Ion Association and Hydration of Some Heavy-Metal Nitrate Salts in Aqueous Solution

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 (Z_t⁰ 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.