Activity coefficient solvation

A quite different approach was adopted by Robinson and Stokes [8], who emphasized, as above, that if the solute dissociated into ions, and a total of h molecules of water are required to solvate these ions, then the real concentration of the ions should be corrected to reflect only the bulk solvent. Robinson and Stokes derive, with these ideas, the following expression for the activity coefficient ... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

Usually SmGo is a small difference between two large numbers, so it is more accurate to measure 8mG directly by the techniques discussed above than to estimate it indirectly. Solvation is then usually considered in terms of transfer free energies or activity coefficients. 

The second group of studies tries to explain the solvent effects on enantioselectivity by means of the contribution of substrate solvation to the energetics of the reaction [38], For instance, a theoretical model based on the thermodynamics of substrate solvation was developed [39]. However, this model, based on the determination of the desolvated portion of the substrate transition state by molecular modeling and on the calculation of the activity coefficient by UNIFAC, gave contradictory results. In fact, it was successful in predicting solvent effects on the enantio- and prochiral selectivity of y-chymotrypsin with racemic 3-hydroxy-2-phenylpropionate and 2-substituted 1,3-propanediols [39], whereas it failed in the case of subtilisin and racemic sec-phenetyl alcohol and traws-sobrerol [40]. That substrate solvation by the solvent can contribute to enzyme enantioselectivity was also claimed in the case of subtilisin-catalyzed resolution of secondary alcohols [41]. 

Therefore, the activity coefficients in solutions are determined primarily by the energy of electrostatic interaction w j between the ions. It is only in concentrated solutions when solvation conditions may change, that changes in (but not the existence of) solvation energy must be included, and that nonelectrostatic interactions between ions must be accounted for. 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

This coefficient has various names (medium effect, solvation activity coefficient, etc.) the name recommended by the responsible IUPAC commission is the transfer activity coefficient. In this book the effect of solvation in various solvents will be expressed exclusively in terms of standard Gibbs transfer energies. 

Thus the free energy of solvation may be calculated from the Henry s law constant or from the vapor pressure of the pure substance and the limiting activity coefficient. Thus, if the deviation of the solution from Raoult s law behavior is known, calculation of the standard state free energy of solvation requires only the vapor pressure of the pure substance (in the standard state... 

This equation has the expected behavior that AG< becomes more positive with decreasing solubility of the solute. However, free energies of solvation for different solutes cannot be related to their relative solubilities unless the vapor pressures of the different solutes are similar or one takes account of this via Equation 76. Furthermore, if the solubility is high enough that Henry s law does not hold, then one must consider finite-concentration activity coefficients, not just the infinite-dilution limit. 

Easier still is John Burgess book, Ions in Solution, Ellis Horwood, Chichester, 1999. Though it does not go into great detail about activity coefficients y, its treatment of ionic interactions and solvation is excellent. 

In principle, Gibbs free energies of transfer for trihalides can be obtained from solubilities in water and in nonaqueous or mixed aqueous solutions. However, there are two major obstacles here. The first is the prevalence of hydrates and solvates. This may complicate the calculation of AGtr(LnX3) values, for application of the standard formula connecting AGt, with solubilities requires that the composition of the solid phase be the same in equilibrium with the two solvent media in question. The other major hurdle is that solubilities of the trichlorides, tribromides, and triiodides in water are so high that knowledge of activity coefficients, which indeed are known to be far from unity 4b), is essential (201). These can, indeed, be measured, but such measurements require much time, care, and patience. 

The degree of solvation of the reactants and activated complex affect the rate of reaction. When the activated complex is solvated to a greater extent in comparison to reactants, the rate of reaction will be greater than that in a non solvating solvent. This is because the activity coefficient of the complex is smaller than it is in a solvent that does not solvate it. This lowers the potential energy of activated complex or causes a decrease in the activation energy of the reaction. 

It is important to stress that the activity coefficients (and the concentrations) in equation 16.18 refer to the species close to the surface of the electrode, and so can be very different from the values in the bulk solution. This is portrayed in figure 16.6, which displays the Stern model of the double layer [332], One (positive) layer is formed by the charges at the surface of the electrode the other layer, called the outer Helmholtz plane (OHP), is created by the solvated ions with negative charge. Beyond the OHP, the concentration of anions decreases until it reaches the bulk value. Although more sophisticated double-layer models have been proposed [332], it is apparent from figure 16.6 that the local environment of the species that are close to the electrode is distinct from that in the bulk solution. Therefore, the activity coefficients are also different. As these quantities are not... 

Note that the tGA are the standard molar Gibbs energies of solvation of the (combined ions of the) electrolyte [5]. Alternatively, a transfer activity coefficient can be defined as... 

When the solvent is a good solvater, the determination of the solvation number b is difficult, unless the dependence of the extractant concentration on the solvent can be obtained. Solvation numbers can be obtained in mixtures of a solvating extractant and an inert diluent like hexane. Further, in these systems the extraction of the metal commonly requires high concentrations of salt or acid in the aqneons phase, so the activity coefficients of the solutes must be taken into acconnt. 

Usnally, only very dilute solutions can be considered ideal. In most aqueous solutions, ions are stabilized because they are solvated by water molecules. As the ionic strength is increased, ions interact with each other. Thus, when calculating the chemical potential of species i, a term that takes into account the deviation from ideal conditions is added. This term is called an excess term and can be either positive or negative. The term usually is written as 7 riny., where y. is the activity coefficient of component i. The complete expression for the chemical potential of species i then becomes... 

Some stability constants for ion pairs on Fe oxides are listed in Table 10.4. This model was applied by Davis and Leckie (1978, 1980) to adsorption of various cations and anions on ferrihydrite. The extended triple layer model of Sahai and Svenjensky (1997) incorporates recent advances in aqueous electrolyte chemistry which enable aqueous activity coefficients for electrolytes to be calculated over a wide range of ionic strengths. The model also considers the free energy of adsorption of an ion to be the sum of the contributions from an electrostatic term, a Born solvation term and a ion intrinsic term. This extended model has been applied to adsorption of Co and Cd on goethite. 

The various factors that contribute to ion solvation were discussed in Section 2.2.1. In this section, we deal with the solvent effects on chemical reactions more quantitatively [5, 22]. To do this, we introduce two quantities, the Gibbs energy of transfer and the transfer activity coefficient. 

A change from a protic to an aprotic solvent can also affect the acidity or basicity, since there is a difference in solvation of anions by a protic solvent (which can form hydrogen bonds) and an aprotic one.158 The effect can be extreme in DMF, picric acid is stronger than HBr,159 though in water HBr is far stronger. This particular result can be attributed to size. That is, the large ion (C N CsE C)- is better solvated by DMF than the smaller ion Br-.160 The ionic strength of the solvent also influences acidity or basicity, since it has an influence on activity coefficients. 

The papers in the second section deal primarily with the liquid phase itself rather than with its equilibrium vapor. They cover effects of electrolytes on mixed solvents with respect to solubilities, solvation and liquid structure, distribution coefficients, chemical potentials, activity coefficients, work functions, heat capacities, heats of solution, volumes of transfer, free energies of transfer, electrical potentials, conductances, ionization constants, electrostatic theory, osmotic coefficients, acidity functions, viscosities, and related properties and behavior. 

Solvation Effects. Many previous accounts of the activity coefficients have considered the connections between the solvation of ions and deviations from the DH limiting-laws in a semi-empirical manner, e.g., the Robinson and Stokes equation (3). In the interpretation of results according to our model, the parameter a also relates to the physical reality of a solvated ion, and the effects of polarization on the interionic forces are closely related to the nature of this entity from an electrostatic viewpoint. Without recourse to specific numerical results, we briefly illustrate the usefulness of the model by defining a polarizable cosphere (or primary solvation shell) as that small region within which the solvent responds to the ionic field in nonlinear manner the solvent outside responds linearly through mild Born-type interactions, described adequately with the use of the dielectric constant of the pure solvent. (Our comments here refer largely to activity coefficients in aqueous solution, and we assume complete dissociation of the solute. The polarizability of cations in some solvents, e.g., DMF and acetonitrile, follows a different sequence, and there is probably some ion-association.)... 

Let us now extend our molecular descriptor model introduced in Chapter 4 (Eqs. 4-26 and 4-27) to the aqueous activity coefficient. We should point out it is not our principal goal to derive an optimized tool for prediction of yw, but to develop further our understanding of how certain structural features determine a compound s partitioning behavior between aqueous and nonaqueous phases. Therefore, we will try to keep our model as simple as possible. For a more comprehensive treatment of this topic [i.e., of so-called linear solvation energy relationships (LSERs)] we refer to the literature (e.g., Kamlet et al., 1983 Abraham et al., 1990 Abraham, 1993 Abraham et al., 1994a and b Sherman et al., 1996). 

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