Ionic radius, values

Fig. 2. 32. Plot of the difference between the relative heats of hydration of oppositely charged ions with equal radii vs. ionic radius. Values are in kilocalories (1 cal = 4.184 J).

Fig. 5. Second order rate constants for the complex formation of the trivalent lanthanide ions and some d i-ions of transition metals with murexide as a function of reciprocal ionic radius (values from ref. 10)...

Plot of the pK of representative metal ions from Table 14.4 versus Z/H for metals having j < 1.50 (a) and versus Z/i +0.096( - 1.50) for metals having >1.50 (b). Electronegativity and ionic radius values are from www.webelements.com. Whenever these values were known, Pauling radii were used otherwise, the Shannon crystal radii were used for the octahedral (HS) metal ion. The pK values are from Wulfsberg. 

With the knowledge now of the magnitude of the mobility, we can use equation A2.4.38 to calculate the radii of the ions thus for lithium, using the value of 0.000 89 kg s for the viscosity of pure water (since we are using the conductivity at infinite dilution), the radius is calculated to be 2.38 x 10 m (=2.38 A). This can be contrasted with the crystalline ionic radius of Li, which has the value 0.78 A. The difference between these values reflects the presence of the hydration sheath of water molecules as we showed above, the... 

The viscosities of liquid metals vaty by a factor of about 10 between the empty metals, and the full metals, and typical values are 0.54 x 10 poise for liquid potassium, and 4.1 x 10 poise for liquid copper, at dreir respective melting points. Empty metals are those in which the ionic radius is small compared to the metallic radius, and full metals are those in which the ionic radius is approximately the same as tire metallic radius. The process was described by Andrade as an activated process following an AiThenius expression... 

Many of the ionic fiuorides of M, M and M dissolve to give highly conducting solutions due to ready dissociation. Some typical values of the solubility of fiuorides in HF are in Table 17.11 the data show the expected trend towards greater solubility with increase in ionic radius within the alkali metals and alkaline earth metals, and the expected decrease in solubility with increase in ionic charge so that MF > MF2 > MF3. This is dramatically illustrated by AgF which is 155 times more soluble than AgF2 and TIF which is over 7000 times more soluble than TIF3. 

The conclusions are evidently relevant to the amount of entropy lost by ions in methanol solution—see Table 29. If, however, the expression (170) is used for an atomic ion, we know that it is applicable only for values of R that are large compared with the ionic radius—that is to say, it will give quantitative results only when applied to the solvent dipoles in the outer parts of the co-sphere. The extent to which it applies also to the dipoles in the inner parts of the co-sphere must depend on the degree to which the behavior of these molecules simulates that of the more distant molecules. This can be determined only by experiment. In Table 29 we have seen that for the ion pair (K+ + Br ) and for the ion pair (K+ + Cl-) in methanol the unitary part of ASa amounts to a loss of 26.8 e.u. and 30.5 e.u., respectively, in contrast to the values for the same ions in aqueous solution, where the loss of entropy in the outer parts of the co-sphere is more than counterbalanced by a gain in entropy that has been attributed to the disorder produced by the ionic field. 

The ionic radius of an element is its share of the distance between neighboring ions in an ionic solid (12). The distance between the centers of a neighboring cation and anion is the sum of the two ionic radii. In practice, we take the radius of the oxide ion to he 140. pm and calculate the radii of other ions on the basis of that value. For example, because the distance between the centers of neighboring Mg2+ and O2 ions in magnesium oxide is 212 pm, the radius of the Mg21 ion is reported as 212 pm - 140 pm = 72 pm. 

Figure 8-16. Correlation of ionic radius and LFSE with log values for divalent transition-metal complexes of 1,2-diaminoethane.

However, consideration in terms of the ionic radius or the LFSE shows that both factors predict that the maximum stabilities will be associated with nickel(ii) complexes, as opposed to the observed maxima at copper(ii). Can we give a satisfactory explanation for this The data presented above involve Ki values and if we consider the case of 1,2-diaminoethane, these refer to the process in Eq. (8.13). 

Fig. 2.3 was constructed using a K2-3 value at 250°C extrapolated from high-temperature data by Orville (1963), liyama (1965) and Hemley (1967). Ion activity coefficients were computed using the extended Debye-Hiickel equation of Helgeson (1969). The values of effective ionic radius were taken from Garrels and Christ (1965). In the calculation of ion activity coefficients, ionic strength is regarded as 0.5 im i ++mci-) (= mc -)- The activity ratio, an-f/aAb, is assumed to be unity. 

Bismuth forms both 3+ and 5+ cations, although the former are by far the more common in nature. The ionic radius of Bi is even closer to that of La, than Ac, so again La is taken as the proxy. As noted above, Bi has the same electronic configuration as Pb, with a lone pair. It is unlikely therefore that the Shannon (1976) radius for Bi is universally applicable. Unfortunately, there is too little known about the magmatic geochemistry of Bi, to use its partitioning behavior to validate the proxy relationship, or propose a revised effective radius for Bi. The values of DWD u derived here should be viewed in the light of this uncertainty. 

Partition coefficients for Po can be derived from those for Th using Equation (8) and the ionic radii in Table 2. We have not modified the ionic radius for Po" from the value... 

Schmidt et al. (1999) report Dpb of 0.034-0.045 for two experiments with leucite lamproite melt composition for a basanitic melt composition La Tourrette et al. (1995) give Z)pb = 0.10. In all three cases Z)pb consistently falls below, by a factor of 3, the parabola defined by the other 2+ cations, as previously noted for several other minerals. Here the implication is that the effective Xll-fold ionic radius of Pb is slightly smaller than the value given in Table 2, i.e., closer in size to rsr. Upb/Usr is between 0.6 and 1.2, in these experiments. In the PIXE partition study of Ewart and Griffin (1994) for acid volcanic rocks, Z)pb ranges from 0.21 to 2.1 (3 samples), with Upb/Usr of 0.29 to 2.9. Until there are further experimental determinations of Upb, or better constraints on its ionic radius, we suggest that Z)pb = E>sr-... 

Water exchange on [Ln(H20)8]3+ for the heavier lanthanides Gd3+-Yb3+ is characterized by a systematic decrease in /feHa0 and an increase in AH as the ionic radius decreases from Tb3+ to Yb3+, and both A Si and AV-t are negative (311-313). The AV are significantly less than either the value of -12.9 cm3 mol-1 calculated for water... 

The ionic radii listed in Tables 6.3 and 6.4 in most cases apply to ions which have coordination number 6. For other coordination numbers slightly different values have to be taken. For every unit by which the coordination number increases or decreases, the ionic radius increases or decreases by 1.5 to 2 %. For coordination number 4 the values are approximately 4 % smaller, and for coordination number 8 about 3 % greater than for coordination number 6. The reason for this is the mutual repulsion of the coordinated ions,... 

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