Hydration number, effective

Effective hydration number, taken as the number of water molecules whose strength of interaction with the cation is large compared to kT, as estimated from activity coefficients of... 

The complex dielectric spectra of water/ChEOjo and water/ChEOi binary systems (at 5, 10, and 15 wt% water) were determined at 25 °C by time-domain reflectom-etry (frequency range of 0.1-20 GHz, [39]). The low-frequency process was assigned to the kinetics of the hydrophiUc layer of micelles, including the motion of hydrated oxyethylene chain and hydrated water. Additionally, the relaxation time of the high-frequency process was attributed to the cooperative rearrangement of the H-bond network of bulk water. Following various calculations, which are reported in the article, the effective hydration number of ethylene chain Zeo was estimated. 

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 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. 

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). 

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... 

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. 

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. 

It is clear from the above equations that numerous parameters (proton exchange rate, kcx = l/rm rotational correlation time, tr electronic relaxation times, 1 /rlj2e Gd proton distance, rGdH hydration number, q) all influence the inner-sphere proton relaxivity. Simulated proton relaxivity curves, like that in Figure 3, are often used to visualize better the effect of the... 

Some caution is required when comparing the association constants obtained from extraction experiments with those measured under anhydrous, homogeneous conditions. Iwachido et al. (1976, 1977) have shown that the extracted cation retains part of its aqueous solvation shell on complexation. In particular, the small univalent cations (Li+, Na+) and bivalent cations give high hydration numbers for their crown-ether complexes. Water molecules completing the co-ordination sphere of the cation have frequently been encountered in the solid state of crown-ether complexes (Bush and Truter, 1970, 1971). The effect of small amounts of water on the equilibria (1) has not been studied yet for crown ethers. However, it has been found that the presence... 

The hydration number (the number of water molecules intimately associated with the salt) of the quaternary ammonium salt is very dependent upon the anion. The change in the order of reactivity is thus believed to be due to the hydration of the anion the highly hydrated chloride and cyanide ions are less reactive than expected, and the poorly hydrated iodide fares better under phase transfer conditions than in homogeneous reactions. Methanol may specifically solvate the anions via hydrogen bonding, and this effect is responsible for the low reactivity of more polar nucleophiles in that solvent. 

When simply hydrated, the number of water molecules bonded to the metal (central) ion correspond to a value N, the coordination number, which is also termed the hydration number. In complexation, ligands displace the hydrate waters, although not necessarily on a 1 1 basis. Charge, steric, and other effects may cause the maximum number of ligands to be less than N. For example, in... 

We can now discuss the solvation number. In systems such as the metha-nol-water-CaCl2 system shown in Figure 5, the hydration number is the greatest, that is, 11 at x3 = 0.020. If the hydration number of ions is calculated from the hydration entropy, Ca2+ is seven and Cl is two (3). If it is assumed that CaC is completely dissociated and both the cation and anion forms hydrate, the hydration number becomes 7 + 2X2 = 11, which agrees with the value obtained from the salt effect. 

The solvation numbers of ions such as Mg2+, Al3+, and Be2+ may be determined by low temperature PMR techniques as mentioned earlier. The solvation number for small spherical ions may be determined in certain circumstances using a titration technique suggested by Van Geet (15). It is based on the competition by water for the solvation sphere of sodium ions in tetrahydrofuran (THF) measured by Na shifts. The salt must contain a large anion, which is assumed to be unhydrated during the titration otherwise a sum of hydration numbers would be determined. The assumptions made by Van Geet are basically those of the present treatment. His apparent constant is for the reverse of the equilibrium of Equation 21 and can be identified as l/K[P]p, where [P]f is the free THF concentration, effectively constant in the early stages of the titration. 

Negative values ofN —N0, the electrolyte effect on the association numbers of water, are called the structure-breaker effect. One can speak of negative hydration31. The estimation of the hydration numbers by spectroscopic or solubility methods gives only an approximation of the sum effect. The spectra of the H-bond bands show in second approximation distinct differences between the ion effects on the H-bonds7 ). — The partial molar volume Vx of water in electrolyte solutions is negative in all solutions but the series of -values corresponds to the Hofmeister ion series too. The negative V1 volume indicates an electrostriction effect around the ions. 

Structure maker ions increase the concentration of micelles and reduce the concentration of monomers. In a very rough model one can assume the fixed hydration sphere around the ions cannot solve the ethylenoxide products and increase its concentrations in the rest bulk water phase (salt-out effect). In this model one can estimate the size of the hydration sphere of the ions. The hydration numbers gained by this method are surprisingly large3 They start at 200 water molecules per ion pair at 0.1 mole solutions of ions and decrease about 20 at 1 mole solutions31,72,130). 

The hydration numbers given are somewhat approximative and are subject to error due to e.g., electroviscous effects and micelle shape effects. However, it seems that possible corrections should lower these numbers which can therefore serve as... 

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