Calculation Of Activity Coefficients Research Articles

Simple model for water wash performance in amine scrubbing for CO2 capture

In amine-based capture systems, a water wash is necessary to remove gaseous amine to minimize atmospheric emissions and maximize amine recovery. Water wash simulation requires rigorous thermodynamic and kinetic models like those for absorption and stripping systems. An offline water wash model has been developed based on simplified thermodynamic and mass transfer assumptions to simulate a single-stage water wash for flue gas from gas-fired turbines with little or no aerosol, and to expedite simulations without needing to utilize process modeling software. Calculation of activity coefficients using both Pitzer–Debye–Hückel and Debye–Hückel theory suggest that the liquid phase in a typical water wash will be ideal due to the dilute concentration of molecular and ionic species.Vapor phase piperazine (PZ) is predicted with a driving force based on the volatility of the free amine that has not reacted with other species or dissociated into its ionic form, and the predicted outlet concentration is nearly identical to that predicted by rigorous Aspen PlusⓇ simulations. The predicted UT FEED outlet concentration is 220 ppb compared to 260 ppb predicted by Aspen PlusⓇ.Single-stage water washes are predicted to have single ppm concentration of MEA leaving the wash outlet flue gas. Amino-methyl-propanol (AMP) is predicted to be reduced to 10–30 ppm by a single-stage wash, and is predicted to be a difficult-to-capture amine without further washing steps. This prediction correlates with published TCM data from an ALIGN-CCUS campaign. Amine compounds at a similar or lower volatility to that of PZ are predicted to be reduced to ppb levels via a single-stage wash.

Phase equilibrium in canonical cubic structure I (sI) and II (sII) and hexagonal (sH) gas hydrate solid solutions

Canonical clathrate or gas hydrates of structure I, II and H are the main interest of engineers and scientists in a variety of technological fields including flow assurance in hydrocarbon pipelines and processing facilities, natural gas recovery from the earth's hydrates, CO2 capture and storage, methane and H2 storage etc. Clathrate hydrate systems exhibit a variety of phase equilibria and the knowledge of the relevant phase diagrams is necessary for the design of relevant processes and facilities. In this work, the various types of canonical hydrate phase equilibria of interest, models of material behaviour for phases encountered in gas hydrate systems and computational methods of phase equilibria are discussed. The term model refers to thermodynamic models for the calculation of fugacities or activity coefficients. The term method refers to hydrate equilibrium computational procedures based on combinations of the hydrate statistical thermodynamics van der Waals and Platteuw (vPW) or its improved versions with various fluid phase thermodynamic models such as equations of state and activity coefficient models. Our discussion and presentation follows a deductive approach to distinguish it from other works that are a collection of all computational methods to calculate hydrate equilibria and which often use the terms method and model interchangeably. Original references are cited as well as the current status and recent advances and challenges are considered. The advent of machine learning techniques for gas hydrate and thermodynamic calculations is also discussed.

Three pesticide-pesticide eutectic systems of boscalid: Mechanochemical preparation, characterization and mechanism analysis

Preparation of eutectic mixture is considered to be an efficient means to improve physical and chemical properties in many fields. In this work, three pesticide-pesticide eutectic systems of boscalid with diniconazole, uniconazole and 3,6-dichloropicolinic acid were prepared by mechanochemical method. The formation of eutectic mixtures was identified by differential scanning calorimetry and powder X-ray diffraction characterizations. From the constructed solid–liquid phase diagrams, it is discovered that these eutectic systems could form a eutectic when the molar fraction of boscalid is 0.500. In addition, all eutectic temperatures are more than 29 K lower than the higher melting points of the constituents in the systems, which eliminates the issue of the poor thermal stability of constituents and enables the treatment of them using melting-based operations. Ideal model and COSMO-RS theory also calculate these solid–liquid phase diagrams relatively accurately, and the calculated activity coefficient values prove that these systems do not deviate significantly from the ideal state. The distinct non-ideality at the eutectic composition of the three systems also suggests that the interactions of the three coformers and the boscalid differ. The formation of eutectic mixtures was further confirmed by other solid state characterizations including mid-infrared spectroscopy, Raman spectroscopy and etc. The accelerated stability test indicates the good stability of the three eutectic mixtures. Furthermore, the water solubility study suggests the boscalid in the eutectic systems has a higher solubility than raw boscalid. By using COSMO-RS modelling, the most typical homo/hetero-molecular complexes of these pesticides were obtained and analyzed. Based on the trend of affinity characterized by the Gibbs free energy of the generation of molecular complexes, it could be inferred that eutectic point could be viewed as the state for which affinity of hetero-molecular complexes is greatest. The affinity of hetero-molecular complexes also presents the interaction between boscalid and 3,6-dichloropicolinic acid is greater than the other two pesticides at the eutectic point. Furthermore, the calculated solvation free energies document the intermolecular interaction plays an important role in stabilizing the three eutectic systems. These eutectic systems solve the problem that the three coformers are unsuitable for melting-based procedures and improve the solubility, making them potential options for future pesticide formulation development.

Isobaric Vapor–Liquid Equilibrium of the Binary Mixtures Toluene + Styrene and Styrene + α-Methylstyrene

Isobaric vapor–liquid equilibria of the binary mixtures toluene + styrene at 30 and 40 kPa and styrene + α-methylstyrene at 20 and 25 kPa were measured applying a recirculation still. The measured vapor–liquid equilibrium data were modeled adopting the non-random two-liquid (NRTL) excess Gibbs energy model with the RK (Redlich–Kwong) equation of state. The NRTL binary interaction parameter optimization was carried out employing own measured data and literature data for the toluene + styrene system. The applied model correlates well with the experimental data at the pressure range of 101–30 kPa. Moreover, the NRTL binary parameter regression was performed applying own measured data and literature data separately for the styrene + α-methylstyrene system. The model fitted with the parameters obtained from own measured data described the multiphase behavior of the system better than the parameters obtained from literature data. Additionally, the binary systems showed ideal behavior over the whole range of investigation as the calculated activity coefficients approached unity and no azeotropes were observed.

Influence of the model used for the calculation of equilibrium constants at moderate temperature for electrolytes

The formation of a solid mineral deposit can cause major problems in the conduct of industrial processes such as high pressure acid leaching. Knowledge of the chemical speciation and solubility product of the mineral can help control or inhibit its formation. This speciation is based on knowledge of the thermodynamic equilibrium constants of the dissociation/complexation reactions involved in the system and their temperature dependence. It also depends on the concentration of the different species in the system, the pressure and the activity coefficients of the chemical species present in their molecular or electrolytic form. From these thermodynamic quantities and the state of the system, it is possible to predict the direction of evolution of the reaction, i.e. whether the reactants or the products of the chemical reactions are favoured. This work presents and compares different models for the calculation of activity coefficients for ionic strengths between 0.001 – 6 molal and the calculation of thermodynamic equilibrium constants at temperatures up to 300°C (at zero ionic strength). It confirms the need for reliable thermodynamic data for modeling aqueous systems.

Chemical speciation models based upon the Pitzer activity coefficient equations, including the propagation of uncertainties. III. Seawater from the freezing point to 45 °C, including acid-base equilibria

A quantitative understanding of pH, acid-base equilibria, and chemical speciation in natural waters including seawater is needed in applications ranging from global change to environmental and water quality management. In a previous study (Humphreys et al., 2022) we implemented a model of solutions containing the ions of artificial seawater, based upon the use of the Pitzer equations for the calculation of activity coefficients and including, for the first time, the propagation of uncertainties. This was extended (Clegg et al., 2022) to include the Tris buffer solutions that are used to calibrate the seawater total pH scale. Here we apply the same methods to develop a model of solutions containing the ions of standard reference seawater, based upon studies by Millero and co-workers. We compare the predictions of the model to literature data for: the dissociation of dissolved CO2 and bicarbonate ion; boric acid dissociation; saturation with respect to calcite, the ion product of water, and osmotic coefficients of seawater. Estimates of the uncertainty contributions of all thermodynamic equilibrium constants and Pitzer parameters to the variance of the calculated quantity are used to determine which elements of the model need improvement, with the aim of agreeing with properties noted above to within their experimental uncertainty. Further studies are recommended. Comparisons made with several datasets for carbonate system dissociation in seawater suggest which are the most reliable, and identify low salinity waters (S < 10) as a region for which dissociation constants of bicarbonate are not yet accurately known. At present, the model is likely to be most useful for the direct calculation of equilibria in natural waters of arbitrary composition, or for adjusting dissociation constants known for seawater media to values for natural waters in which the relative compositions of the major ions are different.

Elements and Chemical Bonds Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures

Based on the contribution of elements and chemical bonds, the UNICAC (Universal Quasi-Chemical elements and chemical bonds Activity Coefficient) method was proposed to estimate the activity coefficients of nonelectrolyte liquid mixtures. The UNICAC method defined 10 elements and 33 chemical bonds as contribution groups. The calculation of activity coefficients was divided into the combination term and the residual term. The combination term represents molecular size differences, and the residual term describes the interaction between molecules. The interaction energy parameters of 43 groups were regressed simultaneously with the experimental data of the vapor–liquid equilibrium of 1085 binary systems. According to the molecular structural information of compounds, the UNICAC method can accurately predict the activity coefficients of nonelectrolyte liquid mixtures. The vapor–liquid equilibrium of 16 groups of the binary system, which were not included in the parameters regress, was predicted using UNICAC. The average relative error of vapor composition was 1.53%. Compared with UNIFAC (2003), UNIFAC (Lyngby), UNIFAC (Dortmund), and ASOG (2011), the UNICAC model employs fewer parameters, provides a broader scope of application, and receives more precise predicted results of the vapor–liquid equilibrium. The UNICAC method would play an important reference role in the design of the chemical separation process.

Liquid-liquid equilibrium of systems encountered in glycerol transesterification with dimethyl carbonate

Glycerol carbonate is a value-added glycerol derivative, which can be obtained by transesterification with dimethyl carbonate. Phase splitting and merging exist in the transesterification due to the low solubilities of glycerol with dimethyl carbonate. The isobaric liquid-liquid equilibrium data for two ternary systems (glycerol – dimethyl carbonate – glycerol carbonate/methanol) and one quaternary system (glycerol – dimethyl carbonate – glycerol carbonate – methanol) involved in the glycerol transesterification were measured at reaction relevant temperatures (333.2, 353.2, 373.2, and 393.2 K) and 1.5 MPa. The equilibrium data were correlated using the NRTL model to calculate activity coefficients, with temperature-dependent interaction parameters, which were estimated through data regression and validated by checking the consistency of the Gibbs free energy. The NRTL model with the regressed parameters could reproduce the phase equilibrium trends of all the studied systems.

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.

Evaluation of mixed micellar interactions of CnBCl and SDBS mixtures using dissociated Margules model and influence of different salts

AbstractThe conductivity measurement has been used to determine the first and second CMC's (CMC1 and CMC2) of alkyldimethylbenzylammonium chloride (CnBCl; n = 12, 14 and 16) as well as gemini surfactant trimethylene‐1,2‐bis‐(dodecyldimethylammonium bromide) (12‐2‐12) with sodium dodecylbenzenesulphonate (SDBS) in aqueous solutions using Rubingh's the regular theory approximation as well as the dissociated Margules Model. The use of Margules model allows us to calculate activity coefficients of the constituents and hence provides better values of micellar parameters for asymmetric mixed systems as compared to the regular solution theory. The CMC1 values for CnBCl/SDBS mixtures were seen to be lower than those predicted from their ideal mixtures suggesting synergistic interactions although the synergism increases with chain length (n) of the cationic surfactant. Both CMC1 and CMC2 experience a decrease with rising values of n. The addition of salts including NaCl, KCl, NaBr, Na3PO4, and Na2SO4 in mixtures of C16BCl and SDBS suggests that salt counterions have a considerable impact on CMC1 when either surfactant is in excess. Zeta potential (ζ) measurements provide more evidence in favor of these observations. The thermodynamic features of micellization have also been scrutinized using isothermal titration calorimetry (ITC).

Thermodynamic properties data of ternary system NH4Cl-NH4H2PO4-H2O at 298.15 K including the solubility data

• Determination of the thermodynamic properties of the system {yNH4Cl+(1-y)NH4H2PO4}(aq) at 25 °C. • Application of the PSC model to describe the thermodynamic behavior of aqueous solutions. • Calculation of NH4Cl and NH4H2PO4 activity coefficients in the system {yNH4Cl+(1-y)NH4H2PO4}(aq). • Prediction of NH4Cl and NH4H2PO4 solubilities in aqueous solution. The mixed aqueous electrolyte system ammonium chloride and ammonium di-hydrogen phosphate has been studied with the hygrometric method at the temperature 298.15 K. The water activities, osmotic coefficient and solubilities are deduced from measurements of relative humidities of this system against total molality ranging from 0.4 mol . kg −1 to about saturation, and for different ionic-strength fractions y of NH 4 H 2 PO 4 ( y = I N H 4 H 2 P O 4 / [ I N H 4 H 2 P O 4 + I N H 4 C l ]) of 0, 1/4, 1/3, 1/2, 2/3, 3/4 and 1. Experimental results are compared to Dinane rule by the Extended Compound Additivity Law (ECA), Leitzke-Stoughton (LS II) and Lin et al. equation. The obtained results were correlated using the PSC model to predict the solute activity coefficients in the mixture for different compositions of the system and are also used to calculate the solubility and excess Gibbs energy in the studied molality range.

On the analogy between the restricted primitive model and capacitor circuits. Part II: A generalized Gibbs-Duhem consistent extension of the Pitzer-Debye-Hückel term with corrections for low and variable relative permittivity

We present a novel, thermodynamically consistent modification of the Pitzer-Debye-Hückel term and its extension for concentration dependent density, molar mass and relative permittivity. This extension is validated for ionic liquids by comparison with a reference model from the literature and, in contrast to similar extensions, also applied to conventional salts with small spherical ions in aqueous, mixed and non-aqueous solvents. The central novelty is the inclusion of a modified parameter of closest approach, which improves the overall qualitative performance of the Pitzer-Debye-Hückel term over the complete relative permittivity range. Gibbs-Duhem consistency is retained in the modified extension and sample calculations for aqueous [BMIM][BF4] and aqueous NaCl are provided. The novel, modified and extended term with concentration dependent properties is combined with the predictive COSMO-RS-ES model for the calculation of phase equilibria and activity coefficients in electrolytes with conventional salts. The performance of the COSMO-RS-ES model for predictions of salt solubility in fully non-aqueous media improves significantly upon introduction of concentration dependent properties within the long-range electrostatics. Modelling performance with the modified extended Pitzer-Debye-Hückel term outperforms modelling with the unmodified extensed term as well as with the conventional term. The correlated relative permittivity of the mixture is overestimated with respect to experimental values and kinetic depolarization effects provide a plausible explanation for this observation. Overall, our results support the consistent introduction of concentration dependent properties within the electrostatic theory in order to improve the modelling of electrolytes with particular emphasis on non-aqueous electrolytes.

Thermal, optical, and volumetric studies on mixing properties of binary nematic mixtures of 9CHBT/11CHBT

• Phase diagrams of a series of binary nematic mixtures (9CHBT/11CHBT) were studied by DSC method. • The modified four-parameter model was used by fitting the experimental data. • The temperature dependence of refractive indices, birefringence and order parameters in nematic phase was investigated. • Quantum chemical calculations on the nematogens provide supportive picture of the optical measurements. Phase diagrams and optical properties of a series of nematic binary mixtures composed of 4-(trans-4′-n-nonylcyclohexyl) isothiocyanatobenzen (9CHBT) and 4-(trans-4′-n-undecylcyclohexyl) isothiocyanatobenzen (11CHBT) were established in the entire range of molar fraction by differential scanning calorimetry method, refractometry as well as density measurements. In this research the thermodynamic, optical, and volumetric properties of the eutectic mixture ( E 9 , 11 ) composed of 9CHBT and 11CHBT ( x 11 C H B T = 0.4 ) were studied and interpreted. The binary phase diagram is in comparable with that predicted from Schroder–van Laar equation. The excess functions were determined using the calculated activity coefficients of the eutectic mixture. Moreover, the temperature dependence of refractive indices, birefringence, and order parameters of the pure nematogens and the binary eutectic mixture was investigated. In contrast to the individual nematogens, the eutectic mixture ( E 9 , 11 ) displays a crossover temperature ( T CO ) based on the four-parameter model. Finally, results from quantum chemical calculations on the studied nematogens provide an overall supportive and coherent picture of the thermal, optical measurements. All calculations were performed using the Turbomole software package. The used methodology allows for an acceptable approximation of effective polarizabilities.

Analysis of the rectifying separation of H2 O–D2 O mixture into light and heavy water by means of mathematical modeling

Objectives. To apply an analytical method for the calculation of a distillation column for the production of D2O at a two-column Kuhn installation operating under vacuum: to simulate the Kuhn installation in the Hysys software; and to compare experimental and calculated data.Methods. Analytical method for the calculation of distillation columns “from stage to stage,” from the lower theoretical separation stage (TSS) to the upper stage. This method is based on phase equilibrium at the TSS with known data of input flows and component concentrations in the column bottoms. Hysys was used as modeling software.Results. Comparison of the calculation results with Kuhn’s experimental data testified to the high calculation accuracy of the vapor–liquid phase equilibrium for the H2O–D2O mixture at the TSS. The convergence of the D2O material balance for the entire installation was 0.005%. The identification parameter was the number of the column feed plate. Simulation of the Kuhn installation in the Hysys software showed a qualitative agreement of D2O concentrations in material flows. The UNIQUAC (UNIversal QUAsiChemical) model was used to calculate activity coefficients. The found values of the number of theoretical separation stages (NTSS) in both columns, were 88 and 153 taking into account the reboiler and condenser. This is less than the experimental 295 and 400, respectively. The discrepancy can be explained by the increased phase equilibrium H2O constant in the UNIQUAC model. However, the convergence of the material balance in terms of D2O was high and amounted to 1.38·10−6 %. The absolute error of the found concentrations in material flows did not exceed 0.12 mol %.Conclusions. The results obtained indicated the possible use of the Hysys modeling software when searching for and optimizing the operating mode of the block diagram of a cascade of distillation columns with direct and recycle flows to separate a mixture of water into light and heavy water. The final results obtained with regard to the operating mode, inlet and outlet material flows (flow rate, composition, temperature, and pressure drop across the column) are recommended for use in the analytical program for the calculation of the distillation column to refine the NTSS and distribution profile of the concentrations of the H2O and D2O components along the height of the column.

Recycling of Lead Pastes from Spent Lead–Acid Batteries: Thermodynamic Constraints for Desulphurization

Lead–acid batteries are important to modern society because of their wide usage and low cost. The primary source for production of new lead–acid batteries is from recycling spent lead–acid batteries. In spent lead–acid batteries, lead is primarily present as lead pastes. In lead pastes, the dominant component is lead sulfate (PbSO4, mineral name anglesite) and lead oxide sulfate (PbO•PbSO4, mineral name lanarkite), which accounts for more than 60% of lead pastes. In the recycling process for lead–acid batteries, the desulphurization of lead sulfate is the key part to the overall process. In this work, the thermodynamic constraints for desulphurization via the hydrometallurgical route for recycling lead pastes are presented. The thermodynamic constraints are established according to the thermodynamic model that is applicable and important to recycling of lead pastes via hydrometallurgical routes in high ionic strength solutions that are expected to be in industrial processes. The thermodynamic database is based on the Pitzer equations for calculations of activity coefficients of aqueous species. The desulphurization of lead sulfates represented by PbSO4 can be achieved through the following routes. (1) conversion to lead oxalate in oxalate-bearing solutions; (2) conversion to lead monoxide in alkaline solutions; and (3) conversion to lead carbonate in carbonate solutions. Among the above three routes, the conversion to lead oxalate is environmentally friendly and has a strong thermodynamic driving force. Oxalate-bearing solutions such as oxalic acid and potassium oxalate solutions will provide high activities of oxalate that are many orders of magnitude higher than those required for conversion of anglesite or lanarkite to lead oxalate, in accordance with the thermodynamic model established for the oxalate system. An additional advantage of the oxalate conversion route is that no additional reductant is needed to reduce lead dioxide to lead oxide or lead sulfate, as there is a strong thermodynamic force to convert lead dioxide directly to lead oxalate. As lanarkite is an important sulfate-bearing phase in lead pastes, this study evaluates the solubility constant for lanarkite regarding the following reaction, based on the solubility data, PbO•PbSO4 + 2H+ ⇌ 2Pb2+ + SO42− + H2O(l).

Comments regarding “Thermodynamic parameters of solvation and volumes of nano Cu(NO3)2·2.5H2O in different concentrations of DMF – Water mixed solvents”

A polemic is provided regarding the calculated thermodynamic properties in the published paper by Sanad for nano Cu(NO3)2·2.5H2O dissolved in binary (water + N,N-dimethylformamide) solvent mixtures. Mathematical expressions used by the author in the calculation of the mean activity coefficients and negative logarithm of the solubility product, pKsp, are incorrect.

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.

Phase equilibria in Hg-Al system during vacuum distillation

   In this work, gas-liquid equilibrium states are calculated, including phase composition dependences on temperature (T-x) and pressure (P-x) for the Hg-Al alloy during vacuum distillation. The objects of research comprised Hg-Al alloys having the following composition, mole %: 20–80 Hg; 80–20 Al, whose formation may occur during the processing of copper anode slime upon producing commercial selenium concentrate. A simplified molecular interaction volume model was used to calculate the activity coefficients of the components in the Hg-Al alloy. Phase diagrams of temperature (T-x) and pressure (P-x) are used for the preliminary selection of temperature and pressure in the system, as well as for the evaluation of the separation efficiency of components. The novelty of the research stems from calculating activity coefficients using the selected simplified model. Saturated vapour pressures for Hg (p*Hg) and Al (p*Al) were calculated in the temperature range of 823–1073 K. The high values of the p*Hg / p*Al ≥ 3 . 1010 ratio and separation coefficient llogβHg ≥ 10 provide theoretical premises for selective extraction of these metals by vacuum distillation, where mercury is concentrated in the gas phase (βHg &gt; 1) and aluminium in the liquid phase. The values of excess Gibb’s energy, enthalpy and entropy changes for the liquid-gas interface of Hg-Al alloy were determined: ΔGE/m = 1–3 кJ/mol;  = 1-3 kJ/mol; +-ΔGE/m = 0,03–0,17 kJ/mol. The practical significance of the research lies in minimising the number of initial experiments during the processing of Hg-Al compositions for optimising the temperature and pressure in the vacuum distillation process.

Activity Coefficients and Solubilities of NaCl in Water-Methanol Solutions from Molecular Dynamics Simulations.

We obtain activity coefficients and solubilities of NaCl in water-methanol solutions at 298.15 K and 1 bar from molecular dynamics (MD) simulations with the Joung-Cheatham, SPC/E, and OPLS-AA force fields for NaCl, water, and methanol, respectively. The Lorentz-Berthelot combining rules were adopted for the unlike-pair interactions of Na+, Cl-, and the oxygen site in SPC/E water, and geometric combining rules were utilized for the remainder of the cross interactions. We found that the selection of appropriate combining rules is important in obtaining physically realistic solubilities. The solvent compositions studied range from pure water to pure methanol. Several salt concentrations were investigated at each solvent composition, from the lowest concentrations permitted by the system size used up to the experimental solubilities. We first calculated individual ion activity coefficients (IIACs) for Na+ and Cl- from the free energy change due to the gradual insertion of a single cation or anion into the solution, accompanied by a neutralizing background. We obtained the salt solubilities by comparing the chemical potentials in solution with solid NaCl chemical potentials calculated previously using the Einstein crystal method. Mean ionic activity coefficients obtained from the IIACs are in reasonable agreement with experimental data, with deviations increasing for solutions of higher methanol content. Predictions for the salt solubility are in surprisingly good agreement with experimental data, despite well-known challenges in the simultaneous calculation of activity coefficients and solubilities with classical MD simulations. The present study demonstrates that good predictions for these two important phase equilibrium properties can be obtained for mixed-solvent electrolyte solutions using existing nonpolarizable models and further suggests that the previously proposed single ion insertion technique can be extended to complex mixed-solvent solutions as well.

ISORROPIA-Lite: A Comprehensive Atmospheric Aerosol Thermodynamics Module for Earth System Models

Aerosol simulations especially for Earth System Models require a thermodynamics module with a good compromise between rigor and computational efficiency. We present and evaluate ISORROPIA-lite, an accelerated and simplified version of the widely used ISORROPIA-II v.2.3 aerosol thermodynamics model, expanded to include the effects of water uptake from organics and an updated interface communicating simulation diagnostics and information. ISORROPIA-lite assumes the aerosol is in metastable equilibrium (i.e., salts do not precipitate from supersaturated solutions) and treats the thermodynamics of Na⁺–NH₄⁺–SO₄^2––NO₃^––Cl^––Ca²⁺–K⁺–Mg²⁺–Organics–H₂O aerosol using binary activity coefficients from precalculated look-up tables. Off-line comparison between ISORROPIA-II and ISORROPIA-lite (without organic water effects) for more than 330,000 atmospherically-relevant states demonstrated that <em>i</em>) ISORROPIA-lite provides virtually identical results with ISORROPIA-II in metastable mode and <em>ii</em>) differences between stable mode ISORROPIA-II and ISORROPIA-lite are less than 25% for the concentrations of the various semivolatile aerosol components and similar to the differences between stable and metastable modes of ISORROPIA-II. Using ISORROPIA-lite reduced computational cost by 35% compared to ISORROPIA-II simulations in stable mode with online calculation of binary activity coefficients. Application of ISORROPIA-lite in the PMCAMx chemical transport model accelerated the 3D simulations by about 10% compared to using ISORROPIA-II in stable mode with changes in the concentrations of the major aerosol components of less than 10%. Simulations considering the effects of the organic aerosol water did not slow down ISORROPIA-lite but increased the concentrations of the inorganic semivolatile components especially at nighttime. Organic water could highly contribute to the total PM₁ water mass and increase the concentrations of fine nitrate and ammonium by as much as 1 μg m^–3 in places where the organic aerosol and RH levels are high.