Handbook of Solvents - George Wypych - ChemTech - Ventech!

770 Roland Schmid
sequently, there are so many different sets of ionic radii and hydration free energies available
that it is very difficult to decide which to prefer.
In a most recent paper, 82 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 Δ hydG*
the Born radii were calculated from
r B (Å) = -695 z 2 /Δ hydG*(kJ) [13.1.30]
as given in Table 13.1.7. This is at first a formal definition whose significance may be tested
in the framework of the position of the first maximum of the radial distribution function
(RDF) measured by solution X-ray and neutron diffraction. 177 However, the procedure is
not unambiguous as is already reflected by the names given to this quantity, viz. (for the
Table 13.1.7. Some radii (Å). Data are from
ref. 82
Atom rB a
raq b
rmetal
Li 1.46 1.50 1.52
Na 1.87 1.87 1.86
K 2.33 2.32 2.27
Rb 2.52 2.48
Cs 2.75 2.58 2.65
Be 1.18 1.06 1.12
Mg 1.53 1.52 1.60
Ca 1.86 1.86 1.97
Sr 2.03 2.02 2.15
Ba 2.24 2.27 2.17
F 1.39 1.29
Cl 1.86 1.85
Br 2.00 2.00
I 2.23 2.30
a From eqn. [13.1.30], b eqns. [13.1.31] and [13.1.32].
case of a cation) ion-water 178 or ion-oxygen
distance. The ambiguity of the underlying
interpretation resides in the circumstance
that the same value of 1.40 Å is assigned in
the literature to the radius of the oxide anion,
the water molecule and the vdW radius
of the oxygen atom.
It seems that many workers would
tend to equate the distance (d) corresponding
to the first RDF peak with the average
distance between the center of the ion and
the centers of the nearest water molecules,
d=r ion +r water. Actually, Marcus 179,180 presented
a nice relationship between d, averaged
over diffraction and simulation data,
and the Pauling crystal radius in the form
d=1.38 + 1.102 r p. Notwithstanding this success,
it is preferable to implicate not the water
radius but instead the oxygen radius.
This follows from the close correspondence
between d and the metal-oxygen bond
lengths in crystalline metal hydrates. 82
The gross coincidence of the solid and
solution state distances is strong evidence
that the value of d measures the distance between
the nuclei of the cation ad the oxygen
rather than the center of the electron cloud
of the whole ligand molecule. Actually, first
RDF peaks for ion solvation in water and in nonaqueous oxygen donor solvents are very
similar despite the different ligand sizes. Examples include methanol, formamide and
dimethyl sulfoxide. 180
Nevertheless, the division of d into ion and ligand components is still not unequivocal.
Since the traditional ionic radius is often considered as a literal measure of size, it is usual to