Raman and Infrared Spectroscopic Investigations on Aqueous Alkali Metal Phosphate Solutions and Density Functional Theory Calculations of Phosphate—Water Clusters

Abstract

Phosphate (PO₄³⁻) solutions in water and heavy water have been studied by Raman and infrared spectroscopy over a broad concentration range (0.0091–5.280 mol/L) including a hydrate melt at 23 °C. In the low wavenumber range, spectra in R-format have been constructed and the R normalization procedure has been briefly discussed. The vibrational modes of the tetrahedral PO₄³⁻(aq) (T_d symmetry) have been assigned and compared to the calculated values derived from the density functional theory (DFT) method for the unhydrated PO₄³⁻ (Td) and phosphate–water clusters: PO₄³⁻ · H₂O (C_2v), PO₄³⁻ · 2H₂O (D_2d), PO₄³⁻ · 4H₂O (D₂d), PO₄³⁻ · 6H₂O (T_d), and PO₄³⁻ · 12H₂O (T), a cluster with a complete first hydration sphere of water molecules. A cluster with a second hydration sphere of 12 water molecules and 6 in the first sphere, PO₄³⁻ · 18H₂O (T), has also been calculated. Agreement between measured and calculated vibrational modes is best in the case of the PO₄³⁻ · 12H2O cluster and the PO₄³⁻ · 18H₂O cluster but far less so in the case of the unhydrated PO₄³⁻ or phosphate–water cluster with a lower number of water molecules than 12. The asymmetric, broad band shape of ν₁(a₁) PO₄³⁻ in aqueous solutions has been measured as a function of concentration and the asymmetric and broad band shape was explained. However, the same mode in heavy water has only half the full width at half-height compared to the mode in normal water. The PO₄³⁻ is strongly hydrated in aqueous solutions. This has been verified by Raman spectroscopy comparing ν₂(H₂O), the deformation mode of water, and the stretching modes, the ν₁OH and ν₃OH of water, in K₃PO₄ solutions as a function of concentration and comparison with the same modes in pure water. A mode at ∼240 cm⁻¹ (isotropic R spectrum) has been detected and assigned to the restricted translational mode of the strong hydrogen bonds formed between phosphate and water, P–O ··· HOH. In very concentrated K₃PO₄ solutions (C₀ ≥ 3.70 mol/L) and in the hydrate melt, formation of contact ion pairs (CIPs) could be detected. The phosphate in the CIPs shows a symmetry lowering of the T_d symmetry to C_3v. In the less concentrated solutions, PO₄³⁻(aq) solvent separated ion pairs and doubly solvent separated ion pairs exist, while in very dilute solutions fully hydrated ions are present (C₀ ≤ 0.005 mol/L). Quantitative Raman measurements have been carried out to follow the hydrolysis of PO₄³⁻(aq) over a very broad concentration range. From the hydrolysis data, the pK₃ value for H₃PO₄ has been determined to be 12.45 at 23 °C.