Ahrlands Softness Parameter

Ahrland29 181 proposes that (/chem/2) for the reaction Eq (30) is a parameter measuring the softness of definite central atoms. Table 3 gives values for aA = 

There is no obvious reason why oA should express Pearson s scale of softness. Nevertheless, it is evident that it succeeds much better than for instance the molar polarizabilities a given in Table 2. The border-line cases between hard and soft central atoms have aA around 3 eV, whereas typical hard behaviour is found when oA is below 2 eV. A mild criticism is that oA has a tendency to increase more with the oxidation number z than appropriate for the chemical softness, producing aA = 

1 eV for iron(III) like for copper(II) and zinc(II). No aqua ions are known for z = 0 but an argument reducing oA ad absurdam for such a case is that it would automatically be zero, or more exactly the slightly negative hydration energy A//hydr expected for a neutral atom. 

Whereas LiCl and CsF with disparate ionic radii dissolve exothermally in water, most halides of the alkaline metals dissolve without much heat evolution. This is a remarkable observation in view of the huge Madelung energy —1.74/(rM + rx) in atomic units (14.3 eV/A) relative to gaseous M+ and X- and it was first pointed out by Fajans183 that this is compatible with the approximate equality 

It is even possible to calculate oA exclusively from the classical E° for the oxidation of the metallic element to the aqua ion and from the heat of atomization AHatom of the element given in Table 3. Neglecting for a moment the difference between AH and AG, it is a matter of constant energy that 

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Ahrland softness parameter (o ) (Ahrland 1968) is correlated with total ionization potential for the formation of M +(g) and the dehydration energy -AH°. The larger the difference between the total ionization potential for the formation of M +(g) and the dehydration energy -AH° are, the softer the ion is. 

Ahrland et al. (1958) classified a number of Lewis acids as of (a) or (b) type based on the relative affinities for various ions of the ligand atoms. The sequence of stability of complexes is different for classes (a) and (b). With acceptor metal ions of class (a), the affinities of the halide ions lie in the sequence F > Cl > Br > I , whereas with class (b), the sequence is F < Cl" < Br < I . Pearson (1963, 1968) classified acids and bases as hard (class (a)), soft (class (b)) and borderline (Table 1.23). Class (a) acids prefer to link with hard bases, whereas class (b) acids prefer soft bases. Yamada and Tanaka (1975) proposed a softness parameter of metal ions, on the basis of the parameters En (electron donor constant) and H (basicity constant) given by Edwards (1954) (Table 1.24). The softness parameter a is given by a/ a - - P), where a and p are constants characteristic of metal ions. 

They indicated that the softness parameter may reasonably be considered as a quantitative measure of the softness of metal ions and is consistent with the HSAB principle by Pearson (1963, 1968). Wood et al. (1987) have shown experimentally that the relative solubilities of the metals in H20-NaCl-C02 solutions from 200°C to 350°C are consistent with the HSAB principle in chloride-poor solutions, the soft ions Au" " and Ag+ prefer to combine with the soft bisulfide ligand the borderline ions Fe +, Zn +, Pb +, Sb + and Bi- + prefer water, hydroxyl, carbonate or bicarbonate ligands, and the extremely hard Mo + bonds only to the hard anions OH and. Tables 1.23 and 1.24 show the classification of metals and ligands according to the HSAB principle of Ahrland et al. (1958), Pearson (1963, 1968) (Table 1.23) and softness parameter of Yamada and Tanaka (1975) (Table 1.24). Compari.son of Table 1.22 with Tables 1.23 and 1.24 makes it evident that the metals associated with the gold-silver deposits have a relatively soft character, whereas those associated with the base-metal deposits have a relatively hard (or borderline) character. For example, metals that tend to form hard acids (Mn +, Ga +, In- +, Fe +, Sn " ", MoO +, WO " ", CO2) and borderline acids (Fe +, Zn +, Pb +, Sb +) are enriched in the base-metal deposits, whereas metals that tend to form soft acids... 

Table 3. Softness parameters according to Ahrland and to Klopman, the sum of the z first ionization energies of the gaseous atom, and the enthalpies and free energies of hydration of M+z according to Rosseinsky, and finally the heats of atomization of the elements, all in the unit 1 eV (= 23.05 kcal/mole)...

Ahrland (10) reasoned that the more completely the energy for positive ion formation in the gas phase is regained by introduction of the ion in a hard solvent (e.g., H2O) the harder the ion is. He then proposed a softness parameter based on the dehydration energy and the ionization potential for the formation of M" (gas). A large difference between the two quantities indicates a soft ion. 

The Pearson-Mawby softness parameter played a central role in this work. Since the use of this parameter does not permit the comparison of ions with different oxidation numbers (Ahrland 1968), the analyses in Turner et al. (1983) and Williams et al. (1982) were confined largely to the application of equation 2 to groups of ions of a given charge. For the 14 divalent ions used in the mouse experiment (Williams et al. 1982), a correlation represented by r = 0.36 was found with standard error s = 0.57. One aim of the present study is to demonstrate a predictive ability for toxicity which can be used for ions of any oxidation number and which is hence independent of ap. 

Many attempts have been made to define physical quantities that relate to softness and the parameter a a of Ahrland as the energy of the process... 

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