Enthalpy hydration, individual

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

Table 8. Gas-phase hydration enthalpies for individual clustering steps, and total...

This increase is due to the partial degradationof the chain structure during displacement of the lattice metal ions (mainly and Fe ) by in the process of acid treatment. From the adsorption isotherm and the integral molar enthalpy isotherm of HDP, it can be seen that hydrated individual molecules and, at higher concentrations, hydrated micelles are adsorbed on the surface of the protonated sepiolite particles. Further evidence of such a mechanism is that the maximum amount of HDP adsorbed is much smaller (2.19 nmVmolecule) than required for close-packed monolayer coverage. 

But what is the enthalpy of the hydration reaction in Equation (3.33) We first met Hess s law on p. 98. We now rephrase it by saying The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which the reaction may be divided. ... 

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. 

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. 

K. Fajans opened the field of study of heats of hydration of ions. In 1919 62) he not only provided the definition of the new quantity and equation (1) but he attempted to derive values for the absolute enthalpies of hydration of individual ions approximately —260 kcal mole i was his estimate for A subsequent paper on the subject 63) was published in 1921. Unfortunately this is not quoted in recent reviews but it lists values for iyM+ and Wx which are quite remarkably similar in magnitude to those given in Table 7. 

The enthalpies of formation of aqueous ions may be estimated in the manner described, but they are all dependent on the assumption of the reference zero that the enthalpy of formation of the hydrated proton is zero. In order to study the effects of the interactions between water and ions, it is helpful to estimate values for the enthalpies of hydration of individual ions, and to compare the results with ionic radii and ionic charges. The standard molar enthalpy of hydration of an ion is defined as the enthalpy change occurring when one mole of the gaseous ion at 100 kPa (1 bar) pressure is hydrated and forms a standard 1 mol dm-3 aqueous solution, i.e. the enthalpy changes for the reactions Mr + (g) — M + (aq) for cations, X (g) — Xr-(aq) for monatomic anions, and XOj (g) —< XO (aq) for oxoanions. M represents an atom of an electropositive element, e.g. Cs or Ca, and X represents an atom of an electronegative element, e.g. Cl or S. 

This treatment illustrates the inherent difficulty of the problem. Any cycle of this type will allow the calculation of sums of enthalpies of hydration of cations and anions, but it will not allow the estimation of the separate quantities. There are two ways of dealing with the matter. One is to use the conventional reference zero that the enthalpy of hydration of the proton is zero, i.e. Ahyti// (H+, g) = 0. The second approach is to estimate an absolute value for A Z/tH h, g) that may be used to estimate the absolute values for enthalpies of hydration of any other ions. Both are exemplified in the text, but only the second is of general use in the study of the hydration of ions and the discussion of the factors that determine the values of enthalpies of hydration of individual ions. 

The discrepancy introduced by ignoring the compression term is only slight and represents no more than a 2% difference from the absolute values usually used. It is normally ignored in view of the uncertainties associated with the problem of dividing the conventional enthalpies of hydration of cation-anion pairs into individual values. 

In these calculations, the electron affinity of the methyl radical has been taken1 as 27 kcal.mole-1. The other enthalpy terms are all well-known quantities the enthalpies of hydration of individual ions have been assigned as done by Valis ev (see ref. 2) and the enthalpy of hydration of the gaseous methyl anion has been taken as that of the bromide ion. It can be seen from Table 1 that not only is the formation of the methyl anion energetically very unfavoured in the gas phase, but it is also endothermic to the extent of 54 kcal.mole-1 in aqueous solution. A check on this final result can be made by consideration of the standard entropy change for the reaction... 

The ionic hydration energies (enthalpies and Gibbs free energies) of metals are consequently roughly a linear function of the square of the oxidation state divided by the effective ion radius (z /r ff. Figure 8.9).It may be added that AH y and AG y, respectively, of the individual alkali halide ion pairs form two linear branches with a maximum at Csl (KBr). 

So-called absolute standard molar enthalpies of hydration of a number of individual ions, including Th", have been obtained by using a combination of experimental data and estimates based on the extra-thermodynamic assumptions that... 

The redox potentials of a number of mixed-ligand complexes of ruthenium and osmium have been, rather thoroughly, analyzed in terms of the individual contribution of ligational and hydrational enthalpy, and of entropy terms (775, 777). The importance of metal-hgand n-bonding on the relative stability of the -)-3 and -f2 complexes, has again been emphasized. For further details the reader is referred to the original work. 

FIGURE 10.12 Enthalpies of Hydration ofTransition-Metal Ions. The lower curves show experimental values for individual ions the blue upper curves result when the LFSE, as well as contributions from spin-orbit splitting, a relaxation effect from contraction of the metal-ligand distance, and interelectronic repulsion energy are subtracted. (Data from D. A. Johnson and P. G. Nelson, Inorg. Chem., 1995,34,5666 (M +data) and D. A. Johnson and P. G. Nelson, Inorg. Chem., 1999,4949 (M3+data).)... 

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