Oscillations, Waves, and Interactions - GWDG

346 R. Pottel, J. Haller and U. Kaatze
Figure 11. Ultrasonic excess absorption spectra for solutions of Sc2(SO4)3 in water at
25 ◦ C and at pH=2.4 (◦, 0.1 mol/l; △, 0.058 mol/l; •, 0.033 mol/l [17]). Dashed lines show
the subdivision of the latter spectrum into three Debye-type relaxation terms as following
from a nonlinear least-squares regression analysis of the experimental data. Full lines are
graphs of the sum of these terms with the parameter values found by the fitting procedure.
and the reaction volumes ∆Vi are given. The values obtained solely from ultrasonic
measurements are reasonable and support the assumption of the Eigen-Tamm
multistep association mechanism.
3.2 Dielectric spectra
The complex dielectric spectrum for a solution of 0.1 mol/l Al2(SO4)3 in water differs
from that of the solvent in various aspects (Fig. 12). Both spectra display a dispersion
(dɛ ′ (ν)/dν < 0)/absorption (ɛ ′′ (ν) > 0) region in the frequency range around 20 GHz
reflecting the dielectric relaxation of water. The solvent contribution ɛ1 to the extrapolated
static permittivity ɛ(0) of the solution, however, is considerably smaller
than the static permittivity ɛW (0) of water. Also the relaxation frequency (2πτ1) −1
of the water contribution to the solution spectrum is slightly shifted with respect to
the relaxation frequency (2πτW ) −1 of water at the same temperature. Both changes
i, j kij kji Ki ∆Vi
s −1
s −1
cm 3 /mol
1,2 (2 ± 0.5) · 10 11 § (9 ± 3) · 10 8
220 ± 100 ∗ 13 ± 3
2,3 (1.4 ± 0.5) · 10 7
(2 ± 0.7) · 10 7
0.7 ± 0.5 7 ± 2
3,4 (9.9 ± 3) · 10 6
(3.3 ± 1) · 10 6
3.0 ± 0.7 7 ± 2
Ka = (800 ± 400)(mol/l) −1
Table 1. Rate constants kij and kji of the coupled reaction scheme of ion association
(Eq.11), equilibrium constants Ki and reaction volumes ∆Vi, as well as association constant
Ka (Eq.14) for aqueous solutions of scandium sulfate [17]; § s −1 (mol/l) −1 , ∗ (mol/l) −1 .