Activity Coefficients Of Solutions Research Articles

Quickly Calculating the Activity Coefficient of a NaCl Solution Based on Machine Learning Algorithms

Quickly Calculating the Activity Coefficient of a NaCl Solution Based on Machine Learning Algorithms

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.

Predicting solvation free energies for neutral molecules in any solvent with openCOSMO-RS

In this study, we introduce openCOSMO-RS 24a, an improved version of the open-source COSMO-RS model parameterized using quantum chemical calculations from ORCA 6.0, leveraging a comprehensive dataset that includes solvation free energies, partition coefficients, and infinite dilution activity coefficients for various solutes and solvents mainly at 25 °C. This is the first version of the model also capable of predicting solvation free energies based on ORCA calculations. Additionally, we develop a Quantitative Structure-Property Relationships model to predict molar volumes of the solvents, an essential requirement for predicting solvation free energies and partition coefficients from structure alone. Our results show that openCOSMO-RS 24a achieves an average absolute deviation of 0.45 kcal mol1 for solvation free energies, 0.76 for the logarithm of the partition coefficients, and 0.51 for the logarithm of infinite dilution activity coefficients, demonstrating improvements over the previous openCOSMO-RS 22 parameterization and comparable results to COSMOtherm 24 BP-TZVP. The user interface was extended to be able use it as solvation model directly from within ORCA 6.0 or from the command line to provide researchers with a robust tool for applications in chemical and materials science.

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.

Quantifying water activity coefficients in PG and VG mixture solutions: A novel approach for assessing E-liquid hygroscopicity

Quantifying water activity coefficients in PG and VG mixture solutions: A novel approach for assessing E-liquid hygroscopicity

Experimental and theoretical studies on thermodynamic activities of binaries ferric and magnesium chlorides in aqueous solutions at various temperatures

The investigation of the thermodynamic properties of binary systems of ferric and magnesium chlorides in aqueous solutions was reported at various temperatures using both the hygrometric method and thermodynamic modeling. Water activities were measured over a molality range of 0.100 up to mmax(FeCl3)= 2.500 mol·kg−1 and to mmax(MgCl2)=(5.798, 6.090, 6.394, and 6.839) mol·kg−1at temperatures from 298.15 K to 353.15 K, respectively. From the new measurements, the osmotic coefficients of water were evaluated and compared with the existing literature data at ambient temperature. These coefficients were treated at various temperatures using established thermodynamic models of the Pitzer, Filippov–Charykov–Rumyantsev, extended ion interaction, and Clegg–Pitzer–Brimblecombe. The relevant properties of ferric and magnesium electrolyte solutions were determined in the temperature range. Indeed, the parameterizations of FeCl3(aq) and MgCl2(aq) were evaluated and employed for the computation of solute activity and osmotic coefficients. Based on literature emf data for MgCl2(aq) at a temperature of 298.15 K, the consistency of the activity coefficients was evaluated using an adequate model, and an excellent description of the prediction activity coefficients is obtained by the extended ion interaction model. Then, the recommended activity coefficients were given at various temperatures by extending this procedure. An experimental investigation was also carried out to evaluate the solubility equilibrium of MgCl2 in aqueous solutions at different temperatures. The solubility product and standard Gibbs energies of dissolution and formation were also calculated at different temperatures and compared with those existing in the literature.

Osmotic and Activity Coefficients of Aqueous Lithium Sulfate Solutions within the Temperature Range 293.15–498.15 K to 40 MPa

Osmotic and Activity Coefficients of Aqueous Lithium Sulfate Solutions within the Temperature Range 293.15–498.15 K to 40 MPa

Gibbs-Helmholtz Graph Neural Network for the Prediction of Activity Coefficients of Polymer Solutions at Infinite Dilution.

Machine learning models have gained prominence for predicting pure-component properties, yet their application to mixture property prediction remains relatively limited. However, the significance of mixtures in our daily lives is undeniable, particularly in industries such as polymer processing. This study presents a modification of the Gibbs-Helmholtz graph neural network (GH-GNN) model for predicting weight-based activity coefficients at infinite dilution (Ωij∞) in polymer solutions. We evaluate various polymer representations ranging from monomer, repeating unit, periodic unit, and oligomer and observe that, in data-scarce scenarios of polymer-solvent mixtures, polymer representation specifics have a reduced impact compared to data-rich environments. Leveraging transfer learning, we harness richer activity coefficient data from small-size systems, enhancing model accuracy and reducing prediction variability. The modified GH-GNN model achieves remarkable prediction results in mixture interpolation and solvent extrapolation tasks having an overall mean absolute error of 0.15, showcasing the potential of graph-neural-network-based models for property prediction of polymer solutions. Comparative analysis with the established models UNIFAC-ZM and Entropic-FV suggests a promising avenue for future research on the use of data-driven models for the prediction of the thermodynamic properties of polymer solutions.

Thermodynamic studies of solute–solute and solute–solvent interactions in ternary aqueous systems containing {betaine + PEGDME250} and {betaine + K3PO4 or K2HPO4} at 298.15 K

In this work, to evaluate solute–solute, solute–solvent and phase separation in aqueous systems containing {betaine + poly ethylene glycol dimethyl ether with molar mass 250 g mol−1 (PEGDME250)}, {betaine + K3PO4} and {betaine + K2HPO4}, first water activity measurements were made at 298.15 K and atmospheric pressure using the isopiestic technique. The water iso-activity lines of these three systems were obtained which have positive deviations from the semi-ideal solutions. This suggests that betaine-polymer and betaine-K3PO4 or betaine-K2HPO4 interactions are unfavorable; and these mixtures may form aqueous two-phase systems (ATPSs) at certain concentrations. Indeed the formation of ATPSs was observed experimentally. Then, osmotic coefficient values were calculated using the obtained water activity data; and, using the polynomial method the solute activity coefficients were determined. Using these activity coefficients, the transfer Gibbs energy (Delta {G}_{tr}^{i}) values were calculated for the transfer of betaine from aqueous binary to ternary systems consisting polymer (PEGDME250) or salts (K3PO4 and K2HPO4). The obtained positive Delta {G}_{tr}^{i} values again indicated that there is unfavorable interaction between betaine and these solutes. Finally, the volumetric and ultrasonic studies were made on these systems to examine the evidence for the nature of interactions between betaine and the studied salts or polymer.

Investigation into Na and Cs activity coefficients in high salt solutions to support Cs removal in Hanford tank waste

Abstract The treatment of Hanford tank waste is one of the most technically challenging environmental cleanup activities for the U.S. Department of Energy to date. To expedite the processing of liquid waste stored in underground tanks in southeastern Washington state, it is necessary to remove the significant dose contributor, 137Cs. Toward this effort, ion exchange with crystalline silicotitanate (CST) has been employed as part of the Tank Side Cesium Removal system. The model used to predict Cs exchange onto CST was developed using activity coefficients calculated from the Bromley equation. A series of batch contact tests that varied in [Na] were conducted to look at the impact of Na concentration on Cs distribution. Experimental distribution ratios (K d) were compared to the distribution ratios predicted using three different activity coefficient models: (1) commercially available HSC software, (2) the Bromley equation, and (3) a simplified approach adapted from Marcos-Arroyo et al. Ultimately, the Bromley method underpredicted the effect of ionic strength on the Na activity coefficient (γ Na+), HSC overestimated the impact of ionic strength on the expected performance due to the Cs activity coefficient (γ Cs+), but the simplified approach predicted the experimental K d values quite well in a binary matrix. Expansion of this approach in complex matrices is necessary for application to Hanford tank waste.

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.

Thermodynamic Properties Data of Ternary System KBr–KH2PO4–H2O at 298.15 K

The OCP Group located in Morocco in Africa is one of the biggest producers of phosphates and fertilizers in the world and delivers products to more than 165 clients on five continents. These products include ammonium and di-ammonium phosphate, sodium phosphate, and others with added micronutrients (potassium–calcium–nitrogen) that are designed to effectively feed degraded soil. OCP has launched a new strategy in Africa called “Green Africa” to transform African agriculture and make it a platform for food production. Therefore, with the aim of developing new fertilizers and increasing the yield of soils and agriculture, we are interested in this work to study the influence of electrolytes on the fertilizer phosphate KBr–KH2PO4–H2O. This system was investigated with our developed hygrometric method at 298.15 K. The thermodynamic parameters of the studied system such as the water activity and osmotic coefficient are determined by measuring the relative humidity at various total molalities from 0.2 mol·kg–1 to about saturation, and for different ionic-strength fractions y of KH2PO4 (y = IKBr/(IKH2PO4+IKBr)) of 0, 1/4, 1/3, 1/2, 2/3, 3/4, and 1. The obtained measurements are compared to four models such the Dinane (ECA), Lin et al., Robinson and Stokes (RS), and Leitzke-Stoughton (LS II) equations. The solubilities of KBr and KH2PO4 in their aqueous mixture are also measured at 298.15 K. The solid state was characterized using powder X-ray diffraction (XRD). The PSC model was used to correlate the results and to predict the solute activity coefficients, excess Gibbs energy, and solubilities of the components in the mixture.

The Role of Debye Charging in Predicting Activity Coefficients in Electrolyte Solutions

The Role of Debye Charging in Predicting Activity Coefficients in Electrolyte Solutions

High-temperature and high-pressure thermodynamic properties of aqueous zinc sulfate solutions

A new method has been proposed to estimate the osmotic and activity coefficients of aqueous electrolyte solutions under non-ambient conditions on the basis of the Pitzer ion-interaction approach using the volumetric data. Following this method, a compact set of Pitzer ion-interaction parameters, valid within the temperature range 293.15 - 373.15 K, and pressure range 0.1 - 10 MPa have been obtained for aqueous ZnSO4 solutions. These parameters helped evaluate the osmotic and activity coefficients of this system to 3.0 mol∙kg−1. The pressure dependences of osmotic and activity coefficients have also been estimated using the equations derived by Rogers and Pitzer (1982). The results obtained by the method proposed in this research agree very well with those calculated using Rogers and Pitzer approach. The advantage of the method proposed here is that it directly provides a compact set of Pitzer ion-interaction parameters required for describing the osmotic and activity coefficients, in contrast to the other method. This study also provided important insight into the ion-association behavior of aqueous ZnSO4 solution with respect to temperature and pressure. Further, the apparent molar enthalpies have been estimated using appropriate temperature derivatives of the Pitzer ion-interaction parameters obtained in this study.

Vapor-liquid-solid equilibria and thermodynamic study of aluminum chloride aqueous solutions at various temperatures

The vapor-liquid-solid equilibria and thermodynamics data relevant to aluminum chloride in aqueous solutions were investigated at various temperatures. The water activity measurements of AlCl3(aq) were carried out from dilution to saturated solutions at temperatures ranging from 298.15 to 353.15 K using the hygrometric method. From new experimental results, the ion interaction of Pitzer, extended ion interaction (EII) and Clegg–Pitzer–Brimblecombe (CPB) models were developed to allow the parametrization of the binary system. The interaction parameters were evaluated for the Al−Cl−H2O system and used to calculate the solute activity and osmotic coefficients form the three models. The standard approach for a 3–1 electrolyte with the ion parameters in the temperature range shows a very good agreement with osmotic coefficient data for unsaturated solutions. The solubility equilibrium of anhydrous AlCl3 in aqueous solutions was determined experimentally up to mmax=(3.383 to 3.606) mol·kg−1from (298.15 to 353.15) K respectively; then, the solubility products as LnKsp∘ of AlCl3(aq) were also given using the obtained activity coefficients at various temperatures.

Graph neural networks for temperature-dependent activity coefficient prediction of solutes in ionic liquids

Ionic liquids (ILs) are important solvents for sustainable processes and predicting activity coefficients (ACs) of solutes in ILs is needed. Recently, matrix completion methods (MCMs), transformers, and graph neural networks (GNNs) have shown high accuracy in predicting ACs of binary mixtures, superior to well-established models, e.g., COSMO-RS and UNIFAC. GNNs are particularly promising here as they learn a molecular graph-to-property relationship without pretraining, typically required for transformers, and are, unlike MCMs, applicable to molecules not included in training. For ILs, however, GNN applications are currently missing. Herein, we present a GNN to predict temperature-dependent infinite dilution ACs of solutes in ILs. We train the GNN on a database including more than 40,000 AC values and compare it to a state-of-the-art MCM. The GNN and MCM achieve similar high prediction performance, with the GNN additionally enabling high-quality predictions for ACs of solutions that contain ILs and solutes not considered during training.

Activity Coefficients of the System {yKCl + (1 – y)KH2PO4}(aq) at T = 298.15 K Determined by Cell Potential Measurements

Zero-current cell potential measurements were used to determine the solution activity coefficient in a ternary system {yKCl + (1 – y) KH2PO4}(aq) at temperature T = 298.15 K. The cell of the type K–ISE|KCl(mKCl), KH2PO4(mKH2PO4)|Ag|AgCl was used in the total ionic strength range, Im = 0.0886–1.0046 mol kg–1. In order to generate a set of parameters that can be applied in a wide range of mixed solution ionic strengths, the Pitzer, Scatchard, and Clegg–Pitzer–Brimblecombe models were used to fit all available experimental data, including cell potential and isopiestic measurements from the literature. The experimental and calculated values of thermodynamic properties for the studied system are in excellent agreement. Potential interactions and solution structure were discussed by means of the excess free energy of mixing via potential pairs, triplets, or quads for the investigated solution using the Scatchard model mixing parameters.

Solubility study and thermodynamic modelling of succinic acid and fumaric acid in bio-based solvents

The solubility and involved energies of organic acids in green solvents are relevant to the design of sustainable biorefinery downstream processes. In this work, the solubility of two important bio-based organic acids such as succinic acid and fumaric acid, in water and four bio-based solvents (i.e., ethyl acetate, 1,8-cineole, cyclopentyl methyl ether, and 2-methyl tetrahydrofuran) were measured within a temperature range of [283 – 313] K. A gravimetric methodology was adopted, previously validated using the organic acid aqueous solubilities available in the literature. The reported data present an average estimated uncertainty of measurement, with a level of confidence of 95%, of 5.2·10-4 mol·mol−1. Experimental results were correlated with the van’t Hoff equation, and the Buchowski–Ksiazaczak λh model, where the root mean squared deviations were <3.9·10-4 for all systems. From the experimental data and the COSMO-RS molecular simulation method, the solid–liquid equilibria were modelled to estimate the excess energies and the solute activity coefficients of the saturated solutions. Excess enthalpy contribution analysis shows that attractive hydrogen-bonding interactions between the organic acids and the green solvents drive the dissolution phenomena. The magnitude of the hydrogen-bonding interactions increases with temperature for all systems, agreeing with the observed solubility trends. The organic acid energies of solution were estimated from the van’t Hoff equation, demonstrating an enthalpy–entropy compensation effect. The energetic analysis shows that the dissolution phenomenon is an enthalpy-driven process for fumaric acid, whereas no predominant effect is observed for succinic acid.

An extended solvation theory for electrolyte osmotic and activity coefficients. Application to 1:1, 1:2, 1:3, 1:4, 2:1, 2:2, 3:1, 3:2 and 4:1 aqueous electrolyte solutions

In this work, we have used two models (DH-MS and PDH-MS) based upon the extended solvation theory to correlate osmotic and activity coefficients of electrolyte aqueous solutions. These models contain the long-range term of the Debye-Hückel (DH) theory or the Pitzer-Debye-Hückel (PDH) modification and a short-range term based upon a modified solvation (MS) theory. We have used literature experimental data of mean ionic activity and osmotic coefficients of 338 aqueous solutions. The electrolytes included in this work are type 1:1, 1:2, 1:3, 1:4, 2:1, 2:2, 3:1, 3:2, and 4:1 at 298.15 K. The results show that the DH-MS and PDH-MS models effectively correlate the experimental data within an average absolute percentage deviation of 0.588% and 0.688%, respectively. We have compared our results with those obtained from the Archer model. This model agrees within 0.769% with the literature data.