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ION–SOLVENT INTERACTIONS 61

where is the velocity of an ultrasonic wave in the medium and is the density.
Note that determined by this equation is an adiabatic not an isothermal one,
because the local compression that occurs when the ultrasound passes through the
solution is too rapid to allow an escape of the heat produced. 12
A word about a particularly clever sound velocity measurement technique is
justified. It is due in its initial form to Richards et al. One creates an ultrasonic vibration
by bringing a piezoelectric crystal with oscillations in the megahertz range into contact
with a fixed transducer. The latter has one face in contact with the liquid and sends out
a beam of sound through it. Another transducer (the receiver) is not fixed and its
position is varied with respect to that of the first transducer over distances that are
small multiples of the wavelengths of the sound waves A stepping
motor is used to bring about exact movements, and hence positions, of the receiver
transducer. As the movable transducer passes through nodes of the sound waves, the
piezoelectric crystal on the receiver transducer reacts and its signal is expressed
through an electronic circuit to project Lissajous figures (somewhat like figures of
eight) on the screen of a cathode ray oscilloscope. When these figures attain a certain
configuration, they indicate the presence of a node (the point in a vibration where the
amplitude is negligible) and by counting the number of nodes observed for a given
distance of travel of the receiver transducer, the distance between two successive
nodes—the wavelength of sound in the liquid —is obtained. The frequency of
piezoelectric crystal used (e.g., barium titanate), v (e.g., 5 MHz), is known. Because

where c 0 is the velocity of sound needed in Eq. (2.12) for the compressibility, the latter
can be found from Eq. (2.13).

2.8. TOTAL SOLVATION NUMBERS OF IONS IN ELECTROLYTES

Total solvation numbers arise directly from the discussion following Passynski’s
Eq. (2.11), which requires measurements only of the compressibility of the solution
(that of the solvent usually being known). Bockris and Saluja used this method in 1972
to obtain the total solvation numbers of both ions in a number of salts (Table 2.5).
In the next section it will be shown how these total solvation numbers for salts
can be turned into individual solvation numbers for the ions in the salt by the use of
information on what are called “ionic vibration potentials,” an electrical potential

I2
A study of the temperature dependence of shows that it is positive for tetraalkylammonium salts.