Radii, ionic

With the knowledge now of the magnitude of the mobility, we can use equation A2.4.38 to calculate the radii of the ions thus for lithium, using the value of 0.000 89 kg s for the viscosity of pure water (since we are using the conductivity at infinite dilution), the radius is calculated to be 2.38 x 10 m (=2.38 A). This can be contrasted with the crystalline ionic radius of Li, which has the value 0.78 A. The difference between these values reflects the presence of the hydration sheath of water molecules as we showed above, the... 

The simplest extension to the DH equation that does at least allow the qualitative trends at higher concentrations to be examined is to treat the excluded volume rationally. This model, in which the ion of charge z-Cq is given an ionic radius d- is temied the primitive model. If we assume an essentially spherical equation for the u. . 

L is Avagadro s constant and k is defined above. It can be seen that there are indeed two corrections to the conductivity at infinite dilution tire first corresponds to the relaxation effect, and is correct in (A2.4.72) only under the assumption of a zero ionic radius. For a finite ionic radius, a, the first tenn needs to be modified Falkenliagen [8] originally showed that simply dividing by a temr (1 -t kiTq) gives a first-order correction, and more complex corrections have been reviewed by Pitts etal [14], who show that, to a second order, the relaxation temr in (A2.4.72) should be divided by (1 + KOfiH I + KUn, . The electrophoretic effect should also... 

The aluminium ion, charge -I- 3. ionic radius 0.045 nm, found in aluminium trifluoride, undergoes a similar reaction when a soluble aluminium salt is placed in water at room temperature. Initially the aluminium ion is surrounded by six water molecules and the complex ion has the predicted octahedral symmetry (see Table 2.5 ) ... 

It will be noted that hydration enthalpy decreases with increasing ionic radius and increases very sharply with increase in ionic charge, these results being what we should expect for an electrostate interaction between a charged ion and the dipole of a water molecule (p, 44). 

Element Ionisation energy (kj mof ) Metallic radius (nm) Ionic radius (nm) Heal oj laporibation at 298 K (kJ mol ) Hydration energy oj gaseous ion (kJ moI ) (V)... 

The data in Table 7.1 show that, as expected, density, ionic radius, and atomic radius increase with increasing atomic number. However, we should also note the marked differences in m.p. and liquid range of boron compared with the other Group III elements here we have the first indication of the very large difference in properties between boron and the other elements in the group. Boron is in fact a non-metal, whilst the remaining elements are metals with closely related properties. 

The reason why lanthanides of high atomic number emerge first is that the stability of a lanthanide ion-citrate ion complex increases with the atomic number. Since these complexes are formed by ions, this must mean that the ion-ligand attraction also increases with atomic number, i.e. that the ionic radius decreases (inverse square law). It is a characteristic of the lanthanides that the ionic radius... 

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. 

Chemical Properties. Although the chemical properties of the trivalent lanthanides are quite similar, some differences occur as a consequence of the lanthanide contraction (see Table 3). The chemical properties of yttrium are very similar too, on account of its external electronic stmcture and ionic radius. Yttrium and the lanthanides are typical hard acids, and bind preferably with hard bases such as oxygen-based ligands. Nevertheless they also bind with soft bases, typicaUy sulfur and nitrogen-based ligands in the absence of hard base ligands. 

Separation Processes. The product of ore digestion contains the rare earths in the same ratio as that in which they were originally present in the ore, with few exceptions, because of the similarity in chemical properties. The various processes for separating individual rare earth from naturally occurring rare-earth mixtures essentially utilize small differences in acidity resulting from the decrease in ionic radius from lanthanum to lutetium. The acidity differences influence the solubiUties of salts, the hydrolysis of cations, and the formation of complex species so as to allow separation by fractional crystallization, fractional precipitation, ion exchange, and solvent extraction. In addition, the existence of tetravalent and divalent species for cerium and europium, respectively, is useful because the chemical behavior of these ions is markedly different from that of the trivalent species. 

Ion Ionic radius, pm CoUoidal hydrous manganese dioxide, mol/mol Hydrated radius, pm 5-Mn02, )J.mol/g... 

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 ... 

The pentahalides of phosphorus, PX, in the gas phase exhibit varying tendencies to dissociate into trihaUde and halogen. InstabiUty increases with increasing ionic radius of the halogen. The pentafluoride appears to be thermally stable. Dissociation of the pentachloride, a few percent at 100°C and 101.3 kPa (1 atm), is essentially completed at 300°C (36). The pentabromide is partially dissociated in the Hquid state and totally dissociated above ca 35°C (39). Pentaiodide does not exist. The molecules of PF and PCl in the vapor phase are trigonal bipyramids. In the crystalline state, both pentachloride and pentabromide have ionic stmctures, ie, [PClJ IPClg] and [PBr4]" PBrJ , respectively. The PX" 4 cations are tetrahedral and the PX anion is octahedral (36,37). 

Impurity atoms having an ionic radius greater than that of silicon cause lattice expansion. 

Only body-centered cubic crystals, lattice constant 428.2 pm at 20°C, are reported for sodium (4). The atomic radius is 185 pm, the ionic radius 97 pm, and electronic configuration is lE2E2 3T (5). Physical properties of sodium are given ia Table 2. Greater detail and other properties are also available... 

A full discussion of thorium electrochemistry is available (3). Thorium is generally more acidic than the lanthanides but less acidic than other light actinides, such as U, Np, and Pu, as expected from the larger Th" " ionic radius (108 pm). 

The physical picture in concentrated electrolytes is more apdy described by the theory of ionic association (18,19). It was pointed out that as the solutions become more concentrated, the opportunity to form ion pairs held by electrostatic attraction increases (18). This tendency increases for ions with smaller ionic radius and in the lower dielectric constant solvents used for lithium batteries. A significant amount of ion-pairing and triple-ion formation exists in the high concentration electrolytes used in batteries. The ions are solvated, causing solvent molecules to be highly oriented and polarized. In concentrated solutions the ions are close together and the attraction between them increases ion-pairing of the electrolyte. Solvation can tie up a considerable amount of solvent and increase the viscosity of concentrated solutions. 

The PTCR effect is complex and not fully understood in terms of the grain boundary states and stmcture. Both the PTCR effect and room temperature resistivities are also highly dependent on dopant type and ionic radius. Figure 11 (32) illustrates this dependence where comparison of the PTCR behavior and resistivity are made for near optimum concentrations of La ", Nd ", and ions separately substituted into BaTiO. As seen, lowest dopant concentration and room temperature resistivity are obtained for the larger radius cation (La " ), but thePTCR effect was sharpest for the smallest radius cation (Y " ), reflecting dual site occupancy of the Y " ion. 

The higher ionisation energy and smaller ionic radius of copper contribute to its forming oxides much less polar, less stable, and less basic than those of the alkah metals (13). Because of the relative instabiUty of its oxides, copper joins silver in occurring in nature in the metallic state. 

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