Step-wise Hydration: Comparison of Debye-Hückel Long-Range interactions and ion pairing

The concentration-based solution activity of representative highly soluble 1–1 (NaCl and NaOH), 2–2 (MnSO₄ and UO₂SO₄), and 3–1 (AlCl₃) salts were modeled with a two-component model. A step-wise hydration component combined with either Debye-Hückel (DH) or ion pairing (IP) component. Step-wise hydration competent models positive deviation from ideality of electrolytes on solution activity (higher activity coefficients or greater effective concentration than the Raoult’s ideal). DH and IP components, both model negative deviations from ideality (lower activity coefficients or less effective concentration than the Raoult’s ideal). Step-wise hydration with either DH or IP can model both solution activity and molal osmotic coefficients, respectively emphasizing the fitting of higher concentration data or lower concentration data. Both the DH and IP based models performed similarly from dilute conditions to saturation. However, modeling the higher valence electrolytes required two modifications that have not been previously reported. First, modification was the development of an equilibrium cluster formation model that decouples the higher order dependance of solute concentration (and various intermediate cluster sizes) from an estimate of a final cluster size. This allowed the IP model to move beyond 1–1 salts and address solutes that are expected to cluster. The second modification was to the DH model so it could address 3–1 salts. The DH model could model 1–1 and 2–2 salts directly without IP, however, to model AlCl₃ with DH the conceptual assumption of irreversible formation of AlCl²⁺ ion was used which is an effective mixing of the DH and IP models.