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58 CHAPTER 2

anion, against the molecular weight ofthe cation (instead ofthe reciprocals ofthe
cations’ volumes) is useful. Extrapolation of this plot to zero cation molecular weight
should give the partial gram-ionic volume forthe partner anion. Conway’splotis given
in Fig. 2.15. The method works because the tetraalkylammonium ions are large and
hence cause little electrostriction (i.e., compression of the surrounding solvent), which
is the reason for the apparent lack of agreement of the other extrapolations. The reason
for the apparent absence of other specific effects, such as the structure breaking which
the big tetraalkylammonium cations would be expected to produce, is less obvious.
The basis for the success claimed by Conway’s method is the agreement (particularly
for of the values it gives with those of an entirely different method, the ionic
vibration approach (Section 2.7). The values for and from the present method
3 –1
are found to be 23.6 and –5.7 cm mol , respectively. Why is one of these values
+
negative? It can only mean that addition of H to the solution causes more contraction
among the surrounding solvent molecules than the volume added by the cation (which
in this case is small).

2.7. COMPRESSIBILITY AND VIBRATION POTENTIAL APPROACH TO
SOLVATION NUMBERS OF ELECTROLYTES

2.7.1. Relation of Compressibility to Solvation
In 1938, Passynski made the following argument, which relates the compressibil-
ity of a solution to the sum of the primary solvation numbers of each ion of an
electrolyte. Primary here means ions that are so compressed by the ions’ field that they
themselves have zero compressibility.
Passynski measured the compressibility of solvent andsolution respec-
tively, by means of sound velocity measurements. The compressible volume of the
solution is V and the incompressible part, The compressibility is defined
in terms of the derivative of the volume with respect to the pressure, P, at constant
temperature, T. Then,

Therefore