Hydrated Cation Radii

The problem of separating them by reactions in aqueous media is aggravated further by the fact that increased charge density, which accompanies lanthanide contraction, promotes a greater overall degree of aquation and renders individual hydrated cationic radii even more similar. 

Hydrated Cation Radius for Various Metals fin- Use with Equation 9.64... 

Metal in oxide Valence Hydrated cation radius (A)... 

The relationship between cation radius and hydrated cation radius, at 298 K, is depicted in Fig. 2 [59N1, OlPl]. The radius of a fully hydrated ion is proportional to the ionic charge, but not proportional to the ionic radius without H2O shell. Cs rm- 1-69 A, rhyd= 3.29 A) is exchanged more easily thanUE (rion= 0.60 A, rhyd= 3.82 A) or Be = 0.31 A, rhyd = 4.59 A) [59N1, 88M2]. The elevated temperatures normally enhance the ion-exchange reactions, while the pH is also critical, particularly in the case of acidic solutions, because small H" cations are very mobile and reactive over many other cations. Other factors concern the solid/liquid ratio, the zeolite particle sizes, and the treatment time. As mentioned above, this discussion is valid in case of alkali or alkaline-earth element cations which are practically stable in aqueous solutions. 

Fig. 2. Heulandite. Relationship of cation radius to hydrated cation radius at 25 °C [59N1, OlPl]. Smaller, divalent cations have larger hydrated radii than larger, monovalent cations.

The other characteristic of the trivalent lanthanide and actinide series that can be exploited in separations is the decrease in ionic radius which occurs with increasing atomic number. This results in increased strength of cation-anion interactions and ion-dipole, ion-induced dipole type interactions. The expected increase in ion-dipole interactions across the series implies that the heavy members of both series should bind solute (and suitable solvent) molecules more tightly than the light members. For certain ion exchange separations, it is thus appropriate to expect elution trends to correlate with the hydrated cation radius rather than the simple cation radius. 

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. 

The type of catalyst influences the rate and reaction mechanism. Reactions catalyzed with both monovalent and divalent metal hydroxides, KOH, NaOH, LiOH and Ba(OH)2, Ca(OH)2, and Mg(OH)2, showed that both valence and ionic radius of hydrated cations affect the formation rate and final concentrations of various reaction intermediates and products.61 For the same valence, a linear relationship was observed between the formaldehyde disappearance rate and ionic radius of hydrated cations where larger cation radii gave rise to higher rate constants. In addition, irrespective of the ionic radii, divalent cations lead to faster formaldehyde disappearance rates titan monovalent cations. For the proposed mechanism where an intermediate chelate participates in the reaction (Fig. 7.30), an increase in positive charge density in smaller cations was suggested to improve the stability of the chelate complex and, therefore, decrease the rate of the reaction. The radii and valence also affect the formation and disappearance of various hydrox-ymethylated phenolic compounds which dictate the composition of final products. 

In Table 3 are also shown the hydrated radii (r ) which are evaluated with n and r by Eq. (25). A good correlation of with the Stokes radius [60] (r ) has been observed for hydrated cations (alkali and alkaline earth metal ions) [46] ... 

Fig. 1.7. Ionic radius r, and charge z, of common forms of elements in water. The solid lines divide (a) elements with Z/r <0.03 pm-1, which form soluble hydrated cations such as Ca2+ (b) ones with 7Jr >0.12 pm-1, soluble as oxyanions such as S042 and (c) those of intermediate Z/r, which form oxides or hydroxides insoluble around neutral pH. (Reproduced with permission from P.A. Cox (1989), see Further Reading.)...

To prevent misunderstanding (94), we emphasize that neither experimental hydration energies nor experimental coordination numbers are necessary for these calculations. Moreover, the coordination numbers obtained are generally not comparable to empirical hydration numbers. The only experimental quantities that enter the calculations are a) cationic radius and charge b) van der Waals radius of water c) dipole and quadrupole moment of water d) polarizabilities e) ionization potentials and f) Born repulsion exponents as well as fundamental constants (see Ref. (92)). 

Figure 4.53 shows the dispersion spectra of hydrated Ca-HC, K-HC, and Na-HC at 300K [120], They are plotted in the x-axis, and the natural logarithm of the frequency (Hz) versus the natural logarithm of the real part of the relative permittivity in the y-axis. This experiment shows once more the higher mobility of monovalent cations in comparison with divalent cations and the higher mobility of Na+ with respect to K+. The cause of this effect is due to the inferior cationic radius of Na+ in comparison with that of K+. 

Hydration Enthalpies (-HJ vs. Cationic Radius (R) for Some Divalent Cations... 

In the case of a neutral non-ionic chelating agent we have neutral carrier-selective electrodes transport is achieved by selective complexa-tion of certain ions. The best-known electrode of this kind is the potassium-selective electrode, whose membrane consists of a valinomycin macrocycle immobilized in phenylether. The important criterion appears to be the size of the cavity in the centre of the macrocycle and interferences are from cations with similar hydrated ionic radius, such as Rb+ and Cs+. 

It is obvious, that the cation and anion radius are mostly different, for example the hydrated radius of r(Na+) = 102 + 116, r(Cs+) = 170 + 49, r(Cl ) = 181 +43, r(I ) = 220 + 26 [pm]. As can be seen, the radii of the hydrated anions are usually larger than that of the hydrated cations. This relation is valid for the ion devoid of the hydration shield. From this reason the assumption of the separate IHP planes for adsorbing cations and anions is rational. 

A large attraction force between interlayer cations and adjacent siloxane cavities allows some cations with certain hydration energy to dehydrate. If the dehydrated cation radius is smaller than the inside diameter of the siloxane cavity, the mineral could collapse and an inner-sphere complex would form (e.g., K-vermiculite) (Fig, 4.3). When vermiculite contains a relatively strongly hydrated cation such as Ca2+ or... 

The negative layer charge is mostly neutralized by the hydrated cations in the interlayer space. These cations are bonded to the internal surfaces by electrostatic forces, and they are exchangeable with other cations. The interaction strength between the hydrated cation and the layers (the internal surface) increases when the charge of the cation increases, and the hydrated ionic radius decreases. Cations with hydrate shell can be considered as outer-sphere complexes. Cation exchange is the determining interfacial process of the internal surfaces of montmorillonite. 

Values are quoted relative to the hydrogen ion for cations and to the chloride ion for anions. As shown, selectivity also increases with increasing degree of. cross-linking. At concentrations greater than 0.1 M selectivity for monovalent over polyvalent ions increases. Ionic properties which determine reSin affinity are complex involving hydration energy, polarizability and hydrated ionic radius. The last shows an approximately inverse relationship to the selectivity coefficient. 

There are four different phases of rare earth orthophosphate (RPO4), mostly depending on the cationic radius of rare earth element Monazite (monoclinic, dehydrate, for light lanthanides), xenotime (also typed as zircon, tetragonal, dehydrate or hydrate, for heavy lanthanides and Y +), rhabdophane (hexagonal, mostly hydrate, across the series), and... 

Let it be assumed that the value of the interaction energy of an ion with a solvent is an inverse function of the ion-first water shell distance, r. Then, if one has a series of salts (R,A, R2A,...) where R is, say, a tetraalkylammonium ion, and the anion is constant, the electrolyte property (e.g., the heat of hydration) can be plotted for the series of RAs, against l/ f (where r represents the cation radius), and the extrapolated value for l/rj" = 0 is then the individual heat of hydration for the common anion. A". 

Fig. 2.40. Heat of hydration against radius of cations forvarious competing models (1 A = 100 pm 1 kcal = 4.184 kJ). (Reprinted from J. O M. Bockris and P. P. S. Saluja, J. Phys. Chem. 76 2298, 1972.)...

---