Ion Radii

As a result of these effects, anions in general are larger than cations. Compare, for example, the Cl- ion (radius = 0.181 nm) with the Na+ ion (radius = 0.095 nm). This means that in sodium chloride, and indeed in the vast majority of all ionic compounds, most of the space in the crystal lattice is taken up by anions. 

ELEMENT z OUTER ELECTRON CONFIGURATION OXIDATION E° states M — - M+3 + 3e +3 ION RADIUS... 

On the basis of the dipole moment, Paik, values computed from the Helmholtz equation (2.21) and the alkali ion radius one can estimate the effective positive charge, q, on the alkali adatom, provided its coordination on the surface is known. Such calculations give q values between 0.4 and 0.9 e (e.g. 0.86e for K on Pt(lll) at low coverages) which indicate that even at very low coverages the alkali adatoms are not fully ionized.6 This is confirmed by rigorous quantum mechanical calculations.27,28... 

Ion Radius ratio Predicted coordination number Observed coordination number Strength of electrostatic bonds... 

Fig. 17. Plot of change in complex stability, Alog K, that occurs for the pairs of ligands THEEN and EN (O), and PDTA-amide and EDDA ( ), as a function of metal ion radius (20). The diagram shows how netural oxygen donors stabilize the complexes of large metal ions relative to small metal ions. Alog Ki for THEEN and EN, for example, is log Kx for the THEEN complex of the particular metal ions, minus log Kx for the EN complex. Data from Ref. (11).

Fig. 19. The variation in logK for alkali metal ions with crown ethers 12-crown-4 (3), 15-crown-5 (O), 18-crown-6 ( ) and dibenzo-30-crown-10 (C) as a function of metal ion radius. Metal ion radii in A from Ref. (20). Formation constants in methanol from Refs. (49 and 50).

Ionic radii are quoted in Tables 2.3 and 2.5 for a large number of cations including those of the elements in groups 13, 14, 15, and 16, which do not form predominately ionic bonds. These values were obtained by subtracting the fluoride or oxide ion radius obtained from predominantly ionic solids from the length of a bond that is not predominantly ionic. The very small values for the radii of cations obtained in this way do not bear much relation to the real size of the atom in the crystal or molecule. 

Ion radius of the cubic sesquioxide in Angstroms (I0 1 m) calculated by Templeton and Dauben (1954). 

Note that the N3- ion (radius 171 pm) is much larger than the nitrogen atom, for which the covalent radius is only 71 pm. The oxygen atom (radius 72 pm) is approximately half the size of the oxide ion... 

Equation (2) contains the value of actual dimensional bond characteristic of the given atom in the structure. In crystals with basic ionic bond, the ion radius can be applied as such dimensional bond characteristic (with a certain approximation), i.e. the stabilization condition for such structures is as follows ... 

For present purposes, the electrical double-layer is represented in terms of Stem s model (Figure 5.8) wherein the double-layer is divided into two parts separated by a plane (Stem plane) located at a distance of about one hydrated-ion radius from the surface. The potential changes from xj/o (surface) to x/s8 (Stem potential) in the Stem layer and decays to zero in the diffuse double-layer quantitative treatment of the diffuse double-layer follows the Gouy-Chapman theory(16,17 ... 

As one traverses through the lanthanide series, there is a reduction in the cation size as the atomic number increases. This results in small differences in the strength of interactions of the ligand with the lanthanide ions. These trends are reflected in the IR spectra of these complexes in a few cases. Cousins and Hart (203) have observed an increase in Pp Q with decreasing lanthanide ion radius for the complexes of TPPO with lanthanide nitrates. This observation has been attributed to an increase in the Ln—O bond strength with an increase in the atomic number of the lanthanide ion. 

Easily ionizable anthracene forms the cation-radical as a result of sorption within Li-ZSM-5. In case of other alkali cations, anthracene was sorbed within M-ZSM-5 as an intact molecule without ionization (Marquis et al. 2005). Among the counterbalancing alkali cations, only Li+ can induce sufficient polarization energy to initiate spontaneous ionization during the anthracene sorption. The lithium cation has the smallest ion radius and its distance to the oxygen net is the shortest. The ejected electron appears to be delocalized in a restricted space around Li+ ion and Al and Si atoms in the zeolite framework. The anthracene cation-radical appears to be in proximity to the space where the electron is delocalized. This opens a possibility for the anthracene cation-radical to be stabilized by the electron s negative field. In other words, a special driving force for one-electron transfer is formed, in case of Li-ZSM-5. 

Ga " complexes are frequently analyzed for two reasons. Ga " also forms octahedral structures and it has almost the same ion radius as Fe " (62 vs. 65 pm). In contrast to Fe " it is diamagnetic and its complexes are therefore amenable to NMR analysis. Also in contrast to Fe " it cannot be reduced and therefore it is used for uptake studies interested in the fate of the complex in the cell. 

It is probable that a primary reason for the lower stability of complexes formed between dicyclohexyl-18-crown-6 and cations larger than the optimum size (e.g. Cs+) is that these cations are too large to "fit into the ligand cavity. On the other hand, as cation size decreases from that affording maximum stability, the hydration energy of the cation becomes predominant and little or no reaction is found, as in the case of Ca2+. Very large cations such as di, tri, and tetramethylammo-nium and trimethyl sulfonium do not appear to form complexes wi h dicyclohexyl-18-crown-6 in aqueous solution (4). Also, tetramethyl-ammonium ion (radius = 3.47 A (30)) complexes less strongly (log K =... 

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