Charge-radius ratio

Charge-radius ratio, denoted by Z/Rk, is the ratio of the number of valence electrons and the radius of cation after all valence electrons ionized. 

Charge-radius ratio is a parameter describing the electrostatic field of the atomic core acting on the valence electrons surrounding it. The values of the charge-radius ratio of elements are listed in Table 5.14. 

We called this kind of maps as maps of parameters of chemical bond . It appears that such kind of two-dimensional maps can provide more powerful tools for structure-property investigation work. 

Although it is obvious that to use a two-parameter map is more powerful than to use a single atomic parameter, it is easy to understand that only two parameters may be not enough for the description of more complicated chemical phenomena yet, and that the data processing in 

In order to investigate the structure-property relationships of the compounds with relatively complex molecules, it is not enough to use atomic parameters only, since the structure of molecules is also a key factor affecting the physico-chemical properties of a compound. This is particularly important for the description of the structure-property relationships of organic compounds. 

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The small lithium Li" and beryllium Be ions have high charge-radius ratios and consequently exert particularly strong attractions on other ions and on polar molecules. These attractions result in both high lattice and hydration energies and it is these high energies which account for many of the abnormal properties of the ionic compounds of lithium and beryllium. 

Fig. 15 Plot of AEm versus charge/radius ratio for the complexation of [24] with...

Electron distribution in carbonyl complexes, 12 112-124 Electronegativity and charge-radius ratio, 24 30-31 and enthalpy of formation of fluorides, 24 24-26... 

In summary, the coordination situations of the M(l) in various MXOr-type framework compounds are presented in Table 5. The variability from AlPO s through GaAsCV s is attributable to the smaller charge/radius ratio of Ga(l) and As(V) in comparison with AKl) and P(V) respectively, although a quantitative assessment of this remains to be done. 

Though the literature on this problem is surprisingly limited and some direct studies would be desirable, there are a few studies which indicate that the above conclusions are reasonable. The factors which need to be considered in determining stability include charge/radius ratio, polarizability, the ability to use empty d orbitals for back bonding, and lattice energy (54). 

The redox chemistry of the actinide elements, especially plutonium, is complex (Katz et al., 1980). Disproportionation reactions are especially important for the +4 and +5 oxidation states. Some of the equilibria are kinetically slow and irreversible. All transuranium elements undergo extensive hydrolysis with the +4 cations reacting most readily due to their large charge/radius ratio. Pu (IV) hydrolyzes extensively in acid solution and forms polymers. The polymers are of colloidal dimensions and are a serious problem in nuclear fuel reprocessing. 

The U(IV) chemistry is similar to that of Th4+, except for the difference in the charge/radius ratio of the ions. U4+ solutions are green in color, stable, and slowly oxidized by air to U02+. Solutions of U4+ are generally prepared by reduction of solutions of the uranyl (U02+) ion. U(IV) forms complexes with many anions (C204-,C2H302, C03-, Cl-, and NO3"). The chlorides and bromides of U(IV) are soluble while the fluorides and hydroxides are insoluble. In aqueous solution, U(IV) hydrolyzes via the reaction,... 

Trivalent yttrium and lanthanide metals, except for promethium, have been complexed to octaethylporphyrin by heating at 210 °C in an imidazole melt.17 The complexes obtained as hydroxides, Mm(OEP)(OH), are unstable in acidic media. As the charge radius ratio rule predicts, the early lanthanide metalloporphyrins, MIU(OEP)(OH) (M = La, Ce, PR, Nd), are demetallated during purification, and the middle series (M = Sm, Eu, Gd, Tb, Dy) in 1 % acetic acid in methanol, while the last five (M = Ho, Er, Tm, Yb, Lu) survive in 2% acetic acid in methanol but are dissociated in dilute hydrochloric acid. The Mnl(OEP)(OH) appears to coordinate more than one equivalent of pyridine and piperidine, and dimerizes in noncoordinating solvents such as benzene and dichloromethane at 10 4 M concentration. The dimer is considered to be a di-p-hydroxo-bridged species, different from the p-oxo dimer, Scin(OEP) 20 (Scheme 6). 

Some pertinent data for the elements are given in Table 4-1. Beryllium has unique chemical behavior with a predominantly covalent chemistry, although it forms an aqua ion [Be(H20)4]2+. Magnesium has a chemistry intermediate between that of Be and the heavier elements, but it does not stand in as close relationship with the predominantly ionic heavier members as might have been expected from the similarity of Na, K, Rb, and Cs. It has considerable tendency to covalent bond formation, consistent with the high charge/radius ratio. For instance, like beryllium, its hydroxide can be precipitated from aqueous solutions, whereas hydroxides of the other elements are all moderately soluble, and it readily forms bonds to carbon. 

All the M2+ ions are smaller and considerably less polarizable than the isoelec-tronic M+ ions. Thus deviations from complete ionicity in their salts due to polarization of the cations are even less important. However, for Mg + and, to an exceptional degree for Be2+, polarization of anions by the cations does produce a degree of covalence for compounds of Mg and makes covalence characteristic for Be. Accordingly, only an estimated ionic radius can be given for Be2+ the charge/radius ratio... 

The water content (y) depends on the ambient water pressure and on the hydration energy of the interlayer cation. At low water partial pressures or for cations with low hydration energies (small charge/radius ratio) a monolayer of water molecules is present between the chalcogen layers. At higher pressures or at a higher cation charge radius ratio, a bilayer structure is observed. 

TABLE 14-1 Ionic Radii, Charge/Radius Ratios, and Hydration Energies for Some Cations ... 

Ion Ionic Radius (A) Charge/Radius Ratio Hydration Energy (kj/mol)... 

The charge/radius ratio is the ionic charge divided by the ionic radius in angstroms. This is a measure of the charge density around the ion. A negative value for heat of hydration indicates that heat is released during hydration. 

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