Activity Coefficients Of Electrolytes Research Articles

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.

Simulation Of Acidic Water Purification Process In Refinery Based On Determining Appropriate Operating Conditions

Acidic process water produced by refineries contains some hazardous pollutants such as (H2S and NH3). Acid water extraction units remove both compounds from the water. The removed contaminants are sent to a sulphur recovery unit to produce sulphur and avoid any acid emissions contrary to environmental regulations. Water pollution is a problem that concerns all people in the world. In view of the importance of preserving the environment and water resources, in this research, the simulation of the acid water treatment unit in the refinery was studied using the Aspen Hysys software based on determining the appropriate operating conditions. The NRTL electrolyte activity coefficient model was used to predict the system's thermodynamic behaviour. The simulation results showed that the suitable temperature for the feed entering the tower is about 38°C and the convenient distance for the trays in the disposal tower is 0.54 mm. Under these conditions, the concentration of hydrogen sulphide 0.1694 and 0.2418 of ammonia in the acid gas exiting the tower reaches its maximum at a molar flow rate of the mixture of about 39.86 kgmol/h, according to the economic considerations of the operating tower.

Mixed Solvent Electrolyte Solutions: A Review and Calculations with the eSAFT-VR Mie Equation of State.

In this work, mixed-solvent mean ionic activity coefficients (MIAC), vapor-liquid equilibrium (VLE), and liquid-liquid equilibrium (LLE) of electrolyte solutions have been addressed. An extended literature review of existing electrolyte activity coefficient models (eGE) and electrolyte equations of state (eEoS) for modeling mixed solvent electrolyte systems is first presented, focusing on the details of the models in terms of physical and electrolyte terms, relative static permittivity, and parameterization. The analysis of this literature reveals that the property predictions can be ranked, from the easiest to the most difficult, in the following order: VLE, MIAC, and LLE. We have then used our previously developed eSAFT-VR Mie model to predict MIAC, VLE, and LLE in mixed solvents without fitting any new adjustable parameters. The model was parameterized on MIAC of aqueous electrolyte solutions and successfully extended to nonaqueous, single solvent electrolyte solutions without any new adjustable parameters by using a salt-dependent expression for the relative static permittivity. Our approach yields excellent results for MIAC and VLE of mixed solvent electrolyte solutions, while being fully predictive. LLE is significantly more challenging, and an accurate model for the salt-free solution is crucial for accurate calculations. When the compositions of the two phases in the binary salt-free system are accurately captured, then the electrolyte extension of our model shows a lot of potential and is currently among the best eEoS for LLE prediction in the literature.

Mean ionic activity coefficient of associative electrolyte solutions: A comparison study

The performance of four implicit solvent models for associative and two models for non-associative electrolyte solutions has been compared and analyzed for the mean ionic activity coefficient (MIAC) of electrolytes in the solution. Two of these models for associative electrolyte solutions are based on a chemical approach (Fisher-Levin-Guillot-Guissani (FLGG) and Ebeling-Grigo (EG)), and one of them is based on the reference cavity approximation (Zhou-Yeh-Stell (ZYS)). The last one is based on the thermodynamic perturbation theory (Binding mean spherical approximation, BiMSA). Models without ion-pairing also consist of hard sphere (HS) contribution in addition to the electrostatic contribution from the Debye-Hückel (HS + DH) and the mean spherical approximation (HS + MSA) theories. To this aim, the models’ predictions are compared with the numerical solution of the Poisson-Boltzmann equation, the Monte Carlo simulations, and the experimental data. We have shown that considering the ion pairing results in a better agreement of the predicted MIAC against both simulations and experimental data of 2:2 electrolytes. We have also adjusted the ionic diameter and the distance between ion pairs to the MIAC experimental data and validated the estimated fractions of free ions with the electrical conductivity measurements. We have shown that the FLGG model captures the physics of the system more accurately compared to other models.

Statistical theory of individual activity coefficients of electrolytes including multiple ionic charges

In previous work we developed a new statistical method for calculating the individual activities of ions including the association of ions. Here we study multi-particle electrostatic interactions connected within higher cluster integrals and identify the ionization constants of the mass action law of associating ion clusters. In contrast to Bjerrum and Fuoss, our concept of association is not based on spatial criteria, but instead on the strength of interaction measured in powers of the Bjerrum parameter (e2/D0kBTa; a is contact) and defined by asymptotic properties of the cluster integrals. For ion pair formation our mass action constant is the classical counterpart of Planck's famous hydrogenic partition function. As a rule, the new association constants are smaller than traditional expressions, e.g., by Fuoss and Kraus, in the interesting regions of interaction parameters about fifty percent. Several examples including CaCl2, MgCl2, Na2SO4, K2SO4, LaCl3 and a model of seawater are studied. For several associating electrolytes and seawater, reasonable agreement with experiments and Monte Carlo results is achieved.

Influence of concentration and temperature dependent dielectric constants on the thermodynamics of electrolytes

The symmetric Poisson–Boltzmann theory, the modified Poisson–Boltzmann theory, and the mean spherical approximation are utilized to calculate the osmotic coefficient, and the individual and mean activity coefficients of model KCl, LiCl, NaCl, and NaClO4 electrolytes all dissociated in water where the dielectric constant depends on concentration. The theories are also employed to compute the same thermodynamic quantities for HCl and NaCl solutions where the dielectric constant is now temperature dependent. In each situation the theoretical predictions are compared with the corresponding exact benchmark Monte Carlo simulation results. The mean spherical approximation and the modified Poisson–Boltzmann theory reproduce the simulation data for osmotic coefficient quantitatively and that for the mean activity almost quantitatively. The individual activities are accurately represented by the modified Poisson–Boltzmann theory but only qualitatively by the symmetric Poisson–Boltzmann and the mean spherical approximation. In general, the symmetric Poisson–Boltzmann theory shows good agreement with the simulations at low concentrations but deviates at higher concentrations.

Generalized Debye–Hückel model for activity coefficients of electrolytes in water–methanol mixtures

We propose a generalized Debye–Hückel model from Poisson–Fermi theory to calculate mean activity coefficients of electrolytes in water–methanol mixtures with arbitrary percentage of methanol from 0 to 100%. The model accounts for both short and long ion–ion, ion–water, ion–methanol, and water–methanol interactions, the size effect of all particles, and the dielectric effect of mixed-solvent solutions. We also present a numerical algorithm with mathematical and physical details for using the model to fit experimental data. The model has only 3 empirical parameters to fit the experimental data of NaF, NaCl, and NaBr, for example, in pure-water solutions. It then uses another 3 parameters to calculate the activities of these salts in mixed-solvent solutions for any percentage of methanol. Values of these parameters show mathematical or physical meaning of ionic activities under variable mixing condition and salt concentration. The algorithm can automatically determine optimal values for the 3 fitting parameters without any manual adjustments.

Estimation of activity coefficients for aqueous organic redox flow batteries: Theoretical basis and equations

SummaryThe field of aqueous organic redox flow batteries (AORFBs) has been developing fast in recent years, and many chemistries are starting to emerge as serious contenders for grid-scale storage. The industrial development of these systems would greatly benefit from accurate physics-based models, allowing to optimize battery operation and design. Many authors in the field of flow battery modeling have brought evidence that the dilute solution hypothesis (the assumption that aqueous electrolytes behave ideally) does not hold for these systems and that calculating cell voltage or chemical potentials through concentrations rather than activities, while serviceable, may become insufficient when greater accuracy is required. This article aims to provide the theoretical basis for calculating activity coefficients of aqueous organic electrolytes used in AORFBs to provide tools to predict the concentrated behavior of aqueous electrolytes, thereby improving the accuracy of physics-based models for flow batteries.

Theoretical Prediction of Freezing Point Depression of Lithium-Ion Battery Electrolytes

Understanding and predicting the freezing point depression of liquid electrolytes is of interest particularly for low-temperature battery applications. We will present a computational methodology to calculate activity coefficients and the freezing point depression of liquid electrolytes relevant to Li-ion batteries. Theoretical expressions for Born solvation, Debye-Huckel ion atmosphere effects and solvent entropy are used with results from classical molecular dynamics simulations and electronic structure methods to calculate the activity coefficients of liquid electrolytes. Using the calculated activity coefficients as well as neat solvent properties, liquidus lines of the studied electrolytes are obtained up to 1 molal. The liquid electrolytes studied include LiPF6 in dimethyl carbonate and LiPF6 in propylene carbonate. It is found that the more significant freezing point depression of the propylene carbonate-based electrolyte versus dimethyl carbonate-based electrolyte originates in large part from the much higher dielectric constant of propylene carbonate versus dimethyl carbonate.

Modelling of the terephthalic acid - disodium terephthalate - sodium chloride - sodium hydroxide - ethylene glycol – water system

The Extended UNIQUAC electrolyte activity coefficient model was used for modeling the aqueous terephthalic acid, disodium terephthalate, sodium chloride, sodium hydroxide, ethylene glycol system. Data for solid-liquid equilibrium (SLE) and vapor-liquid equilibrium (VLE) was used for determining the parameters of the model. Model parameters were determined for terephthalic acid and for the terephthalate ion. Parameters for other species have previously been published and were used in this work. The modeling results are in close agreement with existing experimental data. It has an accurate outcome up to 90 °C based on available experimental measurements; however, the model predicts the reasonable performance of thermodynamics up to several hundred °C. Furthermore, this model can be used to perform simulation and process design of sustainable PET plastic recycling.

Activity coefficients of aqueous electrolytes from implicit-water molecular dynamics simulations.

We obtain activity coefficients in NaCl and KCl solutions from implicit-water molecular dynamics simulations, at 298.15K and 1bar, using two distinct approaches. In the first approach, we consider ions in a continuum with constant relative permittivity (ɛr) equal to that of pure water; in the other approach, we take into account the concentration-dependence of ɛr, as obtained from explicit-water simulations. Individual ion activity coefficients (IIACs) are calculated using gradual insertion of single ions with uniform neutralizing backgrounds to ensure electroneutrality. Mean ionic activity coefficients (MIACs) obtained from the corresponding IIACs in simulations with constant ɛr show reasonable agreement with experimental data for both salts. Surprisingly, large systematic negative deviations are observed for both IIACs and MIACs in simulations with concentration-dependent ɛr. Our results suggest that the absence of hydration structure in implicit-water simulations cannot be compensated by correcting for the concentration-dependence of the relative permittivity ɛr. Moreover, even in simulations with constant ɛr for which the calculated MIACs are reasonable, the relative positioning of IIACs of anions and cations is incorrect for NaCl. We conclude that there are severe inherent limitations associated with implicit-water simulations in providing accurate activities of aqueous electrolytes, a finding with direct relevance to the development of electrolyte theories and to the use and interpretation of implicit-solvent simulations.

Statistical theory of individual ionic activity coefficients of electrolytes with multiple – Charged ions including seawater

Based on methods of statistical mechanics for the calculation of individual activity coefficients for electrolytic solutions we present analytical nonlinear extensions of the standard Debye - Hückel and Mean-Spherical approximations. These extensions, so - called DHX and MSX approximations, respectively, generalize the exact results from cluster theory and are given for the model of charged hard spheres with non - additive contact distances. The flexibility of the fully analytical model which is able to reflect e.g. cationic solvation effects and allows the treatment of ionic activities in a 6-component seawater model. Denoting by e the elementary charge, DHX and MSX include in the third order, e6, the Poirier effects of asymmetry of ion charges, and in the fourth order, e8, as well as in higher orders, weak association effects which are relevant for electrolytes with multivalent ions. Following the Justice method, weak association effects are treated in a semi - chemical description avoiding mass - action laws. An extrapolation of the theory of individual activities to a description of individual conductivities is proposed.

Exploring the thermodynamics of the bromine electrode in concentrated solutions for improved parametrisation of hydrogen–bromine flow battery models

Thermodynamic properties of the bromine electrode in an exemplary hydrogen–bromine flow battery (HBFB) are investigated in detail. Open-circuit potential (OCP) measurements of HBRB electrolytes in a liquid junction-free setup and electrolyte Raman spectra are employed to estimate polybromides speciation. An improved mathematical description of the bromine electrode OCP versus state of charge is provided. This paper addresses the phenomenon of polybromides formation at concentrations up to 7.7 mol L -1 HBr and 3.85 mol L -1 Br 2 and their significant impact on the OCP. The model takes into account tri-, penta- and heptabromides formation, precisely modelled electrolyte activity coefficients (up to 11-molal HBr), electrolyte density, and temperature. It is elucidated that the polybromide formation constants found in literature treating dilute electrolytes are substantially too low. Newly determined equilibrium constants, applicable over a wider concentration range are provided for 25 and 43 °C together with their standard enthalpy changes. The model is successfully validated in an independent experiment using a real, pilot-scale HBFB. It is concluded that the usage of a simple Nernst-like equation to calculate the OCP of flow battery electrodes containing concentrated electrolytes leads to erroneous results. • A novel thermodynamic bromine electrode model is described and validated. • It is applied to describe the open-circuit voltage of a pilot-scale flow battery. • Polybromide formation constants are re-evaluated at high electrolyte concentrations. • Mean activity coefficient of aqueous HBr up to 11 m between 0 and 70 °C is modelled.

Sustainable coastal halophyte farming for biofuel in arid regions: site and feedwater screening using geochemical modeling

Halophyte agriculture in marginal soils using saline water offers a sustainable solution for generating biomass feedstock for carbon-neutral aviation biofuels. A full-scale sustainable energy and agriculture system (SEAS) demonstration is planned for the Abu Dhabi coast, where evaporitic gypsiferous soils pose a challenge to long-term operation because of the potential for land degradation. In this study, geochemical modeling on the Geochemist’s Work Bench (GWB®) platform was employed to (1) evaluate the feasibility of using coastal groundwater versus seawater as irrigation feedwater, (2) determine the change in agricultural return water salinity through site-specific soils upon different seawater irrigation rates, and (3) assess mineral deposition effects in the soil column as a function of site-specific soil characteristics at candidate sites over a 1-year period of continuous seawater irrigation. Evaporation modeling was used to evaluate potential feedwater sources while varying feedwater composition and electrolyte activity coefficient models. 1-D saturated–flow advection–precipitation/dissolution modeling was utilized to assess return water quality and mineral deposition as a function of both the electrolyte activity coefficient model and the mineral composition of site-specific soils. Results pointed to seawater as the more viable feedwater option compared to coastal groundwater because of slower onset of precipitation. This effort demonstrated that soil type did not influence agricultural return water salinity (except for strongly gypsic soils) but influenced mineral precipitation under surficial evaporation conditions. Porosity loss correlated with layers of mineral deposition. The study points to the need for careful screening of land and saline water resources for the sustainable farming of halophytes.

The Activity Coefficients of High-Charge Electrolytes in Aqueous Dilute Solutions

We examine in detail the activity coefficient of higher-charge electrolytes, which, in dilute solutions, can display negative deviations from the Debye–Huckel limiting law instead of the usual positive deviations typical of lower-charge electrolytes. This fact is of considerable relevance for scientists concerned with extrapolation to infinite dilution of thermodynamic and kinetic quantities. It is shown that this “strange” behavior originates merely from the electrostatic interactions between each ion and all other ions, with no necessity of hypothesizing the presence of chemical association; these negative deviations, indeed, are predicted even at the level of the “primitive model” (ions assumed as charged, unpolarizable, rigid spheres inside an unstructured, isotropic, dielectric fluid). Three different approximations for the behavior of the primitive model of low-charge and high-charge electrolytes are tested, in addition to the Debye–Huckel theory; i.e. IPBE (a numerical accurate integration of the Poisson–Boltzmann equation), the Mayer theory of the electrolytes in the so-called DHLL + B2 approximation, and the Bjerrum theory. In the Supporting Information, the fundamentals of the respective algorithms are reported, and the effects produced by the differences of size between cations and anions, are also examined.

Analysis of Some Electrolyte Models Including Their Ability to Predict the Activity Coefficients of Individual Ions

This work presents a modeling study, with selected models, of the mean ionic activity coefficients of electrolytes in aqueous solutions, where predictions of the activity coefficients of individual...

Ionic activity in concentrated electrolytes: Solvent structure effect revisited

We revisit the role of the local solvent structure on the activity coefficients of electrolytes within a nonlocal dielectric function approach. We treat the concentrated electrolyte as a dielectric medium and suggest an interpolation formula for its nonlocal dielectric response. The water dielectric response is approximated based on MD simulations and experimental data, that gives strong over-screening and oscillations in the potential, which are absent in the standard “primitive model” predictions. We obtain mathematically tractable closed-form expressions for the activity coefficients, in reasonable agreement with experimental data.

An extended solvation theory for electrolyte osmotic and activity coefficients. I. Application at 298.15 K

This paper presents a new model to correlate osmotic and activity coefficients of electrolyte solutions. The model contains a long-range interactions term based upon Debye-Hückel theory (Debye- Hückel, DH or Pitzer-Debye-Hückel, PDH) and a short-range interactions term based upon extended solvation theory (ST). Testing the correlative capability of the new model used 56 electrolyte aqueous solutions: 1:1, 1:2, 1:3, 1:4, 2:1, 2:2, 3:1, 3:2 and 4:1 at 298.15 K. The average percentage deviation, standard deviation and its bias from the experimental data are (0.48, 0.25 and −0.001) and (0.69, 0.26 and 0.005) for DH-ST and PDH-ST, respectively. The results demonstrate that the new equation correlates experimental data effectively.

Методы оценки коэффициентов активности сильных кислот в интервале концентраций от 1 до 10 моль/л

The activity coefficient of individual ions is an important parameter in the theory of strong and weak electrolytes in aqueous and non-aqueous solutions. The physical meaning of the average ion coefficient lies in the ratio of the practical and theoretical activity coefficients. If the activity coefficient is set equal to 1 .0, as in the majority of published works, the final calculations can present multiple distorted γ± results. The activity coefficient constitutes a measure of the deviation of real (practical or experimental) parameters from the ideal ones. Ideal parameters are calculated for dilute solutions of non-electrolytes, in which no interactions are assumed to occur. Activity coefficients in high-concentration solutions may reach the values of several tens. However, some empirical data has indicated the dependence of the activity coefficient of electrolytes on their concentration, with some concentrations showing its minimal values. The coefficients equal to several tens, i.e. describing deviations from ideal parameters by the factor of ten, are difficult to adapt for practical application in solutions where association processes or other intermolecular interactions dominate. The present paper describes a number of methods for estimating the average ionic activity coefficients of such strong acids as hydrochloric, hydrobromic, hydroiodic, perchloric, nitric and sulphuric acids across the concentration range from 1 to 10 mol/l. These methods are based on the concepts of nonlinear programming and the method of multi-level modelling of various properties and parameters applied as a calculation tool. According to the performed calculations, the as-estimated activity coefficients of the acids under study are found to be in good agreement with the literature data for the concentration range from 1 to 10 mol/l.

Comment on “Negative Deviations from the Debye–Hückel Limiting Law for High-Charge Polyvalent Electrolytes: Are They Real?”

A work ( Fraenkel , D. J. Chem. Theory Comput. 2018 , 14 , 2609 , DOI: 10.1021/acs.jctc.7b01260 ) was recently published in which, starting from data of activity coefficients of electrolytes determined by Malatesta and co-workers in the years 1992-2000, an incorrect conclusion is reached, i.e., that the negative deviations from the Debye-Hückel limiting law found at high dilution for high-charge polyvalent electrolytes were presumably not real. The present work shows the reasons why we cannot share his opinion. The negative deviations are supported both by the theory and by experimental demonstration.