Limiting Activity Coefficients Research Articles

Activity Coefficients at Infinite Dilution of Polar Solutes in 1-Butyl-3-methylimidazolium Tetrafluoroborate Using Gas−Liquid Chromatography

Activity coefficients at infinite dilution of 17 polar solutes included linear and branched C1 to C5 alcohols, chlorinated methane, acetone, acetonitrile, ethyl acetate, 1,4-dioxane, and cyclohexanone in the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate were determined by gas chromatography using the ionic liquid as the stationary phase. The measurements were carried out at temperatures between (303.15 and 343.15) K. From the temperature dependence of the limiting activity coefficients, partial molar excess enthalpies at infinite dilution of the organic solutes in the ionic liquid have been derived.

Limiting Separation Factors and Limiting Activity Coefficients for Hexanal, 2-Methylbutanal, 3-Methylbutanal, and Dimethylsulfide in Water at (98.1 to 99.0) °C

This work is a continuation of preceding work in which limiting separation factors of important wort flavor components in water at 100 °C were determined. In unpublished experiments, the vapor-liquid equilibrium (VLE) of the same aromatic compounds was also researched at atmospheric conditions. No significant differences between the previous published limiting separation factors at 100 °C and the unpublished ones at atmospheric conditions could be observed. Because of this fact, the results of the measurements were used to calculate residue curves during the atmospheric boiling of wort. This study was only investigated at atmospheric conditions. A recirculating Gillespie-type still was used to determine the limiting separation factor (K∞) for hexanal (x), 2-methylbutanal (x), 3-methylbutanal (x), and dimethylsulfide (x) in water (1 - x). Since the solutions were highly dilute (x < 10 -6 ), infinite dilution was assumed. As the investigated components do not have large absorbances in the UV region, they could not be analyzed by UV spectroscopy. Therefore, in contrary to the preceding work, they were analyzed by gas chromatography. As the boiling point of the solution only changed slightly at the given atmospheric conditions (ΔT ≤ 0.9 °C), the limiting separation factors were acquired assuming a constant average temperature of 98.55 °C. Thus, limiting activity coefficients were calculated at the same average temperature. The calculated limiting activity coefficient depends highly on the reliability of the vapor pressure data of the pure components.

Temperature Dependences of Limiting Activity Coefficients, Henry’s Law Constants, and Derivative Infinite Dilution Properties of Lower (C1–C5) 1-Alkanols in Water. Critical Compilation, Correlation, and Recommended Data

A comprehensive review is presented of experimental data on the limiting activity coefficients γ1∞, infinite dilution partial molar excess enthalpies H¯1E,∞ and heat capacities C¯p,1E,∞ of lower 1-alkanols (C1–C5) in water. For each alkanol, the compiled data are critically evaluated and correlated with a suitable model equation providing adequate simultaneous description of the equilibrium measurements and the calorimetric information. As a result, recommended thermodynamically consistent temperature dependences of γ1∞, H¯1E,∞, and C¯p,1E,∞ of superior accuracy are established in the range from the melting point to the normal boiling point of water. In addition, by employing literature data on the respective residual properties of the pure 1-alkanols, analogous recommendations are also derived for the temperature dependences of the Henry’s law constants, hydration enthalpies, and hydration heat capacities. Evolution of the various infinite dilution thermodynamic properties of aqueous 1-alkanols with temperature and homologous series is briefly discussed.

Experimental Study of Thermodynamic Properties of Mixtures Containing Ionic Liquid 1-Ethyl-3-methylimidazolium Ethyl Sulfate Using Gas−Liquid Chromatography and Transpiration Method

Activity coefficients at infinite dilution of 46 solutes such as alkanes, alkenes, alkylbenzenes, linear and branched C1−C6 alcohols, esters, aldehydes, cyclohexanone oxime, and e-caprolactam in the ionic liquid (IL) 1-ethyl-3-methylimidazolium ethyl sulfate or [EMIM][EtSO4] have been determined by gas chromatography using the IL as the stationary phase. The measurements were carried out at different temperatures between (302 and 396) K. From the temperature dependence of the limiting activity coefficients, partial molar excess enthalpies at infinite dilution of the solutes in the ILs have been derived. Vapor−liquid equilibria (VLE) of binary mixtures containing water with [EMIM][EtSO4] were studied using the transpiration method. VLE measurements were carried out over the broad concentration range at temperatures between (302.9 and 322.9) K. Activity coefficients γi of water in the [EMIM][EtSO4] have been determined from the VLE data and are described formally by using the NRTL equation. Furthermore, act...

Infinite dilution activity coefficients, specific retention volumes and solvation thermodynamics of hydrocarbons in C 78H 158 branched alkane solvent

Kováts's retention indices were determined for 60 hydrocarbons by capillary gas–liquid chromatography at temperatures from 373.15 to 433.15 K using fused silica open tubular column coated with 19,24-dioctadecyldotetracontane (C 78H 158) as stationary phase. Gas–liquid equilibrium parameters (specific retention volumes, standard Gibbs energy differences and limiting activity coefficients) were calculated for isoalkanes, cycloalkanes, alkenes, alkynes, aromatics on the basis of absolute retention data of n-alkanes determined by GLC using packed column with the same stationary phase. It was concluded that molecular shape and size have an important effect on limiting activity coefficient values. The standard Gibbs free energy differences of solute transfer were correlated by a Kirchhoff-type temperature function and the thermodynamic parameters of the solvation (partial molar standard enthalpy and entropy differences at reference temperature T * = 403.15 K, furthermore heat capacity differences) were determined. The predictive ability of various entropic models was investigated on the new experimental data of saturated hydrocarbons and it is shown that the modified UNIFAC-FV model, Kannan-FV, represents satisfactorily the presented experimental limiting activity coefficient data of alkanes in size-asymmetric solutions.

Activity coefficients at infinite dilution and enthalpies of solution of methanol, 1-butanol, and 1-hexanol in 1-hexyl-3-methyl-imidazolium bis(trifluoromethyl-sulfonyl) imide

Activity coefficients at infinite dilution γ i ∞ of methanol, 1-butanol, and 1-hexanol in the ionic liquid 1-hexyl-3-methyl-imidazolium bis(trifluoromethyl-sulfonyl) imide ([HMIM][NTf 2]) have been determined by gas chromatography using the ionic liquids as stationary phase. The measurements were carried out at different temperatures between 298 K and 396 K. From the temperature dependence of the limiting activity coefficients partial molar excess enthalpies at infinite dilution H i E, ∞ of the alcohol in the ionic liquid have been derived. Additionally, enthalpies of solution of the same alcohols in the [HMIM][NTf 2] have been measured at T = 298.15 K in the range of low concentrations using titration calorimetry. Results at infinite dilution, H i E, ∞ , are compared with those indirectly obtained from activity coefficients in infinite dilution γ i ∞ . Within the experimental error of both methods thermodynamic consistency has been confirmed.

Temperature Dependences of Limiting Activity Coefficients and Henry's Law Constants for Nitrobenzene, Aniline, and Cyclohexylamine in Water

Recommended data for the limiting activity coefficients ( ) of nitrobenzene, aniline, and cyclohexylamine in water were established as a function of temperature by the simultaneous correlation of the values resulting from specialized vapor−liquid equilibrium measurements and related thermal data for highly dilute solutions. The new values of were determined by the Rayleigh distillation, circulation still, and headspace analysis methods. The limiting partial molar excess heat capacities were derived from measurements by the Picker flow microcalorimetry. These values were combined with all available literature data on the limiting activity coefficients and the limiting partial molar excess enthalpies. This allowed us to produce a thermodynamically consistent fit of between 273 K and 373 K, which was in turn used in combination with pure solute vapor pressures to calculate the Henry's law constants (kH).

Determination of the infinite dilution diffusion and activity coefficients of alkanes in polypropylene by inverse gas chromatography

AbstractInfinite dilution diffusion and activity coefficients of n‐hexane, n‐heptane, and n‐decane in polypropylene were measured from 373.15 to 393.15 K by inverse gas chromatography. The influences of small molecule solvent and temperature on the infinite dilution diffusion and activity coefficients were investigated. The results showed that the infinite dilution diffusion coefficient decreased but the infinite dilution activity coefficient increased with an increasing number of CH2 group in the aliphatic solvents. The temperature increase resulted in the increase in the infinite dilution diffusion coefficient and the decrease in the infinite dilution activity coefficient. The graphs plotted according to the results of the infinite dilution diffusion coefficient versus temperature were in agreement with the Arrhenius equation. Diffusion constant and activation energy were obtained from the Arrhenius equation. Also, the interdependence on the infinite dilute activity coefficient and temperature accorded with Gibbs‐Helmholtz equation. From the temperature dependence of the limiting activity coefficients partial molar excess enthalpy at infinite dilution HE,∞ was obtained. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 1925–1930, 2006

Limiting Separation Factors and Limiting Activity Coefficients for 2-Furfural, γ-Nonalactone, Benzaldehyde, and Linalool in Water at 100 °C

In combination with previous work in which limiting separation factors of important wort flavor components in water at 100 °C were determined, this work deals with the limiting separation factor (K∞) for 2-furfural (x), γ-nonalactone (x), benzaldehyde (x), and linalool (x) in water (1 − x). As the solutions are highly dilute (x < 10-5), infinite dilution is assumed. The condensed vapor and liquid samples were analyzed using UV spectroscopy. As the confidence intervals are very small, the method showed a good reproducibility. The calculated limiting activity coefficient depends highly on the reliability of the vapor pressure data of the pure components. The measurements of the limiting separation factors of wort aroma compounds in water were investigated to figure out the steaming behavior of these components during the atmospheric boiling of wort. With this knowledge, residue curves can be calculated to predict a needed total evaporation individually for every brew.

New developments in differential ebulliometry: Experimental and theoretical

A new ebulliometer has been developed in which superheat is discharged from the vapour–liquid mixture issuing from the Cottrell pump before it impinges on an otherwise vacuum-insulated temperature sensor. The convoluted chamber through which the mixture passes should also assist the attainment of phase equilibrium in binary mixtures. Measurements for several solvents showed unusually broad plateau regions with slopes much smaller than those reported by other researchers. Vapour pressures for several solvents were in close agreement with literature values. For the measurement of limiting activity coefficients, a new experimentally very simple procedure was developed for finding the difficult-to-determine evaporation ratio, ϕ, based on the steady-state macroscopic energy balance. Results are presented for two pure solvents, viz. ethylacetate and cyclohexane. Exact equations, based on material balances and equilibrium relationships involving ϕ then permit calculation of limiting activity coefficients. Measured temperature-composition data are presented for the ethylacetate (1)–toluene (2) and hexane (1)–ethylacetate (2) systems and the ebulliometer characterization procedure is illustrated for three binary systems. Exact differential equations for the temperature and pressure derivatives with respect to composition, and incorporating the full Gibbs-Duhem equation, are derived. These can be used to find the very useful temperature–pressure derivative (∂ T/∂ p) x 1 at any composition and also form the basis for a new thermodynamic consistency test.

Thermodynamic Properties of Mixtures Containing Ionic Liquids. 8. Activity Coefficients at Infinite Dilution of Hydrocarbons, Alcohols, Esters, and Aldehydes in 1-Hexyl-3-methylimidazolium Bis(trifluoromethylsulfonyl) Imide Using Gas−Liquid Chromatography

Activity coefficients at infinite dilution of alkanes, alkenes, and alkylbenzenes as well as of the linear and branched C1−C6 alcohols, esters, and aldehydes in the ionic liquids 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide have been determined by gas chromatography using the ionic liquids as stationary phase. The measurements were carried out at different temperatures between 301 K and 396 K. From the temperature dependence of the limiting activity coefficients, partial molar excess enthalpies at infinite dilution of the solutes in the ionic liquids have been derived.

Thermodynamic Properties of Mixtures Containing Ionic Liquids. 9. Activity Coefficients at Infinite Dilution of Hydrocarbons, Alcohols, Esters, and Aldehydes in Trimethyl-butylammonium Bis(trifluoromethylsulfonyl) Imide Using Gas−Liquid Chromatography and Static Method

Activity coefficients at infinite dilution of solutes such as alkanes, alkenes, and alkylbenzenes as well as of the linear and branched C1−C6 alcohols, esters, and aldehydes in the ionic liquids trimethyl-butylammonium bis(trifluoromethylsulfonyl) imide [Me3BuN][NTf2] have been determined by gas chromatography using the ionic liquids as stationary phase. The measurements were carried out at different temperatures between 302 K and 393 K. From the temperature dependence of the limiting activity coefficients, partial molar excess enthalpies at infinite dilution of the solutes in the ionic liquids have been derived. Vapor−liquid equilibria (VLE) of binary mixtures containing methanol, ethanol, and propan-1-ol in [Me3BuN][NTf2] were studied by using a static method. VLE measurements were carried out covering the whole concentration range at four different temperatures between 298.15 K and 313.15 K. Activity coefficients γi of solutes in the ionic liquid and their osmotic coefficients φi in the [Me3BuN][NTf2] have been determined from the VLE data and are described formally by using the NRTL equation. and for methanol, ethanol, and propan-1-ol in [Me3BuN][NTf2] are derived from the both the GC and the static method.

Limiting Separation Factors and Limiting Activity Coefficients for 2-Phenylethanol and 2-Phenylethanal in Water at 100 °C

A recirculating Gillespie-type still was used to determine the limiting separation factor (K∞) for 2-phenylethanol (x) or 2-phenylethanal (x) + water (1 − x). Since the solutions are highly dilute (x < 10-5), infinite dilution is assumed. The condensed vapor and liquid samples were analyzed using UV spectroscopy. The confidence intervals are very small, and thus the method has a good reproducibility. The calculated limiting activity coefficient depends highly on the reliability of the pure components vapor pressure data.

Measurement of infinite dilution activity coefficients of 1-alkanols (C1–C5) in water as a function of temperature (273–373 K)

Limiting activity coefficients ( γ 1 ∞ ) of lower (C1–C5) 1-alkanols in water were measured at several temperatures covering the range from the freezing to the normal boiling point of water. Five experimental techniques, namely headspace analysis, inert gas stripping, comparative tensimetry, Rayleigh distillation, and the method of circulation still, were employed for the purpose. To establish reliable temperature dependence of γ 1 ∞ for each of the systems, careful goal-directed measurements were carried out applying the methods alternatively in accordance with the applicability conditions. The method-to-method accord of the results, their thermodynamic consistency with calorimetric data on related thermal properties and their accuracy were verified using two procedures.

Refined non-steady-state gas–liquid chromatography for accurate determination of limiting activity coefficients of volatile organic compounds in water: Application to C 1–C 5 alkanols

This work presents a new refined method of non-steady-state gas–liquid chromatography (NSGLC) suitable for determination of limiting activity coefficients of VOCs in water. The modifications done to the original NSGLC theory address its elements (as the solvent elution rate from the column) as well as other new aspects. The experimental procedure is modified accordingly, taking advantage of current technical innovations. The refined method is used systematically to determine limiting activity coefficients (Henry's law constants, limiting relative volatilities) of isomeric C 1–C 5 alkanols in water at 328.15 K. Applied to retention data measured in this work the refined NSGLC theory gives values 15–20% higher than those from the original approach. The values obtained by the refined NSGLC method agree very well (typically within 3%) with the most reliable literature data determined by other experimental techniques, this result verifying thus the correct performance of the refined method and demonstrating an improved accuracy of the new results.

Thermodynamic Properties of Mixtures Containing Ionic Liquids. 6. Activity Coefficients at Infinite Dilution of Hydrocarbons, Alcohols, Esters, and Aldehydes in 1-Methyl-3-octyl-imidazolium Tetrafluoroborate Using Gas−Liquid Chromatography

Activity coefficients at infinite dilution of alkanes, alkenes, and alkylbenzenes as well as of the linear and branched C1−C6 alcohols, esters, and aldehydes in the ionic liquid 1-methyl-3-octyl-imidazolium tetrafluoroborate were determined by gas chromatography using the ionic liquid as the stationary phase. The measurements were carried out at different temperatures between 302 K and 396 K. Data points (204) have been obtained for 51 solutes. From the temperature dependence of the limiting activity coefficients, partial molar excess enthalpies at infinite dilution of the solutes in the ionic liquid have been derived.

Thermodynamic Properties of Mixtures Containing Ionic Liquids. 5. Activity Coefficients at Infinite Dilution of Hydrocarbons, Alcohols, Esters, and Aldehydes in 1-Methyl-3-butyl-imidazolium Bis(trifluoromethyl-sulfonyl) Imide Using Gas−Liquid Chromatography

Activity coefficients at infinite dilution ( ) of alkanes, alkenes, and alkylbenzenes as well as of the linear and branched C1−C7 alcohols, esters, and aldehydes in the ionic liquids 1-methyl-3-butyl-imidazolium bis(trifluoromethyl-sulfonyl) imide were determined by gas chromatography using the ionic liquid as stationary phase. The measurements were carried out at different temperatures between 302 K and 385 K. From the temperature dependence of the limiting activity coefficients, partial molar excess enthalpies at infinite dilution ( ) of the solutes in the ionic liquids have been derived.

Revision of MOSCED Parameters and Extension to Solid Solubility Calculations

New pure component parameters are presented for the MOSCED limiting activity coefficient model for 133 solvents with an absolute average deviation of 10.6% to experimental literature data. The MOSCED model has been applied to solid−liquid equilibria correlation and compared with the experimental data available in the literature. The correlation of solubility of 26 solids in organic solvents has an average absolute deviation of 25%. This compares favorably to the prediction of the modified UNIFAC model.

Correlation of the critical micelle concentration for aqueous solutions of nonionic surfactants

The critical micelle concentrations (cmc, mole fraction) for nonionic C i E j surfactants in aqueous solution were calculated in this study using a modified excess Gibbs energy model (m-Aranovich and Donohue (AD) model). This local-composition lattice model was derived in our previous study for correlating the limiting activity coefficients. The only adjustable parameter required in the m-AD model is the interchange energy. In surfactant system calculations, this parameter is found as a strong function of the physical properties of surfactants. A generalized correlation for the interchange energy is proposed in this investigation. Satisfactory cmc calculation results (mole fraction) are obtained for 37 systems. The m-AD model has less number of generalized parameters in comparison to the theoretically based method, and shows better accuracy than that from other activity coefficient models. Predictions of the cmc values (mole fraction) for mixed nonionic surfactants systems are also applicable using this m-AD model.

Limiting Activity Coefficients of Phenol in Hydrocarbons

The activity coefficients of phenol in a number of hydrocarbons were determined from experimental data on phenol distribution between aqueous and hydrocarbon liquid phases, using data on the limiting activity coefficients of phenol in water. Ten systems containing saturated and aromatic hydrocarbons were examined in the temperature range 283–328 K.