Ionic radii, solvents

Separation Processes. The product of ore digestion contains the rare earths in the same ratio as that in which they were originally present in the ore, with few exceptions, because of the similarity in chemical properties. The various processes for separating individual rare earth from naturally occurring rare-earth mixtures essentially utilize small differences in acidity resulting from the decrease in ionic radius from lanthanum to lutetium. The acidity differences influence the solubiUties of salts, the hydrolysis of cations, and the formation of complex species so as to allow separation by fractional crystallization, fractional precipitation, ion exchange, and solvent extraction. In addition, the existence of tetravalent and divalent species for cerium and europium, respectively, is useful because the chemical behavior of these ions is markedly different from that of the trivalent species. 

The physical picture in concentrated electrolytes is more apdy described by the theory of ionic association (18,19). It was pointed out that as the solutions become more concentrated, the opportunity to form ion pairs held by electrostatic attraction increases (18). This tendency increases for ions with smaller ionic radius and in the lower dielectric constant solvents used for lithium batteries. A significant amount of ion-pairing and triple-ion formation exists in the high concentration electrolytes used in batteries. The ions are solvated, causing solvent molecules to be highly oriented and polarized. In concentrated solutions the ions are close together and the attraction between them increases ion-pairing of the electrolyte. Solvation can tie up a considerable amount of solvent and increase the viscosity of concentrated solutions. 

Alkali metal alkoxides, r-butyl acetate neat, 45°, 30 min, 98% yield of r-butyl ester from methyl benzoate. The rate constant for the reaction increases with increasing ionic radius of the metal and with decreasing polarity of the solvent. Equilibrium for the reaction is achieved in <10 sec. Other examples eire presented. " ... 

The conclusions are evidently relevant to the amount of entropy lost by ions in methanol solution—see Table 29. If, however, the expression (170) is used for an atomic ion, we know that it is applicable only for values of R that are large compared with the ionic radius—that is to say, it will give quantitative results only when applied to the solvent dipoles in the outer parts of the co-sphere. The extent to which it applies also to the dipoles in the inner parts of the co-sphere must depend on the degree to which the behavior of these molecules simulates that of the more distant molecules. This can be determined only by experiment. In Table 29 we have seen that for the ion pair (K+ + Br ) and for the ion pair (K+ + Cl-) in methanol the unitary part of ASa amounts to a loss of 26.8 e.u. and 30.5 e.u., respectively, in contrast to the values for the same ions in aqueous solution, where the loss of entropy in the outer parts of the co-sphere is more than counterbalanced by a gain in entropy that has been attributed to the disorder produced by the ionic field. 

Fixing attention on this difference between ions in methanol and ions in water, we may next ask whether the difference should be greater for an atomic ion of large or of small radius. The answer is clearly that, according to (18), if we take R equal to or proportional to the ionic radius a, between any two solvents the difference should be greater for the smaller ion greater for Ii+ than for K+ or Cs+, for example. If and 2 denote the dielectric constants of the two solvents, the difference, according to (18), would amount to... 

By using a simple model in which an electron in the surface atom of a polyanion is transferred to a solvent molecule, the effect of z on Alf through is considered as follows if the ionic radius r is much larger than the CT distance d and the radius of the surface atom yq, the z-dependence of can be expressed in terms of the surface field strength E of the polyanion as... 

In almost all theoretical studies of AGf , it is postulated or tacitly understood that when an ion is transferred across the 0/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of AGfr°. Although Abraham and Liszi [17], in considering the transfer between mutually saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB andl,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170mM H2O in NB). In such a medium, hydrophilic ions such as Li, Na, Ca, Ba, CH, and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl-Fischer method [35 5]. Rais et al. [35] and Iwachido and coworkers [36-39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal... 

Electronic configuration = (2g6. Six-coordinate ionic radius = 73 pm (169). b Rate constant for the exchange of a particular coordinated solvent molecule. c All three H20 and MeCN are equivalent. 

Eaq and Caq are the tendency of acid A and base B to undergo ionic and covalent bonding, respectively. Equation (2) resembles that proposed by Drago et al. (18) to model heats of complex formation of acids and bases in solvents of low dielectric constant. Only Lewis acids of ionic radius greater than 1.0 A obey Eq. (2). For all smaller Lewis acids, a third pair of parameters has to be introduced ... 

It follows from Eqs. (2.6.6), (2.6.8) and (2.6.10) that the presence of the solvent has two effects on the ionic mobility the effect of changing viscosity and that of changing the ionic radius as a result of various degrees of solvation of the diffusing particles. If the effective ionic radius does not change in a number of solutions with various viscosities and if ion association does not occur, then the Walden rule is valid for these solutions ... 

Most cations are strongly solvated, since their radii are small, and the free energy of solvation is approximately proportional to z2/r +, where ze0 is the cation charge in coulombs and r+ its ionic radius. The result of this is that even if the charge on the electrode is negative, there is usually little tendency for these cations to shed their water molecules and adsorb directly on the metal surface. Thus, the distance of closest approach of cations is determined by the radius of the inner solvent coordination sphere, and if the metal surface itself constitutes a plane, then the cation nuclei, at the distance of closest approach, will also constitute a plane termed the outer Helmholtz plane (OH P). 

The importance of the size of the solute relative to that of the solvent mentioned above is evident also from experimental determinations of the extent of solid solubility in complex oxides and from theoretical evaluations of the enthalpy of solution of large ranges of solutes in a given solvent (e.g. a mineral). The enthalpy of solution for mono-, di- and trivalent trace elements in pyrope and similar systems shows an approximately parabolic variation with ionic radius [44], For the pure mineral, the calculated solution energies always show a minimum at a radius close to that of the host cation. 

The increase in ionic radius from Be2+ to Mg2+, which is accompanied by an increase in coordination number from 4 to 6, is responsible for a substantial increase in lability (Table III, (37-43)). The two activation volumes measured are positive as well as all the activation entropies. The rate laws determined for non-aqueous solvents in inert diluent are first order, showing a limiting D mechanism for all solvent exchange reactions on [MgS6]2+. 

There are a limited number of fluorescent sensors for anion recognition. An outstanding example is the diprotonated form of hexadecyltetramethylsapphyrin (A-7) that contains a pentaaza macrocydic core (Figure 10.31) the selectivity for fluoride ion was indeed found to be very high in methanol (stability constant of the complex 105) with respect to chloride and bromide (stability constants < 102). Such selectivity can be explained by the fact that F (ionic radius 1.19 A) can be accommodated within the sapphyrin cavity to form a 1 1 complex with the anion in the plane of the sapphyrin, whereas Cl and Br are too big (ionic radii 1.67 and 1.82 A, respectively) and form out-of-plane ion-paired complexes. A two-fold enhancement of the fluorescent intensity is observed upon addition of fluoride. Such enhancement can be explained by the fact that the presence of F reduces the quenching due to coupling of the inner protons with the solvent. 

Because of the small ionic radius of lithium ion, most simple salts of lithium fail to meet the minimum solubility requirement in low dielectric media. Examples are halides, LiX (where X = Cl and F), or the oxides Li20. Although solubility in nonaqueous solvents would increase if the anion is replaced by a so-called soft Lewis base such as Br , I , S , or carboxylates (R—C02 ), the improvement is usually realized at the expense of the anodic stability of the salt because these anions are readily oxidized on the charged surfaces of cathode materials at <4.0 V vs Li. 

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