Lanthanide hydrated radii

The lanthanide ions, Ln are known to contract with increasing atomic number (Z), from La with a hydrated radius of 103 pm to Lu of 86 pm (lanthanide contraction). Thus one expects that the neutral LnAj complex becomes smaller with increasing atomic number, and consequently that P3 should increase and K c decrease with increasing Z. Figure 4.15d shows that measured... 

Fig. 2. Comparison of Gd numbers for lanthanide absorption onto Dowex 50 cation exchange resin [(a) Marcus 1983, (b) Surls and Chopprn 1957] as compared with (c) cation hydrated radius and (d) R-O distance of...

Fig. 7. Hydrated radius of (a) lanthanide cations as compared with (b) free energy and (c) enthalpy of formation...

The experimental measurements that provide the hydration number and hydrated radius information are made on lanthanide solutions of moderate concentration with dilFerent counter ions. The data in Rizkalla and Choppin (1991) indicate that hydration numbers and Ln-O distances change slightly with both the nature of the counter ion and the concentration of the salt. It appears likely that composition of the primary coordination sphere of the lanthanide ion does not vary appreciably with the concentration (or identity of the counterion) of the lanthanide salts. However, the reduced water activity that occurs in concentrated salt solutions would suggest that overall hydration numbers will be higher in dilute solutions. Thus the values reported for overall hydration and hydrated radii determined in concentrated aqueous salt solutions probably underestimate the hydration of lanthanide cations in the dilute solutions that are typical of analytical applications. It has been suggested that as many as 40 water molecules may feel the presence of a trivalent lanthanide ion in solution (Choppin 1997). Using Lundqvist s (1981) estimate of 30 for the volume of a water molecule, the radial distance of the lanthanide iQrdration sphere... 

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. 

One of the consequences of the lanthanide contraction is that some of the +3 lanthanide ions are very similar in size to some of the similarly charged ions of the second-row transition metals. For example, the radius of Y3+ is about 88 pm, which is approximately the same as the radius of Ho3+ or Er3 +. As shown in Figure 11.8, the heats of hydration of the +3 ions show clear indication of the effect of the lanthanide contraction. 

FIGU RE 11.8 Heat of hydration of + 3 lanthanide ions as a function of ionic radius. 

The enthalpies of hydration of the lanthanides are given in Table 8.4 and show a regular increasing negative value with decreasing ionic radius. 

In the case of nitriloacetate complexes, the changes in enthalpy have been explained in terms of the consequences of lanthanide contraction (i) increasingly exothermic complexation with decreasing crystal radius and (ii) decreasing exothermic complexation with decreasing hydration of the cation [22]. In the case of dipicolinates and diglycolates these effects become small as the coordination sphere loses water molecules. Thus AH3 and A S3 vary more regularly than A Hi and A Si. 

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... 

Because of lanthanide contraction, the radius of lanthanide ions decreases gradually as the atomic number increases, resulting in regular changes in the properties of lanthanide elements as the atomic number increases. For example, the stability constant of lanthanide complexes usually increases as the atomic number increases the alkalinity of lanthanide ions decreases as the atomic number increases the pH at which hydrates start to precipitate from an aqueous solution decreases gradually as the atomic number increases. 

When a mixture of lanthanide ions is brought on to an exchange resin (p. 567) in its hydrogen form, the order of absorption follows the atomic numbers. Affinity for the resin decreases with radius of the hydrated ion ... 

Near infrared experiments on lanthanide]III) ions showed no well-defined second hydration shell [118). The residence times for water molecules in the second shells around Nd, Sm and Yb are 13, 12 and 18 ps respectively [70]. The slightly higher value for Yb can be related to its smaller ionic radius, rjon. 

In fig. 6 a clear discontinuity is seen in Ln OHj bond distances of curve A between Nd and Tb with an offset value of 0.045 A. This value agrees with the analysis of Sinha (1976) who calculated a 0.047 A decrease in the effective La radius per unit decrease in the coordination number. In the solid heptahydrate (La Pr) and hexa-hydrates (Nd-Lu), the offset value in the Ln OHj distances between the heavy and the light lanthanides is only 0.039 A. The smaller value was attributed to the differences in the structures of the heptahydrate and hexahydrales (the former form dimers with chloride bridging). 

The peak in the X-ray RDF at 5 A (fig. 4) was assigned to Ln-O distances for water molecules in the second (outer) hydration sphere. Curve B in fig. 6 shows the dependency of the position of this peak on the lanthanide radius. Both ion pair interactions [Ln(H20) (] -Cl and secondary solvation [Ln(H20) ] -H20 are expected to be responsive to differences in ionic radii of the lanthanide ions as well as to changes in the inner-sphere hydration. The decrease in the Ln H2O distance between La " and Lu " " (including the hydration change offset) is 0.24 A (fig. 6, curve A), in good agreement with the difference of 0.22 A for the peak at ca. 5 A. 

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