Evaluation of individual ionic partial molar volumes in aqueous solutions

In a recent H2O–D2O molar volume isotope effect study on the alkali metal halide solutions, individual ionic standard partial molar volume contributions (V¯ion∘(H2O)-V¯ion∘(D2O)=ΔV¯ion∘(H–D)) have been derived, dependent only on the chosen (Pauling) ionic radii, rion. It has been concluded that the isotope effect of the cations (except for Li+) and that of the chloride anion exhibit a linear function of 1/rion, with ΔV¯ion∘(H−D) vanishing when 1/rion approaches zero. On the other hand, the directly measurable hydrodynamic “cosphere” volumes of the ions, V¯cosph∘, derived from the kinetic ionic (Stokes) radii, show a similar pattern, here also the cationic and anionic rion relations cross or meet at V¯cosph∘(Cs+)≅V¯cosph∘(Cl-).Because both ΔV¯ion∘(H–D)andV¯cosph∘ originate in the hydration volumes of the ions, (V¯hydr∘=V¯ion∘-V¯intr∘) determined by electrostriction, this rion pattern of the V¯hydr∘ (ion) provides an “extra-thermodynamic” assumption to evaluate the individual cationic and anionic molar volume contributions in normal water solution. As a basis for the evaluation, this rion pattern is applied to the conventional cationic and anionic V¯hydr∘ (ion) values (related toV¯ion∘(H+,aq.)=0cm3·mol-1), calculated from literature V¯ion∘ data, assuming that the V¯intr∘ (ion) = V¯cryst∘ (ion).To adjust the V¯hydr∘(Cl-) to the V¯hydr∘(Na+,K+,Rb+,Cs+)versus rion relation at T = 298.15 K, the conventional anionic V¯hydr∘ (ion) data have to be increased, the cations have to be decreased by 4.2 cm3 · mol−1. Similar adjustments at five different temperatures between T = (273 and 323) K, result in V¯ion∘(H+,aq.)=-(4.2±0.2)cm3·mol-1 at T = 298.15 K, with an increment of −0.02 cm3 · K−1 · mol−1. Related to these parameters, relations of V¯ion∘versus temperature for the alkali metal and halide ions were calculated.The cationic and anionic V¯hydr∘ (ion) values, when related to V¯ion∘(H+,aq.)=-4.2cm3·mol-1, show strong rion correlation with V¯cosph∘, their ratio versus rion offers a linear equation to compare the influence of the ions on the solvent structure on a well defined “quantitative” scale.The value of the derived V¯ion∘(H+,aq.), while being consistent with that widely accepted ca. − (5 ± 2) cm3 · mol−1, has a higher precision with a reasonable basis of the applied “extra-thermodynamic” assumption. It can serve to verify other partitioning procedures used in non-aqueous solvents.