Enthalpy of ion solvation

Fig. 1. Born-Haber cycle for the formation of solvated ions from an ionic crystal [M+X ]w. U lattice energy, Affsoiv. enthalpy of ion solvation...

You can calculate the enthalpies of ion solvation from the vapor phase to water (dielectric constant D) from the Born model by using the Gibbs-Helmholtz Equation (13.41) ... 

To round off the discussion of solvation enthalpies, reference is made here to the articles by Case 38> and by Friedman and Krishnan 27>, who have reviewed the thermodynamic aspects of ion solvation extensively. 

Despite the simplifying assumptions in the derivation, such as assuming that the medium, water, is a continuum with no structure, and that the only work is electrostatic, and even more assumptions in calculating the properties of individual ions from the measured properties of electrolytes, as estimated by the Born function comes reasonably close to the measured Gibbs energy of ion solvation, as shown in Figure 6.7. Other thermodynamic properties such as the volume, entropy and enthalpy of solvation can also be obtained by appropriate differentiation of Equation (6.5). As a result, ever since its inception the Born equation has been used as a primitive model for the electrostatic contribution to the properties of an ion in a dielectric solvent. 

Differences in the solvation enthalpies of ions with the same charge number are weU-defmed thermodynamic quantities and can serve to test Equation 2.10 according to Coe [33]. 

Estimates of the heat of solvation of various species in DMSO as compared to water have been made and can be expressed as enthalpies of transfer. Some data for some common ions are given below. Discuss their significance. 

It should be born in mind, however, that the activation parameters calculated refer to the sum of several reactions, whose enthalpy and/or entropy changes may have different signs from those of the decrystalUzation proper. Specifically, the contribution to the activation parameters of the interactions that occur in the solvent system should be taken into account. Consider the energetics of association of the solvated ions with the AGU. We may employ the extra-thermodynamic quantities of transfer of single ions from aprotic to protic solvents as a model for the reaction under consideration. This use is appropriate because recent measurements (using solvatochromic indicators) have indicated that the polarity at the surface of cellulose is akin to that of aliphatic alcohols [99]. Single-ion enthalpies of transfer indicate that Li+ is more efficiently solvated by DMAc than by alcohols, hence by cellulose. That is, the equilibrium shown in Eq. 7 is endothermic ... 

Mass spectrometry has been used to study the energetics of solvation and has shown that the enthalpies of attachment of successive water molecules to either alkali metal or halide ions become less exothermic as the number of water molecules increases (Kebarle, 1977). The Gibbs free energies of attachment for water molecules have also been found to be negative. 

A variation of the halide affinity approach was used by Riveros et al. in the investigation of the enthalpy of formation of o-benzyne. Reaction of bromo- or iodobenzene with base in an ICR leads predominantly to the formation the expected M-1 anion, but also leads to the formation of solvated halide ions (Eq. 5.15). By using substrates with known halide affinities, it was possible to assign limits to the enthalpy of formation of the benzyne product. Ultimately, the experiment is comparable to that outlined in Eq. 5.14, although the acidity and halide affinity measurements are made in a single step. 

If a substance is to be dissolved, its ions or molecules must first move apart and then force their way between the solvent molecules which interact with the solute particles. If an ionic crystal is dissolved, electrostatic interaction forces must be overcome between the ions. The higher the dielectric constant of the solvent, the more effective this process is. The solvent-solute interaction is termed ion solvation (ion hydration in aqueous solutions). The importance of this phenomenon follows from comparison of the energy changes accompanying solvation of ions and uncharged molecules for monovalent ions, the enthalpy of hydration is about 400 kJ mol-1, and equals about 12 kJ mol-1 for simple non-polar species such as argon or methane. 

Parker, A. J., Solvation of ions—enthalpies, entropies and free energies of transfer, Electrochim. Acta, 21, 671 (1976). 

The hydration enthalpy of the Al3+ ion is enormous (-4690k) mol-1), and there are some interesting effects produced as a result. When NaCl is dissolved in water and the solvent evaporated, the solid NaCl can be recovered. If A1C13 is dissolved in water, evaporation of the water does not yield the solid A1C13. The Al3+ ion is so strongly solvated that other reactions become energetically more favorable than removing the solvent. This can be shown as follows. 

In 1906, Matignon reported an enthalpy of solution of -21.54 kcal mol-1 (-90 kj mol ) for neodymium trichloride in ethanol (178). His ethanol may have been less than perfectly anhydrous, and the value for pure ethanol somewhat less negative than this, perhaps —80 or — 70 kJ mol 1. Certainly a value in this region is considerably less negative than his value for the enthalpy of solution of neodymium trichloride in water, —148 kj mol-1. The difference may reasonably be attributed to less favorable solvation qf the constituent ions in ethanol than in water. Ion solvation would be expected to be even less favorable in isopropanol, so it is not surprising to find an enthalpy of solution of about + 40 kJ mol-1 for neodymium trichloride in this alcohol. This estimate must be considered as only approximate, as it is derived from... 

Enthalpies of solution of rare-earth trichlorides in dimethyl sulfoxide are markedly more negative than in water, though the difference decreases on going from lanthanum across to ytterbium. Less favorable solvation of the chloride ions by the dimethyl sulfoxide must be more than balanced by favorable solvation of the rare-earth 3+ cations (cf. Section VI,B). This dimethyl sulfoxide-versus-water comparison should be contrasted with the alcohol-versus-water comparisons discussed earlier. 

The enthalpies of solution and solubilities reviewed here provide much of the experimental information required in the derivation of single-ion hydration and solvation enthalpies, Gibbs free energies, and entropies for scandium, yttrium, and lanthanide 3+ cations. 

Table 9 compares ionic enthalpies of hydration from the Bernal and Fowler,164 Latimer et al.165 and Rashin and Honig88 procedures. Given the inherent uncertainty, the latter two sets of data are remarkably similar, considering that they were obtained 46 years apart. A number of tabulations of the thermodynamic solvation properties of ions in various solvents have now appeared. It is important to keep in mind, however, that there is a degree of arbitrariness associated with the experimental AHsoivation and AGSoiVation of individual ions. 

In order to think constructively about these problems we need some scale on which we can measure that intrinsic property of the ions which determines (in part) both stability and reactivity. In practice, we have to content ourselves, as far as carbenium ions are concerned, with the gas-phase standard enthalpy of formation, AHf, of a series of ions, and make estimates of the effects of solvation energies. In this way we can go quite a long way towards rationalising the reactivity of initiating ions with various monomers. 

In the course of our polarographic studies on organic cations we determined the half-wave potentials, 1/2, for various arylmethylium ions [1-11]. The aim of the present work is to extract from these values some new information concerning the relative magnitude of their solvation enthalpies in three very different solvents. A comparison of our results [obtained in methanesulphonic acid (MSA) and dichloromethane (DCM)] with those of Volz and Lotsch [12] [obtained in cyanomethane (CM) solutions] yields some useful conclusions. 

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. 

We report on the measurement of the propagation rate constants kp of styrene, indene, phenyl vinyl ether (PhViE) and 2-chloroethyl vinyl ether (CEViE) in nitrobenzene at (mostly) 298 K with 4-ClC6H4CO+SbF 6 as initiator. The dependence of the conductivity on the [4-ClC6H4CO+SbF"g] = c0 helped to establish that [Pn+] = c0 and thus to validate the foundation of this work. It is shown that most probably the propagating species are the uncomplexed, unpaired, solvated carbenium ions. Some new enthalpies of polymerisation have been found. 

M. D. Tissandier, K.A. Cowen, W.Y. Feng, E. Gundlach, M. H. Cohen,A. D. Earhart, J. V Coe, T. R. Tuttle Jr. The Proton s Absolute Aqueous Enthalpy and Gibbs Free Energy of Solvation from Cluster-Ion Solvation Data. J. Phys. Chem. A 1998, 102, 7787-7794. 

In Table 6 the differences of free enthalpies of solvation for several anion ligands in a donor solvent D and in AN are given. HMPA shows very weak solvation whereas water is a very strong solvating agent for anions. The free enthalpies of solvation of halide and pseudohalide ions are by 4 to 15 keal/mol more negative than in aprotic donor solvents. 

In a donor solvent the iodide ions is much more strongly solvated than the neutral donor and hence the donor properties of the iodide ion are lowered in solution. This event has been described as the thermodynamic solvatation effect. It becomes increasingly important with an increase of the ratio of the free enthalpy of solvation to the free enthalpy of the ligand exchange reaction. 

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