Heats of solvation

Nucleation in a cloud chamber is an important experimental tool to understand nucleation processes. Such nucleation by ions can arise in atmospheric physics theoretical analysis has been made [62, 63] and there are interesting differences in the nucleating ability of positive and negative ions [64]. In water vapor, it appears that the full heat of solvation of an ion is approached after only 5-10 water molecules have associated with... 

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. 

The Solvation Energy of an Ion. The interaction that takes place when an ion is introduced into a solvent is called the solvation of the ion. In recent years the concept of solvation has gradually changed. Formerly, solvation was held to be the attachment of a large or small number of solvent molecules to an ion and heat of solvation meant the heat... 

The theory of the structure of ice and water, proposed by Bernal and Fowler, has already been mentioned. They also discussed the solvation of atomic ions, comparing theoretical values of the heats of solvation with the observed values. As a result of these studies they came to the conclusion that at room temperature the situation of any alkali ion or any halide ion in water was very similar to that of a water molecule itself— namely, that the number of water molecules in contact with such an ion was usually four. At any rate the observed energies were consistent with this conclusion. This would mean that each atomic ion in solution occupies a position which, in pure water, would be occupied by a water moldfcule. In other words, each solute particle occupies a position normally occupied by a solvent particle as already mentioned, a solution of this kind is said to be formed by the process of one-for-one substitution (see also Sec. 39). 

Since the term hydration refers to aqueous solutions only, the word solvation was introduced as a general term for the process of forming a solvate in solution. The terms solvation and heat of solvation were introduced at a time when little or nothing was known about polar molecules. We know now that, when an atomic ion is present in a solvent, the molecular dipoles are subject to the ionic field, whose intensity falls off in 1/r2. We cannot draw a sphere round the ion and say that molecules within this sphere react with the ion to form a solvated ion, while molecules outside do not. The only useful meaning that can now be attached to the term solvation is the total interaction between ion and solvent. As already mentioned, this is the sense in which the term is used in this book. 

This equation is used in calculating heats of solvation of electrolytes. The heat of solution can be determined highly accurately by calorimetry (with an error of <0.1%). This heat is relatively small, and the values are between 100 and +40kJ/mol. Different methods exist to calculate the breakup energies approximately on the basis of indirect experimental data or models. Unfortunately, the accuracy of these calculations is much lower (i.e., not better than 5%). 

TABLE 7.1 Heats of Breakup First Heats of Dissolution and Heats of Solvation for Various lonophors in Water (kj/mol)... 

The second stage is the salvation or hydration of these gaseous ions in water to provide solvated or hydrated ions in solution accompanied by the evolution of their heats of solvation or hydration as represented below ... 

The preceding calculations can also be performed for finite cavity sizes. For this case, there are some additional sources of small amounts of energy associated with cavity formation arising from surface tension, pressure-volume work, and electrostriction. Because of the Franck-Condon principle these do not affect the transition energy, but they have some influence on the heat of solvation. Jortner s (1964) results are summarized as follows ... 

Co2 + is known to give hexasolvated species with most donor molecules. With HMPA, however, the tetrasolvate [Co(HMPA)4 ]2+ is formed and the heat of solvation is smaller than would be expected by mere consideration of the doni-city of HMPA. A plot of the enthalpies for the reaction... 

With a few exceptions solvent dependent coupling constants have been observed only in non-ionic compounds. As a result no data are available concerning correlations of coupling constant changes and heats of solvation, heats of solution, ion pairing, etc. 

The relative bond enthalpies from the photoacoustic calorimetry studies can be placed on an absolute scale by assuming that the value for D//(Et3Si—H) is similar to D/f(Me3Si—H). In Table 2.2 we have converted the D/frei values to absolute T>H values (third column). On the basis of thermodynamic data, an approximate value of D//(Me3SiSiMc2—H) = 378 kJ/mol can be calculated that it is identical to that in Table 2.2 [1]. A recent advancement of photoacoustic calorimetry provides the solvent correction factor for a particular solvent and allows the revision of bond dissociation enthalpies and conversion to an absolute scale, by taking into consideration reaction volume effects and heat of solvation [8]. In the last colunm of Table 2.2 these values are reported and it is gratifying to see the similarities of the two sets of data. 

This overall process can be considered as composed of two parts (1) separation of ions from the lattice (breaking ion-ion bonds in the lattice), and (2) interaction of the ions with water molecules (hydration). Both processes involve ion-water interaction (Fig. 2.10). During crystal dissolution, the two processes are occurring simultaneously. Thus, we can write for the heat of solvation of a salt... 

It seems reasonable to suggest that aUs is proportional to the solvation energy of the species and fi is likely to be inversely proportional to the size of the required accommodation site. Such a model suggests that small molecules with large heats of solvation would have large mass accommodation coefficients and conversely large molecules with small heats of solvation would have small mass accommodation coefficients. Experiments to date support these conclusions. 

In view of the high solubility of ZrCl4 and HfCl4 in MeN02, MeCN, DMF, and DMSO, heats of solvation of the tetrahalides in these solvents have been determined by a calorimetric method as the differences between the heats of solution of the tetrachloride and its solvate 294 the heats of solvation fall in the series DMSO > DMF > MeCN > MeN02 and Hf > Zr... 

Applying the established temperature dependence of A, Cp to the substances listed in Tables II and III, one can find that the enthalpy of the transfer of all these substances from the gaseous phase to water decreases to zero within the temperature range 100-180°C (Fig. 10). As is evident, when one linearly extrapolates A%H values determined at 25°C, using the usual assumption that Ag Cp is temperature-independent, one finds a lower value of the temperature TH(g w) at which the hydration enthalpy is zero (see the last column in Table II). It is clear, however, that these values, obtained by linear extrapolation, i.e., assuming constant heat capacity increment, have only a fictitious meaning. Nevertheless, in all cases one can conclude that the heat of solvation becomes zero at an elevated temperature in the range of 410 40 K. 

The data given in Tables 2 and 3 are, of course, related to one another through a thermochemical cycle. AHi0n(g) and AHaq differ only by the heats of solvation (hydration in aqueous solution) of the reactants and product, and therefore these heats of solvation must affect the absolute bond energies in the gas phases in such a manner as to cause an inversion in the order of stability in cases of class (b) behaviour (see below). 

It will be noted that the energy of activation is greatest in water, next in alcohol, and least in aniline, and it is probable that water tends to solvate more than alcohol, and alcohol to solvate more than aniline. These actual differences in the energies of activation can be attributed to heats of solvation which must be added to the energy of activation before decomposition can occur. The products chloroform and carbon dioxide are not solvated. It will be remembered that the trichloroacetic acid itself is completely stable, as shown by the failure to decompose in such solvents as carbon tetrachloride and sulphuric acid. This stabilizing of the trichloroacetate ion by the proton may be considered as a special limiting case towards which the stabilization by solvation can approach. 

To start with gas-phase data, ionization potentials (IP) and the derived heats of formation of radical cations are available for a large number of organic species (Franklin et al., 1969 Gutmann and Lyons, 1967 Turner, 1966), whereas electron affinities (EA) are far more scarce (for a recent review, see Janousek and Brauman, 1979). For both types of data one has to estimate heats of solvation for participating species in order to obtain E° in solution, and this is known to be an uncertain procedure (Mortimer, 1962). An alternative is to use the rather good correlations that are available between gas phase and solution data for estimating unknown solution values (see below). 

AHa, will be solvent-dependent unless IA//3I = IA Hi + AH2, where A Hi and A H2 are the heats of solvation of the electron donor and the hydrogen compound, respectively, and AH3 is the heat of solvation of the complex. The enthalpy of the formation of the adduct in the gas phase, which would give the actual strength of the hydrogen bond, will be different from that in solution unless the solvation energies cancel. In many cases, this is questionable because of the electron donor properties of the solvent. There is no doubt that many of the hydrogen bond enthalpies reported in the literature may be in error because of this. Moreover, it has been shown that the extent of self-association of... 

The fact that the electrons are completely ionized from the alkali metal atoms at 77°K allows a lower limit to be placed on the heat of solvation of the electron in ice. The reaction which may be represented formally as... 

Baxendale (1964) has estimated that the heat of solvation of the electron in water is 40 kcal mole . However our value is a lower limit because (a) reaction (11) may be considerably exothermic and (b) the... 

---