Hydration and Entropy Model for Ionic and Covalent Monatomic Ions

The hydration model we had proposed has been extended to aquo species having a covalent bond. In this case, the experimental cation−oxygen distance (δ) is shorter than the calculated data obtained with an ionic model. The observed decrease is used to evaluate the effective charge of the covalent species. We discuss the evaluation of the coordination number (N), the number of water molecules in a second hydration shell (H), and the radius (R w) of the water molecule in the two hydration shells and give useful expressions for their determinations. Because the hydration entropy and entropy of the aquo ion (S aq) can be deduced from the derivative of the free hydration energy (ΔG(hyd)) versus temperature, we propose an entropy model, considering six terms corresponding to the derivative versus temperature of the distance δ, the number N, the dielectric constant, the dipole and quadrupole moments of the water molecule, and the binding energy of the water molecule in the second hydration sphere. The two proposed models are tested for ions with charges −1, +1, +2, and +3. The calculated ΔG(hyd) and S°aq data are in excellent agreement with available experimental data. We have shown that the models can be extended to tetravalent ions. Finally, according to the relationships between the main characteristics of the aquo ions, we were able to conclude that the characteristics of an aquo ion can be defined to a great extent by two main parameters: the crystallographic radius and the cation−oxygen distance, which are both measured with accuracy by X-ray diffraction and X-ray absorption spectroscopy. Moreover, the consideration of the proposed equations could be used to predict or determine interesting characteristics such as N, q eff, H, or δ.