Ionic hydration number

The values of r, construed as hydration numbers of electrolytes at high concentrations, are considerably smaller than the sum of the ionic hydration numbers at infinite dilution h°° shown in Tables 4.7,4.8, and 4.9. Theoretically, increasing concentrations necessarily lead to hydration numbers h(c) that diminish with increasing electrolyte concentrations as shown by Padova [22] ... 

The solute-solvent interaction in equation A2.4.19 is a measure of the solvation energy of the solute species at infinite dilution. The basic model for ionic hydration is shown in figure A2.4.3 [5] there is an iimer hydration sheath of water molecules whose orientation is essentially detemiined entirely by the field due to the central ion. The number of water molecules in this iimer sheath depends on the size and chemistry of the central ion ... 

The controhing effect of various ions can be expressed in terms of thermodynamic equhibria [Karger and DeVivo, Sep. Sci., 3, 393 1968)]. Similarities with ion exchange have been noted. The selectivity of counterionic adsorption increases with ionic charge and decreases with hydration number [Jorne and Rubin, Sep. Sci., 4, 313 (1969) and Kato and Nakamori, y. Chem. Eng. Japan, 9, 378 (1976)]. 

The number of water molecules in such a cluster, the hydration number, varies with ionic size it is four for Li, three for Na, but only one for Rb. ... 

The different hydration numbers can have important effects on the solution behaviour of ions. For example, the sodium ion in ionic crystals has a mean radius of 0 095 nm, whereas the potassium ion has a mean radius of 0133 nm. In aqueous solution, these relative sizes are reversed, since the three water molecules clustered around the Na ion give it a radius of 0-24 nm, while the two water molecules around give it a radius of only 017 nm (Moore, 1972). The presence of ions dissolved in water alters the translational freedom of certain molecules and has the effect of considerably modifying both the properties and structure of water in these solutions (Robinson Stokes, 1955). 

AB cements are not only formulated from relatively small ions with well defined hydration numbers. They may also be prepared from macromolecules which dissolve in water to give multiply charged species known as polyelectrolytes. Cements which fall into this category are the zinc polycarboxylates and the glass-ionomers, the polyelectrolytes being poly(acrylic acid) or acrylic add copolymers. The interaction of such polymers is a complicated topic, and one which is of wide importance to a number of scientific disciplines. Molyneux (1975) has highlighted the fact that these substances form the focal point of three complex and contentious territories of sdence , namely aqueous systems, ionic systems and polymeric systems. 

In almost all theoretical studies of AGf , it is postulated or tacitly understood that when an ion is transferred across the 0/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of AGfr°. Although Abraham and Liszi [17], in considering the transfer between mutually saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB andl,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170mM H2O in NB). In such a medium, hydrophilic ions such as Li, Na, Ca, Ba, CH, and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl-Fischer method [35 5]. Rais et al. [35] and Iwachido and coworkers [36-39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal... 

The number of binding sites can be determined in this model by a plot of d Ink /dlnm at constant temperature, pH, and ion valency. To do that, it may be assumed that dlny /dlnm is approximately zero. The actual value is -0.04 for 0.1 to 0.5 M sodium chloride and less at lower concentrations. To a first approximation, the stoichiometry of water molecules released by binding protein could be determined from the slope of the plot of dink /dlnm vs. m. However, especially at low salt concentration and near the isoelectric point, the slope of such plots is nonlinear. The nonlinearity may be due to hydrophobic interaction between stationary phase and protein or a large change of ionic hydration on binding.34... 

The ionic mobility and diffusion coefficient are also affected by the ion hydration. The particle dimensions calculated from these values by using Stokes law (Eq. 2.6.2) do not correspond to the ionic dimensions found, for example, from the crystal structure, and hydration numbers can be calculated from them. In the absence of further assumptions, diffusion measurements again yield only the sum of the hydration numbers of the cation and the anion. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

When an ionic compound is dissolved in a solvent, the crystal lattice is broken apart. As the ions separate, they become strongly attached to solvent molecules by ion-dipole forces. The number of water molecules surrounding an ion is known as its hydration number. However, the water molecules clustered around an ion constitute a shell that is referred to as the primary solvation sphere. The water molecules are in motion and are also attracted to the bulk solvent that surrounds the cluster. Because of this, solvent molecules move into and out of the solvation sphere, giving a hydration number that does not always have a fixed value. Therefore, it is customary to speak of the average hydration number for an ion. 

Table 1. Ionic Radii, hydration numbers, softness parameters a, surface charge densities, polarizabilities, free energies AG° enthalpies AH° and entropies A S° of hydration of metal cations from groups Za o,nd II ...

The four-valent Th4+ ion, which also forms primarily ionic bonds, has a hydration number of eight in aqueous perchlorate solutions (126), which is the same as that of erbium(III), although the Th—H20 bonds are slightly longer, 2.49 A, than for erbium(III), 2.35 A. Diffraction data for an aqueous thorium(IV) chloride solution, with a composition... 

When the ion is hydrated by all the adjacent molecules (it = r — 1), there is a strong lattice-site exclusion effect at high ionic concentrations, since the central site can be available to an ion only when both its first and second neighbors are free of ions (a total of 1 + w 4- w(w — 1) = ia2 + 1 sites). On the other hand, when the hydration number (r — 1) is low, almost any free site can be occupied by an ion, since in this case there is a high chance to find at least (r — 1) free water molecules around a selected site. In the next section it will be shown that there is a strong dependence of the site-exclusion effect on the hydration number and, hence, that specific ion effects can be important in the double layer interactions. 

Table 2. Ionic Radii, Hydration Numbers, Free Energies of Solvation, Surface Charge Densities, and Coordination Geometry of Alkali and Alkaline Earth Cations of Interest...

To obtain individual ionic values, one has to make an assumption. One takes a large ion (e.g., larger than T) and assumes its primary solvation number to be zero," so that if the total solvation number for a series of salts involving this big anion is known, the individual hydration numbers of the cations can be obtained. Of course, once the hydration number for the various cations is determined by this artifice, each cation can be paired with an anion (this time including smaller anions, which may have significant hydration numbers). The total solvation numbers are determined and then, since the cation s solvation number is known, that for the anion can be obtained. 

Primary Hydration Numbers from ionic Mobility Measurements... 

Now, the question is how to get information on the more subtle quantity, the hydration numbers. Some confusion arises here, for in some research papers the coordination number (the average number of ions in the first layer around the ion) is also called the hydration number However, in the physicochemical literature, this latter term is restricted to those water molecules that spend at least one jump time with the ion, so that when its dynamic properties are treated, the effective ionic radius scans to be that of the ion plus one or more waters. A startling difference between co-ordination number and solvation number occurs when the ionic radius exceeds about 0.2 nm (Fig. 2.23a). 

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