Excess Partial Molar Free Energy Research Articles

Isotope Effects in Aqueous Systems. Excess Thermodynamic Properties of 1,3-Dimethylurea Solutions in H2O and D2O

The osmotic coefficients of 1,3-dimethylurea-h2(DMUh2)/H2O and 1,3-dimethylurea-d2(DMUd2)/D2O solutions (1, 2, 4, 12, and 20 maq, 15 < t/°C < 80) were obtained from differential vapor pressure measurements. Excess partial molar free energies, enthalpies, and entropies for the solvent and their isotope effects were calculated from the temperature derivatives of the osmotic coefficients. New partial molar volume data are reported at 25 °C at low and intermediate concentrations. The thermodynamic properties of solution are compared with those of urea and discussed using the cage model of hydrophobic hydration. The results support the mixed (polar−apolar) character of this compound and show that its structural effect on water changes with temperature and concentration.

An electrochemical investigation of the thermodynamic properties of cerium stannide (CeSn 3) and liquid tincerium alloys

The thermodynamic properties of the intermetallic compound CeSn 3 and the tin-rich liquid tincerium alloys in equilibrium with CeSn 3 were studied by a high-temperature galvanic cell technique using the reversible concentration cell Ta, Ce∥CeCl 3, LiClKCl (eutectic)∥CeSn (two-phase alloy), Ta in the temperature range 723–873 K. The standard Gibbs energy of formation of CeSn 3 from pure solid cerium and pure liquid tin varies with temperature according to the equation ΔG f(CeSn 3) 0 = −260.08 + 0.0476 T (±2) kJ mol −1 The activity coefficients, excess partial molar free energies, enthalpies and entropies of cerium in the saturated liquid alloys have been computed from the e.m.f. data obtained in this study and the data for the solubility of cerium in liquid tin. The activity coefficients of cerium in liquid tin with reference to solid cerium can be expressed as G Ce xs = RT ln τ Ce = −249 + 0.059 T (±2) kJ mol −1

溶融Ｃｕ‐Ｚｎ‐Ｆｅ系合金の亜鉛の活量

In order to obtain the fundamental information regarding a new zinc smelting process where zinc is extracted using molten copper as a solvent, the activity of zinc and two-phase region in the Cu-Zn-Fe ternary system were investigated by using the transportation method and the quenching technique respectively.The two-phase of molten Cu-Zn alloy and solid iron determined in this study extends widely in the composition region below 70 at% Zn at 1, 473 K in the Cu-Zn-Fe ternary system. The iron solubility in the Cu-Zn alloy exhibits constancy and is nearly 5.5 at% below 40 at % Zn in the molten alloy phase.The relation between the excess partial molar free energy of zinc, ΔGZnXS and (1-NZn) 2 on the constant composition ratio of NFe/(NFe+NFe) in the homogeneous melt may be expressed by a line, even if the free energies were calculated from the activity measurements at various temperatures between 1, 123 and 1, 373 K. The activity coefficients of zinc, extrapolated by using the relationship between ΔGZnXS and (1-NZn) 2, decrease with increasing iron content in the composition region below 60 at%Zn at 1, 473 K. Above this composition range, the activity coefficient increases.The large solubility of zinc in a molten copper phase is not expected for the new zinc smelting process, because the vapour pressure of zinc is very high even in the composition region of low zinc content in the Cu-Zn-Fe ternary system. Then, the extraction process would require large amount of molten copper to extract zinc from its sinter.

Vaporization study on M 2Zr ( M = FeandCr) by a mass-spectrometric method

The vapor pressures over Fe 2Zr and Cr 2Zr were measured by means of mass spectrometry in the temperature ranges of 1550–1756 K and 1476–1704 K, respectively. The thermodynamic activity of iron (or chromium) in Fe 2Zr(s) (or Cr 2Zr(s)) was determined from the vapor pressure of Fe(g) (or Cr(g)), which was the only gaseous species observed over each intermetallic compound. Applying the regular solution model with Kaufman and Bernstein parameters to the thermodynamic activity of iron (or chromium) determined experimentally, the thermodynamic activity of zirconium in Fe 2Zr (or Cr 2Zr) was calculated as a function of temperature. Thermodynamic quantities such as the partial molar enthalpy and entropy, the partial molar free energy of formation (mixing) and the excess partial molar free energies of iron (or chromium) and zirconium in Fe 2Zr (or Cr 2Zr) were calculated. The integral molar Gibbs free energies, enthalpies and entropies of formation of Fe 2Zr and Cr 2Zr were also calculated from the partial molar quantities. The enthalpy of formation of Fe 2Zr obtained in this study was in good agreement with a previous experimental value by high temperature calorimetry and fell between two predicted values by model calculation. The enthalpy of formation of Cr 2Zr determined in this study was close to one of the two calculated values reported previously. The stabilities (or formations) of Fe 2Zr and Cr 2Zr were briefly discussed in comparison with that of U-Zr solid solution.

Vapour pressure of aqueous tert.-butanol in the water-rich region: transition in the mixing scheme

The total vapour pressure of aqueous tetrt-butanol (TBA) was measured in small increments in the range x TBA < 0.2 at 25.15 and 30.00 ° C, where x TBA is the mole fraction of TBA in the liquid phase. The partial pressure of TBA, and hence the excess partial molar free energy of TBA, G m E(TBA), were calculated by the Boissonnas method. Since the values of the excess partial molar enthalpy, H m E(TBA), had been directly measured in small increments, the values of the excess partial molar entropy, S m E(TBA), were calculated accurately. From the concentration derivative of G m E(TBA), the Kirkwood-Buff parameters were calculated for the range x TBA < 0.05. The concentration dependence of the partial molar entropy, as well as that of the enthalpy, indicated that, at about x TBA = 0.045, there is a transition from one scheme of mixing in the solution to the other. As the temperature increases this threshold value decreases; there is a boundary which is marked by the maxima in various quantities that are proportional to the third derivative of the free energy. Below this boundary, the mixing scheme is consistent with such ideas as the “iceberg formation”, the “structure enhancement of the solvent water”, and the “hydrophobic interaction (attraction)”. The second scheme above this boundary appears to be that of TBA cluster formation.

Excess partial molar free energies and entropies in aqueous tert-butyl alcohol solutions at 25.degree.C

Excess partial molar free energies and entropies in aqueous tert-butyl alcohol solutions at 25.degree.C

Vaporization study on fission-produced noble metal alloys by mass-spectrometric method

Abstract The vapor pressures over the ϵ-phase of the MoxRuyPdz alloys (x = 0.20-0.45, y = 0.15–0.60, z = 0.20–0.40) were measured by means of mass spectrometry in the temperature range 1536–1791 K. Palladium vapor was observed as the only gaseous species. The chemical activities of palladium in the alloys, determined from the vapor pressures of Pd(g), were compared with those calculated on the basis of the regular solution model using the Kaufman and Bernstein parameters. Applying a least-squares fit to the chemical activity of palladium obtained experimentally in this study, the interaction parameters and the free energy of formation were determined for the regular solution model and the Hillert model. The vapor pressures of Mo(g) and Ru(g) over the Mo-Ru-Pd alloys were calculated using the regular solution model. Thermodynamic quantities such as the partial molar free energy of mixing, the excess partial molar free energy of palladium and the partial molar enthalpy and entropy of Pd(g) over the Mo-Ru-Pd alloys were also calculated from the palladium vapor pressures.

Thermodynamics of segregation in alloys

The segregation process is described in terms of thermodynamic equations that use concepts of excess partial molar free energies and activity coefficients. Using such generalized equations, simplified equations are developed that can be used to check the segregation behavior in terms of thermodynamic quantities that are generally available in the literature. These simplified equations can be used to represent segregation semiquantitatively in many situations, including those where the elements form highly stable chemical compounds, such as sulfides, borides, and phosphides. The validity of our equations is checked by comparing the calculated segregation values with those observed on the surface of Ni, Cr, Al, Y, and NiCrAl(Y) alloys containing small concentrations of sulfur.

Thermodynamic properties of DCl in D2O solution from 5 to 50�C

The themodynamic properties of solutions of deuterium chloride (DCl) in deuterium oxide (D2O) have been determined from emf measurements of the electrochemical cell without transference from 5 to 50°C, and from 0.002 to 1.0 mol-kg−1. The standard potential of the silver/silver chloride electrode relative to the platinum/deuterium electrode has been determined. An equation for the Gibbs energy as a function of temperature has been derived from which the enthalpy, entropy, and heat capacity have been computed. Equations for the activity coefficient and the osmotic coefficient of DCl in D2O have been developed. The excess Gibbs energy of the solution and the excess partial molar free energy as a function of temperature have been calculated, from which the other excess thermodynamic properties have been computed. The values for the heat capacity and the apparent molar heat capacity have been compared with calorimetric data in the literature. The relative partial molar enthalpy has been calculated. The solvent isotope effect on the excess thermodynamic functions is discussed.

Selectivity of complexing gas chromatographic stationary phases containing lanthanide β-diketonates

The Rohrschneider—McReynolds series of organic compounds has been used to determine the polarity of gas chromatographic stationary phases containing tris-β-diketonates of praseodymium and europium, dissolved in poly(dimethylsiloxane). The selectivity of the stationary phases studied has been characterized by using the differential excess partial molar free energy of mixing within the temperature range of 90–130°C. Changes in selectivity observed with increasing temperature are discussed in the context of the proposed complexation scheme.

Isotope effects in aqueous systems. 12. Thermodynamics of urea-h4/water and urea-d4/water-d2 solutions

Differential vapor pressure measurements yielding osmotoic coefficients and osmotic coefficient isotope effects for urea h/sub 4//H/sub 2/O and urea-d/sub 4//D/sub 2/O solutions (4, 8, 12, 16, 18, 20 m, and saturated) are reported over the temperature range 15 to 60/sup 0/C. Solubilities and apparent molar volumes and their isotope effects (IE's) have also been measured. From these various data as supplemented by information from published sources, we have calculated standard-state (infinite-dilution) and excess partial molar free energies, volumes, enthalpies, and expansivities (and their isotope effects) as appropriate. Raman spectra in the librational and OH and OD stretching regions are reported. The various data are discussed in terms of solution models of the urea/water system in the context of the theory of isotope effects in condensed phases.

A note on the pyrrhotite-sulfur vapor equilibrium

In the temperature range 600 degrees to 900 degrees C, the activity coefficients of FeS and S in pyrrhotite may be expressed in terms of a two-constant Margules solution model, with a linear temperature dependence of the excess partial molar free energy at infinite dilution of the two components. The pyrrhotite solid solution exhibits no measurable excess volume of mixing; for this reason, the activity coefficients are independent of pressure. This fact and the simple form of the activity coefficients facilitate the calculation of equilibria involving pyrrhotite at pressures other than one atmosphere.

Thermodynamic properties of α Cu-ln alloys by the method of atomic absorption

Atomic absorption spectroscopy was used to measure the vapor pressure of indium over seven binary alloys of the α Cu-ln system. Thermodynamic activity, partial molar enthalpy and partial molar entropy of indium were calculated from the vapor pressure and its tem-perature coefficient. The activity coefficient obtained has a large value for alloys of this type, even when referred to a solid reference state. The partial molar enthalpy values are lower than expected for a trivalent solute. The excess partial molar free energy, when plotted against atom fraction, shows a minimum at about 7 at. pct indium. The reason for the occurrence of a minimum in\(\overline {\Delta G} _{^{In} }^{XS} \) is not known.

Thermodynamische Betrachtung über die Bildung der Komplex-Ionen in des geschmolzenen ThCl4-NaCl Systems

The electromotive force and its temperature-dependence of fused salts of the ThCl 4 –NaCl system were measured with a Th(s)/ThCl 4 –NaCl(l)/Cl 2 (g) cell using highly purified ThCl 4 (ThCl 4 0.22–0.70 mole fraction, 600°–750°C). To discuss the formation and existence of complex ion in the melts, the equation of excess stability d\bar F 1 E /d(1- N 1 ) 2 , where N 1 is the mole fraction of ThCl 4 and \bar F 1 E the excess partial molar free energy of ThCl 4 , derived by Darken was adopted. Curves of the excess stability plotted against N 1 show a maximum at around N 1 =0.35 corresponding to the congruently melting compound Na 2 ThCl 6 . Meanwhile, plots of the equivalent conductivity and the isotherms, calculated from the previously reported values against N 1 revealed a large negative deviation from the additivity at N 1 =0.33(550°C–750°C). From these both results the existence of the anionic complex ion [ThCl 6 ] 2- in the fused state was inferred.

A Consideration on the Excess Partial Molar Free Energy of Fused NaCl and KCl Containing Divalent Salts

A Consideration on the Excess Partial Molar Free Energy of Fused NaCl and KCl Containing Divalent Salts

ニッケルおよびコバルトに溶解する炭素飽和溶解度および第3元素の影響

1) The solubility of graphite in pure cobalt and nickel was determined at various temperatures. Temperature dependence of graphite solubility in nickel and cobalt was as follows:a) Nickel logNc=-875/T 0.521b) Cobalt logNc=-1050/T-0.265(2) The solubility of graphite in nickel-cobalt solutions was also determind at 1400°C. From these data, excess partial molar free energy was calculated to be about -300 cal/gram atom, and it showed that the solution of this alloy was not an ideal.(3) Effects of alloying elements such as Si, Mn, Cr, V and Mo on the solubility of graphite in liquid Ni and Co were investigated at 1400°C. The interaction parameter of Wagner εXC=-(∂ln NXC/∂NX) was calculated and found comparable with that of liquid iron.(4) With the systems Ni-Cr-Mn-C and Co-Cr-Mn-C the solubilities of graphite were determind at 1400°C. The experimental results were in good agreement with calculations from the ternary systems in dilute solution.

Thermodynamics of liquid Mg-Bi alloys

Thermodynamic studies on liquid Mg-Bi alloys have been carried out using the e.m.f. method. A cell is described, suitable for measuring Mg activities in this system. Values of the excess partial molar free energy, the relative partial molar free energy, entropy, and enthalpy are listed along with the corresponding integral quantities. The results are compared with previous vapor pressure and calorimetric measurements as well as investigations of the phase diagram. Wagner's interpretation in terms of electronic constitution is consistent with the present data.