H.F. Holmes

Thermodynamics of aqueous association and ionization reactions at high temperatures and pressures

Electrochemical and electrical conductance cells have been widely used at ORNL over the years to quantitatively determine equilibrium constants and their salt effects to 300°C (EMF) and 800°C (conductance) at the saturation pressure of water (EMF) and to 4000 bars (conductance). The most precise results to 300°C for a large number of weak acids and bases show very similar thermodynamic behavior, which will be discussed. Results for the ionization constants of water, NH3(aq), HCl(aq), and NaCl(aq), which extend well into the supercritical region, have been fitted in terms of a model with dependence on density and temperature. The entropy change is found to be the driving force for ion-association reactions and this tendency increases (as it must) with increasing temperature at a given pressure. Also, the variation of all thermodynamic properties is greatly reduced at high fixed densities. Considerable variation occurs at low densities. From this analysis, the dependence of the reaction thermodynamics on the P-V-T properties of the solvent is shown, and the implication of large changes in hydration for solutes in the vicinity of the critical temperature will be discussed. Finally, the change in the molar compressibility coefficient for all reactions in water is shown to be the same and dependent only on the compressibility of the solvent.

The enthalpy of dilution of HCl(aq) to 648 K and 40 MPa thermodynamic properties

Abstract Enthalpies of dilution of HCl(aq) have been measured to 648 K and 40 MPa over the molality range of about 0.01 to 15.6 mol·kg −1 . At temperatures above 523 K the experimental results approach infinite dilution with a slope greater than the limiting-law slope, a clear indication of ion association. An analysis of the enthalpies of dilution in combination with existing thermodynamic results has produced a comprehensive model for the thermodynamic properties of HCl(aq). Three versions of the ion-interaction model were used depending on the range of temperature or molality. The unmodified ion-interaction model of Pitzer was adequate through 523 K and 7 mol·kg −1 . Addition of a fourth coefficient extended the molality range to 16 mol·kg −1 through 523 K, and for temperatures above 523 K the second coefficient was given additional dependence on molality (a non-zero β (2) parameter). By using the density of water as an independent variable each version of the ion-interaction model covers the entire range of pressure through 40 MPa and the number of adjustable parameters is minimized. A comparison of the thermodynamic properties of HCl(aq) with those of NaCl(aq) demonstrated that HCl(aq) is somewhat more associated than NaCl(aq) at high temperatures and the enthalpy of ionization makes a significant contribution to the observed apparent relative molar enthalpy of HCl(aq).

The enthalpy of dilution of aqueous sodium chloride to 673 K using a new heat-flow and liquid-flow microcalorimeter. Excess thermodynamic properties and their pressure coefficients

Abstract A new heat-flow and liquid-flow calorimeter utilizing a Calvet microcalorimeter is described; it can be used to measure excess enthalpies of liquids at temperatures and pressures up to 700 K and 50 MPa. The sensitivity of the calorimetric apparatus permits observations to be made on sufficiently dilute solutions to allow good extrapolations to infinite dilution required for derivation of excess thermodynamic properties as well as standard-state quantities. The enthalpies of dilution of aqueous solutions of NaCl from 0.1 to 5 mol·kg −1 at temperatures from 323 to 673 K have been measured. Isobaric observations were made at two different pressures at each experimental temperature which permitted derivation of pressure coefficients for the first time. The following excess thermodynamic properties have been calculated from the results from 0.1 to 5 mol·kg −1 at the saturation vapor pressure of water and from 373 K to the temperature indicated: apparent relative molar enthalpy L φ (623 K), activity coefficient λ(623 K), osmotic coefficient φ(623 K), relative partial molar enthalpy L 2 (623 K), and excess molar heat capacity C p , m E (523 K). Pressure coefficients of these excess properties have been calculated from the results. No values of the excess thermodynamic properties for any electrolyte have been previously available above 573 K. In addition, all these excess properties except C p , m E have been calculated to the supercritical temperature 673 K and 41.5 MPa. Comparisons with values in the literature demonstrate that the calorimeter is capable of precise enthalpy measurements which lead to accurate thermodynamic properties and their pressure coefficients at high temperatures and pressures.

Isopiestic studies of aqueous solutions at elevated temperatures I. KCl, CaCl2, and MgCl2

Abstract Isopiestic studies have been made on aqueous solutions of KCl, CaCl2, and MgCl2 over the temperature range 382 to 474 K. Sodium chloride served as the reference solution and provided the basis for the calculation of osmotic coefficients. The molality range covered in this study correspond to about 1 to 6 mol kg−1 for NaCl. An equation recently developed by Pitzer was fitted to each set of osmotic coefficients with a standard deviation of fit (in the osmotic coefficient) ranging from 0.0009 to 0.0029. Parameters obtained from the fit were used to calculate activity coefficients. The activity coefficients showed a monotonic decrease with increasing temperature and became much less dependent on molality at the higher molalities. Osmotic coefficients of KCl and CaCl2 solutions are consistent (by extrapolation) with existing low-temperature (

CaCl2(aq) at elevated temperatures. Enthalpies of dilution, isopiestic molalities, and thermodynamic properties

Enthalpies of dilution of CaCI2(aq) have been measured for molalities ranging from 0.008 mol·kg−1 to 7.26 mol · kg−1, at temperatures from about 298 K to 526 K, and for pressures of approximately 7 MPa to 40 M Pa. Isopiestic molalities of CaCI2(aq) were measured over the temperature range of 444 K to 524 K at molalities ranging from 0.55 mol · kg−1 to 4.8 mol · kg−1 with NaCl(aq) serving as the reference electrolyte. The results can be described quite well within the framework of the ion-interaction model. Our results have been combined with other thermodynamic results for CaCl2(aq), including heat capacities and densities, to produce a general model for the thermodynamic properties of CaCl2(aq) which is valid for molalities to 4.6 mol · kg−1 and pressures to 40 MPa over the temperature range 270 K to 526 K. The model is based on the ion-interaction treatment of Pitzer and allows for a small amount of ion association at the highest temperatures by using the β(2) parameter in the second virial coefficient and making the α1 parameter linearly dependent on temperature. For temperatures greater than 523 K, a description of the thermodynamic properties of CaCl2(aq) will require explicit consideration of ion association.

Isopiestic studies of aqueous solutions at elevated temperatures II. NaCl + KCl mixtures

Abstract Isopiestic studies have been made on aqueous solutions of the mixed electrolyte NaCl + KCl over the temperature range 383 to 474 K. Sodium chloride served as the isopiestic standard for the calculation of osmotic coefficients. The molality range covered in this study corresponded to about 0.6 to 6 mol kg−1 for NaCl. The system of equations developed by Pitzer was fitted to each set of osmotic coefficients with a standard deviation of fit (in the osmotic coefficient) ranging from 0.0025 to 0.0044. Only one mixing parameter (in addition to the pure-electrolyte parameters) was necessary to describe the results adequately. Activity coefficients for NaCl and KCl in the mixed electrolyte system were calculated from the equations. The activity coefficients showed a monotonic decrease with increasing temperature and became much less dependent on molality at the higher molalities. The activity coefficient of NaCl is much more dependent on composition than that of KCl. The trace activity coefficients of NaCl and KCl are very nearly equal over this temperature range. The ability to describe the NaCl + KCl system with only one mixing parameter in Pitzers equation is equivalent to Harneds rule. Excess Gibbs free energies calculated from the mixing parameter were, to a very good approximation, independent of temperature.

pH, Definition and measurement at high temperatures

In this review paper, the NBS scale and its limitations are briefly discussed. The magnitude of liquid junction potentials and some calculated values are presented. The use of a molality scale for hydrogen electrode concentration cells at high temperatures is described, and results from measurements on ionization equilibria are summarized. Use of this scale is also recommended for certain circumstances with cells without liquid junction. As an alternative activity scale, use of the Pitzer ion-interaction treatment for ions is recommended for special cases. Finally, reference data are presented for γ±HCl in HCl(aq) to 350°C and (HCl+NaCl)(aq) to 200°C that were derived by use of the Pitzer ion-interaction treatment.

Isopiestic studies of aqueous solutions at elevated temperatures VIII. The alkali-metal sulfates

Abstract Osmotic coefficients of aqueous solutions of the alkali-metal sulfates over the temperature range 383 to 498 K have been obtained from isopiestic comparisons with NaCl(aq). The ion-interaction model was fitted, by a least-squares computation, to the experimental results. A value of 1.4 for the fixed parameter α gave a better overall fit than the normally used 2.0. In this temperature range the osmotic coefficients of all four solutions decreased with increasing temperature as did activity coefficients calculated from the model. Of the four salts, Cs 2 SO 4 is the most individualistic. For Na 2 SO 4 (aq), there is acceptable agreement with previously reported results.

Isopiestic studies of aqueous solutions at elevated temperatures VII. MgSO4 and NiSO4

Isopiestic measurements have been made on MgSO4(aq) and NiSO4(aq) at 383.14 K with NaCl(aq) serving as the reference electrolyte. Irreversible solubility effects prevented successful measurements at higher temperatures. Osmotic coefficients at 383.14 K are smaller and less dependent on molality than at 298.15 K. The ion interaction model, as modified for 2-2 electrolytes, was fitted to the osmotic coefficients. Only three of the four parameters of the model could be evaluated, thereby precluding the direct calculation of activity coefficients from the isopiestic results. Combination of the present results with published freezing temperatures and enthalpies does permit the computation of activity coefficients in the case of MgSO4(aq). At 383.15 K the activity coefficient of MgSO4(aq) becomes quite small (<0.05) at very moderate molalities (0.5 mol·kg−1). Because of uncertainties in the calculations only general observations concerning trends in the activity coefficient at elevated temperatures and high molalities are warranted.

Isopiestic studies of H2SO4(aq) at elevated temperatures: Thermodynamic properties

Molalities of H 2 SO 4 (aq) and NaCl(aq) in isopiestic equilibrium have been measured over the temperature range 383.45 K to 473.21 K. Molalities of the reference salt (NaCl) ranged from about 0.5 mol·kg −1 to greater than 6 mol·kg −1 . The ion-interaction model gave an excellent fit of the experimental results when the partial ionization of the bisulfate ion was included in the calculations. Coupling available low-temperature results with the present work provided the basis for a relatively simple model for the osmotic and activity coefficients of aqueous sulfuric acid over the temperature range 298.15 K to 473.15 K. The model predicts that at high temperatures and moderate molalities the bisulfate ion is less than 1 per cent ionized. However, at the higher molalities ionization increases with increasing molality (re-ionization).