Hydrate theory

Three theory papers are also included. Determinants of the Polyproline II Helix from Modeling Studies by Creamer and Campbell reexamines and extends an earlier hypothesis about Pn and its determinants. Hydration Theory for Molecular Biophysics by Paulaitis and Pratt discusses the crucial role of water in both folded and unfolded proteins. Unfolded State of Peptides by Daura et al. focuses on the unfolded state of peptides studied primarily by molecular dynamics. 

Table 4.1. Single ion activity coefficients (molal scale) for uni-univalent chlorides at 25° C derived from hydration theory [11].

In connection with the hydration theory proposed by Vaslow (149) and the considerations by Krestov (93), attention is directed to the study by Blandamer and Symons (13). These authors note the importance of peripheral water interactions owing to the presence of both cations and anions. While anions may form H-bonds with the neighboring water molecules, the cation may interact strongly with the lone pair of a neigh-... 

As with all hydrate theory, it is important to interpret calculations at every opportunity in terms of experiments. With computer simulations, it is deceptively alluring to interpret calculations without physical validation, yet such a path can lead to false conclusions. When physical confirmation is not available, simulations should be regarded with caution. For example, at the heart of both MD and MC methods is the potential energy between individual molecules, which is itself an approximation and limits the accuracy of the simulated macroscopic properties. Such potentials should be validated in terms of their ability to predict measured properties, such as phase equilibria. 

Furthermore, he found the critical point and developed the hydrate theory", which made him a great physical chemist. 

This simple hydration theory cannot explain all the known phenomena, as, for example, the opposite effects of calcium chloride and zinc chloride on the colours. Engel2 therefore assumed that the observed colours were due to certain double salts present in the solutions. In the case of pure cobalt chloride, hydrolysis was supposed to occur on heating the solution, the hydrochloric acid liberated uniting with unchanged cobalt chloride and as an explanation of the colour change this is almost certainly incorrect. Ostwald 3 suggested a simple ionic explanation, namely, that the red colour is that of the cobalt cation, and the blue that of the undissociated salt. This is certainly not a complete explanation, and seems to necessitate a very marked decrease in ionisation with rise of temperature, which experiment, so far, does not support.4... 

Pickering SU (1893) The hydrate theory of solutions. Some compounds of the alkylamines and ammonia with water. Thins Chem Soc 63 (I) 141 -195... 

If ionic hydration theory is used as a basis for obtaining single-ion activity coefficients, somewhat different values result. For example, yci- values of 0.620 and 0.586 are obtained when NaCl and KCl are used. At an ionic strength of 0.1... 

The ionic hydration theory has been used to explain the effect of some ofthese factors on selectivity, According to this theory, the ions in aqueous... 

Ion-Association and lon-Hvdration. Aqueous solutions of electrolytes have been chemically described using a variety of theories. The original theoretical approach used by geochemists to model aqueous systems was based on the concept of ion-pairing or ion-association. The ion association approach as described by Carrels and Thompson (1) accurately depicted the speciation of seawater and later many other aqueous solutions. This approach was subsequently found to be inadequate for defining the chemistry of more complex and more concentrated aqueous solutions or those solutions near the critical point of water. This deficiency led to the use of other theoretical approaches to describe these systems, such as the ion-interaction, mean salt, and ion-hydration theories. 

Some other kinds of models have shown parameters that seem to follow useful correlation relationships. Among these are the virial coefficient model of Bums (2), the interaction coefficient model of Helgeson, Kirkham, and Flowers (4), and the hydration theory model of Stokes and Robinson (1). The problem shared by all three of these models is that they employ individual ion size parameters in the Debye-Hiickel submodel. This led to restricted applicability to solutions of pure aqueous electrolytes, or thermodynamic inconsistencies in applications to electrolyte mixtures. Wolery and Jackson (in prep.) discuss empirical modification of the Debye-Huckel model to allow ion-size mixing without introducing thermodynamic inconsistencies. It appears worthwhile to examine what might be gained by modifying these other models. This paper looks at the hydration tlieory approach. 

Hydration theory was first applied to aqueous electrolytes by Stokes and Robinson (1) in 1948. The approach is to correct for the fact that the actual solute species do not exist as bare ions as they are normally written, but as hydrated aqueous complexes. In the case of a solution of an aqueous nonelectrolyte, this reduces to the assumption that the solution is ideal, or nearly so, if one writes the formula of the solute to include the waters of hydration and computes its concentration and that of the solvent on this basis. In the case of an aqueous electrolyte, it reduces to the assumption that the Debye-Hiickel model becomes adequate (or at least more adequate) to describe the activity coefficients if this treatment is applied. 

Hydration theory deals with aqueous solutions in terms of two parallel definitions of the set of components, the usual one in which the solutes are considered formally unhydrated and the amount of solvent is the nominal amount, and a second in which the solutes are formally hydrated and the amount of water is reduced from the nominal amount. The objective is to correct for hydration effects and obtain a model giving activity coefficients in terms of the usual set of components. Quantities pertaining to the second set of components will be denoted by an asterisk. The number of moles of water in the first set is given by... 

The Stokes-Robinson model was later modified by its creators for use in more concentrated solutions by accounting for dehydration equilibria (12). The original model was also modified by Nesbitt (12), who made the hydration number a decreasing function of the ionic strength. Other workers too numerous to mention here have also attempted to do something with hydration theory. 

Figure 1. The fit of our hydration theory model to osmotic coefficient data for sodium perchlorate tabulated by Robinson and Stokes (11).

Future efforts should be directed to develop more advanced hydration theory models than the simple form examined here. Ion pairing should be treated in an explicit manner, even for the 1 1 electrolytes. Other possible changes that might be explored include the use of a more sophisticated electrostatic model and the usage of virial coefficient terms in the phenomenological equations. These models must be tested against not only the ability to fit data, but also the abilities to satisfy additivity relationships and to predict the properties of mixtures of aqueous electrolytes. 

Three other options are presently being studied, with an eye on including them in the forthcoming 3270 version. One of these is the equations of Helgeson, Kirkham, and Flowers (41). for which further model development is required. The second (42) is based on the hydration theory concept of Stokes and Robinson (43). This also requires further model development. The third set is a model (44) recommended by the European Nuclear Energy Agency for obtaining equilibrium constants for the formation of aqueous complexes of interest in nuclear waste disposal, such as of uranium and plutonium. 

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