Hydronium ions solvation free energy

In some circunstances, it might be convenient to take the hydronium ion as the basic unit for a proton in solution. In those cases, what is needed is the hydronium solvation free energy, AG° i (HgO ). Table VII.IO shows the results of theoretical calculations (da Silva [44b]), unless otherwise speci-hed) obtained with different continuum solvation models, according to the Ben-Naim [106] definition of the solvation process. Note that the only experimental value available (Pearson [107]) was obtained assuming AG/oi (H ) = —259.5 kcal/mol, which differs considerable from the more recent experiments of Tissandier et al. [104]. However, if one adopts Tissandier s result for the proton solvation energy, Pearson s scheme furnishes AG/oi (H30 ) = —106.16 kcal/mol, a value in close agreement with some of the theoretical results shown in Table VII.IO. 

However, the hydronium ion is not a regular acid. The trigonal H3O+ geometry on which our estimate for the work function (solvation free energy) is based is only one of the conhgurations that the solvated proton can adopt. The implications of this restriction are quantified below and discussed in detail in [29]. Substituting Equations 13.43 and 13.44 into Equation 13.41, we obtain for the pK of XH, i.e.. 

We may further speculate on the meaning of (15). It is known (Edward, 1964 Boyd, 1969 Yates and McClelland, 1974) that activity coefficients decrease in the series 7 > 7xh > 7x- This is quite reasonable since the increase in acid concentration is accompanied by a reduction in the availability of water, an excellent medium for solvating hydronium ions. This decrease will obviously tend to increase the free energy of the cationic species in particular. The extent of this increase will depend, in turn, on the ability of the individual cation to disperse the positive charge through the residues linked to the protonated atom by hydrogen bonding with the solvent. 

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