Thermodynamics of aqueous electrolytes and hydrogen-bonded non-electrolytes over a wide range of temperature and pressure : the aqueous trivalent lanthanide cations and the methanol-water system

摘要

Partial molar heat capacities and volumes of aqueous solutions are required to calculate the temperature- and pressure-dependence of chemical equilibrium constants over the wide range of conditions encountered in industrial and geochemical processes. Values for the standard partial molar heat capacities Cᴼp,₂ and volumes Vᴼ₂ of aqueous electrolytes also provide much information about the nature of the ionic solvation because both functions are sensitive to the hydrated structure of ions in solution. This research addresses two major topics. The objective of the first part of the program is to explore the solvation of M³⁺(aq) ions by determining the apparent molar volumes and heat capacities of several trivalent lanthanide ions over a wide range of temperature and pressure, and interpreting the results by semi-empirical hydration models. The second objective is to examine the behaviour of partial molar volumes in the methanol-water system, as an example of a hydrogen bonded non-electrolyte, over a range of temperature and pressure that approaches the critical locus of the mixture. -- Apparent molar heat capacities Cpφ and volumes Vφ were derived from specific heat capacities and densities measured in a Sodev Picker flow microcalorimeter and vibrating-tube densimeter at pressure 0.1 MPa. For high-temperature volumetric measurements, a stainless-steel cell vibrating tube densimeter and a platinum cell vibrating-tube densimeter were constructed in the course of this research. These densimeters allowed measurement of the densities of solutions relative to the reference fluid, water, at temperatures up to 600 K and pressures up to 30.0 MPa with an overall uncertainty less than 0.2 kg·m³. -- Data for Cpφ and Vφ for LaC1₃(aq), La(C1O₄)₃(aq), and Gd(C1O₄)₃(aq) from 283.2 K to 338.2 K; Nd(C1O₄)₃(aq), Eu(C1O₄)₃(aq), Er(C1O₄)₃(aq), and Yb(C1O₄)₃(aq) from 283.2 K to 328.2 K; and HCF₃SO₃(aq) and NaCF₃SO₃(aq) from 283.2 K to 328.2 K, were analysed by means of the Pitzer equations to derive Cᴼp,₂, Vᴼ₂, and expressions for the excess properties. The revised Helgeson-Kirkham-Flowers (HKF) model has been used to represent the temperature dependence of these standard partial molar properties within the experimental uncertainty. Plots of Cᴼp,₂ and Vᴼ₂, at T = 298.15 K against the ionic radius of the six lanthanide cations clearly display the discontinuous behaviour known as the "gadolinium break". It was found that the ionic-radius dependence of Vᴼ₂ is consistent with changes in the primary hydration number, while the effect of temperature on the behaviour of Cᴼp,₂ across the series suggests that secondary sphere hydration has a major effect on C° 2. -- Densities of NaCF₃SO₃(aq) and Gd(CF₃SO₃)₃(aq) were measured with the platinum-cell vibrating tube densimeter at temperatures from 323 K to 600 K and at pressures up to 20 MPa. Apparent molar volumes for NaCF₃SO₃(aq) and Gd(CF₃SO₃)₃(aq) calculated from the measured densities were represented by the Pitzer ion-interaction treatment. The temperature and pressure dependence of Vᴼ₂ and the second viriai coefficients in the Pitzer equation were expressed by empirical expressions in which the compressibility of water was used as an independent variable. These treatments led to values of Vᴼ₂(NaCF₃SO₃, aq) from 283 K to 573 K and Vᴼ₂Gd(CF₃SO₃)₃, aq) from 278 K to 473 K as functions of temperature and pressure, which are the first reported in the literature. The conventional values of Vᴼ₂(Gd³⁺, aq) calculated from these data and Vᴼ₂(Na⁺, aq) from the literature are in excellent agreement with extrapolations of low-temperature values of Vᴼ₂(Gd(C1O₄)₃, aq) based on the HKF approach. It was found that the effect of pressure on Vᴼ₂ for Gd(CF₃SO₃)₃(aq) was more pronounced than that for common 1:1 and 2:1 aqueous electrolytes at temperatures near 298 K, and that this behaviour could be explained by the larger primary hydration shell for trivalent lanthanide cations. -- Densities of {xCH₃OH + (1 - x)H₂O} relative to water were measured in the vibrating tube densimeter at the temperatures T = (323, 373, 423, 473, 523, and 573 K) and at pressures of 7.0 MPa and 13.5 MPa. Excess molar volumes VᴱM for {xCH₃OH + (1 - x) H₂O} were calculated from the experimental densities for the mixtures, using accurate equations of state for water and methanol. The data were treated with an extended corresponding-states model based on the properties of pure water. An empirical function was used to fit small differences between the compression factors of {xCH₃OH + (1 - x) H₂O} and the compression factor of H₂O at the same reduced temperature and the same reduced pressure. The corresponding-states treatment reproduces the measured densities to within the experimental uncertainty of 0.0004 g-cm⁻³ at all of the temperatures and pressures studied, except at T = 573 K and p = 13.5 MPa. The densities, excess molar volumes, partial molar volumes, isothermal compressions, and cubic expansion coefficients from the model are consistent with the limited literature data available. The behaviour of VᴱM at T = 573.6 K, and p = 13.7 MPa indicates either a very narrow region of (vapour + liquid) phase separation, or near-critical behaviour at x = 0.44 with the critical pressure pc ≤ 13.5 MPa.