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ION–SOLVENT INTERACTIONS 59

and

Let the g-moles of salt be these are dissolved in g-moles of solvent. Then,
there are g-moles of incompressible solvent per g-mole of solute. This was
called by Passynski (not unreasonably) the primary solvation number of the salt,
although it involves the assumption that water held so tightly as to be incompressible
will qualify for primary status by traveling with the ion.
To obtain individual ionic values, one has to make an assumption. One takes a
large ion (e.g., larger than and assumes its primary solvation number to be zero, 11
so that if the total solvation number for a series of salts involving this big anion is
known, the individual hydration numbers of the cations can be obtained. Of course,
once the hydration number for the various cations is determined by this artifice, each
cation can be paired with an anion (this time including smaller anions, which may have
significant hydration numbers). The total solvation numbers are determined and then,
since the cation’s solvation number is known, that for the anion can be obtained.
In Passynski’s theory, the basic assumption is that the compressibility of water
sufficiently bound to an ion to travel with it is zero. Onori thought this assumption
questionable and decided to test it. He used more concentrated solutions (1–4 mol
–3
dm ) than had been used by earlier workers because he wanted to find the concentra-
tion at which there was the beginning of an overlap of the primary solvation spheres
(alternatively called Gurney co-spheres) of the ion and its attached primary sheath of
solvent molecules.
Figure 2.16 shows the plot of the mean molar volume of the solution multiplied
by the compressibility of the solution as a function of the molar fraction of the NaCl
–3
solute (~4 mol dm ), the values for the three temperatures become
identical. Onori arbitrarily decided to take this to mean that has no further
temperature dependence, thus indicating that all the water in the solution is now in the
hydrated sphere of the ions and these, Onori thought, would have a with no
temperature dependence (for they would be held tight by the ion and be little dependent
on the solvent temperature).
These assumptions allow the compressibility of the hydration sheath itself to be
calculated (Passynski had assumed it to be negligible). To the great consternation of
some workers, Onori found it to be significant—more than one-tenth that of the solvent
value.

11
Thus, whether molecules move off with an ion is determined by the struggle between the thermal energy
of the solution, which tends to take the water molecule away from the ion into the solvent bulk, and the
attractive ion–dipole force. The larger the ion, the less likely it is that the water molecule will remain with
the ion during its darting hither and thither in solution. A sufficiently large ion doesn’t have an adherent
(i.e., primary) solvation shell, i.e.,