Ionic radii in aqueous solutions

Table 8.2 Approximate Effective Ionic Radii in Aqueous Solutions at 25°C 8.4...

Marcus, Y. (1988). Ionic radii in aqueous solution. Chemical Reviews, 88, 1475-98. 

The aqua cations Fe +aq and Fe aq are included in several general reviews " of aqueous solutions, in a comprehensive book and review on aqua-cations, and in a review of ionic radii in aqueous solution. " ... 

Y. Marcus, Ionic Radii in Aqueous Solutions, in Client. Rev., 1988, 88, 1475. 

R. D. Shannon and C. T. Prewitt, Effective ionic radii in oxides and fluorides, Acta Crystallogr. Sec. B 25 925 (1969) Revised values of effective ionic radii, Acta Crystallogr. Sec. B 26 1046(1970). The fact that crystallographic ionic radii are the same as unsolvated ionic radii in aqueous solution is shown by G. Sposito, Distribution of potentially hazardous trace metals. Metal Ions Biol. Systems 20 1 (1986). 

Marcus Y (1977) Introduction to liquid-state chemistry. Wiley, Chichester, pp 241—245,267—279 Marcus Y (1983) Ionic radii in aqueous solutions. J Sol Chem 12 271—275 Marcus Y (1983a) A quasi-lattice quasi-chemical theory of preferential solvation of ions. Austr J Chem 36 1718-1738... 

Marcus Y (1987) The thermodynamics of solvation of ions, part 2. The enthalpy of hydration at 298.15 K. J Chem Soc Faraday Trans 83 339-349 Marcus Y (1988) Ionic radii in aqueous solutions. Chem Rev 88 1475-1498 Marcus Y (1988a) Preferential solvation of ions, part 2. The solvent composition near the ion. J Chem Soc Faraday Trans 1(84) 1465-1475... 

Markus Y (1988) Ionic radii in aqueous solutions. Chem Rev 88 1475-1498... 

Table 3,2. Comparison of Crystal Radii, r, with Ionic Radii in Aqueous Solution, rx, as Estimated from 3.23)...

One anomaly inmrediately obvious from table A2.4.2 is the much higher mobilities of the proton and hydroxide ions than expected from even the most approximate estimates of their ionic radii. The origin of this behaviour lies in the way hr which these ions can be acconmrodated into the water structure described above. Free protons cannot exist as such in aqueous solution the very small radius of the proton would lead to an enomrous electric field that would polarize any molecule, and in an aqueous solution the proton inmrediately... 

Cations in aqueous solutions have an effective radius that is approximately 75 pm larger than the crystallographic radii. The value of 75 pm is approximately the radius of a water molecule. It can be shown that the heat of hydration of cations should be a linear function of Z /r where is the effective ionic radius and Z is the charge on the ion. Using the ionic radii shown in Table 7.4 and hydration enthalpies shown in Table 7.7, test the validity of this relationship. 

This paper starts with a brief description of the Golden ratio and the ( )-based crystal ionic radii and is then followed by the (()-based aqueous ionic radii and hydration lengths. The role of in the sizes of the ions in the crystal and in aqueous solutions and their hydration bonds with water can be seen in Fig. 12.3 for Na" and Cl" ions (used as the examples). 

Fig. 12.2 The ratio of radii, k (=ionic radius/covalent radius), for alkali metal eations (M ) and halide anions (X ) in aqueous solutions (Eqs. 12.6a, b). In the right angled triangle, ABC, E and D are the mid points of AB and AC...

Fig. 12.3 The covalent radii and ionic radii inNaCl crystals and in aqueous solutions, the hydration bond lengths, d( 0) from the ion/water point of contact, P(i/w) to the center of O of water and the length of the hydrogen bon, d(--H) with Cl ...

The Born equations (2.37) and (2.43) are widely used, but suffer from lack of accurate information about the real sizes of ions in aqueous solutions. In the derivations used above, ionic radii have been used, but these give numerical answers that are exaggerated, in particular for those of cations. The values of the absolute enthalpies of hydration of the ions of Table 2.3 are given in Table 2.8, based on the conventional values with that of the proton taken to be — I 110 kJ mol-1. 

Ionic radii in the figure are measured by X-ray diffraction of ions in crystals. Hydrated radii are estimated from diffusion coefficients of ions in solution and from the mobilities of aqueous ions in an electric field.3-4 Smaller, more highly charged ions bind more water molecules and behave as larger species in solution. The activity of aqueous ions, which we study in this chapter, is related to the size of the hydrated species. 

In aqueous media the trivalent rare earth ions are strongly hydrated, and the formation of an aquo complex [M(OHa) ]3+ (where n is larger than six, perhaps eight or nine) takes place. There is also a distinct lowering of pH on dissolving the salts of rare earths in water. The extent of lowering of pH depends essentially on the concentration of the salt and the nature of the particular rare earth ion. The heavier rare earth ions which possess small ionic radii show a greater tendency to hydrolyse. Certain anions like the halides, sulphates and nitrates tend to form ion-pairs in aqueous solution. There is, however, spectroscopic evidence [258] that the formation of an ion-pair readily takes place in an alcoholic medium also. 

Due to its 5t/-6.v- electron configuration, hafnium forms tctravalent compounds readily, although the Ilf1 ion docs not exist as such In aqueous solution except at very low pH values, Ihe common cation being HfO lor Hf OH)i ) and many of the tctravalent compounds are partly covalent. There are also less stable Hf(lll) compounds, There is close similarity in chemical properties to those of zirconium due to the similar outer electron configuration (4identical ionic radii (ZrJ is 0.80 A) the relatively low value for Hf being due lo the Lanthanide contraction. 

In spite of considerable similarities between the chemical properties of lanthanides and actinides, the trivalent oxidation state is not stable for the early members of the actinide series. Due to larger ionic radii and the presence of shielding electrons, the 5f electrons of actinides are subjected to a weaker attraction from the nuclear charge than the corresponding 4f electrons of lanthanides. The greater stability of tetrapositive ions of actinides such as Th and Pu is attributed to the smaller values of fourth ionization potential for 5f electrons compared to 4f electrons of lanthanides, an effect that has been observed in aqueous solution of Th and Ce (2). Thus, thorium... 

The crystallographic ionic radii of the rare-earth elements in oxidation states +2 (CN = 6), +3 (CN = 6), and +4 (CN = 6) are presented in Table 18.1.3. The data provide a set of conventional size parameters for the calculation of hydration energies. It should be noted that in most lanthanide(III) complexes the Ln3+ center is surrounded by eight or more ligands, and that in aqueous solution the primary coordination sphere has eight and nine aqua ligands for light and heavy Ln3+ ions, respectively. The crystal radii of Ln3+ ions with CN = 8 are listed in Table 18.1.1. 

Many naturally occurring ionic polysaccharides are mixed salts of alkali, alkali-earth, and transition metals with different insolubilities. Salts of alkali metals are invariably soluble. Sodium, the most ubiquitous alkali, possesses a single valence electron, large atomic and ionic radii, and very low ionization potential. Na+ hydrates in aqueous solution and retains its coordination water in the solid state. Prior to use, native polysaccharide salts are usually converted to the sodium form whence they acquire functionality. 

In aqueous solution metal ions are surrounded by water molecules.36 In some cases, such as the alkali ions, they are weakly bound, whereas in others, such as [Cr(H20)6]3+ or [Rh(H20)6]3+, they may be firmly bound and exchange with solvent water molecules only very slowly for the lanthanides water exchange decreases with decreasing ionic radii.37 Coordination numbers vary extensively, depending on the size of the metal ion. For example, coordination number four is common for lithium, six is most frequently found for transition metal ions 38 higher coordination numbers are not unusual for larger ions, e.g., Bi3+ can form Bi(H20)93+.39... 

Table 7.2 gives the coordination numbers in aqueous solution of a number of [M(H20) ] + ions, together with their ionic radii (for six coordination, for a fair comparison of size), showing why Sc + might have been predicted to form a seven-coordinate aqua ion, purely on grounds of size. 

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