Partial Molar Excess Free Energy Research Articles

Thermodynamic investigations of Sn–Zn–Ga liquid solutions

Activity of zinc in liquid Sn–Zn–Ga alloys has been measured by electrochemical technique based on molten salt electrolyte galvanic cell in the temperature range 723–823 K along three pseudo-binary lines of Zn x (Sn y Ga 1− y ) 1− x where y = 0.75, 0.50 and 0.25. The excess molar free energy, enthalpy and entropy have been computed by the Darken's treatment of the ternary solutions using published data of the relevant binary solutions and ternary system investigated. Slope–intercept method has been used to compute the partial molar quantities. The activities of tin and gallium are computed from the partial molar excess free energies of three components at 750 K. The activities of all the three components show positive deviation from the Raoult's law. Thermodynamic properties of Sn–Ga binary system have been predicted at 750 K from the ternary data and compared with those published in the literature.

Formation Enthalpy, Free-Energy and Activity Coefficients of Sn-Pb Eutectic Solders

Based on Miedema’s model, the enthalpy of formation, excess free-energy and partial molar excess free-energy of Sn-Pb binary alloy solders were calculated. The model of the activity coefficient for each component in the solders was established. The diagrams of enthalpy of formation, free energy versus composition and activity versus composition and temperature as well as activity coefficients as a function of composition and/or temperature were drawn. And then the relationship between the activity coefficients of elements Sn/Pb in the solders and temperature was obtained. The approaches to reduction in the volatilization of lead at high temperature were proposed from the point of views that the lead pollution to environment results from its chemical activity in the solder alloys.

Thermodynamic Investigations of Cd-Zn-Ga Liquid Solutions

Activity of zinc in liquid Cd-Zn-Ga alloys has been measured by electrochemical technique based on molten salt electrolyte galvanic cell in the temperature range 723 to 823 K along three pseudo-binary lines of Zn-(Cd y Ga1−y ), where y = 0.75, 0.50, and 0.25. The excess molar free energy, enthalpy, and entropy were computed by the Darken’s treatment of the ternary solutions using published data of the relevant binary solutions and the ternary system investigated. The excess molar free energy surface of the ternary confirms substantially what one would expect from the knowledge of the corresponding curves of the component binary systems. The excess molar free energy surfaces have the maxima in the Cd-Ga side. The extremum value of molar excess free energy was found to be 3.24 kJ/mol (x Cd = 0.5, x Zn = 0.125, and x Ga = 0.375) at 800 K. The excess molar enthalpy curves have been found to be tilted toward the Zn-Cd and Cd-Ga sides. The extremum value of excess molar enthalpy was found to be 2.58 kJ/mol (x Ga = 0.3 and x Zn = x Cd = 0.35) at 800 K. The excess molar entropy surfaces have the maxima in the Zn-Ga side and minima in the Cd-Ga side. The slope-intercept method was used to compute the partial molar quantities. The activities are computed from the partial molar excess free energy for three components at 800 K. The isoactivity surfaces of the three components are depicted by the isoactivity lines. The activities of all three components show positive deviation from the Raoult’s law. The excess molar free energies of the Cd-Zn-Ga system obtained experimentally are compared with those estimated from the theoretical models.

Analyzing solubility and diffusion of solvents in novel hybrid materials of poly(vinyl alcohol)/γ-aminopropyltriethoxysilane by inverse gas chromatography

Novel hybrid materials were prepared through sol–gel reaction of poly(vinyl alcohol) (PVA) and γ-aminopropyltriethoxysilane (APTEOS). Solubility and diffusion behavior of a series of solvents in the PVA/APTEOS hybrid materials were studied by inverse gas chromatography (IGC) fitted with a packed column. Solubility thermodynamics parameters at infinite dilution, such as the activity coefficient Ω∞1 and the solubility coefficient S of solvents in the hybrid materials, the partial molar excess free energy of mixture ΔGm, and the Flory–Huggins interaction parameter χ∞12 were determined. The infinite dilution diffusion coefficients D∞ of the solvents in the hybrid materials were also calculated. Effects of APTEOS content in the stationary phase and the column temperature on the solubility and diffusion of solvents in the hybrid materials were investigated. The hybrid material containing 5.0 wt% APTEOS has the strongest interaction with water, the largest S and D∞ for water, and the hybrid material has a promising application in membrane separation, such as pervaporation dehydration of alcohol solution. The solubility parameter δ2 of the hybrid materials was estimated, and it decreased with increasing APTEOS content. The dependence of D∞ on temperature was in good agreement with the Arrhenius equation.

Thermodynamic studies on infinitely dilute solutions of xylenes and ethyltoluenes on 3,4′-dimethyl-4-[(4-chlorobenzyl)oxy]azobenzene liquid crystal

Specific retention volumes, activity coefficients at infinite dilution, partial molar excess free energies, partial molar excess enthalpies and entropies, partial molar enthalpies and entropies of solution for m-, p-, o-xylenes and m-, p-, o-ethyltoluenes in 3,4′-dimethyl-4-[(4-chlorobenzyl)oxy] azobenzene (DMCBOA) as solvent were determined. The separation of m-, p-, o-xylenes and m-, p-, o-ethyltoluenes was studied on a packed column with 2.5% DMCBOA on Chromosorb W HP 100–120 mesh. The synthesis of this liquid crystal is presented. At cooling, starting from isotropic liquid (129.5°C) a nematic phase of DMCBOA was identified in the range of 109.6–103.6°C, but m-, p-, o-xylenes and m-, p-, o-ethyltoluenes were separated at temperature ranges 65–48°C and 90–55°C, respectively.

Estimation of the surface tensions of binary liquid alloys

A simple method to estimate the surface tensions of binary alloys has been developed by assuming that the partial molar excess free energies are proportional to the number of nearest neighbors in both the bulk solution and in the surface itself. In order to estimate the surface tension of the alloys, excess free energies of the alloys and the surface tensions of the pure components are required. This method has been applied to ten alloys exhibiting positive, positive as well as negative, and negative deviations from ideal solution behavior. The method depends upon the reliability of the thermodynamic data for the bulk solutions, and, further, it is important to use an interpolation scheme that is consistent with the Gibbs-Duhem requirement, when the thermodynamic data are presented in tabular form as a function of composition. To accomplish this interpolation, a special calculation technique is presented.

Extension of binary analytical equations to ternary ones

A series of analytical expressions of predicting and representing ternary thermodynamic properties using binary data has been derived by applying the subregular solution model and the Krupkowski equation. The geometrical methods employed for the derivation are the Muggianu-, the Kohler-, the Colinet- and the Toop- methods. The expressions have been used to predict the partial molar excess free energy in the Cd-Pb-Sn system at 760K. The experimental data of the liquid Cd-Pb-Sn solutions are found to be excellently represented by the derived expressions.

Thermodynamic characteristics of solute-solvent interactions in liquid organic salt solvents, studied by gas chromatography

A number of thermodynamic constants were measured for five McReynolds selectivity probes and a series of aromatic selectivity probes on thirteen tetra-n-butylammonium salts and eleven 4-toluenesulfonate salts to elucidate the nature of intermolecular interactions of solute—liquid organic salts by gas chromatography (GC). The molar free energy of solution for a methylene group was used to determine dispersive contributions of individual cations and anions to retention. The partial molar, mole fraction, and molal free energy of solution and partial mole fraction enthalpy and entropy of solution were determined to estimate the contribution of various intermolecular forces to retention and to compare the magnitude of these interactions to those of non-ionic, polar phases. Weak dispersive interactions increasing with the size of the cation, strong orientation interactions of a relatively constant nature, and proton acceptor interactions that varied greatly and correlated with the properties of the anion were observed for the liquid organic salts. The magnitude of the orientation and proton acceptor interactions in several cases were much larger than equivalent interactions for polar, non-ionic phases. The infinite dilution activity coefficient and partial molar excess free energy of solution were determined for the five McReynolds probes on the tetra-n-butylammonium salts. With the exception of butanol the range of values observed were similar to literature values for polar, non-ionic GC phases.

Thermodynamic characteristics of solute—solvent interactions in liquid organic salt solvents, studied by gas chromatography

A number of thermodynamic constants were measured for five McReynolds selectivity probes and a series of aromatic selectivity probes on thirteen tetra- n-butylammonium salts and eleven 4-toluenesulfonate salts to elucidate the nature of intermolecular interactions of solute—liquid organic salts by gas chromatography (GC). The molar free energy of solution for a methylene group was used to determine dispersive contributions of individual cations and anions to retention. The partial molar, mole fraction, and molal free energy of solution and partial mole fraction enthalpy and entropy of solution were determined to estimate the contribution of various intermolecular forces to retention and to compare the magnitude of these interactions to those of non-ionic, polar phases. Weak dispersive interactions increasing with the size of the cation, strong orientation interactions of a relatively constant nature, and proton acceptor interactions that varied greatly and correlated with the properties of the anion were observed for the liquid organic salts. The magnitude of the orientation and proton acceptor interactions in several cases were much larger than equivalent interactions for polar, non-ionic phases. The infinite dilution activity coefficient and partial molar excess free energy of solution were determined for the five McReynolds probes on the tetra- n-butylammonium salts. With the exception of butanol the range of values observed were similar to literature values for polar, non-ionic GC phases.

A regular solution model for met-aluminous silicate liquids: Applications to geothermometry, immiscibility, and the source regions of basic magmas

Adopting a set of multioxide components and using published compositional data on olivineand plagioclase-liquid equilibria we have developed a 17 component regular solution model for met-aluminous silicate liquids. The partial molar excess free energies predicted from this model can be used together with phenocryst compositions as an effective geothermometer, with an approximate error of 20 °C (30 °C for olivine, 12 °C for plagioclase). The regular solution formulation is also successful in predicting liquid immiscibility at (1) high mole fractions of silica commonly observed in phase diagrams, and at (2) lower temperatures in lunar basalts and intermediate lavas. The model yields activities of silica which are consistent with those obtained from solid-liquid silica buffers in rocks which contain olivine and enstatite or quartz. From predicted activities of KAlSi3O8 in liquids coexisting with plagioclase a value is obtained for the limiting Henry's law activity coefficient of KAlSi3O8 in the solid. This coefficient agrees well with that inferred from plagioclase-sanidine equilibrium phenocryst assemblages in rhyolites. The activities of silica obtained from this model are used to place constraints on the pressure-temperature regions where various types of basic magmas are generated. In conjunction with plagioclase geothermometry an application is given where the pressure, temperature, and water content of an olivine andesite is predicted from the activity of silica.

Über die extrem hohe thermodynamische Stabilität von Pd-Th-Legierungen / On the Extremely High Thermodynamic Stability of Pd-Th Alloys

The thermodynamic properties of Pd-Th solid solutions containing up to 16 at.% Th have been determined by the e.m.f. method between 700 and 800 °C with CaF2 solid electrolyte cells. The mixing behaviour of the alloys is characterized by extreme negative deviations from ideality, up to -410 kJ/mol for the partial molar excess free energy of Thorium. The extraordinary stability is attributed to electronic interactions brought about by the transfer of the Thorium valence electrons to the electron gas of the alloy. At vanishing Thorium concentration the resulting bonding contribution to the thermodynamic excess quantities is determined by the difference of the Fermi energies of the pure components, approximately equal to the difference of the work functions. Including the lattice distortion as a small additional effect, the mixing behaviour of these and other palladium alloys can be well described

The Activity of AgCl in AgCl–LiCl–KCl Melts

Thermodynamic properties of silver chloride in molten silver chloride – lithium chloride – potassium chloride melts were studied using a silver chloride formation cell employing a chlorine electrode of novel design which facilitated measurements in ternary melts. The data were treated by analytical methods resulting in the generation of activity and the partial molar excess free energy at 500 °C.The measured properties were interpreted with the aid of a model which presupposed the existence of free silver ions as well as those "bonded" to adjacent chloride ions. With three adjustable parameters it was possible to account for the thermodynamic behavior of silver chloride.

Thermodynamics of ternary systems. Quasichemical approximation and the excess ternary term

Based on the quasichemical theory, second order expressions in terms of the nearest-neighbor interaction parameters are given for the molar energy of mixing, ΔE, and the partial molar excess free energy of mixing, ḠCE, of a ternary system. In order to improve the applicability, the quasichemical binary contributions are replaced by the experimental binary values. The ``leftover'' term or the ``excess'' ternary term is discussed in more detail. The quasichemical theory suggests the ternary excess energy term is of a more complex form than N AN BNC × const. The expressions are useful in calorimetric work and in discussing phase stabilities (miscibility gaps).

Thermodynamics of the Molten AgCl ‐ RbCl ‐ NaCl System by Electromotive Force Measurements

Electromotive force measurements have been made using the reversible formation cell Partial molar excess free energies, enthalpies, and excess entropies of mixing of have been measured over the entire composition range of the ternary system. Partial properties of mixing of and and integral properties of mixing have been calculated using an analytical solution of the Gibbs‐Duhem equation. The partial properties of and can be explained on the basis of simple considerations of regular solution behavior. The partial properties of , however, cannot be explained in this way.

Thermodynamic and structural properties of some mixtures of molten fluorides

The thermodynamic and structural properties for mixtures of the type (A + - B +)F − and (A + - M z+)F − are discussed, where A + and B + are alkali metal ions and M z+ is a divalent or a trivalent metal ion. The discussion is based on the partial molar excess free energy Δ G 1 E calculated from the observed freezing point depression of the component AF on addition of univalent, bivalent or tervalent fluorides. It is shown that the parameter b = Δ G 1 E N 2 2 , where N 2 is the ion fraction of the second component, ▪, is a function of charge and radius of the added cation. The possibility of formation of complex ions in the different systems is briefly discussed.