Thermochemical radius

There is another use of the Kapustinskii equation that is perhaps even more important. For many crystals, it is possible to determine a value for the lattice energy from other thermodynamic data or the Bom-Lande equation. When that is done, it is possible to solve the Kapustinskii equation for the sum of the ionic radii, ra + rc. When the radius of one ion is known, carrying out the calculations for a series of compounds that contain that ion enables the radii of the counterions to be determined. In other words, if we know the radius of Na+ from other measurements or calculations, it is possible to determine the radii of F, Cl, and Br if the lattice energies of NaF, NaCl, and NaBr are known. In fact, a radius could be determined for the N( )3 ion if the lattice energy of NaNOa were known. Using this approach, which is based on thermochemical data, to determine ionic radii yields values that are known as thermochemical radii. For a planar ion such as N03 or C032, it is a sort of average or effective radius, but it is still a very useful quantity. For many of the ions shown in Table 7.4, the radii were obtained by precisely this approach. 

Although Br and CN have approximately the same thermochemical radii, there is a great difference in the basicity of the ions. Which is the stronger base Explain your answer. 

Yatsimirskii s thermochemical radii are obtained from Kapustinskii s empirical formula for the lattice energy of crystalline salts. The lattice energy is the heat evolved when the gaseous cation and anion combine to form the salt ... 

Yatsimirskii, K.B. "Thermochemical Radii and Heats of Hydration of Ions," Izvest. Akad. Nauk, S.S.S.R., Otdel. 

Table 1.13 Thermochemical radii for polyanionic complexes (Greenwood, 1970). ...

Table 3.1-1 Melting points (°C) and thermochemical radii of the anions (A) for Na and [EMIMj salts. The ionic radii of the cations are 1.2 A (Na ) and 2x2.7 A ([EMIMjh non-spherical).

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. 

Tetranuclear clusters, 815-816 Thermal ellipsoids, 234, 724 Thermochemical calculations, predictive power of, 127-129 Thermochemical radii. 117 Thermodynamics, and chelate effect. 523... 

In cases where the lattice energy is known from the Born-Haber cycle, the Kapustinskii equation can be used to derive the ionic radii of complex anions such as S042- and P043-. The values determined in this way are known as thermochemical radii some values are shown in Table 4.2.6. 

This expression has turned out to be remarkably useful in correlating the heats of formation of the salts of tetrahedral ions, provided suitable values are assumed for the ionic radii R+ and R. Kapustinskii and his coworkers recognized that these quantities are not necessarily equal to the packing radii of the ions in the actual structure of the crystal consequently, they have come to be known as thermochemical radii. The thermochemical radius and heat of formation for a tetrahedral ion are normally determined from Equation 1 and the known heats of formation of two of its salts. 

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... 

Calculations can be extended to complex ions such as carbonate and sulfate by the use of thermochemical radii, chosen to give the best match between experimental lattice energies and those estimated by the Kapustinskii equation. 

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