Activity Coefficients Of Aqueous Solutions Research Articles

Relationship of the Permittivity with the Activity Coefficients of Water and Ions in Aqueous Solutions of Lithium and Sodium Sulfates

The activity coefficients in aqueous solutions of lithium and sodium sulfates at 298 K were calculated by the generalized Debye–Huckel theory using the experimental values of the static permittivity of the solutions. The effect of the hydration and ion association on the dielectric and thermodynamic properties of the electrolyte solutions was considered.

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.

Thermodynamic Properties of Aqueous Sodium Nitrate Solutions Under Superambient Conditions

Use has been made of the Pitzer ion-interaction or virial coefficient approach to estimate the pressure dependence of the osmotic and activity coefficients of aqueous solutions of sodium nitrate (NaNO3) up to 423.15 K and 6.0 mol·kg−1 using published volumetric data on NaNO3(aq). In particular, volumetric Pitzer ion-interaction parameters have been evaluated from a mathematical fit of published apparent molar volume data with the appropriate Pitzer equation. The Pitzer parameters were then fitted as a function of temperature and pressure. These results were then used to calculate the change in the osmotic and activity coefficients in going from the state of an initial pressure p1 to one of a final pressure p2. These pressure dependences have been combined with the osmotic and activity coefficient values of NaNO3(aq) at 0.1 MPa or vapor-saturation pressures (psat) obtained from the model of Archer to yield a comprehensive set of thermodynamic parameters for NaNO3(aq) at temperatures from 293.15 K through 423.15 K, at pressures of (5, 10, 15, 20) MPa, and molalities to 6.0 mol·kg−1.

Effect of hydrophobicity and H-bonding abilities of ions on osmotic coefficients of aqueous diethylammonium based protic ionic liquid solutions at 298.15 K

The osmotic and activity coefficients of aqueous solutions of diethylammonium based protic ionic liquids (PILs) were determined experimentally using vapor pressure osmometry in the concentration range of (~0.02 to ~0.5) mol·kg−1 at 298.15 K. Osmotic coefficient data show positive deviation from Debye-Hückel limiting law for all the studied PILs. Also a minimum in osmotic coefficient data was observed at higher concentrations and is explained in terms of ion-pair formation. Data of experimental osmotic coefficient were used to obtain activities (aw) and activity coefficients (γ1) of water, mean molal activity coefficient (γ±) of PILs and excess Gibbs free energy change (ΔGE) due to mixing. Observed variations in osmotic coefficients data were explained in terms of hydrophobicity as well as H-bonding. The data of osmotic and activity coefficients were further subjected to analysis through Pitzer ion-interaction model to get an information of ion-ion and ion-solvent interaction to understand ion-pairing, ion hydration and hydrophobic effects in aqueous solutions of PILs. For this, Pitzer ion interaction parameters β(0) and β(1) were estimated and compared with literature data available for other relevant systems. Finally, the results are interpreted in terms ion-ion, ion-solvent interaction along with effect of hydrophobicity on ion-pairing and further discussed the effect of alkyl chain length of anions on solvation behavior of protic ionic liquids in aqueous solutions.

Novel solutions for closed-loop reverse electrodialysis: Thermodynamic characterisation and perspective analysis

Closed-loop Reverse Electrodialysis is a novel technology to directly convert low-grade heat into electricity. It consists of a reverse electrodialysis (RED) unit where electricity is produced exploiting the salinity gradient between two salt-water solutions, coupled with a regeneration unit where waste-heat is used to treat the solutions exiting from the RED unit and restore their initial composition. One of the most important advantages of closed-loop systems compared to the open systems is the possibility to select ad-hoc salt solutions to achieve high efficiencies. Therefore, the properties of the salt solutions are essential to assess the performance of the energy generation and solution regeneration processes. The aim of this study is to analyse the influence of thermodynamic properties of non-conventional salt solutions (i.e. other than NaCl-aqueous solutions) and their influence on the operation of the closed-loop RED. New data for caesium and potassium acetate salts, i.e. osmotic and activity coefficients in aqueous solutions, at temperature between 20 and 90 °C are reported as a function of molality. The data are correlated using Pitzer's model, which is then used to assess the theoretical performance of the whole closed-loop RED system considering both single and multi-stage regeneration units. Results indicate that KAc, CsAc and LiCl are the most promising salts among those screened.

Activity Coefficient Modelling of Aqueous Solutions of Alkyl Ammonium Salts using the Extended UNIQUAC Model

Certain alkyl ammonium salts are called ionic liquids They can be used as green solvents without toxicity, effects on the ozone layer depletion, effects on climate change, and any other significant environmental impacts; in this regard knowledge about their thermo-physical properties are really important. In this work activity coefficients of aqueous solutions of alkyl ammonium salts at 298.15 and 293.15 K are modelled using the Extended UNIQUAC (Universal Quasi Chemical) thermodynamic model. Adjustable parameters of the Extended UNIQUAC thermodynamic model were obtained by non-linear regression between experimental data and the results calculated from the model. The results of the model are in good agreement with the experimental values in most cases, the average absolute deviation of the model being less than 2 %, which is acceptable considering the uncertainty of the experimental data. Additionally, the results gained from the Extended UNIQUAC model are also compared with the results obtained from Electrolyte NRTL and Pitzer thermodynamic methods.

New Data on Activity Coefficients of Potassium, Nitrate, and Chloride Ions in Aqueous Solutions of KNO3 and KCl by Ion Selective Electrodes

Ion selective electrodes (ISEs) are used to measure the single-ion activity coefficients in aqueous solutions of KNO3 and KCl at 298.15 K against a double-junction reference electrode. The EMF responses of ISEs up to 0.01 m are plotted to obtain the slope and intercept values. The obtained slopes and intercepts are used in Nernst equation for higher concentrated solutions for calculation of individual ion activity coefficient. The mean ionic activity coefficients are estimated from single ion activity coefficient, and the obtained results are compared with the literature values.

Activity coefficients of aqueous solutions of aceto-hydroxamic acid solutions at 298.15 K and 0.1 MPa

Aceto-hydroxamic acid (AHA) is a novel reductant and complexant for actinides. Information on the thermodynamic parameters for AHA–water system is scarce. For simulation of solvent extraction flowsheets utilizing AHA, these parameters are required for accurate prediction of complexation and other goals. In this paper, activity coefficients, osmotic coefficients and excess Gibbs energies of AHA–water solutions at 298.15K and 0.1MPa are reported.

Isopiestic Determination of the Osmotic and Activity Coefficients of Aqueous Solutions of Symmetrical and Unsymmetrical Quaternary Ammonium Bromides at T = (283.15 and 288.15) K

Osmotic coefficients of aqueous solutions of Bu4NBr, sec-Bu4NBr, iso-Bu4NBr, Bu2Et2NBr, and Bu3EtNBr are measured at T = (283.15 and 288.15) K by the isopiestic method. A branched isopiestic apparatus was used. The osmotic data of the solutions were compared at T = (283.15 and 298.15) K. Osmotic coefficient data are correlated using the Pitzer model. The parameters obtained with the Pitzer model are used to calculate the mean molal activity coefficients. Vapor pressures of the solutions are evaluated from osmotic coefficients, and their depression was used for qualitative deduction of solute−solvent interactions occurring in these solutions.

Standard State Thermodynamic Properties of Completely Ionized Aqueous Sodium Sulfate Using High Dilution Calorimetry up to 598.15 K

Pabalan and Pitzer (Geochim. Cosmochim. Acta 1988, 52, 2393-2404) reported a comprehensive set of thermodynamic properties of aqueous solutions of sodium sulfate without using ion association or hydrolysis. However, there is now ample evidence available indicating that the ion association cannot be ignored at temperatures T>or=373 K. For example, even at the lowest concentration of their studies (m>or=0.05) and at 573.15 K, less than 20% of SO4(2-)(aq) is available as free ions. In the present study, the integral heats of solution of sodium sulfate were measured to very low concentrations (10(-4) m) up to 573.16 K. The data were analyzed correcting for the hydrolysis of SO4(2-)(aq) and the association of Na+(aq) with SO4(2-)(aq) and NaSO4-(aq) in order to obtain the final standard state thermodynamic properties of completely ionized aqueous sodium sulfate, Na2SO4(aq). From these and the available solubility data, the stoichiometric activity coefficients of saturated aqueous solutions of sodium sulfate were calculated up to 573.15 K and compared with literature data. The stoichiometric activity coefficients of aqueous solutions of sodium sulfate, as a function of temperature at all concentrations (0<or=m<or=msat), were also calculated up to 573.15 K.

Dynamic surface tension, critical micelle concentration, and activity coefficients of aqueous solutions of nonyl phenol ethoxylates

Dynamic surface tensions, σ( t) for aqueous solutions of nonyl phenol ethoxylates (NPEOs) at the temperature 298.15 K were measured using a Lauda drop volume tensiometer. The non-ionic surfactants analyzed in this work were Tergitol NP-9, NP-35 and NP-40. By using the classical Ward and Torday equation, the diffusion coefficient for each bulk surfactant concentration was calculated. The equilibrium surface tension values were determined by extrapolating the dynamic surface tension to t → ∞ on the σ( t) vs. t −1/2 curves. These values were used to determine the critical micelle concentrations (CMC) of the surfactant aqueous solutions as well as to calculate the infinite dilution activity coefficient of the surfactant, following a model that combines the Volmer surface equation of state and the Gibbs adsorption equation.

Measurement of Ion Activity Coefficients in Aqueous Solutions of Mixed Electrolyte with a Common Ion: NaNO3 + KNO3, NaCl + KCl and NaBr + NaCl

Measurement of Ion Activity Coefficients in Aqueous Solutions of Mixed Electrolyte with a Common Ion: NaNO₃ + KNO₃, NaCl + KCl and NaBr + NaCl

Measurement of Ion Activity Coefficients in Aqueous Solutions of Mixed Electrolyte with a Common Ion: NaNO3 + KNO3, NaCl + KCl, and NaBr + NaCl

This work reports individual ion activity coefficients in aqueous solutions of mixed 1:1 electrolytes with a common ion for the systems NaNO3 + KNO3, NaCl + KCl, and NaCl + NaBr at 298.15 K. These values were obtained from electrode potential measurements of ion-selective-electrodes (ISEs) of the common ion against an Ag−AgCl single-junction reference electrode filled with 4 mol·kg−1 KCl solution saturated with AgCl. For the NaNO3 + KNO3 and NaCl + KCl systems, experiments were carried out at cation molal fractions of sodium of 0.75, 0.5, and 0.25, and for the NaCl + NaBr system, experiments were carried out at an anion molal fraction of chloride of 0.5. For NaNO3 + KNO3, single ion activity coefficients were obtained up to 2.4 mol·kg−1 total nitrate concentration, and for the NaCl + KCl and NaCl + NaBr systems, up to 4 mol·kg−1 of total chloride and sodium concentrations, respectively. The Henderson equation was used to estimate the value of the liquid−junction potential.

Correlation of Activity Coefficients in Aqueous Solutions of Ammonium Salts Using Local Composition Models and Stochastic Optimization Methods

In this study, several local composition models and stochastic optimization methods have been used and compared in data fitting of activity coefficients in aqueous electrolytes. We have utilized the electrolyte-NRTL model of Chen et al. and the modified Wilson models proposed by Xu and Macedo, and Zhao et al. to fit the activity coefficients of several quaternary ammonium salts in water at 25°C. These electrolytes have interesting properties for their application as ionic liquids. However, the modeling of their thermodynamic behavior using local composition models is a global optimization problem. In this study, several stochastic optimization methods have been used to solve this optimization problem and their numerical performances have been compared. Specifically, we have tested the classical Simulated Annealing and the hybrid methods: Direct Search Simulated Annealing, Simplex Coding Genetic Algorithm, Simulated Annealing Heuristic Pattern Search, and Directed Tabu Search. Our results show that Simulated Annealing is a suitable tool for data fitting of the activity coefficients of aqueous electrolytes. Finally, the tested models can satisfactorily correlate the mean activity coefficients of electrolytes treated in this study, and are suitable for process design.

Gex-Model Using Local Area Fraction for Binary Electrolyte Systems

The correlation and prediction of phase equilibria of electrolyte systems are essential in the design and operation of many industrial processes such as downstream processing in biotechnology, desalination, hydrometallurgy, etc. In this research, the local composition non-random two liquid-nonrandom factor (NRTL-NRF) model of Haghtalab and Vera was extended for uni-univalent aqueous electrolyte solutions. Based on the assumptions of the NRTL-NRF model, excess Gibbs free energy (g E) functions were derived for binary electrolyte systems. In this work, the local area fraction was applied and the modified model of NRTL-NRF was developed with either an equal or unequal surface area of an anion to the surface area of a cation. The modified NRTL-NRF models consist of two contributions, one due to long-range forces represented by the Debye–Huckel theory, and the other due to short-range forces, represented by local area fractions of species through nonrandom factors. Each model contains only two adjustable parameters per electrolyte. In addition, the model with unequal surface area of ionic species gives better results in comparison with the second new model with equal surface area of ions. The results for the mean activity coefficients for aqueous solutions of uni-univalent electrolytes at 298.15 K showed that the present model is more accurate than the original NRTL-NRF model.

Modeling of Aqueous 3–1 Rare Earth Electrolytes and Their Mixtures to Very High Concentrations

A simple modification to the Pitzer ion–interaction model has been presented for osmotic and activity coefficients of aqueous solutions of highly soluble and highly unsymmetrical electrolytes and their mixtures. The equations extending to the C(3) parameter enable the literature osmotic and activity coefficients of aqueous rare earth nitrates, perchlorates and chlorides at 298.15 K to be represented accurately from infinite dilution to maximum saturation or supersaturation concentrations available. The ionic interactions have also been investigated from the isopiestic measurements on aqueous mixtures Y(NO3)3–La(NO3)3, Y(NO3)3–Pr(NO3)3, Y(NO3)3–Nd(NO3)3, La(NO3)3–Pr(NO3)3, La(NO3)3–Nd(NO3)3 and Pr(NO3)3–Nd(NO3)3 at 298.15 K to near saturation, and the simple modification can represent the new measurements within experimental uncertainty over the full concentration range. In addition, the Zdanovskii-Stokes-Robinson model or partial ideal solution model is obeyed by all the mixtures within isopiestic accuracy, which is consistent with the nature of rare earth elements.

A new model for the activity coefficients of individual ions in aqueous electrolyte solutions

In this study, the individual ion activity coefficient in an aqueous solution is modeled with a new model. This model contains two physical significant ionic parameters regarding the ionic solvation and the closest distance of approach between ions in a solution. The present model was evaluated by the estimation of the individual activity coefficients of the ions of thirty electrolytes in aqueous solutions. The results showed that this model suitably predicts the individual ion activity coefficients in aqueous two-electrolyte solutions consisting of the binary pairs of electrolytes of NaCl, KCl, KBr and CaCl 2 in a temperature range from 298.15 to 243.15 K. The results by this model were compared to the literature values. The average absolute relative deviations of vapor pressures showed acceptable agreement between experimental data and the results of this model.

Isopiestic determination of osmotic and activity coefficients of aqueous solutions of aliphatic polyols at 298.15 K

The osmotic coefficients of 1,2-butanediol (12BD), 1,3-butanediol (13BD), 1,4-butanediol (14BD), 2,3-butanediol (23BD), 1,2,4-butanetriol (124BT) and 1,2,3,4-butanetetrol (1234BT) in water were measured by the isopiestic method at 298.15 K. Experimental osmotic coefficients were used to calculate water activity, solute activity coefficients and the pairwise Gibbs energy coefficients for solute–solute interactions.

Correlation and prediction of osmotic coefficient and water activity of aqueous electrolyte solutions by a two-ionic parameter model

In this study, osmotic coefficients and water activities in aqueous solutions have been modeled using a new approach based on the Pitzer model. This model contains two physically significant ionic parameters regarding ionic solvation and the closest distance of approach between ions in a solution. The proposed model was evaluated by estimating the osmotic coefficients of nine electrolytes in aqueous solutions. The obtained results showed that the model is suitable for predicting the osmotic coefficients in aqueous electrolyte solutions. Using adjustable parameters, which have been calculated from regression between the experimental osmotic coefficient and the results of this model, the water activity coefficients of aqueous solutions were calculated. The average absolute relative deviations of the osmotic coefficients between the experimental data and the calculated results were in agreement.

Osmotic and activity coefficients of aqueous solutions of KCl at temperatures of 283.15, 288.15, 293.15 and 298.15 K: A new isopiestic apparatus

Osmotic coefficients of aqueous KCl solutions have been determined by the isopiestic method using standard NaCl reference solutions for comparison. Measurements were made at 283.15, 288.15, 293.15, and 298.15 K. A modified isopiestic apparatus is described. Equilibrium times ranged from 4 to around 15 days. The equilibrium molalities went up to 1.0 m. The average relative uncertainty of the observed water activities of the solutions was less than 0.005%. The activity and osmotic coefficients of KCl aqueous solutions at several temperatures are compared with literature data.