The solution ionic radius

The solution ionic radius is arguably one of flie most important microscopic parameters. Although detailed atomic models are needed for a full understanding of solvation, simpler phenomenological models are useful to interpret the results for more complex systems. The 

Irrespective of these ambiguities, fiie desired scheme of relating the Bom radius wifii some other radius is facing an awkward situation Any ionic radius depends on arbitrary divisions of the lattice spacings into anion and cation components, on the one hand, and on the other, file properties of individual ions in condensed matter are derived by means of some extra-thermodynamic principle. In ofiier words, both properties, values of r and AG, to be compared wifii one another, involve uncertain apportionments of observed quantities. Con- 

In a most recent paper,a new table of absolute single-ion thermodynamic quantities of hydration at 298 K has been presented, based on conventional enthalpies and entropies upon implication of the thermodynamics of water dissociation. From the values of AiydG the Bom radii were calculated from 

It seems that many workers would tend to equate die distanee (d) eorrespond-ing to the first RDF peak with the average distance between the center of the ion and the centers of the nearest water molecules, d=Tion + Twater Actually, Marcus presented a nice relationship between d, averaged over diffraction and simulation data, and the Pauling crystal radius in the form d=1.38 +1.102 rp. Notwithstanding this success, it is preferable to implicate not the water radius but instead the oxygen radius. This follows from the close correspondence between d and the metal-oxygen bond lengths in crystalline metal hydrates.  

The gross coincidence of the solid and solution state distances is strong evidence that the value of d measures the distance between die nuclei of the cation ad the oxygen raflier than die center of the electron cloud ofdie whole ligand molecule. Actually, first RDF peaks for ion solvation in water and in nonaqueous oxygen donor solvents are very similar despite the different ligand sizes. Examples include methanol, formamide and dimethyl sulfoxide.  

While Bom assumes that the dielectric response of the solvent is linear, nonlinear effects such as dielectric saturation and electrostriction should occur due to the high electric field near the ion. Dielectric saturation is the effect that the dipoles are completely aUgned in the direction of the field so that any fiuther increase in the field cannot change the degree of ahgnment. Electrostriction, on the other hand, is defined as the volume change or compression of the solvent caused by an electric field, which tends to concentrate dipoles in the first solvation shell of an ion. Dielectric saturation is calculated to occur at field intensities exceeding 10 V/cm while the actual fields around monovalent ions are on the order of 10 V/cm.  

Indeed, the number of modifications of the Bom equation is hardly countable. Rashin and Honig, as example, used the covalent radii for cations and the crystal radii for anions as the cavity radii, on the basis of electron density distributions in ionic crystals. On the other hand, Stokes put forward that the ion s radius in the gas-phase might be appreciably larger than that in solution (or in a crystal lattice of the salt of the ion). Therefore, the loss in self-energy of the ion in the gas-phase should be the dominant contributor. He could show indeed that the Bom equation works well if the vdW radius of the ion is used, as calculated by a quantum mechanical scaling principle applied to an isoelectronic series centering around the crystal radii of the noble gases. More recent accounts of the subject are avail-able.  

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The most common oxidation state of niobium is +5, although many anhydrous compounds have been made with lower oxidation states, notably +4 and +3, and Nb can be reduced in aqueous solution to Nb by zinc. The aqueous chemistry primarily involves halo- and organic acid anionic complexes. Virtually no cationic chemistry exists because of the irreversible hydrolysis of the cation in dilute solutions. Metal—metal bonding is common. Extensive polymeric anions form. Niobium resembles tantalum and titanium in its chemistry, and separation from these elements is difficult. In the soHd state, niobium has the same atomic radius as tantalum and essentially the same ionic radius as well, ie, Nb Ta = 68 pm. This is the same size as Ti ... 

It follows from Eqs. (2.6.6), (2.6.8) and (2.6.10) that the presence of the solvent has two effects on the ionic mobility the effect of changing viscosity and that of changing the ionic radius as a result of various degrees of solvation of the diffusing particles. If the effective ionic radius does not change in a number of solutions with various viscosities and if ion association does not occur, then the Walden rule is valid for these solutions ... 

The chemistry of aluminium combines features in common with two other groups of elements, namely (i) divalent magnesium and calcium, and (ii) trivalent chromium and iron (Williams, 1999). It is likely that the toxic effects of aluminium are related to its interference with calcium directed processes, whereas its access to tissues is probably a function of its similarity to ferric iron (Ward and Crichton, 2001). The effective ionic radius of Al3+ in sixfold coordination (54 pm) is most like that of Fe3+ (65 pm), as is its hydrolysis behaviour in aqueous solution ... 

Cations in aqueous solutions have an effective radius that is approximately 75 pm larger than the crystallographic radii. The value of 75 pm is approximately the radius of a water molecule. It can be shown that the heat of hydration of cations should be a linear function of Z /r where is the effective ionic radius and Z is the charge on the ion. Using the ionic radii shown in Table 7.4 and hydration enthalpies shown in Table 7.7, test the validity of this relationship. 

The simple pore was originally considered in the context of osmosis as an explanation of how water might move across a biological structure (e.g. an epithelium) in the absence of solute movement. This notion introduced by Brucke in the mid 19th century, (see Hille, 1984) was subsequently extended by Boyle and Conway (1941) to consider the selective ionic permeability of the resting cell membrane. Here the explanation for the high membrane permeability to potassium and to chloride, as compared to sodium, was simple. The hydrated ionic radius of sodium was greater than that of either the hydrated potassium or chloride ion, hence the pores postulated to be present in the membrane would act as a molecular sieve and permit the movement of potassium and of chloride but not of sodium. 

The effective ionic radius of an ion in solution is an important quantity in the discussion of the behaviour of electrolyte solutions. Mobilities are thus fundamental to both Debye-Hiickel theory and conductance theory. 

It is clear from Table 11.1 that the effective ionic radius found from Stokes Law is greater than the crystallographic radius for the cations, suggesting that these ions are probably hydrated in solution. The situation is much less clear for the anions. F (aq) is the only anion where the effective radius gives evidence for hydration. Chapter 13 looks at this in more detail. 

The reaction (1) shows that fluorine severely catalyses hydrolysis reaction [3]. In the hydrolysis reaction, because of the smaller ionic radius of the fluorine, which approaches a molecule of TEOS in the solution forming a highly unstable pentacovalent activated intermediate. This complex rapidly decomposes, forming a partially fluorinated and hydroxylated silicon alkoxide. 

Figure 18 Dm or log K (formation constant for the M" "/18-crown-6 complexes in water) versus the effective ionic radius of several group 1 and 2 cations. The ABS was prepared by mixing equal aliquots of a 40% PEG-2000 solution 1.25 M in 18-crown-6 with a 20% NaOH solution 2.0 M in NaNOs.

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