Hydrate number

Figure A2.4.3. The localized structure of a hydrated metal cation in aqueous solution (the metal ion being assumed to have a primary hydration number of six). From [5].

Hydration and solvation have also been studied by conductivity measurements these measurements give rise to an effective radius for the ion, from which a hydration number can be calculated. These effective radii are reviewed in the next section. 

The complete hydration shell of the proton consists of both the central FI O unit and fiirther associated water molecules mass spectrometric evidence would suggest that a total of four water molecules fomr the actual FIgOj unit, givmg a hydration number of four for the proton. Of course, the measurement of this number by... 

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)]. 

Bell has calculated Hq values with fair accuracy by assuming that the increase in acidity in strongly acid solutions is due to hydration of hydrogen ions and that the hydration number is 4. The addition of neutral salts to acid solutions produces a marked increase in acidity, and this too is probably a hydration effect in the main. Critchfield and Johnson have made use of this salt effect to titrate very weak bases in concentrated aqueous salt solutions. The addition of DMSO to aqueous solutions of strong bases increases the alkalinity of the solutions. 

There has been considerable discussion about the extent of hydration of the proton and the hydroxide ion in aqueous solution. There is little doubt that this is variable (as for many other ions) and the hydration number derived depends both on the precise definition adopted for this quantity and on the experimental method used to determine it. H30" has definitely been detected by vibration spectroscopy, and by O nmr spectroscopy on a solution of HF/SbFs/Ha O in SO2 a quartet was observed at —15° which collapsed to a singlet on proton decoupling, 7( 0- H) 106 Hz. In crystalline hydrates there are a growing number of well-characterized hydrates of the series H3O+, H5O2+, H7O3+, H9O4+ and H13O6+, i.e. [H(0H2) ]+ n = 1-4, Thus... 

The coordination chemistry of the large, electropositive Ln ions is complicated, especially in solution, by ill-defined stereochemistries and uncertain coordination numbers. This is well illustrated by the aquo ions themselves.These are known for all the lanthanides, providing the solutions are moderately acidic to prevent hydrolysis, with hydration numbers probably about 8 or 9 but with reported values depending on the methods used to measure them. It is likely that the primary hydration number decreases as the cationic radius falls across the series. However, confusion arises because the polarization of the H2O molecules attached directly to the cation facilitates hydrogen bonding to other H2O molecules. As this tendency will be the greater, the smaller the cation, it is quite reasonable that the secondary hydration number increases across the series. 

Fig. 18. Hydration number and a-helix content of (Glu Na) as a function of solvent composition in mixtures of water with 1-PrOH (O), 2-PrOH (A) and t-BuOH (O) 1J<)...

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. 

TABLE 7.2 Heats of Hydration of Individual Ions (kj/mol) and Hydration Numbers h. 

The values of hj for different ions are between 0 and 15 (see Table 7.2). As a rule it is found that the solvation number will be larger the smaller the true (crystal) radius of the ion. Hence, the overall (effective) sizes of different hydrated ions tend to become similar. This is why different ions in solution have similar values of mobilities or diffusion coefficients. The solvation numbers of cations (which are relatively small) are usually higher than those of anions. Yet for large cations, of the type of N(C4H9)4, the hydration number is zero. 

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... 

Recently, the abilities of primary to tertiary alkylammonium ions with Me, Et, and -Bu groups to transport water to NB have been studied [48]. As the result of careful consideration of the ion-pair formation, it has been shown that the hydration numbers (w ) of the ammonium ions in NB, being little affected by the alkyl chain length, are simply dependent on the class of the ammonium ion % = 1.64, 1.04, 0.66, respectively, for the primary, secondary, and tertiary ammonium ions. 

TABLE 3 Charge Numbers and Radii of Ions and Their Hydration Numbers and Hydrated Radii in NB at 25° C... 

Unless noted otherwise, it has been assumed that the number of the solvent molecules (S = 0 or W) that can interact directly with a hydrated ion in phase S is equal to the hydration number ... 

The sequential reactions 4.1 and 4.2 represent the self-dissociation of water as the exchange of a proton between water molecules, where hydration of the proton according to reaction 4.2 is the driving force for its separation (reaction 4.1) although the proton hydration is not limited to one H20 (hydration number 1), nor is the occurrence of unhydrated OH ion realistic, the overall reaction 4.3 is generally written as the simplest form to show the principle of proton acidity. 

As every solvent has its characteristic structure, its molecules are bonded more or less strongly to the ions in the course of solvation. Again, solvation has a marked effect on the structure of the surrounding solvent. The number of molecules bound in this way to a single ion is termed the solvation (hydration) number of this ion. 

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. 

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. 

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. 

Remarkable data on primary hydration shells are obtained in non-aqueous solvents containing a definite amount of water. Thus, nitrobenzene saturated with water contains about 0.2 m H20. Because of much higher dipole moment of water than of nitrobenzene, the ions will be preferentially solvated by water. Under these conditions the following values of hydration numbers were obtained Li+ 6.5, H+ 5.5, Ag+ 4.4, Na+ 3.9, K+ 1.5, Tl+ 1.0, Rb+ 0.8, Cs+0.5, tetraethylammonium ion 0.0, CIO4 0.4, NO3 1.4 and tetraphenylborate anion 0.0 (assumption). 

The method of calculating these values was proposed by R. A. Robinson and R. H. Stokes. The Gibbs energy G of a system containing 1 mole of uni-univalent electrolyte ( t = 1, total number of moles of ions being 2) and n0 moles of solvent is expressed for solvated ions (dashed quantities) on one hand and for non-solvated ions (without dash) on the other it is assumed that jU0 = jUo and that the hydration number h (number of moles of the solvent bound to 1 mole of the electrolyte) is independent of concentration ... 

---