Oscillations, Waves, and Interactions - GWDG

Multistep association of cations and anions 355
Figure 20. Concentration ratios C0/C(•) and C1/C(◦) of completely dissociated Zn 2+
ions and of (Zn(H2O)Cl) + complexes, respectively, as following from dielectric spectra of
aqueous solutions of ZnCl2 with salt concentration C [23]. The lines show the predictions
from a set of equilibrium constants [95] for the zinc chloride association scheme.
each other. Therefore, the solute contribution ɛ(0) − ɛ1 (Fig. 18) to the static permittivity
of zinc chloride solutions appears to be mainly due to monochloro complexes.
We used the relation
C1 = (ɛ(0) − ɛ1) ɛ0
N
� �2 2 3kBT
3 µ 2
to derive the concentration C1 of monochloro complexes from the relaxation amplitude
ɛ(0) − ɛ1 and the dipole moment µ of the ion pairs [23]. Here N is Avogadro’s
number and kB is the Boltzmann constant. Using the simple relation
(18)
µ = e · l (19)
for the dipole moment in solution, where e denotes the elementary charge and l the
cation-anion distance, perfect agreement of the C1 values with those from the set of
equilibrium constants Ki, i = 1, ..., 4 is observed (Fig. 20), if l = 4.2 ˚Ais assumed.
This is the cation-anion distance in an outer-sphere complex. Hence, obviously, the
monochloro complex exists predominantly as solvent-separated species.
The ultrasonic absorption spectra of zinc chloride solutions extend over a broader
frequency band than a single Debye type relaxation term, thus indicating a distribution
of relaxation times [30]. A relaxation time distribution had been already
inferred from previous ultrasonic measurements, in a reduced frequency range, of
zinc(II)halide aqueous solutions [96] and also from a combined ultrasonic and Bril-