Partial Molar Heat Of Solution Research Articles

Ab initio evaluations of the He solubility in liquid Li

Modified embedding atom methods (MEAM) are developed to have predictions of the partial molar heat of solution (− H s) by direct simulation of metal cohesion, He-metal and He–He interaction. Transitions from crystalline Li to configurations, having the liquid Li structure's factors ( h ˆ ( q ) ), are simulated ab initio. Once h ˆ ( q ) reproduced, He atoms are added, one by one, to the Li system. Parallel lines for each case, with slopes clearly independent on the number of He atoms in the system, are obtained for energy versus pressure at given temperatures. Average differences between two adjacent parallels at zero pressure, once kinetic energy of the system discounted, represents the energy gained by an He atom when added to the Li system, related to the solution energy − H s. The molar excess entropy of gas in solution ( S ¯ l ex ) is previously evaluated following diverse fundamental approaches: a “thermodynamic liquid-hole” (TL-H) model for alkali liquids and a statistical-mechanics (Neff & McQuarrie's) model (SMM). Between 600 and 900 °C, a typical range of interest for the use of Li in fusion technology, the computed values for the (He) Henry's constant in Li range from 8 × 10 −14 to 10 −13 at. fr. Pa −1.

Heats of solution/substitution and of fusion of Cs (1− x) K xCl compositions 0< x

Measurements of the change in heat (enthalpy) of solid–solid transition Δ H t and of fusion Δ H fus in crystalline CsCl effected by the presence of guest ion K + up to 56.5 mol% using differential scanning calorimetry are reported. The range of K + solubility is found to be higher and at variance with the subsolidus region described in earlier reports. Novel features of Δ H t and Δ H fus dependence on solute composition are in contrast to parallel binary systems, viz. CsNO 3–RbNO 3, CsNO 3–TlNO 3 and RbNO 3–TlNO 3. Some fundamental solution quantities are calculated from heat of transition, viz. slope Δ H t/ x or Δ H ̄ solute and χ-apparent partial molar heat of solution and partial molar heat of solution at infinite dilution, respectively.

Heats of solution/substitution of Tl+, Rb+, K+, Br−, I− in crystalline CsCl from heats of solid phase transition by differential scanning calorimetry

Measurements of the change in heat (enthalpy) of transition in crystalline CsCl effected by the presence of guest ions K+, Rb+, Tl+, Br−, I− using differential scanning calorimetry are reported. The nature of each mixed-ion solid, ‘mixed crystal’ or ‘crystalline solid solution’ is discussed. The limits of solubility of each guest ion are found to be consistent with the subsolidus region described in its respective phase diagram. The quantitative heat of transition values are used to calculate some fundamental solution quantities, viz. slope ΔHt/x or ΔH̄solute,χ, ΔHS0, ΔHL0—apparent partial molar heat of solution, partial molar heat of solution at infinite dilution, the heat of solution, recovered lattice energy, respectively.

Heats of solution/substitution in TlNO 3 and CsNO 3 crystals and in RbNO 3 and CsNO 3 crystals from heats of transition: the complete phase diagrams of TlNO 3–CsNO 3 and RbNO 3–CsNO 3 systems

From measurements of the decrease in the heat (enthalpy) of transition in the solid phase using differential scanning calorimetry, the apparent molar heats of solution, slope Δ H t/ x, the partial molar heats of solution at infinite dilution, χ, and the heats of solution, Δ H s °, of Tl + in CsNO 3 crystal and Cs + in TlNO 3 crystal and Rb + in CsNO 3 crystal and Cs + in RbNO 3 crystal along with their recovered lattice energies, Δ H L °, are reported. Δ H s ° of Tl + and Rb + in CsNO 3 crystal are each found to be negligible or zero representing an ideal solid solution, i.e. Δ H mix=0. The complete phase diagrams of the TlNO 3–CsNO 3 and RbNO 3–CsNO 3 systems with details of the sub-solidus regions are included. The properties of Tl (1− x) Cs x NO 3 and Rb (1− x) Cs x NO 3 compositions are discussed in terms of a ‘mixed crystal’ or ‘crystalline solid solution’ in relation to parallel compositions of Tl (1− x) Rb x NO 3.

Heats of solution of TlI in TlNO3 and TlBr in TlI crystals. Phase diagrams of TlNO3–TlI and TlBr–TlI systems

From differential scanning calorimetry (DSC) measurements of the decrease in the heat (enthalpy) of transition in the solid phase, the partial molar heats of solution at infinite dilution, χ, and the heats of solution or substitution, ΔHs° of I− in TlNO3 crystal, Br− and NO3− in TlI crystal along with their recovered lattice energies ΔHL° are reported. The phase diagram of the TlNO3–TlI system with details of the subsolidus region along with subsolidus region of the TlBr–TlI diagram are reported. The TlIx(NO3)1−x compositions exhibit properties, viz. structure, transition temperatures and melting temperature characteristic of a “mixed crystal” or “crystalline solid-solution” paralleling Tl(1−x)RbxNO3 behavior.

Heats of solution/substitution in TlNO3 and RbNO3 crystals from heats of transition. The complete phase diagram of the TlNO3–RbNO3 system

From measurements of the decrease in the heat (enthalpy) of transition in the solid phase by differential scanning calorimetry, the partial molar heats of solution at infinite dilution, χ, and the heats of solution or substitution, ΔHs°, of Tl+ in RbNO3 crystal and Rb+ in TlNO3 crystal along with their recovered lattice energies, ΔHL°, are reported. The complete phase diagram of the TlNO3–RbNO3 system with details of the sub-solidus regions is reported. The properties of a “mixed crystal’' or “crystalline solid solution’' of Tl(1-x)RbxNO3, viz., structure, transition temperatures, melting temperature, etc., are presented and discussed.

Thermodynamic Study on MnO Behavior in MgO-saturated Slag Containing FeO.

In order to understand the behavior of manganese oxide in smelting reduction process, the manganese equilibrium between ironmaking slag containing FeO and silver melt was investigated over the temperature range of 1400-1500°C. The oxygen partial pressure was controlled by CO/CO2 ratio. Test results on Mn content in silver have been thermodynamically converted into those in supercooled or carbon-saturated iron melts and the activity coefficient of MnO in slag was determined experimentally. The activity of MnO decreased with increasing FeO content in slag. Higher FeO content as well as lower slag basicity resulted in larger equilibrium manganese distribution ratio between slag and iron. The temperature dependence of equilibrium manganese distribution was determined in the temperature range of 1400-1500°C. The relative partial molar heats of solution of MnO and Mn were also experimentally determined.

Hydrogen solubility in a titanium aluminide alloy

The dissolution of hydrogen in a titanum aluminide alloy based on Ti3Al, Ti-24 Al-11 Nb, has been measured as a function of temperature and hydrogen pressure. Both the terminal solubility and the overall solubility, or total uptake of hydrogen, were determined. The terminal solubility of hydrogen in the α2 matric phase increases with temperature, while the overall solubility decreases with increasing temperature in the high-temperature region. The partial molar heat of solution in the α2 phase was determined to be−(21.97 ± 1.46) kJ/mol [H], while the partial molar heat of formation of the hydride phase was −(70.29 ± 2.34) kJ/mol [H]. The standard partial molar free energy of hydrogen in the α2 phase in equilibrium with the hydride was −(74,060 ± 2000) + (87.8 ± 2.1) T J/mol [H].

NPT ensemble Monte-Carlo simulation of ethanol in water

NPT ensemble Monte-Carlo simulation has been carried out on a dilute aqueous solution of ethanol (108 water molecules) m using a Jorgensen-type potential for ethanol-water interactions and the TIP4P model of water. The hydrogen bonding of water to the ethanol OH group has been detailed by the use of primary pair correlation functions and from pair-interaction-energy distribution functions. The calculation shows 2.3 water molecules hydrogen bonded to the ethanol molecule with 1.4 of the OH oxygen proton-acceptor and 0.9 of the OH hydrogen proton-donor type. In addition, the partial molar heat of solution of −31.8 kJ mol −1 is in better agreement with experimental results than previously published results.

Permeation, diffusion, and solution of cyclopropane in silicone rubber

AbstractPermeability, solubility, and diffusion coefficients have been determined for cyclopropane (c‐C3H6) in silicone rubber at temperatures between −8 and 70°C at relative pressures from 0.04 to 0.30. The permeability coefficients, $&amp;\[\bar P\]$, are of the order of 10−6 cm3 (STP) · cm/(s · cm2 · cmHg). $&amp;\[\bar P\]$ increases slightly with increasing penetrant pressure and decreases with increasing temperature, the energy of activation for permeation being −1.27 kcal/gmol at zero pressure. The solubility of cyclopropane in silicone rubber can be represented over the experimental concentration range by the Flory‐Huggins equation. The solubility decreases with increasing temperature and the partial molar heat of solution is −4.95 kcal/gmol. The solubility coefficient in the Henry's law limit, S(0), for cyclopropane and many other gases and vapors can be correlated with (Tc/T)2, where T and Tc are the experimental and critical temperatures, respectively. The mutual diffusion coefficients, D, increase with increasing concentration and temperature, the energy of activation for diffusion being 3.68 kcal/gmol. The pressure dependence of &amp;\[\bar P\] is described satisfactorily by a free‐volume model proposed by Fujita and extended by Stern, Frisch, and coworkers. The permeability, diffusion, and solubility behavior of cyclopropane in silicone rubber is similar to that of propane (C3H8).

Thermodynamics of hydrogen bonding polymer‐solute interactions by inverse gas chromatography

AbstractThe gaschromatographic retention behaviour of a series of solutes with potential hydrogen bonding activity has been studied, using polyethylene, poly(ethylene‐vinyl acetate), poly(vinyl acetate), and poly(ethylene glycol) as stationary phases. Measurements were performed at various temperatures above the melting point and/or glass transition temperature of the polymers and the slopes of the ln V versus 1/T‐functions (where V is the specific retention volume) were used to calculate partial molar heats of solution (ΔHs). Correspondingly, the temperature dependence of the activity coefficient can be used to calculate partial molar heats of mixing (ΔH̄1infin;) of the solute at infinite dilution in the polymer. Based on a “homomorph” concept with the inherent assumption of additive group contributions to the total interaction energy, hydrogen bonding energies of polymer‐solute systems could be separated using polyethylene on one hand and appropriate model solutes on the other hand as reference materials.

Lattice Constant and Nonstoichiometry in Mn–Fe Ferrites

The lattice constant of Mn1-xFe2+xO4+δ(x=0.050, 0.084, 0.139 or 0.198) equilibrated at 1200°C, 1300°C and 1350°C in an atmosphere of oxygen whose partial pressure ranges from about 10-5 atm to 1 atm is measured with an X-ray diffractometer at room temperature. The lattice constant of Mn-Fe ferrites depends on the oxygen partial pressure and the temperature as well as the ratio of Fe to Mn in the composition. The lattice constant versus the oxygen partial pressure curves at each temperature show a maximum. The Mn-Fe ferrites with the maximum lattice constant are thought to be nearly stoichiometric. The partial molar heat of solution of oxygen in Mn1-xFe2+xO4.000(x=0.084 or 0.198) calculated from the temperature dependence of the equilibrium oxygen partial pressure is about -77 kcal/mol in the temperature range from 1200°C to 1350°C.

The U 0.8Pu 0.2C-W system

A phase diagram of the U 0.8Pu 0.2C-W system has been established based on X-ray diffraction measurements and metallographic observations. A peritectic four-phase reaction has been found to occur at 2100 ± 40° C: ▪ The peritectic point is close to U 0.8Pu 0.2C-27 wt.%W. Composition of the peritectic liquid is near 48(U + Pu)/18W/34C (at %) by analogy with the UC-W system. The liquid phase transforms, during rapid cooling, to a metastable mixture [(U, Pu)C + (U, Pu)metal + W] with accompanied retention of (U, Pu)WC 1.75. The (U, Pu)WC 1.75 phase crystallizes in a UWC 1.75-type monoclinic structure. Essentially single-phase (U 0.8Pu 0.2)WC 1.75 has been produced by sufficient annealing of the arc-melted specimen, with lattice parameters: a 0 = 5.6257 ± 0.0008 Å, b 0= 3.2498 ± 0.0005Å, c 0 = 11.623 ± 0.002 Å, β = 109.61 ± 0.01°. This compound perhaps melts incongruently as: ▪ The terminal solid solubility limit of tungsten in U 0.8Pu 0.2C increases from about 0.8 wt%W at 1500°C to a maximum of about 3.2 wt%W at 2100°C. The partial molar heat of solution of tungsten in U 0.8Pu 0.2C is approximately 14.4 kcal/mole. Un diagramme de phase du système U 0,8Pu 0,2C-W a étée'tabli en se basant sur les mesures par diffraction aux rayons X et par examen métallographique. Une réaction péritectique a quatre phases a été observée à 2100 ± 40°C: ▪

Partial Molar Heats of Solution of Hydrated Electrolytes in Saturated Solutions

Partial Molar Heats of Solution of Hydrated Electrolytes in Saturated Solutions

Use of thermodynamic functions of solution for identification in gas-liquid chromatography

A new method of identification in GLC based on the application of themodynamic functions of solution has been developed. Relative partial molar heats of solution for the expected components in the mixture are calculated on a semiempirical basis. Then the calculated values are compared with the experimental values for unknown components in the mixture. The coincidence between the calculated and experimental data shows the structure of the unknown molecule. Some relationships between thermodynamic functions of solution in GLC and the structure of molecules are discussed in the paper.

溶融Fe-V系の窒素溶解度

The solubility of nitrogen in liquid V and Fe-V system has been measured in the temperature range from 1800° to 2200°C over wide composition range using the levitationmelting method.The solubility of nitrogen in liquid V was very high and decreased with increasing temperature. In the Fe-V system, it was increased with increasing V content and decreased with increasing temperature. The departure of this system from Sieverts’ law deserves attention because the activity coefficient was decreased with increasing nitrogen partial pressure.Values of the partial molar heat of solution Δ\barHN of nitrogen and interaction coefficient eN(v) were determined as functions of composition and of temperature, respectively. Δ\barHN in Fe-V system showed a higher negative value than that in the Fe-Cr system. Enthalpy coefficient hN(v) was estimated as −2.26 kcal/mol.

A resistometric study of the solution and precipitation of hydrides in unalloyed zirconium

A resistometric technique has been used to study the terminal solid solubility of hydrogen and the kinetics of hydride precipitation in α-zirconium. The terminal solid solubility of hydrogen in unalloyed zirconium is determined to be 65–70 ppm at 300 °C. Δ H, the difference in partial molar heat of solution of hydrogen in the hydride and in α-phase zirconium, is found to be 10.8 kcal/mole. The resistivity increase is 1.9 ± 0.2 μΩ · cm per atomic percent of solute hydrogen. The rate of hydride precipitation is more rapid than reported earlier. In annealed specimens containing more than 100 ppm of hydrogen, obtaining a supersaturated solid solution by quenching into ice water is almost impossible, whereas in annealed materials containing less than 20 ppm of hydrogen, it is possible to get the solid solution state by quenching from about 300 °C into ice water. However, in cold worked specimens, this is again impossible. An activation energy of 7.6 kcal/mole is obtained for hydride precipitation in α-zirconium at ageing temperatures of 14 °C to −35 °C. The reaction rate for hydride precipitation is nearly of the first order in the temperature range 14 °C to −35 °C, and nearly of the second order in the range −50 °C to −67 °C

Hard-Sphere Model of Binary Liquid Mixtures

An equation of state [Eq. (2) of the text] which has been successfully applied to pure liquids composed of small, nonpolar molecules was generalized to the case of binary mixtures. The generalized equation was used to calculate excess thermodynamic functions for 10 equimolar mixtures, and agreement with experiment was found to be generally good. The partial molar heat of solution of gaseous neon in liquid argon was also calculated, but good agreement with experiment was not obtained in this calculation.

The solubilities of MgO and UO 2 in molten MgF 2

Liquidus curves have been determined over a limited composition range for the systems MgOMgF 2 and UO 2MgF 2. Pure MgF 2 was observed to melt at 1260 ± 0·5°C and the system MgOMgF 2 forms a simple eutectic containing 8·35 mole % MgO and melting at 1229·5°C. The saturation solubility for UO 2 in MgF 2 was determined for the temperature range 1268–1434°C. The calculated partial molar heat of solution of the UO 2 in MgF 2 is +28·0 kcal mole −1 and the eutectic is estimated to be at 0·35 mole % UO 2 and 1256°C. A technique is also described for the estimation of true liquidus temperatures for samples that exhibit random supercooling.

Polymer–filler interaction. Thermodynamic calculations and a proposed model

AbstractFrom a study of the sorption of water vapor by epoxy polymers filled with titanium dioxide, the differences in enthalpy and entropy of the filled and the unfilled polymers are calculated. The enthalpy and the entropy of the filled polymer are smaller than those of the unfilled polymer by about 2 cal./g. and 6 × 10−3 e.u., respectively. These differences may be explained by the existence of a higher degree of local ordering of the polymer segments. A model is proposed to describe the interaction between the polymer and the filler as a function of the distance from the interface. It appears that polymer segments at a distance less than 1500 A. from the surface of the filler particle are within the sphere of influence of the filler. The effects of filler incorporation of the thermal expansion coefficient, heat capacity, and partial molar heat of solution of the polymer are discussed in terms of the model.