Experimental Activity Coefficients Research Articles

Force field for halide and alkali ions in water based on single-ion and ion-pair thermodynamic properties for a wide range of concentrations.

A classical non-polarizable force field for the common halide (F-, Cl-, Br-, and I-) and alkali (Li+, Na+, K+, and Cs+) ions in SPC/E water is presented. This is an extension of the force field developed by Loche et al. for Na+, K+, Cl-, and Br- (JPCB 125, 8581-8587, 2021): in the present work, we additionally optimize Lennard-Jones parameters for Li+, I-, Cs+, and F- ions. Li+ and F- are particularly challenging ions to model due to their small size. The force field is optimized with respect to experimental solvation free energies and activity coefficients, which are the necessary and sufficient quantities to accurately reproduce the electrolyte thermodynamics. Good agreement with experimental reference data is achieved for a wide range of concentrations (up to 4 mol/l). We find that standard Lorentz-Berthelot combination rules are sufficient for all ions except F-, for which modified combination rules are necessary. With the optimized parameters, we show that, although the force field is only optimized based on thermodynamic properties, structural properties are reproduced quantitatively, while ion diffusion coefficients are in qualitative agreement with experimental values.

Machine learning for determination of activity of water and activity coefficients of electrolytes in binary solutions

Activity of water and electrolytes in aqueous solutions is of utmost importance for multiple industrial applications. However, experimental determination of such values is time-consuming, while calculation of activity coefficients using numerical methods is challenging. By training neural networks models on literature data, one could predict activity of water and electrolytes easily, without requiring any experiment. In this paper, multiple descriptors (or features) are compared to predict activity coefficients of electrolytes and activity of water in electrolyte solutions. A neural network based on the Levenberg-Marquardt algorithm (LM-NN) showed high accuracy to calculate values, despite the small size of the training datasets. Both activity coefficients of electrolytes and activity of water in electrolyte solutions can be predicted accurately even on unseen data, using simple descriptors such as electrolyte concentration, ion sizes and charges. However, some discrepancies were observed due to the lack of representativeness of the training dataset. This could be solved by selecting training data sets that are similar (e.g. same group of the periodic table) to the unknown values, or by including available experimental data for the salt considered. The ability of the LM-NN to solve non-linear least square curve fitting problems makes it a good candidate to fit experimental activity coefficient data, with the advantage of simplicity as compared to e-NRTL or UNIQUAC methods. This method paves the way for accurate and quick determination of thermodynamic data for electrolyte solutions (and beyond) using machine learning, without necessitating large training datasets.

When Ions Defy Electrostatics: The Case of Superchaotropic Nanoion Adsorption

Nanometer-sized anions, like polyoxometalates and borate clusters, bind to nonionic hydrated matter driven by the chaotropic effect, which arises from the favorable dehydration of the ions. Herein, we evaluate the adsorption and activity coefficient of the superchaotropic Keggin polyoxometalate SiW12O404- (SiW) on nonionic surfactant (C8E4) micelles by modeling small-angle X-ray and neutron-scattering spectra. Neither hard sphere nor electrostatic repulsion models reproduce the experimental activity coefficient of adsorbed SiW ions on the micelles. However, the activity and binding of SiW on the micelles is well-described by a Langmuir adsorption isotherm. These results imply that adsorbed SiW ions are non-interacting and "create" around themselves adsorption sites on the micelle. The temperature dependence of the adsorption constant showed that the SiW adsorption is enthalpically driven and entropically unfavorable, in line with the typical chaotropic thermochemical signature. The adsorption enthalpy can be split into an electrostatic term and a water-recovery term to evaluate and qualitatively predict the superchaotropicity of a nanoion.

Measurements of infinite dilution activity coefficient for aromatic and aliphatic hydrocarbons in Deep Eutectic Solvent, 1-ethyl-1-methylpyrrolidinium bromide + ethylene glycol at different temperatures and a stated molar ratio

It is reported data concerning the thermodynamic properties of organic mixtures in pyrrolidinium based DES with ethylene glycol at different temperatures ranging from T = 313.15 to 343.15 K. The infinite dilution activity coefficients (IDACs) for 32 various organic solutes (e.g., alkanes, alkenes, alkynes, aromatics, cycloalkanes, cycloalkenes, alcohols, and ketones) as part of the limiting thermodynamic properties were studied using Gas Liquid Chromatography (GLC). The excess thermodynamic properties (enthalpies, entropies, and Gibbs free energies) were subsequently calculated from the experimental infinite dilution activity coefficients. Moreover, the values of the selectivities and capacities at infinite dilution were determined from the experimental infinite dilution activity coefficients achieved at the fixed experimental temperature, T = 313.15 K. The obtained selectivity and capacity values were compared to those found in the literature. Lastly, the results of the investigated [[EMPYR]Br + EG] DES in a molar ratio of 1:4 proved that this investigated system could be utilized for all the selected separation problems: benzene/toluene, cyclohexane/benzene, acetone/ethanol, and n-butanol/MEK.

Evaluation of the activity coefficients of ternary molecular solutions from osmotic coefficient data

A method is proposed for the evaluation of the activity coefficients of a solution constituted by a solvent (1) and two non-volatile molecular solutes (2,3) from the experimental dependence of the osmotic coefficient of the ternary solution (1,2,3) on composition. A generalized analytical expression is derived to describe such dependence, based on the sum of the weighted contributions of both binary systems and the contribution due to the mixing effect. With the resulting expression and using the solution of the Gibbs-Duhem differential equation for ternary systems, the equations that allows the evaluation of the corresponding experimental activity coefficients of both solutes in ideal dilute solution reference state (molality scale) are derived. From the comparative analysis and discussion of the results obtained for three ternary systems, it was possible to verify that the proposed methodology provides a rigorous alternative to evaluate suitable values ​​of activity coefficients from experimental data of osmotic coefficients. Finally, in order to facilitate the correlation of these values with equations originated in molecular solution modelling (NRTL, UNIQUAC, etc.), the relationships between the corresponding reference states and concentration scales were established.

Infinite Dilution Activity Coefficient Measurements for 1-Methyl-4-(1-methylethenyl)-cyclohexene as a Green Solvent for Separation

Infinite dilution activity coefficients for various solutes, which include alkanes, alkenes, alkynes, cycloalkanes, heterocycles, alcohols, aromatics, ketones, ethers, nitrile, and water, in a 1-methyl-4-(1-methylethenyl)-cyclohexene solvent were measured using gas–liquid chromatography at 303.15, 313.15, and 323.15 K. The focus of this study was to assess 1-methyl-4-(1-methylethenyl)-cyclohexene as a green solvent for separation processes. 1-Methyl-4-(1-methylethenyl)-cyclohexene, a nonpolar monoterpene solvent extracted from essential oils of citrus peels, was investigated as an alternative solvent to currently employed conventional organic solvents in separation processes. Through experimental infinite dilution activity coefficients, γ13∞, the values of partial molar excess enthalpy at infinite (ΔHiE,∞) were obtained using the Gibbs–Helmholtz equation. The infinite dilution selectivity (Sij∞) and capacity (Δkj∞) values were calculated from the experimental limiting activity coefficients and were compared with deep eutectic solvents, ionic liquids, and industrial solvents. From this study, it was observed that 1-methyl-4-(1-methylethenyl)-cyclohexene is not suitable to be used as an alternative for separation processes. In addition, activity coefficients at infinite dilution of different organic solutes in hexadecane were measured at various temperatures to validate the reliability and accuracy of gas–liquid chromatography. Finally, the experimental data were modeled using Aspen Plus, compared with experimental data, and found to be in good agreement.

Development of an Infinite Dilution Activity Coefficient Prediction Model for Organic Solutes in Ionic Liquids with Modified Partial Equalization Orbital Electronegativity Method Derived Descriptors.

The objective of this study was to develop a robust prediction model for the infinite dilution activity coefficients (γ∞) of organic molecules in diverse ionic liquid (IL) solvents. Electrostatic, hydrogen bond, polarizability, molecular structure, and temperature terms were used in model development. A feed-forward model based on artificial neural networks was developed with 34,754 experimental activity coefficients, a combination of 195 IL solvents (88 cations and 38 anions), and 147 organic solutes at a temperature range of 298 to 408 K. The root mean squared error (RMSE) of the training set and test set was 0.219 and 0.235, respectively. The R2 of the training set and the test set was 0.984 and 0.981, respectively. The applicability domain was determined through a Williams plot, which implied that water and halogenated compounds were outside of the applicability domain. The robustness test shows that the developed model is robust. The web server supports using the developed prediction model and is freely available at https://preadmet.bmdrc.kr/activitycoefficient_mainpage/prediction/.

Solubility Calculations of Methane and Ethane in Aqueous Electrolyte Solutions

Accurate calculation of light hydrocarbon solubilities in aqueous electrolyte solutions is critical for petroleum and geochemical applications. However, very few electrolyte Equations of State (e-EoS) have been used for calculation of light hydrocarbon solubilities. Thermodynamic calculation of gas (methane and ethane) solubilities in aqueous solutions of chloride salts are presented. This work introduces a new parameter estimation approach (which can predict well the liquid densities of aqueous solutions) for the electrolyte Cubic Plus Association EoS (e-CPA). The cation/anion–water interaction parameters are obtained from the regression of experimental mean ionic activity coefficients and liquid densities. The results show that the e-CPA with the new parameter estimation approach gives good agreements with the corresponding experimental data. The cation/anion–gas interaction parameters are obtained from the regression of experimental gas solubilities. The results show that the e-CPA with the new parameter estimation approach correlates the gas solubilities reasonably well. The gas dissolution mechanisms and salting effects are extensively analyzed and discussed for a deeper understanding of gas dissolution in aqueous electrolyte solutions.

Determination of the dispersion forces in the gas phase structures of ionic liquids using exclusively thermodynamic methods.

Ionic liquids are described by a delicate balance of Coulomb interaction, hydrogen bonding and dispersion forces. Dissecting the different types of interactions from thermodynamic properties is still a challenge. Here, we show that comparison of vaporization enthalpies of tetra-alkyl-ammonium ionic liquids with bis(trifluoromethylsulfonyl)imide [NTf2]- anions and the related molecular liquids, trialkylamines, allows for determining dispersion interactions in the gas phase ion-pairs. For this purpose, we measured vapor pressures and vaporization enthalpies of these ionic and molecular liquids by using a quartz-crystal microbalance. For supporting these data, we determined the vaporization enthalpies additionally from experimental activity coefficients at infinite dilution. Characteristic alkyl chain length dependences of the vaporization enthalpies have been established and were used for quantifying the dispersion forces in the gas phase species. The dissected dispersion contributions suggest that the alkyl chains do not show star-like topologies but embrace the anion maximizing the dispersion interactions. For the longest alkyl chains with eight carbon atoms, the dispersion interaction is as strong as two and a half hydrogen bonds. The proportion of dispersion in the gas phase species depending on the number of methylene groups in the ammonium cations is strongly supported by quantum chemical calculations.

Technical note: Estimating aqueous solubilities and activity coefficients of mono- and <i>α</i>,<i>ω</i>-dicarboxylic acids using COSMO<i>therm</i>

Abstract. We have used the COSMOtherm program to estimate activity coefficients and solubilities of mono- and α,ω-dicarboxylic acids and water in binary acid–water systems. The deviation from ideality was found to be larger in the systems containing larger acids than in the systems containing smaller acids. COnductor-like Screening MOdel for Real Solvents (COSMO-RS) underestimates experimental monocarboxylic acid activity coefficients by less than a factor of 2, but experimental water activity coefficients are underestimated more especially at high acid mole fractions. We found a better agreement between COSMOtherm-estimated and experimental activity coefficients of monocarboxylic acids when the water clustering with a carboxylic acid and itself was taken into account using the dimerization, aggregation, and reaction extension (COSMO-RS-DARE) of COSMOtherm. COSMO-RS-DARE is not fully predictive, but fit parameters found here for water–water and acid–water clustering interactions can be used to estimate thermodynamic properties of monocarboxylic acids in other aqueous solvents, such as salt solutions. For the dicarboxylic acids, COSMO-RS is sufficient for predicting aqueous solubility and activity coefficients, and no fitting to experimental values is needed. This is highly beneficial for applications to atmospheric systems, as these data are typically not available for a wide range of mixing states realized in the atmosphere, due to a lack of either feasibility of the experiments or sample availability. Based on effective equilibrium constants of different clustering reactions in the binary solutions, acid dimer formation is more dominant in systems containing larger dicarboxylic acids (C5–C8), while for monocarboxylic acids (C1–C6) and smaller dicarboxylic acids (C2–C4), hydrate formation is more favorable, especially in dilute solutions.

Consistent description of ion-specificity in bulk and at interfaces by solvent implicit simulations and mean-field theory.

Solvent-implicit Monte Carlo (MC) simulations and mean-field theory are used to predict activity coefficients and excess interfacial tensions for NaF, NaCl, NaI, KF, KCl, and KI solutions in good agreement with experimental data over the entire experimentally available concentration range. The effective ionic diameters of the solvent-implicit simulation model are obtained by fits to experimental activity coefficient data. The experimental activity coefficients at high salt concentrations are only reproduced if the ion-specific concentration-dependent decrement of the dielectric constant is included. The dielectric-constant dependent contribution of the single-ion solvation free energy to the activity coefficient is significant and is included. To account for the ion-specific excess interfacial tension of salt solutions, in addition to non-ideal solution effects and the salt-concentration-dependent dielectric decrement, an ion-specific ion-interface interaction must be included. This ion-interface interaction, which acts in addition to the dielectric image-charge repulsion, is modeled as a box potential, is considerably more long-ranged than the ion radius, and is repulsive for all ions considered except iodide, in agreement with previous findings and arguments. By comparing different models that include or exclude bulk non-ideal solution behavior, dielectric decrement effects, and ion-interface interaction potentials, we demonstrate how bulk and interfacial ion-specific effects couple and partially compensate each other. Our MC simulations, which correctly include ionic correlations and interfacial dielectric image-charge repulsion, are used to determine effective ion-surface interaction potentials that can be used in a modified Poisson-Boltzmann theory.

Infinite dilution activity coefficients and thermodynamic properties of selected organic solutes and water dissolved in 1, 6-hexanediol

The experimental activity coefficients (γ13∞) and gas-to-liquid partition coefficients (KL) at infinite dilution for 34 organic solutes and water were determined in 1.6-hexanediol (HDO) by the gas–liquid chromatography technique (GLC) in the temperature range from (323.15 to 353.15) K. Fundamental thermodynamic functions such as excess partial molar enthalpy (ΔHiE,(∞)), excess partial molar Gibbs energy, (ΔGiE,∞) and entropy, (TrefΔSiE,∞) at infinite dilution were calculated from experimental values of γ13∞. Reported data were discussed in terms of solvent-solute interactions, heat effects and mixing spontaneity. Selectivity (Sij∞) and capacity (kj∞) related to different separation problems were calculated from γ13∞ data and compared to the literature values for selected ionic liquids (ILs), deep eutectic solvents (DESs) and industrial solvents. New data reported in this study suggest that HDO may be proposed as an alternative solvent for the separation of alkanes-pyridine and alkanes-thiophene systems. Furthermore, it was found that adding a hydrogen bond acceptor to HDO enhances its performance as a separation solvent.

Extension of Cubic-Plus-Polar (CPP) equation of state (EoS) for application in aqueous electrolyte solutions

In this study, an extension of Cubic-Plus-Polar (CPP) equation of state (EoS), i.e. electrolyte CPP (eCPP), was proposed to study various aqueous binary electrolyte solutions as well as water-CO2-NaCl, water-CO2-Na2SO4, and water-H2S-NaCl ternary systems. To avoid complexity, polar (dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole) interactions were only considered for water, CO2, and H2S components, not for the studied ionic species in electrolyte solutions. In this work, the long-range electrostatic contribution was taken into account by Pitzer-Debye-Huckel equation. The proposed model has three adjustable parameters for each electrolyte, which were determined by fitting to experimental mean activity coefficient and liquid molar volume data of 79 aqueous strong electrolyte solutions at 0.1 MPa and 298.15 K. The overall average absolute relative deviation (AARD) between model-calculated values and experimental data were 1.05% and 1.44% for liquid molar volume and mean activity coefficient, respectively, while this value was 1.27% for predicted results of osmotic coefficient. Moreover, eCPP EoS predicted the liquid molar volumes of 15 different electrolyte solutions with an overall AARD of 0.6% in a wide range of pressure, temperature, and electrolyte concentration. The reliability of the proposed EoS (eCPP) was verified by the obtained AARDs.

The influence of the ionic liquids functionalization on interaction in binary systems with organic solutes and water – Thermodynamic data of activity coefficients at infinite dilution

In this work, the effect of IL’s functionalization of the interaction of IL with organic solutes and water at infinite dilution has been investigated. Based on the experimental activity coefficients at infinite dilution, (γ13∞) the possibility of using ionic liquids (ILs) in different separation processes, such as aliphatic from aromatic hydrocarbon (heptane/benzene, or cyclohexane/benzene), desulfurization and denitrification of model fuel (heptane/thiophene and heptane/pyridine) were investigated based on the experimental study of the activity coefficients at infinite dilution. The (γ13∞) values were determined for more than fifty different solutes including alkanes, cycloalkanes, alkenes, alkynes, aromatic hydrocarbons, alcohols, ethers, ketones, thiophene, acetonitrile, pyridine, 1-nitropropane and water in two ionic liquids: 4-(3-cyanopropyl)-4-methylmorpholinium tricyanomethanide, [Mo1,3CN][TCM] and 4-(3-hydroxypropyl)-4-methylmorpholinium tricyanomethanide, [Mo1,3OH][TCM]. The experiment was performed using inverse gas–liquid chromatography at a wide temperature range from T = (308.15 to 358.15) K. From the experimental data, the partial molar excess Gibbs energy (ΔG1E,∞), enthalpy (ΔH1E,∞) and entropy (Tref ΔS1E,∞) at infinite dilution were determined. The gas–liquid partition coefficients of the solutes, KL were also calculated. Finally, two the values of two factors important from separation point of view: selectivity (S12∞) and capacity (k2) at infinite dilution for few separation problems as hexane/benzene, cyclohexane/benzene, heptane/thiophene, and heptane/pyridine were calculated from γ13∞ and compared to literature values for other ionic liquids taken from available literature. Moreover, physicochemical properties of pure IL including liquid density and dynamic viscosity data, important from the technological point of view was determined at a wide temperature range.

Activity Coefficient Measuring and Modeling for a Single and Symmetrical Mixture in a Mixed Solvent and Friedman’s Footprint of a Higher-Order Limiting Law

This study is conducted to investigate the HCl + NaCl + H2O + C2H5OH mixed electrolyte systems. The experimental activity coefficients are collected through measuring the electromotive force by using a cell containing pH and silver chloride electrodes in different alcohol mass fractions w(C2H5OH) in H2O (where w = 0.10, 0.20, and 0.50). All the used electrolyte molalities are between 0.01 and 2.5 mol kg–1, at 298.15 ± 0.01 K. Modeling is achieved using mean activity coefficients data for single and mixed HCl and NaCl in mixed solvent. A detailed study of Pitzer’s equations regarding effectiveness of nonionic species is taken into account. The result shows that this approach is a valuable aspect of the Pitzer equation for activity coefficient correlation of pure and mixed electrolytes, in mixed solvent media. The result underlines the importance of including Friedman’s higher-order limiting law (HOLL) regarding fitting the activity coefficient data for symmetric mixture, that is, not only theoretically accurate but also practically important. It seems that this work would be considered as the first experimental observation for the HOLL to correlate the activity coefficient of symmetrical mixture.

Extending the UNIFAC model for ionic liquid–solute systems by combining experimental and computational databases

AbstractConsidering that the predictive UNIFAC model is highly valuable for the solvent selection, process design and optimization of separation tasks, a large extension of this model to ionic liquid (IL)–solute systems is presented by combining experimental and COSMO‐RS derived databases. The experimental infinite dilution activity coefficient (γ∞) data of different solutes in ILs are first collected exhaustively to extend UNIFAC‐IL to cover all involved IL and conventional functional groups. Afterwards, the experimental and COSMO‐RS calculated γ∞ are compared for different types of solutes to evaluate the potential of using COSMO‐RS predictions as quasi‐experimental data for further UNIFAC‐IL extension. In the cases where COSMO‐RS can provide quantitatively accurate predictions after calibration, additional γ∞ database is specifically generated to regress more group interaction parameters in the UNIFAC‐IL model. Finally, a large experimental liquid–liquid and vapor–liquid equilibria database is collected and employed to evaluate the predictive performance of the obtained γ∞‐based UNIFAC‐IL model.

Volumetric, enthalpic and VLE studies of binary mixtures of isomers of butyl chloride with cyclohexane at 298.15 K

Excess molar volumes (VmE), excess molar enthalpy (HmE) and isothermal vapor-liquid equilibrium data for n-, sec- and tert-butyl chloride (A) + cyclohexane (B) systems were measured at 298.15 K. Excess molar Gibbs free energy (GmE) for these systems were calculated by Barker's method. The VmE and HmE for these mixtures follow the sequence: n- > sec- > tert-butyl chloride while it is reverse for GmE. Prigogine-Flory-Patterson theory (PFP) predicts the experimental VmE and HmE data for these systems quite well except for HmE of n-butyl chloride (xA>0.5) mixtures and tert-butyl chloride mixtures for xA<0.5. The activity coefficients γA and γB of the components in binary (A+B) mixtures were also predicted by Singh and Maken activity coefficient model employing limited experimental activity coefficient data.

Investigation of Thermodynamic Nonideality of Solid Li-ion Electrodes Using Concentrated Solution Theory

Li-Ion batteries (LIBs) is poised to dominate the energy storage market of electric vehicles (EVs) and renewable-energy-integrated grids over the next few decades. To address safety and lifetime concerns of the technology, significant efforts have been devoted to advancing online battery diagnostic tools and evolving charging/discharging protocols to enhance their stability and elongate their lifetime, and both have been found to be highly amenable to physics-based models (PBMs). With the continuous improvements and breakthroughs of computer technology, PBMs in substitute of equivalent circuit models (ECMs) have been employed to produce high-fidelity, low-computational-cost reduced-order-models (ROMs) for battery management system (BMS), despite the fact that simplifications have regularly been made. For example, in a general PBM of LIBs, Li-ion diffusion is governed by Fick’s second law of diffusion in a dilute solution (Fig. 1), which neglected the thermodynamic nonideality of a solid active material which experiences large concentration variation in electrochemical processes. Though the above fact likely indicates that such PBMs contain some battery physics to represent the key electrochemical processes, it does not exclude the possibility that important correlations could be associated with physics that have been neglected. For example, although both ks (solid/liquid interface reaction rate) and D (diffusivity of Li-ion in a solid phase) exhibited correlations with battery State-Of-Charge (SOC), especially at the end of discharge, they have been assumed to be constants over the entire range of SOC. In fact, their values reported from different researchers show variation spanning over 2 to 5 order of magnitude. With this large variation, both battery SOC and State-Of-Health (SOH) will remain unpredictable, which means that ultimately the battery management and diagnosis remains uncertain. Numerous theoretical and experimental studies support the inevitable Li-Li interactions when Li-ion deintercalation/intercalation from/into the active materials, especially with a sufficiently large concentration. This Li-Li interaction introduces thermodynamic nonideality which could not be described by the Fick’s second law of diffusion. Consequently, critical electrochemical kinetic and transport properties such as ks and D will have a strong correlation with the SOC. In this research, we will try to understand the nonideality of a solid Li-ion solution by the concentrated solution theory, as shown in Fig.1. We will use nonequilibrium thermodynamics in a concentrated solution to correlate ks/D with the activity coefficient of the solid solution γ and elaborate new governing equations for D and ks. Then, utilize the new correlations to process experimental data tested by EIS method and to regress the experimental activity coefficient γ. Furthermore, a methodology in determining the most appropriate constants for ks and D with a minimum discrepancy for a full charge/discharge cycle will be provided. Figure 1. (a) Inconsistency in KsS and D values between dilute solution model prediction and experimental results; (b) Ks and D comparison between dilute solution theory and concentrated solution theory; (c) Experimental and model prediction based on concentrated solution theory. Figure 1

Dispersion activity coefficient models. Part 1: Cubic equations of state

An explicit expression for dispersion in activity coefficient models can be derived from cubic equations of state (cEoS). Here we show that all the two-parameter cEoS deliver a van Laar type of equation. The difference between these equations can be characterized by a single parameter K, which can be computed directly from the cEoS characteristic parameters. The theoretical values for K are always higher than experimental activity coefficient data of alkane mixtures indicate. We show that mixtures of linear and branched alkanes require K=4.13 and K=3.04, respectively, while the lowest theoretical value, K=9, is given by the van der Waals equation. This mismatch in results is caused by the assumptions, which are made in the derivation of the van der Waals equation of state and which remain present in later developed cEoS. One of these is that all molecules are spherical, which leads to the inconsistency that the ratio of the covolume and the van der Waals volume is always 4, while this ratio for linear alkanes decreases rapidly to nearly 2 with increasing chain length. Another assumption is that all molecules experience the same number of external interactions, which neglects the fact that polyatomic molecules have less intermolecular interactions per spherical segment due to presence of covalent bonds and the occurrence of intramolecular interaction. Therefore, the van Laar type of activity coefficient equations are limited in their use as predictive model for dispersion. Perturbed hard-sphere chain equation of state will be discussed in part 2.

Abraham model correlations for solute transfer into 2-methyl-2-butanol based on measured activity coefficient and solubility data at 298.15 K

Experimental infinite dilution activity coefficients, gas-to-liquid partition coefficients and mole fraction solubilities are reported for numerous liquid and solid organic compounds dissolved in 2-methyl-2-butanol at 298.15 K. Experimental values were determined using headspace chromatographic and spectroscopic methods of analysis. Abraham model correlations were developed by combining our measured values with solubility data gathered from the published chemical literature. The mathematical correlations that we have developed described the measured partition coefficient and solubility data to within 0.14 log units (or less).