The Properties of Isolated Ions

Thermodynamic quantities that pertain to isolated ions in the ideal gas state (designated as ig ) and to their formation from the elements in their standard states are well defined. The standard molar entropy and constant-pressure heat capacity, 5°(I , ig) and Cp°(F ,ig), of isolated ions are recoded in Table 2.2 in J K mol for the standard temperature T° = 298.15 K and pressure P =0.1 MPa. The standard molar Gibbs energy and the enthalpy of formation, AfC (r , ig) and Af//°(I , ig), in kJ mol of many ions are also recorded in Table 2.2, The values of the Gibbs energies having been obtained from the enthalpies and entropies AfG°(P, ig) = Af//°( = =,ig) r°[5°(P= =,ig) — E5 (elements,ig)] in a manner that is thermodynamically consistent. 

The standard molar entropy of isolated monatomic ions with no unpaired electrons reflects the translational entropy alone and depends only on the mass of the ion. At T° =298.15 K and P° = 0.1 MPa the standard molar entropy is then 5°(P, ig) = 108.85 - -3 2ln(M/M°)J moP, where M/M° is the relative 

Values are provided for some ions not to be found in molten salts (e.g., H ) and for a few cations relevant to low-melting salts and RTILs, but for most of the latter no data could be found, nor for most of the polyatomic anions relevant to the RTILs. 

The shape of isolated monatomic ions is spherical, but ions that consist of several atoms may have any shape. The common ones are planar (NO3-, COs ), tetrahedral (NH4 , BF4-), octahedral (PFs ), elongated (SCN ), or more irregular, as they are for the ions constituting RTILs that generally have low symmetry (otherwise higher melting salts result). Tetrahedral and octahedral ions approximate spherical shape for many purposes and are termed globular. The size of an isolated ion cannot be specified readily, because its outer electron shell extends indefinitely around the inner ones and the nucleus. The sizes of ions in condensed liquid phases 

References are provided for data not found in those given in this caption 

When an ion exists in an ideal gaseous state, that is, when it is devoid of interactions with other particles or its surroundings in general, it is termed an isolated ion. Commonly, isolated ions consist of relatively few atoms, but some quite large ones are produced in mass spectrometers. They may also be the centers of clusters consisting of the ion proper surrounded by a small number of solvent molecules. 

The masses of ions are generally specified as their molar mass, that is, of Avo-gadro s number, 1Va = 6.02214 x 10 mol , of ions. The units of the molar mass. Ml, are therefore kg mol , but generally Mi is given in g mol .  

The polarizibility, aj, of an ion also has the dimension of a volume, of the order of 10 ° m per ion. The molar refractivity (at infinite frequency) is proportional to the polarizability  

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The properties of ionic liquids, because they are dissociated to a major extent into ions, depend on those of the constituting cations and anions. Therefore, Chap. 2 of the book is devoted in part to the properties of isolated ions that do not interact with their environment. These properties comprise their mass and charge, their standard thermodynamics of formation, and their entropy and heat capacity under standard conditions. The sizes of ions, once they are in a condensed phase, depends on their being constrained by their neighboring particles due to the repulsion of their outer electron shells. These properties of the individual constituting ions of ionic liquids are assumed to be portable when they form the ionic liquid, some of them being subject to changes induced by the mutual interactions of the ions. 

In solution, ions are produced by the heterolysis of covalent bonds in ionogens. This ionization reaction is favored by solvents due to their cooperative EPD and EPA properties (c/ Section 2.6). In the gas phase, however, ionization of neutral molecules to form free ions is rarely observed because this reaction is very endothermic. For example, in order to ionize gaseous H—Cl into H and Cl , an energy of 1393 kJ/mol (333 kcal/ mol) must be provided. This considerably exceeds the 428 kJ/mol (102 kcal/mol) needed to homolytically cleave H—Cl into hydrogen and chlorine atoms. Thus, for the creation of isolated ions in the gas phase, energy must be supplied by some means other than solvation with EPD/EPA solvents. The most widely used method is ionization by elec-... 

The ability of mass spectrometry to induce chemical transformations makes this method a unique technique for obtaining information about the intrinsic properties of isolated ions and molecules, solvates, clusters, non-covalent complexes, etc. Mass spectrometry is a convenient method for measuring basic thermochemical values of neutral molecules, ions, and radicals. Various molecular properties, such as ionization energy, proton affinity, electron affinity, energy of solvation/ desolvation, and bond dissociation energy can be directly measured in the gas phase by mass spectrometric methods (see also Chapter 2.12). 

The preceding methods may be characterized as collisionless, i.e., they determine the properties of isolated atoms or molecules in the gas phase. In contrast, ion/molecule equilibrium processes maintained by collision and characterized by a specific temperature... 

Some other properties of isolated ions have been determined the magnetic susceptibility, the polarizability, and the softness/hardness. These properties of isolated ions are portable and additive. This means that these properties of ions are not appreciably sensitive to the enviromnent of the ions, wheflier they are isolated, in crystalline compounds, or in molten salts. The property of a compound is the sum of the stoichiometrically weighted properties of its constituting cations and anions. These values for many ions were critically selected and reported by Marcus [4]. 

Kawa, M., and Frechet, J.M.J. (1998) Self-assembled lanthanide-cored dendrimer complexes enhancement of the luminescence properties of lanthanide ions through site-isolation and antenna effects. Chem. Mater. 10, 286-296. 

The direct access to the electrical-energetic properties of an ion-in-solution which polarography and related electro-analytical techniques seem to offer, has invited many attempts to interpret the results in terms of fundamental energetic quantities, such as ionization potentials and solvation enthalpies. An early and seminal analysis by Case etal., [16] was followed up by an extension of the theory to various aromatic cations by Kothe et al. [17]. They attempted the absolute calculation of the solvation enthalpies of cations, molecules, and anions of the triphenylmethyl series, and our Equations (4) and (6) are derived by implicit arguments closely related to theirs, but we have preferred not to follow their attempts at absolute calculations. Such calculations are inevitably beset by a lack of data (in this instance especially the ionization energies of the radicals) and by the need for approximations of various kinds. For example, Kothe et al., attempted to calculate the electrical contribution to the solvation enthalpy by Born s equation, applicable to an isolated spherical ion, uninhibited by the fact that they then combined it with half-wave potentials obtained for planar ions at high ionic strength. 

Note Although the discussion of common fragmentation pathways of organic ions is embedded here in the context of EI mass spectrometry, their occurrence is not restricted to this technique. The reactions of isolated gaseous ions do not directly depend on the ionization method, but are almost exclusively governed by intrinsic properties of the respective ion and by its internal energy (Chap. 2). 

The volume properties of crystalline mixtures must be related to the crystal chemical properties of the various cations that occupy the nonequivalent lattice sites in variable proportions. This is particularly true for olivines, in which the relatively rigid [Si04] groups are isolated by Ml and M2 sites with distorted octahedral symmetry. To link the various interionic distances to the properties of cations, the concept of ionic radius is insufficient it is preferable to adopt the concept of crystal radius (Tosi, 1964 see section 1.9). This concept, as we have already noted, is associated with the radial extension of the ion in conjunction with its neighboring atoms. Experimental electron density maps for olivines (Fujino et al., 1981) delineate well-defined minima (cf figure 1.7) marking the maximum radial extension (rn, ,x) of the neighboring ions ... 

The most important approach to reducing the computational burden due to core electrons is to use pseudopotentials. Conceptually, a pseudopotential replaces the electron density from a chosen set of core electrons with a smoothed density chosen to match various important physical and mathematical properties of the true ion core. The properties of the core electrons are then fixed in this approximate fashion in all subsequent calculations this is the frozen core approximation. Calculations that do not include a frozen core are called all-electron calculations, and they are used much less widely than frozen core methods. Ideally, a pseudopotential is developed by considering an isolated atom of one element, but the resulting pseudopotential can then be used reliably for calculations that place this atom in any chemical environment without further adjustment of the pseudopotential. This desirable property is referred to as the transferability of the pseudopotential. Current DFT codes typically provide a library of pseudopotentials that includes an entry for each (or at least most) elements in the periodic table. 

The ion selectivities displayed by these antibiotics are lower than those of the neutral ionophores, and are given in Table 11. Many studies have been made on the properties of these ionophores, particularly with reference to the calcium-transporting abilities of A 23187 (146) and lasolocid (145). The search for new antibiotics is ongoing and there is constant addition to a list of about 50 distinct polyether antibiotics which have been isolated from various streptomycetes. Representative structures will be discussed here to illustrate the nature of complexation with alkali and alkaline earth metal cations. 

The resolution of tris(catecholato)chromate(III) has been achieved by crystallization with L-[Co(en)3]3+ the diastereomeric salt isolated contained the L-[Cr(cat)3]3 ion.793 Comparison of the properties of this anion with the chromium(III) enterobactin complex suggested that the natural product stereospeeifically forms the L-cis complex with chromium(III) (190). The tris(catecholate) complex K3[Cr(Cat)3]-5H20 crystallizes in space group C2/c with a = 20.796, 6 = 15.847 and c = 12.273 A and jS = 91.84° the chelate rings are planar.794 Electrochemical and spectroscopic studies of this complex have also been undertaken.795 Recent molecular orbital calculations796 on quinone complexes are consistent with the ligand-centred redox chemistry generally proposed for these systems.788... 

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