Radii of polyatomic ions

Yatrimirskii has provided an ingwious method for estimating the radii of polyatomic ions. A Bom-Haber calculation utilizing the enthalpy of formation and related data can provide an estimate of the lattice energy, ft is then possible to find what value of the radius of the ion in question is consistent with this lattice encroy. These values are thus termed thermochemical radii. The most recent set of such values is given in Table 4.5. In many cases the feet that the ions (such a COf", CNS", CHjCOO") are markedly nonspherical limits the use of these radii. Obviously they... 

We start this second and last chapter on the solid state with a description of the theoretical determination of lattice energy. Next, we consider how the lattice energy can be determined experimentally using the principles of thermochemistry that you learned in previous chemistry courses. A discussion of such topics as the degree of covalent character in ionic crystals, the source of values for electron affinities, the estimation of heats of formation of unknown compounds, and the establishment of thermochemical radii of polyatomic ions follows. We conclude with a special section on the effects of crystal fields on transition metal radii and lattice energies. 

Using a combination of the theoretical and experimental approaches, (1) more reliable values of electron affinities including those of monoatomic anions like and S, (2) heats of formation of unknown compounds like CaCl or NaCl2, and (3) thermochemical (or effective) radii of polyatomic ions can be calculated. 

Radii of Polyatomic The sizes of polyatomic ions such as NH and SO are of interest for the under-Iona standing of the properties of ionic compounds such as (NH4)2S04, but the experimen-... 

With the availability of thermochemical lattice energies (see Table 8.6 for some representative values) for salts involving polyatomic anions and cations, Kapustinskii s equation can be used to estimate the radii of these ions. As an example, let s take sodium perchlorate. The thermochemical lattice energy for NaC104 is given in Table 8.6 as —648 kj/mol. We use this value as the lattice energy in the Kapustinskii equation as shown in Equation (8.22) and solve for r . 

Radii derived in this manner from thermochemical cycles and calculated lattice energies are known as thermochemical radii. Some representative values are presented in Table 8.7. These are values averaged over a series of salts involving the ion listed. Interpretation of these results must be approached with caution, but they do give some indication of the effective size of polyatomic ions. 

Table 7.4 Radii of Common Monatomic and Polyatomic Ions. ...

Table 13 gives the three contributions to AGhydration for five polyatomic ions, as computed by the PCM technique of Barone et al.,95 using their radii. As mentioned earlier, Gelectrostetic, Gcavitatlon and Gvdw are generally of the same order of magnitude for molecular solutes (Table 8) however this is not true for ionic ones, as can be seen in Table 13. Geiectrostatic is now often an order of magnitude larger.

As we end this section, let us reconsider ionic radii briefly. Many ionic compounds contain complex or polyatomic ions. Clearly, it is going to be extremely difficult to measure the radii of ions such as ammonium, NH4, or carbonate, COs, for instance. However, Yatsimirskii has devised a method which determines a value of the radius of a polyatomic ion by applying the Kapustinskii equation to lattice energies determined from thermochemical cycles. Such values are called thermochemical radii, and Table 1.17 lists some values. 

Radii have also been tabulated for polyatomic ions [7]. Since these species are not truly spherical, such radii must be regarded as effective. However, it is useful to have estimates of effective radii when comparing ionic solvation parameters. In the following section, methods of determining the solvation parameters of single ions in infinitely dilute electrolyte solutions are considered. This is followed by a discussion of simple models of ionic solvation in which ionic size is an important factor. 

In summary, the empirical approach to ionic solvation based on the MSA is quite successful for monoatomic ions of the main group elements. It helps one to understand the important differences between the way cations and anions are solvated in water. It can also be applied to other ions, including polyatomic ions, provided the solvation is essentially electrostatic in character. Thus, one may estimate effective radii for anions such as nitrate and perchlorate from the Gibbs solvation energy using the value of 8s calculated for the halide ions. Considering the simplicity of the model, it provides an useful means of understanding the thermodynamics of solvation. 

The sizes of polyatomic (nonglobular) ions in crystals are also expressed by their thermochemical radii according to Jenkins and coworkers [47], Circular reasoning may be involved in their determination, because these radii depend on calculated lattice energies of crystals that in turn depend on the interionic distances. The assigned uncertainties of these radii are 19 pm for univalent and divalent anions increasing to twice this amount for trivalent ones and they are listed in Table 2.8 too. A further problem with these values is the use of the Goldschmidt radii for the alkali metal counterions, r°, rather than the Shannon-Prewitt ones [43,44] appropriate for ions in solution. 

Using Marcus data, that is, interparticle distances, two approximations were performed in order to obtain the a values of several salts in aqueous solution. Initially, the a values were determined as the sum of the ionic radii (R ) reported by Marcus in the same woik. The R values were obtained as the difference among the mean intemuclear distance between a monoatomic ion, or the central atoms of a polyatomic ion, and the oxygen atom of a water molecule in its first hydration shell and the... 

Small shifts in band position may be observed for different cations. The various radii and charges of different cations alter the electrical environment of polyatomic anions and hence affect their vibrational frequencies. Obviously, different crystalline arrangements may result when the cation is altered. Normally, with increase in mass of the cation there is a shift to lower frequency. The characteristic bands of particular polyatomic ions are given in Table 22.1... 

It should not be inferred that the crystal structures described so far apply to only binary compounds. Either the cation or anion may be a polyatomic species. For example, many ammonium compounds have crystal structures that are identical to those of the corresponding rubidium or potassium compounds because the radius NH4+ ion (148 pm) is similar to that of K+ (133 pm) or Rb+ (148 pm). Both NO j and CO, have ionic radii (189 and 185 pm, respectively) that are very close to that of Cl- (181 pm), so many nitrates and carbonates have structures identical to the corresponding chloride compounds. Keep in mind that the structures shown so far are general types that are not necessarily restricted to binary compounds or the compounds from which they are named. 

The difference in ionic radii between isobaric isotopes of different elements is too small for KED to be practical for suppression of atomic isobaric interferences. In our view, the most universal method of interference suppression in ICP-MS is chemical resolution via ion-molecule reactions, since it can provide a way of resolving both atomic and polyatomic interferences, and can be more specific compared to the use of energy and momentum transfer processes. 

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