Single-ion hydration enthalpies

Another result of considerable interest is the fact that the total single ion hydration enthalpies AH% are nicely paralleled by the values for individual clustering steps in the gas phase, and hence even more markedly by the AH%t n values (Figs. 7 and 8). It is not at all trivial that properties brought about by an infinite number of solvent molecules should be displayed already by such small complexes. Nevertheless, the shapes of the plots for AH% and AHo,n are quite similar. 

Table 9 Single-ion Hydration Enthalpies (kJmol-1) for Metal Cations (at 298.2K)a 1 ...

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. 

The quantitative comparisons with the available experimental data are less favorable in this case. The transition state and product in water appear to be shifted up in energy by about 15 kcal/mol. The computed curves are more in line with experimental data for ketones, where formation of hydrates is far less favorable than for formaldehyde. The discrepancy likely comes from an overly exothermic hydration energy for the charge-localized hydroxide ion, which lowers the reactant end of the pmfs. This results from the use of two-body potential functions, that is, the TIP4P water molecules are not polarized by the ion, so water-water repulsions between molecules in the first solvent shell are underestimated. Until the polarization can be explicitly treated, ions that have attractive interactions with single water molecules greater than about 18-20 kcal/mol should probably be avoided. For example, CN would be less problematic since its single molecule hydration enthalpy is only 14 kcal/mol, versus 25 for... 

The overall strength of interaction between a metal ion and its hydration shell, which will parallel the strength of bonding within the [M(OH2 ),]" , can be assessed from ion hydration enthalpies. The values listed in Table are based on the single ion assumption of Halliwell and Nyburg... 

Similar to the total single hydration enthalpies, the individual magnitudes n decrease with increasing ion size in a given group. 

For reference, the standard Gibbs energies and enthalpies of hydration of some single ions and neutral molecules are given in Table 2.2. 

This, of course, is always negative, and plays the same role in aqueous thermochemistry as the lattice energy does in the energetics of ionic solids. The hydration enthalpy cannot be measured directly, and many thermodynamicists frown upon this or any other single-ion quantity. For example, the enthalpy of solution of sodium chloride can be measured and subjected to the following analysis ... 

Although for solutions at infinite dilution the absolute enthalpy of hydration of a single ion is clearly defined, there is no purely thermodynamic way to separate the sum of the hydration energies of a cation and an anion into constituent parts. Hence it has been common practice to use conventional standard enthalpies of hydration related in the case of a cation Mz+ and an anion Xz to the absolute enthalpies of hydration by... 

Probably the most satisfactory approach which has been used to estimate absolute enthalpies of hydration of single ions is that of Halliwell and Nyburg (39). The method makes use of a simple model of aqueous solutions, and is based on the significance of differences between thermodynamic functions for ions of opposite charge rather than attempting to split the enthalpy of hydration of pairs of ions. Values of the differences between conventional enthalpies of hydration are plotted against (R -fa) - , where R is the effective radius of the ion and a is the effective radius of the water molecule. This plot yields the absolute enthalpy of hydration of the proton. 

When is it most likely that Ln +(aq) ions will be stable For the first of the two reactions above to be favoured, the single factor that will help make A// positive is a high value of h. Less important would be the size of the ions, as this could affect the hydration enthalpies the difference between the hydration enthalpies will be less, the larger the lanthanide ions. Substituting into the above equation, we can investigate the relative stabilities of La +(aq) and Eu +(aq), making use of ionization energies from... 

For a comprehensive compilation of Gibbs energies of solvation, see C. M. Criss and M. Salomon Thermodynamic Measurements - Interpretation of Thermodynamic Data. In A. K. Covington and T. Dickinson (eds.) Physical Chemistry of Organic Solvent Systems, Plenum Press, London New York 1973, p. 253 ff. - Cf also D. W. Smith Ionic Hydration Enthalpies, J. Chem. Educ. 54, 540 (1977). - A critical selection of standard molar heat capacities of hydration, AhydC°/ (J K") moF ), of single ions has been given by M. H. Abraham and Y. Marcus, J. Chem. Soc., Faraday Trans. 1 82, 3255 (1986). 

An electrostatic hydration model, previously developed for ions of the noble gas structure, has been applied to the tervalent lanthanide and actinide ions. For lanthanides the application of a single primary hydration number resulted in a satisfactory fit of the model to the experimentally determined free energy and enthalpy data. The atomization enthalpies of lanthanide trihalide molecules have been calculated in terms of a covalent model of a polarized ion. Comparison with values obtained from a hard sphere modeP showed that a satisfactory description of the bonding in these molecules must ultimately be formulated from the covalent perspective. 

For the non-aqueous solvents, the solvation enthalpies were calculated from the hydration enthalpies and the single ion enthalpies of transfer i.c., = + from H2O-> solvent... 

Enthalpies of transfer from water to PC, as seen in Fig. 2.15.5b show the same qualitative behaviour as A/fpc.-DMso th simple ions, but different interpretations are offered for the two cases, ° specifically a difference in basicity for the PC DMSO process, but specific hydration effects for the PC HgO transfer. This can be justified on the basis of the difference in the single-ion values for the two systems. The basic assumption supporting this view is that the single-ion enthalpies have been correctly assigned. 

In a most recent paper,a new table of absolute single-ion thermodynamic quantities of hydration at 298 K has been presented, based on conventional enthalpies and entropies upon implication of the thermodynamics of water dissociation. From the values of AiydG the Bom radii were calculated from... 

Tabulated are single-ion entropies of about 110 diatomic and polyatomic ions in water Gibbs energies, enthalpies, and entropies of hydration of monatomic ions at 25 C partial molar volumes of about 120 common ions at 25 C ionic partial molar heat capacities of ions Gibbs energies of transfer of inorganic electrolytes from HjO to 020 and calorimetrically determined enthalpies of solution of salts in H2O and 020. 

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