may lead to production problems associated with crystal size, shape and solubility, and to dissolution and bioavailability effects in the formulated product. 

It is therefore the right time to give a first comprehensive overview of fullerene chemistry, which is the aim of this book. This summary addresses chemists, material scientists and a broad readership in industry and the scientific community. The number of publications in this field meanwhile gains such dimensions that for nonspecialists it is very difficult to obtain a facile access to the topics of interest. In this book, which contains the complete important literature, the reader will find all aspects of fullerene chemistry as well as the properties of fullerene derivatives. After a short description of the discovery of the fullerenes all methods of the production and isolation of the parent fullerenes and endohedrals are discussed in detail (Chapter 1). In this first chapter the mechanism of the fullerene formation, the physical properties, for example the molecular structure, the thermodynamic, electronic and spectroscopic properties as well as solubilities are also summarized. This knowledge is necessary to understand the chemical behavior of the fullerenes. 

This section describes further developments to May, 2007. A new topic relevant to thermodynamic aspects (Section 8.03.4.1) is solubility of pyrazine and its derivatives in supercritical carbon dioxide <2006CED2056>. A notable example of nucleophilic displacement of substituents (Section 8.03.5.4.2) is represented by highly selective monosubstitution of chloro substituent in 2,3-dichloropyrazine, which is converted by treatment with a-lithio ketones into a-(3-chloropyrazin-2-yl) ketones <2006T9919>. Similarly a-(chloropyrazinyl) acetic ester or acetonitrile derivatives are synthesized by using a-lithio acetic esters or acetonitriles, respectively. 

This book offers no solutions to such severe problems. It consists of a review of the inorganic chemistry of the elements in all their oxidation states in an aqueous environment. Chapters 1 and 2 deal with the properties of liquid water and the hydration of ions. Acids and bases, hydrolysis and solubility are the main topics of Chapter 3. Chapters 4 and 5 deal with aspects of ionic form and stability in aqueous conditions. Chapters 6 (s- and p-block). 7 (d-block) and 8 (f-block) represent a survey of the aqueous chemistry of the elements of the Periodic Table. The chapters from 4 to 8 could form a separate course in the study of the periodicity of the chemistry of the elements in aqueous solution, chapters 4 and 5 giving the necessary thermodynamic background. A more extensive course, or possibly a second course, would include the very detailed treatment of enthalpies and entropies of hydration of ions, acids and bases, hydrolysis and solubility. 

The next main section deals with thermodynamic aspects. It starts by consideration of the intramolecular forces between heterocyclic molecules which influence melting and boiling points, solubility and chromatographic characteristics. This is followed by a section on stability and stabilization, including thermochemistry and conformation of the saturated ring systems, and then a discussion of aromaticity. 

Ben-Naim (1972b, c) has examined hydrophobic association using statistical mechanical theories of the liquid state, e.g. the Percus-Yevick equations. He has also examined quantitative aspects of solvophobic interactions between solutes using solubility data for ethane and methane. The changes in thermodynamic parameters can be calculated when two methane molecules approach to a separation of, 1-533 x 10-8 cm, the C—C distance in ethane, and the solvophobic quantities 8SI/i, s 2 and 8SiS2 can be calculated. In water (solvophobic = hydrophobic) 5si/i is more negative than in other solvents and decreases as the temperature rises both 8s iH%... 

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