Gibbs Free Energy Of Solution Research Articles

Influence of electric field strength applied during the solution heat treatment of the Al–Mg–Si–Cu Alloy AA6111

Abstract In the present paper, the effect of electric field strength in the range E = 0.1 – 5.0 kV/cm applied during the solution heat treatment (SHT) of the AA6111 alloy at 475° –550 °C has been determined employing resistivity. An increase in the as-quenched resistivity ρ w occurred for all field strengths, the increase being relatively rapid up to E ≈ 1 kV/cm and only slight, if at all, for higher fields. Analysis of the results gave that the field reduced the enthalpy, entropy and Gibbs free energy of solution, the amount of reduction increasing with field strength. The electric current, which occurred with application of the field during SHT, ranged from (7 × 10 –3 to 4 × 102) μA, increasing with field strength and SHT temperature, but decreasing with time during the SHT. The role of the current in the enhancement of ρ w by the field is not clear.

Experimental measurement and correlation of solubility of β-carotene in pure and ethanol-modified subcritical water

For the first time, the solubility of β-carotene in pure and ethanol-modified subcritical water (SW) using the static method was determined. The experimental runs were performed at a temperature ranging from 298.15 to 403.15 K and 0–10% (w/w) of ethanol as a modifier at a constant pressure of 5 MPa. Samples were analyzed by UV–vis spectrophotometer. The solubility of β-carotene was found to range from 1.084 × 10 −8 to 227.1 × 10 −8 mol fractions in the subcritical water in above mentioned conditions. The obtained β-carotene solubility data were correlated using the linear model and modified Apelblat model. The obtained results showed the modified Apelblat model was better for estimating the solubility of β-carotene in SW. The values of the root-mean-square deviation (RMSD) between experimental and correlated data were calculated and used as the index of validity and accuracy for the model. Also, thermodynamic properties of the solution such as the Gibbs free energy of solution, enthalpy, and entropy of solution were estimated. • The solubility of β-carotene in pure and ethanol-modified subcritical water using static method was measured for the first time. • Solubility of β-carotene was measured at different temperatures (298.15–403.15 K) and constant pressures (5 MPa). • Solubility data were correlated by semi-empirical models. • Thermodynamic properties of solution were estimated.

Thermodynamic analysis of celecoxib in amphiprotic and amphiprotic-aprotic solvent mixtures at several temperatures

The solubilities of celecoxib (CLX), a COX-2 selective nonsteroidal anti-inflammatory drug, were determined in water-ethanol and ethanol-ethyl acetate mixtures at several temperatures (288.15-308.15 K). The solubility curves as a function of ethanol ratio were studied at five temperatures, they showed a single maximum located at 50% ethanol-ethyl acetate (δ1 = 22.50 MPa1/2). The measurements of the variation of inherent drug solubility with temperature were used to estimate different thermodynamic parameters, enthalpy, entropy and Gibbs free energy of solution (ΔHS,ΔSS and ΔGShm, respectively). The apparent enthalpies of the solution were a nonlinear function of the ethanol ratio in aqueous mixture. Non-linear enthalpy-entropy compensation analysis was observed indicating different dissolution mechanism with the variation in mixtures composition. The solubility enhancement is entropy driven at water-rich region (0-40% v/v ethanol) and enthalpy controlled at ethanol-rich region (40–100% v/v ethanol), likely due to water-structure loss around nonpolar moieties of the drug and for the ethanol-rich mixtures it is the enthalpy, probably due to the drug better solvation.

Volumetric and viscometric investigation of aqueous solution of [Bmim][BF4] from 288.15 to 318.15 K

Density and viscosity of aqueous [Bmim][BF4] were measured at the temperature range from 288.15 to 318.15K with a step of 5K under atmospheric pressure. All the concentrations of the aqueous solutions were controlled bellow 1.000mol·kg−1. The values of apparent molar volumes were obtained at different temperatures with the corresponding concentrations. According to Redlich-Mayer equation, the empirical parameters (SV and BV) and the limiting apparent molar volume at infinite dilution, ϕVi0, were acquired. The volume properties were also investigated using Pitzer's equation the result showed that Redlich-Mayer's and Pitzer's equation were mutually proved. Based on the equation of ϕVi0 and T, the limiting apparent molar expansibilities, Eϕ∞, were calculated and discussed. Through the Jones-Dole empirical equation, the viscosity coefficient A and B of aqueous [Bmim][BF4] were obtained. In addition, the standard molar activation Gibbs free energy of solute, Δμ2≠0, were obtained, and the activation entropy, ΔS2≠0, as well as activation enthalpy, ΔH2≠0, can be calculated by fitting Δμ2≠0 against T. Using a semi-empirical method the viscosity of aqueous [Bmim][BF4] was predicted and the result showed a good agreement with experimental values.

Thermodynamic properties for MMoO4 (M = Mg, Sr and Ba) as the end-members of the yellow phases formed in the nuclear fuel waste glasses

The standard molar entropyΔ0TSm°, at 298.15 K of MgMoO4(cr) of the end-members of the yellow phases formed in the nuclear fuel waste glasses was determined by measuring Cp,m° at the temperature of 2 K and above using the most recent Debye-Einstein formula. The Δ0TSm° data obtained in our previous study for SrMoO4(cr) and BaMoO4(cr) were re-evaluated using this most recent formula. The standard Gibbs free energies of formation, ΔfGm°, of MgMoO4, SrMoO4(cr) and BaMoO4(cr) were determined by combining the Δ0TSm° data with the reference data for the standard enthalpy of formation,ΔfHm°. The ΔfGm° of MoO42−(aq) was updated from the thermodynamic cycle based on the data obtained in the present work. The unknown standard Gibbs free energy of solution, ΔslnGm°, and the solubility product, Ks, at 298.15 K for MgMoO4 were predicted. The thermodynamic values were obtained as follows:Δ0TSm°(MgMoO4(cr), 298.15 K)/(J K−1 mol−1) = 119.11 ± 1.19;Δ0TSm°(SrMoO4(cr), 298.15 K)/(J K−1 mol−1) = 136.44 ± 1.36;Δ0TSm°(BaMoO4(cr), 298.15 K)/(J K−1 mol−1) = 152.61 ± 1.53;ΔfGm°(MgMoO4(cr), 298.15 K)/(kJ mol−1) = −1295.73 ± 0.91;ΔfGm°(SrMoO4(cr), 298.15 K)/(kJ mol−1) = −1441.32 ± 1.36;ΔfGm°(BaMoO4(cr), 298.15 K)/(kJ mol−1) = −1443.29 ± 1.33;ΔfGm°(MoO42−(aq), 298.15 K)/(kJ mol−1) = −836.63 ± 0.97.ΔslnGm°(MgMoO4(aq),298.15 K)/(kJ (mol of MoO42−(aq))−1) = 3.72 ± 1.88.Ks(MgMoO4(aq), 298.15) = 2.23×10−1± 4.46×10−2The thermodynamic data obtained in this work are expected to be useful for nuclear fuel waste safety management.

Below the room temperature measurements of solubilities in ester absorbents for CO2 capture

Six ester absorbents were selected for CO2 capture, such as methyl benzoate, methyl heptanoate, ethyl hexanoate, butyl butyrate, triethyl phosphate and tributyl phosphate. CO2 solubilities in these absorbents were determined under temperatures of 273.15–283.15 K, and pressures up to 1.2 MPa. Henry’s constants of CO2 + the selected absorbent systems at 273.15 K and 283.15 K were calculated and compared with those at higher temperature. It seemed that decreasing the absorption temperature is obviously beneficial for enhancing absorption performance. In order to assess the absorption capacity for different physical absorbents, Henry’s constants and volumetric solubilities of the selected absorbents were compared with ionic liquids, common solvents and the selected absorbents in our previous work. The result showed that tributyl phosphate and triethyl phosphate were found to be relatively good absorbents by mole and volumetric fraction respectively, and they have potential value for CO2 capture. Moreover, thermodynamic properties such as entropy of solution, enthalpy of solution and Gibbs free energy of solution for the selected systems were calculated and assessed to study the absorption behavior.

Below the room temperature measurements of CO 2 solubilities in six physical absorbents

Abstract An isothermal synthetic apparatus was established as the absorbing device. Six physical absorbents with ether and ester groups were selected: ethylene glycol methyl ether acetate (EGMEA), propylene glycol methyl ether acetate (PGMEA), 3-methoxy butyl acetate (MBA), diethylene glycol diethyl ether (DGDE), ethylene glycol butyl ether acetate (EGBEA) and carbitol acetate (CA). CO2 solubilities in the selected absorbents were measured at temperatures of 273.15–283.15 K, and pressures up to 1.2 MPa. Henry’s constants of CO2 + selected absorbents systems at 273.15 K and 283.15 K were regressed and compared with those at higher temperature. It turned out that decreasing the temperature has a large effect on improving absorption capacity. Henry’s constants and volumetric solubilities of the selected absorbents were compared with other solvents and ionic liquids for the purpose of judging the absorption capacity. CA and EGMEA were found to be relatively good absorbents by mole and volumetric fraction respectively, and they have potential value for CO2 capture. In order to study absorption behavior, thermodynamic properties such as entropy of solution, enthalpy of solution and Gibbs free energy of solution for the selected systems were calculated and assessed.

A Contribution to the Solution Thermodynamics of Chiral Lactide

AbstractSolubilities and solution enthalpies of enantiopure L‐lactide and the racemic molecular compound DL‐lactide are examined. Different experimental methods are used to isolate and specify relevant thermodynamic contributions of the solution enthalpy. Thus, measurements of the dissolution process have been carried out by means of solution calorimetry. Additionally, solubilities of both chiral species have been measured at different temperatures to derive the van't Hoff enthalpy of solution from their temperature dependency and the enthalpy of solution at saturation concentration from the experimental Gibbs free energy of solution. The solution thermodynamic quantities are compared to the respective enthalpies of melting to isolate excess enthalpies, which incorporate different parts of the solution nonidealities. The solution nonidealities for the enantiomer and racemic compound in toluene incorporate solute‐solute interactions that depend on the concentration of the solute. A trend is identified that shows the absolute and relative solid‐liquid phase transition enthalpies from the melt to the saturated solution and their dependency on temperature.

Modeling of systems with aqueous solutions of UO 2 2+ salts. Asymmetric model of excess thermodynamic functions, based on virial expansion of the Gibbs free energy of the solution, VD-AS

An asymmetric model of virial expansion of the Gibbs free energy of solution, VD-AS, was suggested. Partial and molar thermodynamic functions of UO2(ClO4)2–H2O, UO2Cl2–H2O, and UO2(NO3)2–H2O binary solutions at 25°C were calculated using this model. The calculations show that the solutions are characterized by different, sometimes extremely large, deviations from ideality. The suggested model is considerably more accurate and stable than the most widely used Pitzer’s model of electrolyte solutions.

Determination and correlation of solubility of phenylphosphonic acid in selected solvents

In this study, the solubility of phenylphosphonic acid in n-propanol, acetone, acetonitrile, ethyl acetate, and chloroform was determined by the static analytical method over the temperature range from 288.15 to 318.15K. At a given temperature, the order of solubility is n-propanol>acetone>acetonitrile>ethyl acetate>chloroform. The modified Apelblat equation and λh model were used to represent the experimental data with satisfactory correlation results. Moreover, the enthalpy, entropy, and Gibbs free energy of solution of phenylphosphonic acid in the selected organic solvents were calculated from the measured solubility data by the modified van't Hoff equation.

Equation for solvent activity correlation in ternary solutions with electrolyte and molecular components

An analytical thermodynamically self-consistent equation is proposed for the dependence on composition of the solvent activity of ternary solutions with electrolytic and molecular components (polyols, sugars, etc.). This equation was derived on the basis of the sum of contributions from short and long range interactions to the excess Gibbs free energy of solution. The correlation of experimental data corresponding to 20 aqueous ternary systems was successfully carried out. The results obtained demonstrate an excellent fitting capability of the proposed equation.

Determination and correlation of solubility of tylosin tartrate in alcohol mixtures

Data on (solid+liquid) equilibrium of tylosin tartrate in {methanol+(ethanol, 1-propanol or 2-propanol)} solvents will provide essential support for industrial design and further theoretical studies. In this study, the solubility of tylosin tartrate in alcohol mixtures was measured over temperature range from (278.15 to 323.15)K under atmospheric pressure by a gravimetric method. From the experimental results, the solubility of tylosin tartrate in selected solvents noted above was found to increase with increasing temperature and mass fraction of methanol. The solubility data were correlated with the modified Apelblat equation, the λh equation and van’t Hoff equation. The results showed that the three equations agreed well with the experimental values, and that the modified Apelblat equation was more accurate than the λh equation and van’t Hoff equation. Further, the standard enthalpy, standard entropy and standard Gibbs free energy of solution of tylosin tartrate in mixed solvents were calculated according to solubility results, model parameters with modified Apelblat equation and van’t Hoff equation.

Solubilities of carbon dioxide in 2-methoxyethyl acetate, 1-methoxy-2-propyl acetate and 3-methoxybutyl acetate

The solubilities of CO2 in 2-methoxyethyl acetate, 1-methoxy-2-propyl acetate, and 3-methoxybutyl acetate were measured by isothermal synthesis method under pressures up to 1.2MPa and at temperatures ranging from (293.15 to 333.15)K. Henry’s constant was calculated based on experimental data regression. The solubilities of CO2 were found to increase with decreased temperature and increased the methyl group to the molecular structure of the absorbent. Henry’s constant and volumetric solubility of selected absorbents at T=298.15K were compared with those of commercial absorbents and common solvents. 3-Methoxybutyl acetate showed the best performance by mole fraction, and 2-methoxyethyl acetate behaved the best by volumetric fraction. Based on Henry’s constant, thermodynamic properties such as Gibbs free energy of solution, enthalpy of solution, and absorption entropy of solution were determined. These properties are very essential for designing an absorption process.

Thermodynamics of solvation and solvophobic effect in formamide

Using semi-adiabatic calorimetry, we measured the enthalpies of solution for various low-polar compounds including alkanes, aromatic hydrocarbons and their halogenated derivatives in formamide at temperature of 298K. For the same compounds, the values of limiting activity coefficients in formamide were determined using GC headspace analysis at 298K, and Gibbs free energies of solution and solvation were calculated. Based on these data and the available literature values of the Gibbs free energy of solvation in formamide for a number of other low-polar solutes, a study of the solvophobic effect in this solvent is performed, and its resemblance to the hydrophobic effect in aqueous solutions is demonstrated. It is shown that the contribution of the solvophobic effect into the solvation Gibbs free energy in formamide is much higher than that in aliphatic alcohols, but lower than that in water. Like in water, the magnitude of this contribution for different solutes linearly increases with the solute molecular volume. Solvophobic effect also significantly affects the enthalpies of dissolution in formamide, causing them to be more negative in the case of alkanes and more positive in the case of arenes.

Solubility of Terephthalic Acid in Subcritical Water

The solubility of terephthalic acid (TPA) in subcritical water was measured as a function of the temperature from (349 to 547) K at a pressure of 10.0 MPa. A semibatch flow apparatus was developed for the solubility measurement. N-Methylpyrrolidone was used as a good solvent for collection of TPA saturated in subcritical water without deposition upon cooling. The solubility of TPA in water showed an exponential increase with increasing temperature from 1.25·10–5 at 349 K to 2.99·10–2 at 547 K. The aqueous solubility of TPA was found to be lower than those of m- and o-phthalic acids by one and three orders of magnitude, respectively. The Gibbs free energy of solution (ΔGsol) as well as the enthalpic and entropic components (ΔHsol and –TΔSsol) were calculated from the temperature dependence of the solubility. The thermodynamic analysis showed that the ΔGsol gradually decreases with increasing temperature, as a result of the competition between a large increase in ΔHsol and a large decrease in –TΔSsol. The ΔGsol value decreased in the order of (p-phthalic acid) > (m-phthalic acid) > (o-phthalic acid) due to a decrease in –TΔSsol, whereas ΔHsol showed a small variation among the three isomers.

Thermodynamic investigation of the ternary mixed aqueous electrolyte (MgCl 2 + MgSO 4) system by potentiometric method at T = 298.15 K

This work reports the results of thermodynamic investigation of the ternary mixed-electrolyte system (MgCl 2 + MgSO 4 + H 2O). The investigation was performed based on Pitzer ion interaction model by using the potentiometric technique at T = 298.15 K. The mean activity coefficients of MgCl 2 in the mixed aqueous electrolyte system were determined on the galvanic cell without liquid junction of the type: Mg-ISE|MgCl 2 ( m A ), MgSO 4 ( m B ), H 2O|Ag/AgCl over total ionic strengths from (0.001 to 8.000) mol · kg −1 for different series of salt ratio r ( r = m MgCl 2 / m MgSO 4 = 2.5 , 5.0 , 7.5 , 10.0 , 15.0 and pure MgCl 2). The PVC based magnesium ion-selective electrode (Mg-ISE) and the Ag/AgCl electrode used in this work were made in our laboratory and had a reasonably good Nernst response. The experimental results obeyed the Harned rule, and the Pitzer model could be used to describe this ternary system satisfactorily. Pitzer ion-interaction parameters for mixed salts were determined for this system. Then, these parameters ( θ ClSO 4 = 0.0252 ± 0.0042 , ψ MgClSO 4 = - 0.0049 ± 0.0003 ) were used to calculate the values of the mean activity coefficients of MgSO 4, the osmotic coefficients of water ( ϕ) and the excess Gibbs free energies of solution ( G E ) for the whole series of the studied electrolyte systems.

Thermodynamic investigation of the ternary mixed electrolyte (CoCl 2 + CoSO 4 + H 2O) system by EMF measurements at T = 298.15 K

In this work, the ternary mixed electrolyte system (CoCl 2 + CoSO 4 + H 2O) was investigated based on the Pitzer ion-interaction model by using the potentiometric technique at T = 298.15 K. The mean activity coefficients of CoCl 2 in the mixed aqueous electrolyte system were determined on the galvanic cell without liquid junction of the type: Co-ISE|CoCl 2 ( m A ), CoSO 4 ( m B ), H 2O|Ag/AgCl over total ionic strengths from (0.001 to 6.000) mol · kg −1 for different series of salt ratio r ( r = m CoCl 2 / m CoSO 4 = 1.00 , 2.50 , 5.00 , 10.00 and pure). The PVC based cobalt ion-selective electrode (Co-ISE) and the Ag/AgCl electrode used in this work were made in our laboratory and had a reasonably good Nernst response. The experimental results obeyed the Harned rule, and the Pitzer model could be used to describe this ternary system satisfactorily. Furthermore, the parameters obtained with the Pitzer model ( θ ClSO 4 = 0.0719 ± 0.0099 , ψ CoClSO 4 = 0.0088 ± 0.0003 ) were used to calculate the values of the mean activity coefficients of CoSO 4, the osmotic coefficients of water ( ϕ) and the excess Gibbs free energies of solution ( G E ) for the whole series of the studied electrolyte systems.

On algorithm for the calculation of the equilibrium composition of water-salt systems on the basis of the Pitzer model

Calculating the equilibrium composition of systems under given conditions (usually, temperature and pressure) is a core in the majority of the existing computer models of geochemical processes. Recently, Shvarov [1] investigated the thermodynamic consistency of the models of nonideal aqueous solutions that are used in geochemical calculations. He distinguished necessary and sufficient conditions for the thermodynamic consistency of the physicochemical models of real (nonideal) solutions and presented particular examples of errors appearing when these criteria are not met. In addition, Shvarov [1] claimed that the models that are currently used for concentrated electrolyte solutions are thermodynamically inconsistent. Such a pessimistic conclusion is related to a large extent to the fact that Shvarov’s [1] analysis was limited to the Debye‐Huckel model, which is applicable to diluted aqueous solutions, and its empirical modifications aimed at extending to concentrated aqueous solutions. Indeed, such models are thermodynamically inconsistent. However, models have been developed allowing adequate description of the behavior of concentrated aqueous solutions. One of them is the wellknown Pitzer model [2, 3] proposed for the description of the properties of dense electrolyte solutions in a wide range of temperatures, pressures, and compositions. The Pitzer model was developed on the basis of the Gibbs method and is, consequently, thermodynamically sound. If correct numerical algorithms are employed, the Pitzer model allows for the calculation of chemical equilibria in water‐ salt systems within a wide concentration range. The Pitzer model is an example of the rigorous statistical mechanical description of a multicomponent fluid system and the calculation of free energy by the Gibbs method. The derivation of an expression for free energy in the Pitzer model was described in detail in [2, 3], and only its basic principles are shortly discussed here. It is based on the approach developed by McMillan and Mayer [4], who described interactions between dissolved species within the mean field approximation and ignored the detailed description of interactions between individual particles. It should be emphasized that these approximations concern interactions between particles, i.e., a microscopic Hamiltonian. The free energy function is further derived in accordance with the statistical method of Gibbs using the methods of group expansion of Mayer [5, 6] and divergence elimination [6, 7] for the calculation of the configuration integrals of the long-range potentials of electrostatic interactions. Eventually, the excess Gibbs free energy of solution is given in the Pitzer model, after transition from volume concentrations to molalities, as [2]

Flame Emission Spectrometry in General Chemistry Labs: Solubility Product (Ksp) of Potassium Hydrogen Phthalate

In this general chemistry laboratory, flame emission spectrometry is used to determine the potassium ion concentration in saturated solutions of potassium hydrogen phthalate (KHP) in the 0–65 °C temperature range. From these data the solubility products (Ksp), the Gibbs free energies of solution (ΔsolnG°), the standard enthalpy of solution (ΔsolnH°), and the standard entropy of solution (ΔsolnS° are calculated. Students also determine Ksp in 0.50 M KCl at room temperature wherein the K+ concentration is determined by flame emission and HP- concentration is determined via titrating with NaOH. In determining both the K+ and HP- concentrations in a saturated solution of KHP in 0.50 M KCl, students verify that Ksp is a constant by showing that the same numerical values are obtained, with and without KCl. This experiment also addresses one of the serious problems we and many others have noticed; students do not know how to prepare solutions accurately, especially dilute solutions. We therefore require our stud...

Osmotic coefficients and solvation thermodynamics of aqueous solutions of some lower poly(ethylene glycol)s at different temperatures

The osmotic coefficients of aqueous solutions of ethylene glycol (MEG), diethylene glycol (DEG), triethylene glycol (TEG) and tetraethylene glycol (TTEG) were determined by freezing point measurements. On the basis of these data the activity coefficient of the solute, the excess Gibbs free energies of solution as well as the respective partial molar functions of solute and solvent were determined. The linear coefficient of the thermodynamic function characterising the limiting effect of a solute on the solvation quantities of a water molecule was calculated from the partial molar volume and expansibilities of the investigated compounds. For more concentrated solutions the difference in Gibbs free energy of a solvent molecule relative to the pure solvent were estimated and from the temperature dependence of the difference in the Gibbs free energy, the difference in the enthalpy and entropy of a solvent molecule in solution were calculated.