Charge-to-size ratio

Compounds of beryllium and aluminum are substantially covalent as a result of the high charge -to-size ratio, which causes polarization of anions and very high heats of hydration of the ions ( —2487kJ mol-1 for Be2+ and — 4690kJ mol-1 for Al3+). 

Metal ions that have a high charge-to-size ratio (charge density) undergo hydrolysis to produce acidic solutions. As a result of the decrease in size of the +3 ions across the lanthanide series, there is a general increase in acidity of the aquated ions as a result of the reaction... 

As is the case with numerous other metal alkyls, beryllium alkyls are spontaneously flammable in air. Beryllium oxide is produced, and it has a heat of formation of — 611kJ/mol. Dimethylberyllium also reacts explosively with water, and some of its other properties resemble those of trimethylaluminum. This should not be surprising because the metals have a strong diagonal relationship that relates to their similar charge-to-size ratios. 

Hydration and hydrolysis reactions. We have seen (Chapters 4 and 8) that large charge-to-size ratios for cations result in an increase in hydration energies. Closely related to hydration and, in fact, inseparable from it except in degree is the phenomenon of hydrolysis. In genera], we speak of hydration if no reaction beyond simple coordination of water molecules to the cation occurs ... 

In the case of hydrolysis reactions, the acidity (charge-to-size ratio) of the cation is so great as to cause rupture of H—O bonds with ionization of the hydrate to yield hydronium ions ... 

Ultimate acids and bases." Familiarity with the idea that acidity and basicity are related to electron density at reacting sites and charge-to-size ratio... 

FIGURE 7.15 Plot of d(-U(r))/d( NO, orRlol) versus (a) the charge-to-size ratio or (b) the enthalpy of hydration for the extraction of the nitrates of various cations. (From R. Chiarizia, M. P. Jensen, P. G. Rickest, Z. Kolarik, M. Borowski, and P. Thiyagerrajan, Langmuir, 20 10798-10808, 2004. With permission.)... 

For small molecules (metabolites, monomers, and small oligomers) the mobility equation may be empirically approached with the Offord model (linear relation to charge-to-size ratio, the charge being obtained directly from the ionization constants and the size being approached with the molecular mass exponent a factor a) [see Offord (1966)]. 

Metal Radii (pm), Atom Radii (pm), Ion M-M Bond Energy (kj mol-1) Ionization Enthalpy (k mol-1) -A Hhyd (k mol-1) Charge to Size Ratio... 

The stability of complexes of alkali metals with various complexing agents is known to depend on matching the size of the alkali metal to the size of the opening in the molecule. However, for most complexes of the ions of Group IA metals, the stability decreases in the order Li+ > Na+ > K+ in accord with the decrease in the charge to size ratio. 

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