Activity Coefficients Of Aqueous Solutions Research Articles

Calculations of mean ionic activity coefficients of copper and manganese salts in aqueous solutions

Accurately predicting the activity coefficients of copper and manganese salts in aqueous solutions is crucial for treating industrial wastewater, and it is of practical interest to calculate the activity coefficients of heavy metals in aqueous solutions using the Equation of State because of its high flexibility and wide range of applicability. This work conducts a modeling study on the mean ionic activity coefficients of copper and manganese salts in aqueous solutions. The thermodynamic framework used in this work is an electrolyte version of the Cubic Plus Association Equation of State (e-CPA). The model's ion-water binary interaction parameters are obtained by regressing the osmotic coefficients and mean ionic activity coefficients in aqueous solutions. The modeling results indicate that the electrolyte Equation of State can satisfactorily correlate the water activity, osmotic coefficients, and mean ionic activity coefficients of copper and manganese salts in aqueous solutions over a wide range of salt concentrations. Among all the systems at 298.15 K, the biggest average relative deviation between calculated and experimental values is within 6.7 % and 2.3 % for the mean ionic activity coefficients and water activity, respectively. Furthermore, this work discusses the impact of ion pairs on the phase equilibrium of aqueous systems from a microscopic mechanism perspective and analyzes and discusses the model's adaptability. The model used in this work can accurately predict the activity coefficients of a variety of copper and manganese salts in aqueous solutions over wide concentration ranges and provides an improved interface for improving the calculation accuracy of the model under high concentration or other complex conditions.

Understanding water behavior through activity coefficients in aqueous solutions: insights from experimental and modeled relative static permittivity

Understanding water behavior through activity coefficients in aqueous solutions: insights from experimental and modeled relative static permittivity

The SIT model parameters for interactions of carbonate compounds with sodium and potassium ions accounting for association

The current study is devoted to the determination of the SIT coefficients at 298.15 K for interactions, involving CO2(aq), HCO3−, and CO32‐, with mostly Na+ and K+ ions. The SIT model is a simple yet physically sound model for activity coefficients in aqueous solutions, that has just one parameter for each cation-anion or a dissolved gas – electrolyte interaction. Among the issues that were met for carbonate systems are the side reactions of hydrolysis and disproportionation in the carbonate solutions, that complicate the analysis of data and lead to unusually large difference, up to 9%, in the values of activity coefficients, determined in different authoritative laboratories. For Na2CO3 and K2CO3 solutions, it was necessary to take into account the reaction of formation of the ionic pair M++CO32‐=MCO3−, with the equilibrium constants β1o equal to log10β1o= 0.75 ± 0.08 for M+=Na+ and to log10β1o= 0.67 ± 0.11 for M+=K+. In all, there are values for more than 20 binary SIT interaction coefficients. All results are valid at 298.15 K, 0.1 MPa.

Analysis of Activity Coefficients in Aqueous Solutions of Alkali Metal Bromides Based on Dielectric Properties

Extended Debye–Hückel (EDH) theory was used to calculate activity coefficients in aqueous solutions of alkali-metal bromides at 298 K from experimentally determined values of their static permittivities. Calculations with non-optimized model parameters fit the nonmonotonic concentration-dependent trend of the activity coefficients and the cation radius–dependent trend of the activity coefficients. The latter is explained by hydration weakening and ion association strengthening in response to increasing cation radius in the salt series.

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.