Mean Activity Coefficients Research Articles

Mixed Electrolyte in Mixed Solvent: Activity Coefficient Measuring and Modeling for the HCl + NaCl + Methanol + Water System

The emf of the cell is measured to investigate the HCl + NaCl + H2O + CH3OH mixed electrolyte systems. The experimental data are obtained over the electrolyte molality ranging from 0.005 mol kg–1 up to about 3.5 mol kg–1, at 298.15 ± 0.01 K, by using a cell containing a pH and a silver chloride electrode in different alcohol mass fractions x(CH3OH) in H2O (where x = 0.10, 0.20, 0.30, 0.40, and 0.50). The mean activity coefficients of HCl in the mixtures are computed. Modeling is implemented by the classical Pitzer (CP) equation and original Pitzer (OP) equation that are included by the additional terms which are arising from interactions of neutral species and finally the modified Pitzer equation by Merida et al. (MP). The different aspects of proper parameter choosing in fitting processes especially for pure and mixed electrolytes in mixed solvent systems are signified in the results.

Solubility, density and refractive index of formamide/N-methylformamide/N, N-dimethylformamide + rubidium bromide/cesium bromide + water ternary systems

The Solubility, density and refractive index of the formamide(FA)/N-methylformamide(NMF)/N,N-dimethylformamide(DMF) + rubidim bromide/cesium bromide+ water ternary systems were determined at (283.15, 298.15 and 313.15) K. The solubility of the RbBr and CsBr decrease significantly when adding amides into the aqueous solution. The variation trend of density is consistent with solubility, and the change of the refractive index is different. The isothermal experimental solubility was correlated by the NRTL model and the UNIQUAC model. The isothermal solubility, density and refractive index of the ternary systems were fitted by the four parameter equation. Moreover, the mean activity coefficients of the FA/NMF/DMF + RbBr/CsBr + H2O systems at experimental temperatures were obtained through the UNIQUAC model. Besides, to investigate the temperature effect on the solid-liquid equilibrium, the multiple temperatures solubility was fitted by the modified Apelbl at equation and the λh equation.

Thermodynamically Consistent Force Field for Coarse-Grained Modeling of Aqueous Electrolyte Solution.

We propose a thermodynamically consistent methodology to parameterize interactions between charged particles inside the dissipative particle dynamics (DPD) formalism. We used osmotic pressure experimental data as a function of the salinity in order to optimize the interaction parameters. Results for NaCl aqueous solution show that both mean osmotic and activity coefficients of individual ions allowed the determination of Na+-water, Cl--water, and Na+-Cl- DPD repulsion parameters. A simple linear relationship between the hydration-free energies of ions and the ion-water repulsion parameters that allows the parameterization of the complete series of halide and alkaline ions is proposed. Two strategies have been used to obtain the anion-cation interaction parameters for halide and alkaline ions. In the first one, the parameters are obtained based on the numerical optimization of the anion-cation repulsion parameter with respect to the experimental osmotic pressure data (with mean average deviations <4%). Second, we propose a predictive approach based on the free-energy difference of hydration energies of anions and cations in the spirit of the law of matching water affinities [with a mean absolute relative deviation of about 13%, better than 6% if small ions (Li+ and F-) are removed].

Anion-Specific Effects on Activity Coefficients in Aqueous Solutions of Sodium Salts: Modeling with the Extended Debye–Hückel Theory

The extended Debye–Huckel theory, which allows for concentration variation of electrolyte solution static permittivity, is employed to predict activity coefficients in aqueous solutions of sodium salts with various univalent anions (NaCl, NaBr, NaI, NaNO3, NaClO4 and NaSCN) at ambient conditions. Calculations without empirical adjustments reproduced the activity coefficients for NaI in the concentration range up to 6 mol·kg−1 and for NaSCN up to 2 mol·kg−1. In the case of other solutions, calculations underestimate water activity coefficients and overestimate mean ionic activity coefficients at concentrations beyond 0.5 mol·kg−1. In order to improve the representations, the model was extended to include ion pairing, which resulted in a better agreement between calculated activity coefficients and experimental data, especially for NaNO3. The ion pairing equilibrium constants were estimated and compared with available literature values. The extent of ion pairing was found to increase in the sequence NaI < NaSCN < NaBr < NaCl < NaClO4 < NaNO3, with violation of the Collins rule in the case of polyatomic oxygen-containing anions.

Mean Activity Coefficients of NaCl in the NaCl–SrCl2–H2O Ternary System at 308 K by EMF Method

The mean activity coefficient of NaCl in NaCl–SrCl2–H2O was measured at 308 K by the electromotive force method. The total ion strength range of the mixed solution was 0.0100–1.0000 mol·kg–1, and the ion intensity fraction of yb of SrCl2, i.e., yb = (0.8, 0.6, 0.4, 0.2, 0). A liquid-free electrochemical cell (Na-ISE | NaCl(m1) SrCl2(m2)| Cl-ISE) was used to determine the electromotive force of a NaCl single salt and mixed solution. According to experimental data, the activity coefficient diagrams were drawn. The experimental results show that the measured activity coefficients are accurate and reliable, and the average activity coefficient of NaCl decreases with the increase of the ion strength of SrCl2. Using the measured average activity coefficient of NaCl, the parameters of the mixed ion action of the Pitzer equation θNa+·Sr2+ and φNa+·Cl–·Sr2+ are fitted. Furthermore, the Pitzer equation is used to calculate the average activity coefficents of SrCl2, the water activities aw, osmotic coefficients Φ, a...

Modeling Tetra-n-butyl ammonium halides aqueous solutions with the electrolyte cubic plus association equation of state

This work presents the thermodynamic modeling of the fluid phases of Tetra-n-butyl ammonium halides aqueous solutions with the electrolyte Cubic-Plus-Association (e-CPA) Equation of State (EOS). The adjustable model parameters are obtained by fitting the experimental data of mean ionic activity coefficients and osmotic coefficients. Several other thermodynamic properties of the aqueous solutions, such as relative static permittivity, liquid density and saturation pressure, are subsequently predicted by the e-CPA EOS. The results of Tetra-n-butyl ammonium bromide aqueous solution show that the model can satisfactorily correlate the mean ionic activity coefficients and osmotic coefficients with the percentage average absolute deviations being 7.2% and 5.9%. The model overpredicts the liquid density with a deviation of 9.2%, while it can correlate the liquid density within 0.2% with a volume translation parameter. In order to have a more complete picture of the capabilities and limitations of the model, the consistencies of experimental data, parameter estimation approaches and the ion sizes are extensively analyzed and discussed.

Water content, relative permittivity, and ion sorption properties of polymers for membrane desalination

The interplay of polymer water content, dielectric relative permittivity, and ion sorption properties was studied using a cross-linked poly(glycidyl methacrylate) (XL-pGMA) polymer. The water content of the base XL-pGMA polymer was increased, by partial hydrolysis of the epoxide ring on the polymer side chain, to prepare a series of hydrolyzed XL-pGMA materials. Microwave dielectric spectroscopy, performed from 45 MHz to 26.5 GHz, revealed lower relative permittivity at a given water content compared to Nafion® 117. This observation suggests that knowledge of polymer water content alone may be insufficient for estimating relative permittivity properties of hydrated polymers. State of water analysis suggested that (for polymers that contain similar total amounts of sorbed water) more water in hydrolyzed XL-pGMA interacts with the polymer compared to that in Nafion® 117, and this result may be related to the observed differences in the relative permittivity properties of the two materials. The hydrolyzed polymers were more water/ion sorption selective, important for desalination applications, compared to many uncharged materials reported in the literature but less selective compared to Nafion® 117. Membrane phase mean ionic activity coefficients suggest that Nafion® 117 is more thermodynamically ideal (i.e., the mean ionic activity coefficients are closer to unity) than the hydrolyzed XL-pGMA materials, and thus, ion exclusion in Nafion® 117 is primarily due to Donnan exclusion. Measured static relative permittivity values were used to estimate, via electrostatic theory, the free energy barrier for ion sorption in each material, and these values were qualitatively consistent with values determined using measured ion sorption data. This study suggests that polymer chemistry, not water content alone, influences the relative permittivity properties of hydrated polymers and that relative permittivity measurements can provide qualitative insight into ion sorption properties, which is important for designing advanced desalination membranes.

Osmotic and activity coefficients for five lithium salts in three non–aqueous solvents

To obtain osmotic coefficients, a classic static–view apparatus was used to measure the difference between the vapor pressure of a solvent and that of its salt solution at 25 °C. Vapor–pressure lowering was measured for solutions containing a lithium salt (LiCl, LiBr, LiNO3, LiPF6 and LITFSI) dissolved in a non–aqueous solvent (dimethyl carbonate, dimethyl sulfoxide and acetonitrile) that may be used in a lithium–ion battery. The osmotic–coefficient data are represented by Archer’s extended Pitzer equation. Mean ionic activity coefficients for the salts are calculated from the osmotic–coefficient data.

Mathematical modelling of surface tension of nanoparticles in electrolyte solutions

Nanoparticles (NPs) have been successfully applied to reservoirs for enhanced oil recovery and fines migration mitigation at laboratory scale. Despite the successful implementation at laboratory scale, it is rarely applied at field scale. One of the major reasons for the delay in implementation is the lack of an appropriate model to predict the fluid-particles behaviour in the reservoir. An accurate prediction of the surface tension of the fluid system is particularly important in field design and development in the petroleum sector.The surface tension of NPs in deionized water increases with increase in concentration of NPs. This study exploits the Debye-Hückel constants to calculate the mean activity coefficients of NPs in solution combined with the equation proposed by Li and Lu (2001) for single electrolyte solutions to estimate the change in surface tension.However, NPs behaviour in brine (electrolyte solution) is different from the behaviour of mixture of different electrolytes. In deionized water, the surface tension of the fluid increases with increase in the NPs concentration, but NPs in electrolyte solutions behave as surface active agent decreasing the surface tension with increase in NPs concentration. This work includes the dipole-dipole interaction and structural effects along with the equation developed by Borwankar and Wasan (1988) for surface excess adsorption. This surface excess adsorption is applied to Li and Lu's equation for mixed electrolyte solutions to estimate the change in surface tension.This study is able to model the surface tension of NPs with or without electrolyte. Here, the molecular interaction of NPs in deionized water and electrolyte solutions is considered to predict the fluid-surface tension. The free energy at the interface is affected by the intermolecular interaction of the NPs. This intermolecular interaction includes electrical double layer, dipole-dipole interaction, and structural effects. The proposed model shows a good agreement with the experimental data from previous studies.

Determination and Modeling the Activity Coefficients of 1-Propyl-3- methylimidazolium Bromide in the Ethanol + Water Mixtures at T = (298.2, 308.2 and 318.2) K

In this work, the results relating to the mean activity coefficient measurements for ionic liquid of 1- propyl -3 methylimidazolium bromide, [PMIm]Br in ethanol+ water mixtures have been reported using potentiometric measurements at T=( 298.2, 308.2 and 318.2)K. The electromotive force (emf) measurements were performed on the galvanic cell of the type:Br-ISE│[PrMIm] (m) ethanol (wt.%), H2O (1−wt) %│ [PrMIm] -ISE, in mixed solvent system containing 0, 10, 20, 30% mass fractions of ethanol over ionic strength ranging from 0.0010 to 2.0000 mol•kg−1. The Pitzer ion-interaction model was used to analyze the activity coefficients for studied system. The Pitzer ion-interaction parameters (β(0), β(1) and Cϕ) were determined and employed to calculate the mean activity coefficients, the osmotic coefficients and excess Gibbs free energies for the whole series the studied system.

A Nonextensive Electrolyte UNIQUAC Model for Prediction of Mean Activity Coefficients of Binary Electrolyte Solutions

In this work, an electrolyte-UNIQUAC model was developed by replacement of Boltzmann weight binary interaction parameters by the nonextensive Tsallis weight. A summation of the long-range electrostatic term (Debye-Huckel equation) and a short-range interaction term were considered in the calculation of thermodynamic properties. A framework proposed by Chen and co-workers was employed for the derivation of the local mole fractions. Application of the nonextensive theory increased the degree of freedom of the present model (T-E-UNIQUAC). Furthermore, the strength of the model lies in its ability to calculate individual activity coefficients of ions. The applicability of the T-E-UNIQUAC model has been tested using aqueous electrolyte solutions and results have been compared with Messnaoui, Chen and Pitzer models.

Thermodynamic Study of LiClO4 Activity Coefficients in Aqueous Solution at (288.15, 298.15, and 308.18) K

The use of various electrolyte materials in a lithium ion battery must be studied under stable electrochemical conditions; therefore, the LiClO4 activity coefficients in water at the temperatures described in this work are the result of an electrochemical cell (ISE): Na-ISE|LiClO4(m)|ClO4-ISE. For this study, the determination of activity coefficients was carried out using the Pitzer and Debye–Huckel equations to represent the relationship between log γ and molality. For the system used with the electrochemical cell, it has good the behavior of mean ionic activity coefficients of LiClO4 for all temperatures, and at a temperature of 298.15 K, there is good agreement between the experimental data and the data in the literature.

Generalized Quasi-Random Lattice model for electrolyte solutions: Mean activity and osmotic coefficients, apparent and partial molal volumes and enthalpies

Electrolytes are the subject of a vast number of theoretical and experimental investigations concerned with a variety of modern applications. The modeling of thermodynamic properties of ionic solutions is thus a fundamental research topic that has been supported in many ways for many decades. There is however still a lack of models that are truly predictive over wide ranges of concentration, temperature and pressure conditions.In this article, the Quasi-Random Lattice (QRL) model is presented in a generalized form that allows for evaluating relevant thermodynamic properties of binary electrolyte solutions. The semi-predictive character of the model yields a powerful and competitive representation of electrolyte data over well defined concentration ranges. The additional experimental information to support the generalized version of QRL is very modest compared to the number of data points typically used in regression techniques for best-fit purposes. The thermodynamic consistency of the improved QRL model is demonstrated by the level of agreement with experimental data concerning mean activity and osmotic coefficients, apparent and partial molal volumes and enthalpies, for a variety of aqueous 1:1, 2:1, and 3:1 electrolytes.

THERMODYNAMIC PROPERTIES AND PITZER PARAMETER DETERMINATION FOR ORTHOPHOSPHORIC ACID FROM FREEZING POINT AND ISOPIESTIC MEASUREMENT DATA

Abstract The freezing depression points of aqueous phosphoric acid have been determined using a method based on measurement of solution conductivity. The osmotic coefficient for freezing point lowering was calculated by the condition of solid-liquid equilibrium and by the equation proposed by Bjerrum (1918). A calculation method is presented in this study to evaluate the ion interaction parameters for the Pitzer model from freezing point and isopiestic molalities of aqueous phosphoric acid solution. The model of Chen, Bromely and the Three-Characteristic Parameter Correlation (TCPC) are also used to model this system. The isopiestic molality values from literature data are used to optimize these models. Using these parameters, we were able to estimate thermodynamic properties: osmotic coefficient, mean activity coefficient and water activity for the H3PO4-H2O system, and contribution to a better understanding of the thermodynamic behaviour of the aqueous system containing phosphoric acid.

Isopiestic Measurements of Osmotic and Activity Coefficients of NiCl2–NH4Cl–H2O Systems at 308.15 K

In this work, the osmotic coefficients and water activities of NiCl2–NH4Cl–H2O ternary system and its two subsystems were obtained by isopiestic measurements at 308.15 K. The mean ion activity coefficients of NiCl2–H2O and NH4Cl–H2O systems with different molalities at 308.15 K were calculated by the Pitzer ion interaction model. Meanwhile, the self-consistency of experimental data was validated by Gibbs–Duhem equation, showing the calculated results have a good self-consistency between Pitzer ion interaction model and Gibbs–Duhem equation in the whole experimental molality range for NH4Cl–H2O system. Whereas for the NiCl2–H2O system, the Pitzer equation has its limitation of the molality range. Similarly, the osmotic coefficients of NiCl2–NH4Cl–H2O ternary system with different ionic strength can be obtained. Furthermore, the relative deviation between the experimental and calculated results indicated that the mixing parameters of Pitzer equation can be ignored in estimating the osmotic coefficients at the ionic strength of less than 2.5 mol·kg–1, whereas it cannot be omitted at the higher ionic strength.

Comparison Among Pitzer Model and Solvation Models. Calculation of Osmotic and Activity Coefficients and Dilution Enthalpy for Single-Electrolyte Aqueous Solutions

We have compared the performance of the Pitzer model and solvation models in the correlation of the mean activity and osmotic coefficients of 338 electrolyte solutions at 298.15 K and the temperatu...

Thermodynamic Study of (KCl + N,N-Dimethylformamide + Water) System Based on Potentiometric Measurements

In this research, the thermodynamic properties of (KCl + N,N-dimethylformamide + water) system were determined based on potentiometric technique. The electromotive force measurements were carried out by using self-made electrodes on the galvanic cell of type Ag|AgCl|KCl (m), N,N-dimethylformamide (w), and H2O (1 – w)|K-ISE in various mass fractions of N,N-dimethylformamide in water (0, 0.10, 0.20, and 0.30) in the molality ranging from 0.0094 to 2.5200 mol·kg–1 at T = (298.2 and 308.2) K and P = 0.1 MPa. Thermodynamic properties modeling was implemented using the Debye–Huckel extended equation, Pitzer ion interaction, and Pitzer–Simonson–Clegg models. Subsequently, unknown parameters for each model were determined and utilized to calculate the thermodynamic properties such as the mean activity coefficients, the osmotic coefficients, the excess Gibbs free energy, and the solvent activity for the system under investigation.

Revisiting electrolyte thermodynamic models: Insights from molecular simulations

Pitzer and electrolyte nonrandom two‐liquid (eNRTL) models are the two most widely used electrolyte thermodynamic models. For aqueous sodium chloride (NaCl) solution, both models correlate the experimental mean ionic activity coefficient (γ±) data satisfactorily up to salt saturation concentration, that is, ionic strength around 6 m. However, beyond 6 m, the model extrapolations deviate significantly and diverge from each other. We examine this divergence by calculating the mean ionic activity coefficient over a wide range of concentration based on molecular simulations and Kirkwood–Buff theory. The asymptotic behavior of the activity coefficient predicted by the eNRTL model is consistent with the molecular simulation results and supersaturation experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3728–3734, 2018

Thermodynamics of primitive model electrolytes in the symmetric and modified Poisson-Boltzmann theories. A comparative study with Monte Carlo simulations

Osmotic coefficients, individual and mean activity coefficients of primitive model electrolyte solutions are computed at different molar concentrations using the symmetric Poisson-Boltzmann and modified Poisson-Boltzmann theories. The theoretical results are compared with an extensive series of Monte Carlo simulation data obtained by Abbas et al. [Fluid Phase Equilib., 2007, 260, 233; J. Phys. Chem. B, 2009, 113, 5905]. The agreement between modified Poisson-Boltzmann predictions with the "exact" simulation results is almost quantitative for monovalent salts, while being semi-quantitative or better for higher and multivalent salts. The symmetric Poisson-Boltzmann results, on the other hand, are very good for monovalent systems but tend to deviate at higher concentrations and/or for multi-valent systems. Some recent experimental values for activity coefficients of HCl solution (individual and mean activities) and NaCl solution (mean activity only) have also been compared with the symmetric and modified Poisson-Boltzmann theories, and with the Monte Carlo simulations.

Semi-quantitative determination of ion transfers at an interface between water and quaternary ammonium polybromide droplets through stochastic electrochemical analysis

In this article, we present stochastic electrochemical analyses for the semi-quantitative determination of ion transfers (ITs) at an interface between water and electrochemically generated quaternary ammonium polybromide (QBr2n+1) droplets (water|QBr2n+1) in QBr aqueous solutions containing different acids (HAs).The concentration of Br− in QBr2n+1, CBr−(QBr2n+1) is linearly proportional to CA−(aq) with the proportionality constant, which was estimated from the difference between the two partition coefficients of H+ and A− from water toward QBr2n+1, KH+−KA−, and the ratio of the mean activity coefficient of the aqueous over that of the QBr2n+1 phase, γ±,aq/γ±,QBr2n+1. CBr−(QBr2n+1) also shows the linear function of CQ+(aq) with (γ±,aq/γ±,QBr2n+1)KQ+ as its proportionality constant.The stochastic chronoamperometric analyses of QBr2n+1 droplets during their particle-impacts on Pt UME in acidic solutions containing either N-methyl-N-ethyl pyrrolidinium bromide (MEPBr) or ethylpyridinium bromide (EPyBr) as model QBrs can provide indirect information about CBr−(QBr2n+1), and we estimated the relative order to be KC+(Li+orNa+), KH+, and KA−: KC+(Li+orNa+)<KH+<KA−, where KHSO4−<KClO4−<KCl− in KA− and KNa+<KLi+ in KC+. Also, we found that Br−-IT at water|QBr2n+1 is effectively limited by A−-IT in the acidic solutions, and Cl− is most significantly transferred to QBr2n+1, leading to the complete inhibition of Br−-IT into QBr2n+1.