Aqueous solutions of four heavy-metal nitrate salts
(AgNO3, TlNO3, Cd(NO3)2 and Pb(NO3)2) have been studied at
25 °C using broadband dielectric relaxation spectroscopy (DRS) at
frequencies 0.27 ≤ ν/GHz ≤ 115 over the approximate
concentration range 0.2 ≲ c/mol L−1 ≲ 2.0 (0.08 ≲ c/mol L−1 ≲
0.4 for the less-soluble TlNO3). The spectra for AgNO3, TlNO3,
and Pb(NO3)2 were best described by assuming the presence of
three relaxation processes. These consisted of one solute-related
Debye mode centered at ∼2 GHz and two higher-frequency
solvent-related modes: one an intense Cole−Cole mode centered
at ∼18 GHz and the other a small-amplitude Debye mode at ∼500
GHz. These modes can be assigned, respectively, to the rotational
diffusion of contact ion pairs (CIPs), the cooperative relaxation of
solvent water molecules, and its preceding fast H-bond flip. For Cd(NO3)2 solutions an additional solute-related Debye mode of
small-amplitude, centered at ∼0.5 GHz, was required to adequately fit the spectra. This mode was consistent with the presence of
small amounts of solvent-shared ion pairs. Detailed analysis of the solvent modes indicated that all the cations are strongly solvated
with, at infinite dilution, effective total hydration numbers (Zt
0 values) of irrotationally bound water molecules of ∼5 for both Ag+
and Tl+, ∼10 for Pb2+, and ∼20 for Cd2+. These results clearly indicate the presence of a partial second hydration shell for Pb2+(aq)
and an almost complete second shell for Cd2+(aq). However, the hydration numbers decline considerably with increasing solute
concentration due to ion−ion interactions. Association constants for the formation of contact ion pairs indicated weak complexation
that varies in the order: Tl+ < Ag+ < Pb2+ < Cd2+, consistent with the charge/radius ratios of the cations and their Gibbs energies of
hydration. Where comparisons were possible the present constants mostly agreed well with the rather uncertain literature values.