Ionic contributions to partial molal volumes in aqueous solutions

Abstract

The ionic components of the partial molal volumes of aqueous electrolyte solutions at 25 °C have been analysed on the basis of the TTG model with reference to molecular data. Twenty cations and seventeen anions were considered. The limiting value, ν°, for each ion is summarised by ν°(ion)=V(edi)+ΔV(ed H₂O)+ΔV(HB)+V(Born), where V(edi) is the effective volume of the ion in solution, which includes the electrical deformation effects. V(edi)=Mψ_s= 4/3πN× 10^–24(r+Δ_geom+Δ_el)³, where r is the crystal radius (Pauling), Δ_geom is the geometric packing factor and Δ_el the electrical deformation effect. For small cations Δ_el is proportional to the number of water molecules that have lost their orientation polarization per mole per unit charge. ΔV(ed H₂O) is the volume change due to the electrical deformation of the water molecules close to the ion and equals kzΔ_el, where z is the charge on the ion and k is a function of the internal pressures and dielectric properties of pure water. ΔV(HB) is the volume change associated with rupture or formation of hydrogen bonds and V(Born) is the Born volume.

The Masson (or TTG) slope S_v was split into the ionic components via an equation given previously. The cations all have positive slopes (in cm³ kg^1/2 mol^–3/2 for I^1/2, where I is the molal ionic strength) ranging from 1.03 for H⁺ to 5.67 for Ce³⁺. The monovalent anions have small slopes (usually < 0.5 and negative). The F^– ion (S^–_v= 1.18), HCO^–₃ ion (S^–_v= 0.83) and OH^– ion (S^–_v= 2.22) are exceptions. The divalent oxyanions have large (> 3) positive slopes. The deviations of the ionic slopes from the Debye–Hückel slope are the result of an anion versus cation factor, plus the specific ionic effect on the reorientation time of the water molecules (resulting either from rotational or translational diffusion). All the slopes can be summarised by the relationships (S⁺_v–S^K+_v)∝(1/Q°)(dQ⁺/dm)_m→0 and (S^–_v–S^Cl_v)∝(1/Q°)(dQ^–/dm)_m→0, where Q represents either the self-diffusion coefficient of water or the reciprocal of the proton magnetic relaxation rate. For the halide ions, Q can also be represented by the relative molal shift of the dielectric relaxation time. This result and those for ν° are consistent with the concept of hydration water exchange of dielectrically mismatched water molecules near small cations.