Joseph A. Rard

Thermodynamic properties of 0–6 mol kg–1 aqueous sulfuric acid from 273.15 to 328.15 K

Generalised equations are presented for an extended form of the Pitzer molality-based thermodynamic model, involving an ionic strength-dependent third virial coefficient. Compatibility with the established formulation is retained. Osmotic coefficients, emf measurements, degrees of dissociation of the HSO–4 ion, differential enthalpies of dilution and heat capacities for aqueous H2SO4 from 273.15 to 328.15 K, 0–6.1 mol kg–1 and at 1 atm pressure have been critically evaluated. Treating this solution as the mixture H+–HSO–4–SO2–4–H2O, and using hydrogen sulfate dissociation constants from the literature, the model parameters were fitted to the data yielding a self-consistent representation of activities, speciation and thermal properties together with the standard potentials of four electrochemical cells and standard-state heat capacities of the SO2–4 ion as functions of temperature. The model equations represent the experimental data accurately (without the use of mixture parameters θHSO4, SO4 and ψHSO4, SO4, H), and should yield values of the osmotic coefficient that are suitable for use as an isopiestic standard over this temperature and molality range. The new model will also enable improved prediction of the properties of mixed acidic sulfate systems.

Thermodynamics of electrolytes. 13. Ionic strength dependence of higher-order terms; Equations for CaCl2 and MgCl2

While the original ion-interaction (Pitzer) equations of 1973 were adequate for many electrolytes to the limit of solubility, additional terms are needed for some systems of large solubility. A simple pattern of ionic-strength dependence is proposed for third, fourth, and higher virial coefficients. It is found to be very effective in representing the complex behavior of CaCl2(aq) as well as that of MgCl2(aq) at 25°C. Equations without ion association are presented for each system that are valid for the full range to 11.0 and 5.9 mol-kg−1, respectively, as well as simpler equations for limited molality ranges.

Isopiestic Determination of the Osmotic Coefficients of Na2SO4(aq) at 25 and 50°C, and Representation with Ion-Interaction (Pitzer) and Mole Fraction Thermodynamic Models

Isopiestic vapor-pressure measurements were made for Na2SO4(aq) from 0.11 to3.74 mol-kg−1 at 25.00°C and from 0.12 to 3.57 mol-kg−1 at 50.00°C, usingNaCl(aq) as the reference standard. Published isopiestic data, direct vaporpressures, emfs of reversible cells, freezing temperature depressions, boilingtemperature elevations, heat capacities, and dilution enthalpies for this system have beencritically assessed and recalculated in a consistent manner. Parameters for Pitzersmodel and a mole fraction-based thermodynamic model were evaluated. Themole fraction-based thermodynamic model for Na2SO4(aq) is valid from thefreezing temperatures of the solutions to 150.5°C. Pitzers model represents theosmotic coefficients and emfs essentially to experimental accuracy at 25 and50°C provided that the third virial coefficient was ionic-strength dependent.

Isopiestic determination of the osmotic and activity coefficients of Rb 2SO4 (aq) and Cs 2SO 4(aq) at T = (298.15 and 323.15) K, and representation with an extended ion-interaction (Pitzer) model

Isopiestic vapor-pressure measurements were made for Rb 2SO 4(aq) from molalitym = (0.16886 to 1.5679 )mol · kg − 1atT = 298.15 K and from m = (0.32902 to 1.2282 )mol · kg − 1at T = 323.15 K, and for Cs 2SO4 (aq) from m = (0.11213 to 3.10815 )mol · kg − 1at T = 298.15 K and fromm = (0.11872 to 3.5095 )mol · kg − 1atT = 323.15 K, with NaCl(aq) as the reference standard. Published thermodynamic information for these systems were reviewed and the isopiestic equilibrium molalities and dilution enthalpies were critically assessed and recalculated in a consistent manner. Values of the four parameters of an extended version of Pitzer`s model for osmotic and activity coefficients with an ionic-strength dependent third virial coefficient were evaluated for both systems at both temperatures, as were those of the usual three-parameter Pitzer model. Similarly, parameters of Pitzer`s model for the relative apparent molar enthalpies of dilution were evaluated at T = 298.15 K for both Rb 2SO 4(aq) and Cs 2SO 4(aq) for the more restricted range of m⩽ 0.101 mol · kg − 1. Values of the thermodynamic solubility product Ks(Rb2 SO 4, cr, 298.15 K ) = (0.1392 ± 0.0154) and the CODATA compatible standard molar Gibbs free energy of formationΔfGmo (Rb 2SO 4, cr, 298.15 K ) = − (1316.91 ± 0.59)kJ · mol − 1, standard molar enthalpy of formationΔfHmo (Rb 2SO 4, cr, 298.15 K ) = − (1435.07 ± 0.60)kJ · mol − 1, and standard molar entropy S mo(Rb2 SO 4, cr, 298.15 K ) = (199.60 ± 2.88)J · K − 1· mol − 1were derived. A sample of one of the lots of Rb 2SO 4(s) used for part of our isopiestic measurements was analyzed by ion chromatography, and was found to be contaminated with potassium and cesium in amounts that significantly exceeded the claims of the supplier. In contrast, analysis by ion chromatography of a lot of Cs 2SO 4(s) used for some of our experiments showed it was highly pure.

Solubility determinations by the isopiestic method and application to aqueous lanthanide nitrates at 25°C

The isopiestic method is one of the most accurate methods for solubility determinations; an additional advantage is that solvent activity can be simultaneously determined for the saturated solution. In spite of this the method is rarely used for that purpose, and then almost exclusively for aqueous solutions at 25°C. This method is described, and its advantages and disadvantages discussed. Examples are given of the application of this method to solubility determinations, and new data are presented for the aqueous solubilities of Pr(NO3)3, Ho(NO3)3, Er(NO3)3, and Y(NO3)3 at 25°C. These new data are designed to refine results recently reviewed in the IUPAC Solubility Data Series.

Conversion of parameters between different variants of Pitzer’s ion-interaction model, both with and without ionic strength dependent higher-order terms

Abstract In this article we present a method for converting the parameters between different variants of Pitzer’s ion-interaction model for electrolyte solutions. The original version of Pitzer’s ion-interaction model contains an ionic-strength dependent virial coefficient for two-ion interactions, but the virial coefficient for three-ion interactions is set to an empirically determined constant value. Extended versions of the ion-interaction model are now in common use, where the virial coefficient for three-ion interactions is also allowed to depend on the ionic strength, and terms for higher-order interactions may also be included. These extended ion-interaction equations may have one or more additional ionic-strength dependent terms, and are particularly useful for representing the thermodynamic activity values of highly soluble electrolytes. However, the parameters of the original Pitzer model are often needed to supplement existing databases based on this model. Analytical equations presented here allow the parameters of these extended ion-interaction models to be directly transformed to the parameters of the original Pitzer model. The parameters of the original Pitzer model derived by this approach are compared against parameter values obtained by directly fitting the parameters to values of the osmotic coefficients calculated using the equations and parameters of the extended Pitzer models, with excellent agreement. This approach is demonstrated by application to Rb2SO4(aq), Cs2SO4(aq), NaNO3(aq), and Ca(NO3)2(aq).

Aqueous solubilities of praseodymium Europium, and lutetium sulfates

The aqueous solubilities of finely divided Pr2(SO4)3·8H2O(cr), Eu2(SO4)3·8H2O(cr), and Lu2(SO4)3·8H2O(cr) have been measured as a function of time at 25°C using isothermal saturation. Solubilities of the latter two salts showed a steady decrease with time, whereas Pr2(SO4)3·8H2O(cr) showed no such variation within the accuracy of the determinations. The turbidities of these filtered saturated solutions also decreased with time, and indicate that some colloidal rare earth sulfates were present. These colloidal particles (<0.2 μm) have a large surface area, which contributes to the Gibbs energy of the solid phase, thus giving rise to enhanced solubilities. The micro-particles also grow with time, thereby reducing the surface area contribution to the Gibbs energy and also leaving fewer particles to pass through the filters. Extrapolation of solubilities to infinite time gives the solubilities of macrocurstalline Eu2(SO4)3·8H2O and Lu2(SO4)3·8H2O. Previous solubility data for Lu2(SO4)3, at 20 and 40°C, yield an interpolated value at 25°C that is about 30% low. Densities were also measured at several concentrations of each salt.

Ternary diffusion coefficients of the brine systems NaCl (0.5 M)-Na2SO4 (0.5 M)-H2O and NaCl (0.489 M)-MgCl2 (0.051 M)-H2O (seawater composition) at 25°C☆

Abstract Mutual diffusion coefficients have been measured by Rayleigh interferometry for two ternary brine compositions at 25°C: NaCl (0.5 M)-Na 2 SO 4 (0.5 M)-H 2 O and NaCl (0.489 M)-MgCl 2 (0.051 M)H 2 O. The latter is a ternary analog of seawater. Four diffusion coefficients are required to characterize a ternary system. The data show that the cross term diffusion coefficients are significant, and cannot be neglected in accurate geochemical modeling. Since D 21 for NaCl-Na 2 SO 4 -H 2 O is negative, a sufficient gradient of NaCl can cause Na 2 SO 4 to move “uphill” against its own gradient. One of the cross term coefficients for NaClMgCl 2 -H 2 O is nearly as large as one of the main term coefficients.

Ternary mutual diffusion coefficients and densities of the system {z1NaCl +(1 –z1)Na2SO4}(aq) at 298.15 K and a total molarity of 0.5000 mol dm–3

Isothermal ternary mutual diffusion coefficients (interdiffusion coefficients) have been measured for the system {z1NaCl +(1 –z1)Na2SO4}(aq) at a constant total molarity of 0.5000 mol dm–3 and 298.15 K using either Rayleigh or Gouy interferometry. Measurements were performed at NaCl molarity fractions of z1= 1, 0.90, 0.75, 0.50, 0.25 and 0. Densities of all solutions used in the diffusion experiments were measured using pycnometers and/or a vibrating densimeter. Trace diffusion coefficients have been evaluated from these results for the Cl–(aq) ion in 0.5 mol dm–3 Na2SO4(aq) and for the SO42–(aq) ion in 0.5 mol dm–3 NaCl(aq). The resulting values are D*(Cl–)=(1.681 ± 0.002)× 10–9 m2 s–1 and D*(SO42–)=(0.900 ± 0.006)× 10–9 m2 s–1, respectively. At all compositions, (D21)v, the cross-term diffusion coefficient of Na2SO4 due to a concentration gradient of NaCl, was found to be negative, whereas (D12)v, the cross-term diffusion coefficient of NaCl due to a concentration gradient of Na2SO4, was found to be positive.

Effects of different sized concentration differences across free diffusion boundaries and comparison of Gouy and Rrayleigh diffusion measurements using NaCl−KCl−H2O

Diffusion was systematically studied in the ternary system NaCl (0.5M)−KCl (0.5M)−H2O at 25°C. There were four purposes. First, current methods to extractDij from Gouy and Rayleigh interferometry data depend on treating theDij as effectively constant. If concentration differences ΔCi across the boundary are large, this may not be true. To explore this issue, four sets of experiments were performed. Each set had four experiments with approximately the same total number of fringesJ. Each set also had the same corresponding ΔC1/ΔC2 ratios as the other three, but the ΔCi were adjusted such that the four sets hadJ≈30, 60, 90, and 120, respectively. Noclear dependence of theDij on ΔCi was found within their realistic errors. Second, the Gosting diffusiometer can yield both Rayleigh and Gouy fringe patterns during the same experiment. Therefore, theDij from both methods were compared, and agree well. Third, a new method for analyzing Gouy fringe positions (Miller; program TNY) can be compared to the classical one (Fujita-Gosting; program RFG). TheDij from both analyses agree well. Fourth, we compared results from the Gosting diffusiometer with those at the same composition from other diffusiometers: one data set by O[Donnell and Gosting from an older Gouy apparatus, and three Rayleigh sets at differentJ values from our older Model H diffusiometer. Results from older diffusiometers were more scattered, but correspondingDij agree within realistic errors. As reported previously, realistic errors are approximately four times the statistical errors obtained by least squares. Recommended Rayleigh and GouyDij are presented for this composition.