Thermodynamic Properties Of Dilute Solutions Research Articles

Thermodynamic properties of dilute solutions of various elements in liquid lead

Published evidence about the thermodynamic properties of dilute solutions of various elements in liquid lead are reviewed. Particular attention is given to the characteristic impurities in lead smelted both from ores and from secondary raw materials and also to alkali and alkaline-earth metals whose behavior is of interest for electrolysis processes with a liquid lead cathode. In experimental data processing, the activity coefficient of a component at infinite dilution was estimated by using, when necessary, the analytical representation of the concentration dependence of thermodynamic functions and various graphical extrapolation procedures.

Thermodynamic Properties of Dilute Solutions of Lead(II) Oxide in an Equimolar Mixture of KCl–PbCl2

The electromotive forces of the electrochemical system (GC)Pb|(1–N)·KCl–PbCl2+N·PbO|ZrO2(Y2O3)|O2(Pt) in the mole fraction range of PbO 0.0016 to 0.0732 were measured at temperatures of (776, 821, and 874) K. The activities, the activity coefficients, and the basic thermodynamic functions of lead(II) oxide for dilute solutions were calculated from the experimental EMF values.

Mean Activity Coefficients and Osmotic Coefficients in Aqueous Solutions of Salts of Ammonium Ions with Univalent Anions at 25 °C

The Hückel equation used in this study to describe the thermodynamic properties of dilute solutions of the ammonium salts of NH4Cl, NH4Br, NH4I, NH4NO3, NH4SCN, and NH4H2PO4 up to 1.5 mol·kg–1 is consisted of two electrolyte-dependent parameters B and b1. Parameter B is linearly related to the ion-size parameter a* in the Debye–Hückel equation, and parameter b1 is the coefficient of the linear correction term with respect to the molality. This coefficient is associated with the hydration numbers of the ions forming the electrolyte. For NH4ClO4 solutions, the estimated Hückel equation applies up to 2.1 mol·kg–1, and the equation was obtained from the isopiestic data measured by Esval and Tyree (J. Phys. Chem.1962, 66, 940–942) against KCl solutions. For molalities above 1.5 mol·kg–1 (in the best case up to 10 mol·kg–1), an extended Hückel equation was used. For this equation, the Hückel equation is supplemented with a quadratic term in molality, and the coefficient of this term is parameter b2. All of the parameters for the Hückel equations of NH4Cl and NH4NO3 solutions were estimated from isopiestic data of Wishaw and Stokes (Trans. Faraday Soc.1953, 49, 27–31). The former data were measured against KCl solutions and the latter against NaCl solutions. The Hückel parameters for NH4Br, NH4I, NH4SCN, and NH4H2PO4 solutions were estimated from the data measured by Covington and Irish (J. Chem. Eng. Data1972, 17, 175–176), Bonner (J. Chem. Eng. Data1976, 21, 498–499), Covington and Matheson (J. Solution Chem.1977, 6, 263–267), and Filippov et al. (J. Appl. Chem., U.S.S.R., 1985, 58, 1807–1811), respectively, using the same experimental technique against NaCl solutions. In all of these estimations, the Hückel parameters of a recent KCl and NaCl study (J. Chem. Eng. Data2009, 54, 208–219) were used for the solutions of the reference electrolyte. In the tests of the new parameter values, the cell potential difference, vapor pressure, and isopiestic data available in the literature were used. These data support well the tested Hückel parameters in most cases at least up to 3.5 mol·kg–1. Reliable thermodynamic activity quantities for ammonium salt solutions are, therefore, obtained using the new Hückel parameters. The activity coefficients, osmotic coefficients, and the vapor pressures obtained using these equations are tabulated here at rounded molalities. These values were compared to those suggested by Robinson and Stokes (Electrolyte Solutions, 2nd ed.; Butterworths Scientific Publications: London, 1959), to those obtained using Pitzer equations (Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, 1991; pp 100–101), and to those obtained using the extended Hückel equations presented by Hamer and Wu (J. Phys. Chem. Ref. Data1972, 1, 1047–1099).

Thermodynamic properties of dilute solutions of selenium in liquid lead

The activity coefficients and activities of selenium in liquid alloys of the Pb-Se system at low selenium content were estimated from the available experimental data.

Thermodynamic properties of dilute solutions of bismuth in liquid lead

Value of the limiting activity coefficients in liquid alloys of bismuth with lead at 673, 773 and 873 K were assessed with application of various analytical expressions.

Thermodynamic properties of dilute solutions of antimony in liquid lead

Various methods of assessing the limiting activity coeffi cient of antimony and the area of the Henry’s Law holding in liquid alloys of antimony-lead system were considered.

Jacobus Henricus van’ t Hoff

J H van’ t Hoff is considered as one of the greatest chemists of all time. He started his career as an organic chemist. He solved the vexing problem of optical isomerism by proposing an asymmetric tetrahedral carbon bonded to form different groups. He extended this to include geometric isomerism, and to compounds with heteroatoms in place of asymmetric carbon. Thus he established the ‘chemistry in space’ or stereochemistry. He moved on to work on reaction kinetics, equilibria, thermodynamic properties of dilute solutions and related areas. He laid the foundation for physical chemistry through these discoveries and was awarded the first Nobel Prize in Chemistry in 1901. van’ t Hoff died of tuberculosis at a relatively early age of 59.

Excess thermodynamic properties of dilute solutions

Appropriate equations for representation of excess thermodynamic properties of moderately dilute solutions are presented with discussions. Illustrative examples are given, based largely on the experimental results of Morita et al. It is shown that the statistical thermodynamic treatments with enumeration of configurations, and with the free volume concept yield the best existing equations. Future developments will depend on realistic enumeration of configurations with models having attractive and repulsive forces. The lack of adequate data on the physical properties, such as the excess volume, electronic configuration, etc., have discouraged further realistic developments.

Solubility near the solvent's critical point

The thermodynamic properties of dilute solutions near the critical point of the solvent — such as phase equilibria, critical lines, partial molar properties, Henry constants, K factors, and solubility — are all shown to be determined by the critical value of one thermodynamic derivative, ( ϖP/ ϖχ) V, T c , which we call the Krichevskii parameter. This parameter also governs the linear increase of In χx with density in supercritical solvents. We relate the derivative to direct correlation function integrals. We make some remarks about the nature of the divergence of total correlation function integrals. Contrary to statements we made in the literature, the divergence of the partial molar volume of the solute does not lead to an additional increase of solubility in dilute supercritical solutions, as we will show here.

Modelling aqueous solutions near the critical point of water

We review the thermodynamic properties of dilute solution near the critical point of the solvent. Two examples are discussed, a solution of a non-electrolyte and a solution of an electrolyte. The limiting behavior of the electrolyte solutions is modelled with a Debye-Huckel term in the Helmholtz free energy. The partial molar properties, in particular the volume and isobaric thermal expansion are examined in detail. The derivation of these properties is introduced by considering the geometry of the thermodynamic surfaces near to and far from the critical point of the solvent. We conclude that the properties of solutions near the solvent critical point are dominated by that feature; solution properties cannot be adequately modelled without including the functional forms associated with the critical point.

Thermodynamic properties of dilute solutions of (C2-C6) n-alkanoic acids in sulfolane

Mesures a 303,16 K des volumes molaires partiels des 5 premiers membres de la serie des acides n-alcanoiques en solutions diluees dans le sulfolane

ChemInform Abstract: THERMODYNAMIC PROPERTIES OF DILUTE SOLUTIONS OF CARBON MONOXIDE IN A HYDROCARBON

Chemischer InformationsdienstVolume 16, Issue 17 Article ChemInform Abstract: THERMODYNAMIC PROPERTIES OF DILUTE SOLUTIONS OF CARBON MONOXIDE IN A HYDROCARBON J. F. CONNOLLY, J. F. CONNOLLYSearch for more papers by this authorG. A. KANDALIC, G. A. KANDALICSearch for more papers by this author J. F. CONNOLLY, J. F. CONNOLLYSearch for more papers by this authorG. A. KANDALIC, G. A. KANDALICSearch for more papers by this author First published: April 30, 1985 https://doi.org/10.1002/chin.198517068AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume16, Issue17April 30, 1985 RelatedInformation

Thermodynamic properties of dilute solutions of carbon monoxide in a hydrocarbon

Partial molar volumes, enthalpies, entropies, and energies have been obtained for dilute solutions of carbon monoxide in liquid benzene and in liquid n-octane up to 523 K and 15 MPa. As for (hydrogen + a hydrocarbon), the ratio a 12 a 11 of the cohesive energy densities is independent of hydrocarbon type.

Thermodynamics of solutions of hydrogen in palladium–manganese alloys. II. Pd to PdMn

The thermodynamic properties of dilute solutions of hydrogen in alloys of palladium with up to 50 at. % manganese have been studied by a combined calorimetric-equilibrium method between 555 and 909 K. The results are compared with corresponding data for hydrogen in pure palladium and in the alloy Pd3Mn; the latter undergoes an order–disorder transformation at 750–800 K. In some cases data also were obtained for deuterium; a comparison between the properties of the two hydrogen isotopes provides approximate information on the vibrational frequency of hydrogen in the alloy. For the disordered solid solution of manganese in palladium we find little change in the vibrational frequency with alloy composition. Particular interest is attached to the ’’decomposition’’ of the excess Gibbs energy into its enthalpy and entropy ’’parts’’. Our results show that for alloys up to 25 at. % manganese increasing manganese content. The dependence of the enthalpy on temperature also becomes increasingly sharp and there is a corresponding large increase in the excess entropy of hydrogen. These changes are attributed to increased occupation by the hydrogen atoms at higher temperatures of energetically less favorable sites.

A calorimetric-equilibrium study of dilute solutions of hydrogen and deuterium in palladium at 555 to 909 K

The thermodynamic properties of dilute solutions of hydrogen and deuterium in palladium have been studied by a calorimetric-equilibrium method in the temperature range 555–909 K. The new enthalpy data are compared with data for lower temperatures reported in the literature, and are used to obtain analytical expressions for the relative partial enthalpies and heat capacities of hydrogen and deuterium. The derived partial heat capacities are larger than values calculated from the harmonic oscillator model and show distinct maxima in the temperature range 500–600 K. It is possible that this may reflect a localized-mobile transition of the hydrogen atoms.

Thermodynamics of solutions of hydrogen in palladium–manganese alloys. I. Pd3Mn from 555 to 909 K

The thermodynamic properties of dilute solutions of hydrogen and deuterium in Pd3Mn have been determined by a calorimetric-equilibrium method between 555 and 909 K. This alloy undergoes an order–disorder transition at 750–800 K, i.e., in the temperature range of our measurements. In this temperature region the thermodynamic properties of hydrogen change very significantly. The partial entropies of hydrogen in the alloy are quite low compared to the values in pure palladium; this points toward a highly nonrandom distribution of the hydrogen atoms among the available interstitial sites. From the isotope effect the vibrational frequencies of hydrogen are calculated to be 600 cm−1 at 555 K, 650 cm−1 at 700 K, 770 cm−1 at 777 K, and 860 cm−1 at 807 K, i.e, increasing significantly with increasing temperature. Note in particular the increase in frequency in the transition region. This change correlates with a reduction in the partial entropy of hydrogen of about 1.8 cal K−1 mol−1 from the ordered to the disordered alloy.

Thermodynamics of dilute solutions of hydrogen and deuterium in manganese at 555 to 700 K

The thermodynamic properties of dilute solutions of hydrogen and deuterium in manganese have been studied between 555 and 700 K. If the harmonic-oscillator model is assumed, we calculate from the isotope effect at 555 K a vibrational wavenumber of hydrogen of 980 cm −1. The corresponding vibrational entropy of hydrogen is quite large compared with the observed values. This indicates that the number of interstitial sites accessible to hydrogen is significantly smaller (about 1 2 ) than the number of manganese atoms.

Solution properties of poly( N-vinyl carbazole)—III : Excluded volume theories and theta temperature

Thermodynamic properties of dilute solutions of poly- N-vinylcarbazole have been studied by viscometry in chlorobenzene and nitrobenzene at several temperatures. The validities of some excluded volume theories have been tested and the unperturbed dimensions have been calculated; for two of these theories in particular, no dependence of unperturbed dimensions on temperature and solvent has been found. The viscometric equations have also been determined. The theta temperatures for PNVC in chlorobenzene and nitrobenzene are − 36.5 and − 20.4°C respectively.

High temperature thermodynamics of dilute solutions of hydrogen in palladium–copper alloys

The thermodynamic properties of dilute solutions of hydrogen and deuterium in palladium-copper alloys with copper contents of 10, 25, and 40 at.% have been determined by a calorimetric-equilibrium method at 555 K. The results are compared (a) with corresponding data for hydrogen in palladium–silver at the same temperature and (b) with equilibrium data for palladium–copper measured near room temperature. (1) The partial excess entropies of hydrogen in dilute solutions in palladium–copper alloys are reduced significantly compared to pure palladium. In palladium–copper this effect is only about one-half that in palladium-silver. Even so, it is believed to reflect in both systems a nonrandom distribution of the hydrogen atoms among the available interstitial sites. (2) It is shown that to a first approximation the dissolved hydrogen atoms may be considered to be isotropic, three-dimensional Einstein oscillators. In this approximation the observed differences between hydrogen and deuterium may be used to calculate the vibrational frequency of hydrogen. For palladium–copper these differences do not vary with copper content within experimental error. This points towards ?H being essentially independent of alloy composition. This behavior contrasts with that of hydrogen in palladium–silver, for which Picard et al. [J. Chem. Phys. 70, 2710 (1979)] recently found increasing values of ?H with increasing silver content. It is suggested that the different behavior of ?H in large measure may account for the observed difference between the concentration dependence of the excess entropy of hydrogen in palladium–copper and in palladium–silver.

Solution properties of poly( N-vinyl carbazole)—II. Thermodynamic properties in various solvents

Thermodynamic properties of dilute solutions of Poly- N-vinyl carbazole obtained by cationic polimerization have been studied by viscometry in various solvents. The validities of some excluded volume theories have been tested and the unperturbed dimensions have been calculated. The dependence of molecular dimensions, 〈 s 2〉, on molecular weight and viscometric equations have also been determined.