Gibbs Energy Equation Research Articles

Four‐chamber cochlea box model: Establishing acoustic comfort, illustrating injury and toward therapy.

The unrolled cochlea is modeled using the finite‐element software ANSYS with four inner chambers representing the Scala Vestibuli contiguous with the Scala Tympani thru a rounded helicotrema, the Scala Media, the inner and the outer hair cells. The tectorial membrane is represented as a plate in contact with the hair cells. An improvement from previously presented results is the inclusion of a tapered helicotrema. Various geometries are compared, i.e. with straight sides and with tapered sides, and differences in the frequency response of the models are seen. Applying real values for material properties and the human hearing range and using characteristic frequency at certain nodes inside the Scala Media, the tapered model is calibrated to establish the reference comfort sound level. Hearing injury is regarded by subjecting nodes to increased sound pressure levels until the frequency response disappears. This is done at the same time monitoring the change in electrical potential in the inner and outer hair cell regions. The potential change between the normal and the injured conditions is inputted to the Gibbs energy equation for the ATP‐ADPase glycolysis to identify a possible route to remedy.

XSEOS: An evolving tool for teaching chemical engineering thermodynamics

XSEOS – excess Gibbs energy models and equations of state – is an Excel ® add-in for computing properties with thermodynamic models often used in chemical process design. The program is free, has open source, and runs on a platform, Excel, commonly available in personal computers. The main targets are undergraduate and graduate courses in chemical engineering thermodynamics whose syllabi include phase and chemical equilibrium calculations, but XSEOS may also be useful for research. The thermodynamic models available in XSEOS allow computing excess or residual properties, and activity or fugacity coefficients of pure components and mixtures (with any number of components). The recent addition of several methods to characterize petroleum fluids and to estimate surface tensions extends the potential application of the package to oil refining and petroleum engineering courses. We also report assessments of XSEOS's use in assignments and course projects, based on feedback provided by students.

Application of a New Gibbs Energy Equation to Model a Distillation Tower for Production of Pure Ethanol

AbstractA steady‐state equilibrium‐stage model based on MESH equations was proposed to simulate saline extractive distillation columns. The interaction parameters between each component of water‐CaCl2 and ethanol‐water were obtained from mean ionic activity coefficients and vapor‐liquid equilibrium (VLE) experimental data. Additionally, the interaction coefficients for the ethanol‐CaCl2 pair were fitted to experimental VLE data which were reported by Nishi for the ethanol‐water‐CaCl2 system. It should be noted that adjustable parameters between each pair were considered to be temperature dependent. The results confirmed that the proposed model could accurately predict the experimental vapor‐liquid equilibrium data for ethanol‐CaCl2‐water systems. Finally, the validated model was coded using MATLAB software and was solved using the Wang‐Henke method, including the VLE and enthalpy models.

Solubilities of Biologically Active Phenolic Compounds: Measurements and Modeling

Aqueous solubilities of natural phenolic compounds from different families (hydroxyphenyl, polyphenol, hydroxybenzoic, and phenylpropenoic) were experimentally obtained. Measurements were performed on tyrosol and ellagic, protocatechuic, syringic, and o-coumaric acids, at five different temperatures (from 288.2 to 323.2 K), using the standard shake-flask method, followed by compositional analysis using UV spectropho-tometry. To verify the accuracy of the spectrophotometric method, some data points were measured by gravimetry, and in general, the values obtained with the two methods are in good agreement (deviations lower than 11%). To adequately understand the solubilization process, melting properties of the pure phenolics were obtained by differential scanning calorimetry (DSC), and apparent acid dissociation constants were measured by potentiometry titration. The aqueous solubilities followed the expected general exponential trend. The melting temperatures did not follow the same solubility tendency, and for tyrosol and ellagic acid, not only the size and extent of hydrogen bonding, but also the energy associated with their crystal structures, determine the solubility. For these binary systems, acid dissociation is not important. Approaches for modeling the measured data were evaluated. These included an excess Gibbs energy equation, the modified UNIQUAC model, and the cubic-plus-association (CPA) equation of state. Particularly for the CPA approach, a new methodology that explicitly takes into account the number and nature of the associating sites and the prediction of the pure-component parameters from molecular structure is proposed. The results indicate that these are appropriate tools for representing the water solubilities of these molecules.

Solubilities of Biologically Active Phenolic Compounds: Measurements and Modeling

Aqueous solubilities of natural phenolic compounds from different families (hydroxyphenyl, polyphenol, hydroxybenzoic, and phenylpropenoic) were experimentally obtained. Measurements were performed on tyrosol and ellagic, protocatechuic, syringic, and o-coumaric acids, at five different temperatures (from 288.2 to 323.2 K), using the standard shake-flask method, followed by compositional analysis using UV spectrophotometry. To verify the accuracy of the spectrophotometric method, some data points were measured by gravimetry, and in general, the values obtained with the two methods are in good agreement (deviations lower than 11%). To adequately understand the solubilization process, melting properties of the pure phenolics were obtained by differential scanning calorimetry (DSC), and apparent acid dissociation constants were measured by potentiometry titration. The aqueous solubilities followed the expected general exponential trend. The melting temperatures did not follow the same solubility tendency, and for tyrosol and ellagic acid, not only the size and extent of hydrogen bonding, but also the energy associated with their crystal structures, determine the solubility. For these binary systems, acid dissociation is not important. Approaches for modeling the measured data were evaluated. These included an excess Gibbs energy equation, the modified UNIQUAC model, and the cubic-plus-association (CPA) equation of state. Particularly for the CPA approach, a new methodology that explicitly takes into account the number and nature of the associating sites and the prediction of the pure-component parameters from molecular structure is proposed. The results indicate that these are appropriate tools for representing the water solubilities of these molecules.

Thermodynamic properties of the LiCl–H 2O system at vapor–liquid equilibrium from 273 K to 400 K

A formulation of the thermodynamic properties of the LiCl–H 2O system at vapor–liquid equilibrium is presented in the form of separate Gibbs energy equations for the vapor and solution phases. Explicit thermodynamically consistent equations for density, isobaric heat capacity, enthalpy, entropy, enthalpy of dilution and osmotic coefficient are given. The pressure at vapor–liquid equilibrium is calculated from the condition of phase equilibrium. The description of the properties is valid from 273 K or from the crystallization line up to 400 K in temperatures and for solution composition from 0 to 50 wt% of LiCl in the solution, which is the region covewred by available experimental data. The thermodynamic properties of the gas phase are approximated by the properties of pure water vapor computed from the IAPWS formulation 1995. The Gibbs energy equation for solution is based upon a body of experimental data that have been critically assessed. Within the present study, 136 experimental works have been collected containing a total of 2921 data points on various thermodynamic properties of the LiCl–H 2O solutions. Gaps in the database are shown to give experimenters orientation for future research. The uncertainties associated with correlation are estimated to be ±0.4% for density, ±2.0% for pressure and ±2.4% for isobaric heat capacity. The uncertainty in values of enthalpy is estimated to be less than ±10 kJ kg −1 and less than ±0.03 kJ kg −1 K −1 for entropy. Values of the particular properties generated by the representative equations are provided to assist with the confirmation of computer implementation of the calculation procedure.

Thermodynamic assessment of the Mg–Zn–Sr system

The phase equilibria and thermodynamic properties of the Mg–Sr–Zn system were analyzed in this work for the first time and a thermodynamic description of the system was obtained using a computerized optimization procedure. The available thermodynamic and phase diagram data were critically assessed for the Mg–Sr, Mg–Zn and Sr–Zn binary systems. Optimized thermodynamic properties of the binary systems were then used to construct a database and calculate the ternary phase diagram. The excess terms of the liquid phase in the binary Gibbs energy equation, for all binaries, were described by the Redlich–Kister polynomial equation. The established database predicted 4 saddle points, 11 ternary quasi-peritectics, 1 ternary peritectic and 3 ternary eutectics. Lack of ternary experimental data led to the following assumptions: no ternary solid solution and/or compounds are present in the system and no ternary terms were added to the model parameters for the thermodynamic properties of the liquid. The calculated ternary phase diagram can be improved by the addition of new experimental data and can help in establishing Mg multi-component database.

Compact Layer of Alkali Ions at the Surface of Colloidal Silica

The forces of electrical imaging strongly polarize the surface of colloidal silica. I used X-ray scattering to study the adsorbed 2-nm-thick compact layer of alkali ions at the surface of concentrated solutions of 5-nm, 7-nm, and 22-nm particles, stabilized either by NaOH or a mixture of NaOH and CsOH, with the total bulk concentration of alkali ions ranging from 0.1- to 0.7-mol/L. The observed structure of the compact layer is almost independent of the size of the particles and concentration of alkali base in the sol; it can be described by a two-layer model, i.e., an ~ 8 Angstrom thick layer of directly adsorbed hydrated alkali ions with a surface concentration 3x10(18) m(-2), and a ~ 13 Angstrom thick layer with a surface concentration of sodium ions 8x10(18) m(-2). In cesium-enriched sols, Cs+ ions preferentially adsorb in the first layer replacing Na+; their density in the second layer does not depend on the presence of cesium in the sol. The difference in the adsorption of Cs+ and Na+ ions can be explained by the ion-size-dependent term in the electrostatic Gibbs energy equation derived earlier by others. I also discuss the surface charge density and the value of surface tension at the sol's surface.

A Gibbs energy equation for LiBr aqueous solutions

LiBr aqueous solution has been the most popular choice in absorption cooling industry. As increasing interest is paid to the exploitation of its unconventional working range for various new applications, the need of a wide-ranging thermodynamic description of the solution has been growing. In order to meet the observed need, this paper presents a Gibbs energy equation valid for the solutions in the concentration range from 0 to 70 LiBr wt% and the temperatures from 0 to 210 °C with the equilibrium pressures ranging from 74 to 1 MPa. The osmotic coefficients were determined for 405 experimental density and 487 vapor pressure data collected from the literature. A function for the partial molar enthalpy of infinitely dilute solution has been developed and the resulting enthalpy and entropy values are evaluated.

Microstructural and thermodynamic study of γ-Ga2O3

The metastable nanocrystalline y form of gallium oxide has been prepared and its microstructure and thermochemistry have been studied for the first time by employing X-ray and electron diffraction, high-resolution transmission electron microscopy, adiabatic and differential scanning calorimetry. The randomly oriented crystallites of maximum 5 nm in size have been observed. The sponge-like morphology of γ-Ga 2 O 3 particles may explain the high specific surface area, previously reported for this material. The defect spinel-type structure of γ-Ga 2 O 3 is similar to that of y and η-Al 2 O 3 . Up to 5.7 wt.% of water can be stored in γ-Ga 2 O 3 and subsequently released at elevated temperatures. Dry γ-Ga 2 O 3 specifically absorbs atmospheric water at room temperature. The transformation of γ-Ga 2 O 3 into stable β-Ga 2 O 3 occurs in two steps. In the range 650-800 K, γ'-Ga 2 O 3 is formed in the course of a reversible higher-order phase transition. The latter irreversibly transforms into β-form above 873 K. The enthalpy of this exothermic transformation is determined as -19.3 ± 0.4 kJ . mol -1 . The coefficients of the Gibbs energy equation for y and γ'-Ga 2 O 3 have been assessed.

Thermodynamics and Phase Stability in the Si—O System

AbstractFor Abstract see ChemInform Abstract in Full Text.

Thermodynamics and phase stability in the Si–O system

A comprehensive thermodynamic assessment has been carried out on the phases SiO 2(L), including SiO 2(glass), the amorphous monoxide SiO(am) and on the solubility of oxygen in solid and liquid silicon, jointly with the equilibrium partition coefficient k. Contradictions in the sparse thermodynamic data of SiO(am) are pointed out. Our key experiments were performed on the decomposition and condensation of SiO(am). X-ray diffraction on samples heated in evacuated silica capsules was used. The condensation experiment was performed in local equilibrium on a silica rod in a commercial CZ-Si apparatus. With the Calphad method a complete set of Gibbs energy equations was developed for the phase SiO 2(L), comprising glass, supercooled liquid and stable liquid silica, the phase SiO(am) and the solid and liquid silicon solution phases. Combining this with the data for crystalline silica and the gas phase, a consistent thermodynamic description of the entire Si–O system is constructed, covering the complete composition range. Based on that, a number of stable and metastable phase diagrams at various pressures are calculated and applied to better understand important process steps in the production of semiconductor silicon.

Correlation and comparison of the infinite dilution activity coefficients in aqueous and organic mixtures from a modified excess Gibbs energy model

Activity coefficients at infinite dilution (ln γ ∞) of aqueous systems were calculated using a modified excess Gibbs energy model. More than 95 binary systems with 15 solute families from nonpolar alkanes to polar alcohols and acids were employed in this study. Based on the local composition lattice model developed by Aranovich and Donohue, a modified excess Gibbs energy equation (m-AD model) was derived in this study. With two generalized parameters for each homologous series of solutes, this modified model yields satisfactory results for the limiting activity coefficients. The overall absolute average deviation (AAD) of ln γ ∞ for all aqueous systems investigated in this study is 2% for the m-AD model, and the corresponding AAD in γ ∞ unit is 7%. The calculated infinite dilution activity coefficients from the m-AD model are comparable to those from the MOSCED, SPACE, PDD, LSER or the modified UNIFAC model. The m-AD model shows lower peak deviation than those from other methods. Satisfactory generalized correlation results are also observed for organic solvents other than water. With the generalized parameters, the m-AD model satisfactorily predicts the limiting activity coefficients for other solutes not included in the correlation.

The modified quasi-chemical model: Part II. Multicomponent solutions

Further improvements to the modified quasi-chemical model in the pair approximation for shortrange ordering (SRO) in liquids are extended to multicomponent solutions. The energy of pair formation may be expanded in terms of the pair fractions or in terms of the component fractions, and coordination numbers are permitted to vary with composition. The model permits complete freedom of choice to treat any ternary subsystem with a symmetric or an asymmetric model. An improved general functional form for “ternary terms” in the excess Gibbs energy expression is proposed. These terms are related to the effect of a third component upon the binary pair interaction energies. It is shown how binary subsystems that have been optimized with the quasi-chemical model can be combined in the same multicomponent Gibbs energy equation with binary subsystems that have been optimized with a random-mixing Bragg-Williams model and a polynomial expression for the excess Gibbs energy. This is of much practical importance in the development of large databases for multicomponent solutions. The model also applies to SRO in solid solutions as a special case, when the number of lattice sites and coordination numbers are constant.

ChemInform Abstract: Phase Stability Analysis in Binary Systems

Stability analysis should be a standard practice for testing the physical validity of phase equilibrium states predicted by thermodynamic models however, it is seldom used in routine work of experimental data modeling. Lack of stability analysis may result in potential modeling pitfalls or in an inadequate prediction of data. In this contribution the concept of stability is reviewed from a general viewpoint, showing how it applies to completely general cases of binary phase equilibrium, from low to high-pressure ranges. Graphical examples are given using excess Gibbs energy models and equations of state.

Phase Stability Analysis in Binary Systems

Stability analysis should be a standard practice for testing the physical validity of phase equilibrium states predicted by thermodynamic models however, it is seldom used in routine work of experimental data modeling. Lack of stability analysis may result in potential modeling pitfalls or in an inadequate prediction of data. In this contribution the concept of stability is reviewed from a general viewpoint, showing how it applies to completely general cases of binary phase equilibrium, from low to high-pressure ranges. Graphical examples are given using excess Gibbs energy models and equations of state.

Partitioning of some biomolecules at high pressures to aqueous/organic liquid–liquid phases of the carbon dioxide+water+1-propanol system

A completely miscible, binary liquid mixture of water and an organic solvent can reveal a liquid–liquid phase split, when it is pressurised with a ‘near-critical’ gas. The coexisting liquid phases in such a high-pressure three-phase equilibrium can be used to enable an extraction of biomolecules from an aqueous phase into a water-like organic phase. The basic design of such a process requires, at first, information on the behaviour of the phase forming ternary system of ‘near critical’ gas+water+water-soluble organic solvent, at second, experimental data on the partitioning of biomolecules to the coexisting phases and, at third, a method to correlate and predict such phase equilibrium. After a short introduction to the basic phase equilibrium phenomena, experimental results are reported for the partitioning of small amounts of six biomolecules — adenine, caffeine, methyl anthranilate, l-phenylalanine, salicyl alcohol and vanillin — on coexisting liquid phases in high-pressure three-phase vapour–liquid–liquid equilibrium of the ternary system ‘near critical’ carbon dioxide+water+1-propanol at 313 and 333 K. The experimental results for the partition coefficients are correlated with a semi-empirical approach, which combines an equation of state for describing the high-pressure multiphase equilibrium and the UNIQUAC excess Gibbs energy equation for describing the partitioning of the biomolecules.

Prediction of vapor-liquid equilibria and thermodynamic properties for a quinary hydrocarbon system from optimized binary data using the kohler method

For organic systems, the models usually used to predict thermodynamic properties of multicomponent liquid solutions from data for binary sub-systems (Wilson, NRTL, UNIQUAC) suffer from the drawback that the binary data must be fitted to a specific Gibbs energy equation of fixed functional form with a limited number of adjustable parameters. Furthermore, these models do not permit all binary data to be optimized simultaneously. The “CALPHAD approach” of simultaneous optimization of binary data to general polynomial expansions followed by the prediction of multicomponent properties with the Kohler (or Muggianu) equation, yields superior results. An example of an optimization of a binary system is presented for the hexane + benzene system. The Kohler equation is then used to calculate phase equilibria in the quinary hexane + benzene + toluene + methylcyclopentane + cyclohexane system and the results are compared with published experimental data.

The influence of the structure of molybdenum disulphide on its reactivity

The equilibrium in the system Mo-MoS2-H2S-H2 was studied between 569.4 and 1 276.8 K. The equilibrium gaseous mixture was analyzed by an iodometric method, the solid phase was studied by X-ray powder diffraction. The structure of MoS2 changed in the course of measurements from a “poorly crystalline” form at lower temperatures to a “well crystalline” one with a small number of stacking faults at higher temperatures. The poorly crystalline form is more reactive than the well crystalline one. For the formation of the well crystalline form of MoS2 a Gibbs-energy equation, ΔG0 (J mol-1) = -390 100 + 176.7T, was derived. It is in excellent agreement with the equation derived from the data obtained by fluorine calorimetry.

A thermodynamic evaluation of the Copper — Bismuth and Copper — Lead systems

Optimized descriptions of the phase diagrams and thermodynamic functions for the systems Bi-Cu and Cu-Pb have been obtained from published experimental values using computer programs based on a least squares method. The results of the optimization are presented in the form of Gibbs energy equations for the phases of the two systems.