Effective ionic radii, Table

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. 

The remaining compounds listed in Table II all adopt structures with infinite metal-metal bonded chains consisting of octahedral cluster units fused on opposite edges. However, because of the large difference in effective ionic radius of the cations concerned, very different lattice types are dictated. The compounds NaMoi 06 (19,22) and Bas(Moit06)8 (17) adopt tunnel structures with the Na+ or Ba2+ ions located in sites along the tunnels with 8-fold coordination by oxygen atoms. 

Table 1. Partial Molar Volume (Vj°°). Effective Ionic Radius (rjf), Stokes Radius (rs), and Temperature CoefScient of Walden Product (dln( A °°Tj ldT) at 25 ...

It is clear from Table 11.1 that the effective ionic radius found from Stokes Law is greater than the crystallographic radius for the cations, suggesting that these ions are probably hydrated in solution. The situation is much less clear for the anions. F (aq) is the only anion where the effective radius gives evidence for hydration. Chapter 13 looks at this in more detail. 

The cationic head of acetylcholine. It is useful to pause here and compare acetylcholine cations with inorganic cations likely to be present at the receptor surface. Whereas potassium has a stimulant action on all of the muscle, the action of acetylcholine is normally confined to the small end-plate region. The shielding effect of the alkyl-groups (on the nitrogen atom in a quaternary amine) ensures that the ion is virtually anhydrous in aqueous solution (Robinson and Stokes, 1959). Thus the effective ionic radius in solution may be taken as the same as the radius obtained from X-ray crystallography. It is seen from Table 13.1 that the tetramethylam-monium ions has a radius of 2.41 A, and this must also be the radius of the cationic head of acetylcholine. 

The uncertainty of the proper coordination number of any particular plutonium species in solution leads to a corresponding uncertainty in the correct cationic radius. Shannon has evaluated much of the available data and obtained sets of "effective ionic radii" for metal ions in different oxidation states and coordination numbers (6). Unfortunately, the data for plutonium is quite sparse. By using Shannon s radii for other actinides (e.g., Th(iv), U(Vl)) and for Ln(III) ions, the values listed in Table I have been obtained for plutonium. These radii are estimated to have an uncertainty of 0.02 X ... 

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-... 

We focus attention on the fact that the crystal radii (CRs) for the various cations listed in table 1.11 are simply equivalent to the effective ionic radii (IRs) augmented by 0.14 A. Wittaker and Muntus (1970) observed that the CR radii of Shannon and Prewitt (1969) conform better than IR radii to the radius ratio principle and proposed a tabulation with intermediate values, consistent with the above principle (defined by the authors as ionic radii for geochemistry ), as particularly useful for sihcates. It was not considered necessary to reproduce the... 

In 1967, C. J. Pederson of DuPont deNemours Co. synthesized the cyclic polyethers ( ) These cyclic polyethers are commonly referred to as "crown ethers" (see Figure 3). In solution, crown ethers are extremely effective ligands for a wide range of metal ions. The size of the ring cavity and the ionic radius of the metal affect the stability of the complex. Tables I and II list the cavity diameters for the crown ethers and the ionic radii of a number of metal ions (6-11). 

Inspection of the values for the entropies of hydration of the Group 2 cations in Table 2.17 shows that, with the exception of that for Be2 +, the values become less negative as the ionic radius increases. This effect is similar to that observed for the Group 1 cations. The exception of Be2+ to the general trend is possibly because of its tendency to have a tetrahedral coordination that causes it to affect fewer molecules of water in the hydration process. 

MacNevin and Ogle (87) investigated the effects of impurities on the photochromism of barium and calcium titanates as shown in Table V. Pure samples of barium and calcium titanate were not photochromic and doping with Ag+1, Cu+2, Sb+3, Sn+4, Zn+4, and Co+2 produced no enhancement of photochromism. However, increases in the concentrations of impurities such as Fe+3, Zn+2, Sb+5, and V+6 promote photochromic activity. MacNevin and Ogle concluded that the photochromism in these systems depends on the insertion into the lattice of an impurity ion having, (a) an ionic radius near that of Ti+4, and (b) an oxidation number other than 4 to make electron transfer possible. 

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