Page 114 - MODERN ELECTROCHEMISTRY

56 CHAPTER 2

ion changes the volume of the solution not only by its own volume, but by the change
due, respectively, to a breakup of the solvent structure near the ion and the compression
of the solvent under the influence of the ion’s electric field (called electrostriction; see
Section 2.22).
The effective ionic volume of an ion in solution, the partial molar volume, can be
determined via a quantity that is directly obtainable. This is the apparent molar volume
of a salt, defined by

where V is the volume of a solution containing moles of the solvent and moles
of the solute and is the molar volume of the solvent. It is easily obtained by
measuring the density of the solution.
Now, if the volume of the solvent were not affected by the presence of the ion,
would indeed be the volume occupied by moles of ions. However, the
complicating fact is that the solvent volume is no longer per mole of solvent; the
molar volume of the solvent is affected by the presence of the ion, and so is called
the apparent molar volume of the ion of the salt. Obviously, as when the
apparent molar volume of the solvent in the solution must become the real one, because
the disturbing effect of the ion on the solvent’s volume will diminish to zero. Hence,
at finite concentration, it seems reasonable to write the following equation:

This equation tells one that the density of the solution that gives for a series
of concentrations gives the partial molar volume at any value of Knowing
from and Eq. (2.7) can be used to obtain as a function of Extrapolation
of to gives the partial molar volume of the electrolyte at infinite dilution,
(i.e., free of interionic effects).
Once partial molar volumes are broken down into the individual partial ionic
volumes (see Section 2.6.2), the information given by partial molar volume measure-
ments includes the net change in volume of the solvent that the ion causes upon entry
and hence it provides information relevant to the general question of the structure near
the ion, that is, its solvation.

2.6.2. How Does One Obtain Individual Ionic Volume from the Partial
Molar Volume of Electrolytes?

From an interpretive and structural point of view, it is not much use to know the
partial molar volumes of electrolytes unless one can separate them into values for each
ion. One way of doing this might be to find electrolytes having ions with the same