Ionic Radii in Solution

David and Fourest (1990) challenged the concept of a constant radius for the water molecule, rw- The electric field of the ions polarizes the water molecules adjacent to them and for multiply charged ions squeezes these molecules somewhat in the direction of the ions. The values of rw decrease according to these authors from 0.143 nm for the alkali metal cations down to 0.133nm for the divalent lanthanide cations. Therefore, using the mean value, rw = 0.138 nm, increases accordingly the uncertainty of the ionic radii in solution from 0.002 to 0.005 nm. 

The radii of multi-atomic ions was estimated as thermochemical radii by Jenkins and co-workers (Jenkins and Thakur 1979 Jenkins et al. 1999 Roobottom et al. 1999) from the lattice potential energies f/iat of crystals containing them with a monatomic counter-ion of known radius. The sum of the radii of the cation and anion is  

The temperature dependence of the ionic radii of monatomic- as well as multi-atomic ions is negligible within the temperature range of the existence of water as a liquid at ambient pressures (Krestov 1991). 

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Another important topic of interest has been the interpretation of the observed ion-water distances d(i...w) [4-6] in terms of the ionic radii in solutions and the radii of water molecules. The present author made the surprising observation recently [7] that d(i...w) increases linearly with the covalent radius d(A) of the atom [9], for mary ions according to the eqrration. 

The radius thus calculated from the theory of Smith and Symons does not correspond to any known property of halide ions. However, when the acceptable physical model of Franck and Platzman is combined with the concept of a variable radius, as proposed by Smith and Symons, both absolute value and environmental effects can be accounted for. This was done in the theory of Stein and Treinin (18, 19, 47), using an improved energetic cycle to obtain absolute values of r, the spectroscopically effective radius of the cavity containing the X ion. These values were then found to correspond to the known partial ionic radii in solution, as did values of dr/dT to values obtained from other experiments. The specific effects of temperature, solvents, and added salts could be used to differentiate between internal and such CTTS transitions where the electron interacts in the excited state strongly with the medium. These spectroscopic aspects of the theory were examined later in detail and compared with experiment by Treinin and his co-workers (3, 4, 32, 33, 42,48). 

Another important topic of interest has been the interpretation of the observed ion-water distances d(i.. [4-6] in terms of the ionic radii in solutions and the... 

Tables 2.1-2.4 relative to sodiiun, lithium, potassium, rubidium, and cesium salts, also show that, in general, the values of a obtained by fitting experimental data of activity coefficients are larger than the sum of ionic radii in solutions (or crystal-lattice spacing) and the interatomic distances, d. Also they are close to the values obtained from Kielland sdata and toab initio values calculated by using two models model I and model II, considering the absence and the presence of five water molecules between anion and cation, optimized in the gas phase, respectively), and also to those obtained fi om MM studies, where no water molecules are consid-...

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. 

In chapter 2, Profs. Contreras, Perez and Aizman present the density functional (DF) theory in the framework of the reaction field (RF) approach to solvent effects. In spite of the fact that the electrostatic potentials for cations and anions display quite a different functional dependence with the radial variable, they show that it is possible in both cases to build up an unified procedure consistent with the Bom model of ion solvation. The proposed procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy. Especially interesting is the introduction of local indices in the solvation energy expression, the effect of the polarizable medium is directly expressed in terms of the natural reactivity indices of DF theory. The paper provides the theoretical basis for the treatment of chemical reactivity in solution. 

Plotting ixbase VS. pH gives a sigmoidal curve, whose inflection point reflects the apparent base-pAi, which may be corrected for ionic strength, I, using Equation 6.11 in order to obtain the thermodynamic pATa value in the respective solvent composition. Parameters A and B are Debye-Hiickel parameters, which are functions of temperature (T) and dielectric constant (e) of the solvent medium. For the buffers used, z = 1 for all ions ao expresses the distance of closest approach of the ions, that is, the sum of their effective radii in solution (solvated radii). Examples of the plots are shown in Figure 6.12. 

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. 

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. 

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). 

Fig. 12.3 The covalent radii and ionic radii in NaCl 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 Q...

A is the length of the hydrogen bond. Note that d(H ) = d(HH)/t ) = 0.28 A, the radius of the proton, is the cationic radius of H. Fig. 12.3 for Na and Cf ions shows a comparison of the covalent radii with the ionic radii in the crystal and in aqueous solutions. The results for many other ions (including Lanthanides) can be found in [7]. 

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... 

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