Effective ionic radii, metal ions

The remaining compounds listed in Table II all adopt structures with infinite metal-metal bonded chains consisting of octahedral cluster units fused on opposite edges. However, because of the large difference in effective ionic radius of the cations concerned, very different lattice types are dictated. The compounds NaMoi 06 (19,22) and Bas(Moit06)8 (17) adopt tunnel structures with the Na+ or Ba2+ ions located in sites along the tunnels with 8-fold coordination by oxygen atoms. 

Much work has been carried out in which these cations have been replaced by other cations having suitable electronic or nuclear properties to allow the application of instrumental techniques to the characterization of the metal-binding site. For such substitutions to be effective, the probe metal ion should be of similar ionic radius and chemistry to the natiye metal ion. 

The entropies of formation of the 1 1 bivalent metal complexes of the structurally related ligands, Formulas IX-XIII, reported by Martell (10) show a linear correlation with the square of the reciprocal of the effective ionic radius of the metal ions, r , in Equation 8, and with the number of negative carboxylate groups of the ligand that combine with the metal ion. 

Shannon and Prewitt base their effective ionic radii on the assumption that the ionic radius of (CN 6) is 140 pm and that of (CN 6) is 133 pm. Also taken into consideration is the coordination number (CN) and electronic spin state (HS and LS, high spin and low spin) of first-row transition metal ions. These radii are empirical and include effects of covalence in specific metal-oxygen or metal-fiuorine bonds. Older crystal ionic radii were based on the radius of (CN 6) equal to 119 pm these radii are 14-18 percent larger than the effective ionic radii. 

The uncertainty of the proper coordination number of any particular plutonium species in solution leads to a corresponding uncertainty in the correct cationic radius. Shannon has evaluated much of the available data and obtained sets of "effective ionic radii" for metal ions in different oxidation states and coordination numbers (6). Unfortunately, the data for plutonium is quite sparse. By using Shannon s radii for other actinides (e.g., Th(iv), U(Vl)) and for Ln(III) ions, the values listed in Table I have been obtained for plutonium. These radii are estimated to have an uncertainty of 0.02 X ... 

The dominant features which control the stoichiometry of transition-metal complexes relate to the relative sizes of the metal ions and the ligands, rather than the niceties of electronic configuration. You will recall that the structures of simple ionic solids may be predicted with reasonable accuracy on the basis of radius-ratio rules in which the relative ionic sizes of the cations and anions in the lattice determine the structure adopted. Similar effects are important in determining coordination numbers in transition-metal compounds. In short, it is possible to pack more small ligands than large ligands about a metal ion of a given size. 

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... 

The chelate ring size principle can have structural effects as well as effects on thermodynamic stability in aqueous solution. An example is coordination of metal ions by sugars (44). The cyclic polyol cts-inositol can coordinate metal ions in two distinct ways (Fig. 14) (45). In ax-ax-ax bonding (Fig. 14), the metal ion is part of three fused six-membered chelate rings. Alternatively, in ax-eq-ax coordination, the metal ion is part of two fused five-membered and one six-membered chelate rings. Angyal has noted that metal ions of radius more than 0.8 A adopt the ax-eq-ax structure (44), whereas with an ionic radius... 

In 1967, C. J. Pederson of DuPont deNemours Co. synthesized the cyclic polyethers ( ) These cyclic polyethers are commonly referred to as "crown ethers" (see Figure 3). In solution, crown ethers are extremely effective ligands for a wide range of metal ions. The size of the ring cavity and the ionic radius of the metal affect the stability of the complex. Tables I and II list the cavity diameters for the crown ethers and the ionic radii of a number of metal ions (6-11). 

As concerns the spatial fit of host and guest, 44 forms the most stable complex with K+ (Figure 3.1) [10], since its radius of ca. 138 pm is approximately equal to the ionic radius of the guest. The dependence of stability constants of the complexes of 47, 48 and 44 with alkali metal cations on the ion diameters is shown in Figure 3.2. The complicated character of the depicted relations indicates that more factors (e.g., solvent effect) are at play in the ions recognition. 

Although there is no space to develop a detailed discussion of the solubilities of compounds of the transition elements, the general insolubility of their + 2 and + 3 hydroxides is important. The rationale underlying their insolubility can be summarized (i) the hydroxide ion is relatively small (152 pm ionic radius) and the ions of the +2 and +3 transition metals assume a similar size if their radii are increased by 60-80 pm, and (ii) the enthalpy of hydration of the hydroxide ion (—519 kJ mol ) is sufficiently negative to represent a reasonable degree of competition with the metal ions for the available water molecules, thus preventing the metal ions from becoming fully hydrated. Such effects combine to allow the lattice enthalpies of the hydroxides to become dominant. 

By contrast, the chlorides of the metal ions are soluble because the chloride ion (181 pm ionic radius) is considerably larger than the hydroxide ion, and its enthalpy of hydration ( — 359 kJ mol l) is less negative than that of OH. This allows the metal cations to exert more nearly their full effect on the solvent molecules, thus overcoming the lattice enthalpy terms, and this leads to their general solubility as chlorides. 

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