Evaluation of individual ionic partial molar volumes in aqueous solutions

Abstract

In a recent H 2O–D 2O molar volume isotope effect study on the alkali metal halide solutions, individual ionic standard partial molar volume contributions ( V ¯ ion ∘ ( H 2 O ) - V ¯ ion ∘ ( D 2 O ) = Δ V ¯ ion ∘ ( H–D ) ) have been derived, dependent only on the chosen (Pauling) ionic radii, r ion. 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/ r ion, with Δ V ¯ ion ∘ ( H − D ) vanishing when 1/ r ion 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 r ion relations cross or meet at V ¯ cosph ∘ ( Cs + ) ≅ V ¯ cosph ∘ ( Cl - ) . Because both Δ V ¯ ion ∘ ( H–D ) and V ¯ cosph ∘ originate in the hydration volumes of the ions, ( V ¯ hydr ∘ = V ¯ ion ∘ - V ¯ intr ∘ ) determined by electrostriction, this r ion 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 r ion pattern is applied to the conventional cationic and anionic V ¯ hydr ∘ (ion) values (related to V ¯ ion ∘ ( H + ,aq . ) = 0 cm 3 · 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 r ion 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 cm 3 · mol −1. Similar adjustments at five different temperatures between T = (273 and 323) K, result in V ¯ ion ∘ ( H + ,aq . ) = - ( 4.2 ± 0.2 ) cm 3 · mol - 1 at T = 298.15 K, with an increment of −0.02 cm 3 · 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 . ) = - 4.2 cm 3 · mol - 1 , show strong r ion correlation with V ¯ cosph ∘ , their ratio versus r ion 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) cm 3 · 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.