Estimation Of Activity Coefficients Research Articles

Application of Davis method to estimation of ions activity coefficients at the evaluation of dissociation constants of aromatic dicarboxylic acids in organic solvents

Validity of the Davis method for the estimation of activity coefficients of the ions forming in an acid-base system at the evaluation of thermodynamic dissociation constants of aromatic acids in dimethylformamide medium is evidenced.

Binary Mutual Diffusion Coefficients of Isoniazid Aqueous Solutions at (298.15 and 310.15) K

Binary mutual diffusion coefficients measured by the Taylor dispersion method in two different laboratories (University of Naples, Federico II, Italy, and University of Coimbra, Portugal) are reported for aqueous solutions of isoniazid at concentrations from (0.000 to 0.100) mol·dm−3 and at two temperatures (298.15 and 310.15) K. The hydrodynamic radii for the isoniazid in aqueous solution are calculated from the experimental results. In addition, the Hartley equation and the experimental diffusion coefficients are used to estimate activity coefficients for aqueous isoniazid at both temperatures.

Finitely limited group contribution correlations for boiling temperatures

Group contribution correlations are presented for the boiling temperatures at (101.33 and 1.33) kPa and for critical temperature applicable to a broad range of organic compounds. The group contributions are based on UNIFAC groups to facilitate simultaneous group identification for estimation of activity coefficients. These correlations recognize a finite limit in boiling temperature and critical temperature as infinite molar mass is approached. The existence of this limit is suggested by: extrapolation of the experimentally measured boiling temperatures, by critical behavior polymer solutions, by engineering equations of state, and by molecular simulation results. The availability of two vapor pressures enables straightforward application of the Clausius–Clapeyron equation to estimate boiling temperatures at other points. In the presented approach, there are three parameters for the boiling temperature correlations and one parameter for the critical temperature plus 72 functional groups. The parameters are regressed through a database consisting of 336 hydrocarbons and 642 non-hydrocarbons. The database consists of various chemical families including aliphatics, olefinics, naphthenics, aromatics, alcohols, amines, nitriles, thiols, sulfides, aldehydes, ketones, esters, ethers, halocarbons, silicones, and acids. The average absolute percent deviations (AAD%) between the correlated and experimental temperatures are calculated in comparison with the Joback–Reid and Gani approaches. For the enthalpy of vaporization at T = 298 K, the Joback model makes calculations possible at 1.33 kPa by assuming that Hvap is constant over this range. Also, Kolska and Gani have reported a correlation for heat of vaporization at the normal boiling point which is used in this study. We obtain (3.5, 4.7, and 4.1) AAD% in temperature for the present work using the Joback–Reid and Gani methods, respectively. Additionally, the accuracy of the present work is evaluated by calculating the vapor pressures from the DIPPR correlation at the predicted temperatures of each model. We obtained (33, 104, and 48) AAD% in pressure for the present work by means of the Joback–Reid, and Gani methods. The critical temperature correlation results in a 2.6 AAD% in critical temperature. Asher and Pankow have reported a UNIFAC- P L ∘ method to predict the vapor pressure of oxygen-containing compounds to model the behavior of organic aerosols over the temperature range of (290 to 320) K. The Asher et al. model is compared to this approach for 66 volatile species. For the vapor pressure at the 1.33 kPa boiling temperature, we obtain 37 AAD% for the present work and 95 AAD% using the Asher–Pankow method.

Estimation of Drug–Polymer Miscibility and Solubility in Amorphous Solid Dispersions Using Experimentally Determined Interaction Parameters

The amorphous form of a drug may provide enhanced solubility, dissolution rate, and bioavailability but will also potentially crystallize over time. Miscible polymeric additives provide a means to increase physical stability. Understanding the miscibility of drug-polymer systems is of interest to optimize the formulation of such systems. The purpose of this work was to develop experimental models which allow for more quantitative estimates of the thermodynamics of mixing amorphous drugs with glassy polymers. The thermodynamics of mixing several amorphous drugs with amorphous polymers was estimated by coupling solution theory with experimental data. The entropy of mixing was estimated using Flory-Huggins lattice theory. The enthalpy of mixing and any deviations from the entropy as predicted by Flory-Huggins lattice theory were estimated using two separate experimental techniques; (1) melting point depression of the crystalline drug in the presence of the amorphous polymer was measured using differential scanning calorimetry and (2) determination of the solubility of the drug in 1-ethyl-2-pyrrolidone. The estimated activity coefficient was used to calculate the free energy of mixing of the drugs in the polymers and the corresponding solubility. Mixtures previously reported as miscible showed various degrees of melting point depression while systems reported as immiscible or partially miscible showed little or no melting point depression. The solubility of several compounds in 1-ethyl-2-pyrrolidone predicts that most drugs have a rather low solubility in poly(vinylpyrrolidone). Miscibility of various drugs with polymers can be explored by coupling solution theories with experimental data. These approximations provide insight into the physical stability of drug-polymer mixtures and the thermodynamic driving force for crystallization.

Predicted Reaction Rates of HxNyOz Intermediates in the Oxidation of Hydroxylamine by Aqueous Nitric Acid

This work reports computed rate coefficients of 90 reactions important in the autocatalytic oxidation of hydroxylamine in aqueous nitric acid. Rate coefficients were calculated using four approaches: Smoluchowski (Stokes-Einstein) diffusion, a solution-phase incarnation of transition state theory based on quantum chemistry calculations, simple Marcus theory for electron-transfer reactions, and a variational TST approach for dissociative isomerization reactions that occur in the solvent cage. Available experimental data were used to test the accuracy of the computations. There were significant discrepancies between the computed and experimental values for some key parameters, indicating a need for improvements in computational methodology. Nonetheless, the 90-reaction mechanism showed the ability to reproduce many of the trends seen in experimental studies of this very complicated kinetic system. This work highlights reactions that may govern the system evolution and branching behavior critical to the stability of the system. We hope that this analysis will guide experimental investigations to reduce the uncertainties in the critical rate coefficients and thermochemistry, allowing an unambiguous determination of the dominant reaction pathways in the system. Advances in efficient and accurate solvation models that effectively separate entropic and enthalpic contributions will most directly benefit solution-phase modeling efforts. Methods for more accurately estimating activity coefficients, including at infinite dilution in multicomponent mixtures, are needed for modeling high ionic strength aqueous systems. A detailed derivation of the solution-phase equilibrium and transition state theory rate expressions in solution is included in the Supporting Information.

Some Transport Properties of γ-Cyclodextrin Aqueous Solutions at (298.15 and 310.15) K

Values of binary mutual diffusion (interdiffusion) coefficients, obtained by using the Taylor dispersion method, for aqueous solutions of γ-cyclodextrin in the concentration range from (0.002 to 0.010) mol·dm−3 and temperatures (298.15 and 310.15) K are reported. From these experimental results, the hydrodynamic radius values for the γ-cyclodextrin are estimated. Also, the measured diffusion coefficients are used with both Hartley’s and Gordon’s equations to estimate activity coefficients for aqueous γ-cyclodextrin. These studies are complemented by some density and viscosity measurements, carried out at the same range of concentrations and temperatures. The effect of both the viscosity of the medium and the formation of γ-cyclodextrin dimers on the estimated hydrodynamic radius is discussed.

Nikolai Izmailov (1907-1961): An appreciation

Nikolai Izmailov (1907-1961): An appreciation

The form of the rate constant for elementary reactions at equilibrium from MD: framework and proposals for thermokinetics

The rates of formation and concentration distributions of a dimer reaction showing hysteresis behavior are examined in an ab initio chemical reaction designed as elementary and where the hysteresis structure precludes the formation of transition states (TS) with pre-equilibrium and internal sub-reactions. It was discovered that the the reactivity coefficients, defined as a measure of departure from the zero density rate constant for the forward and backward steps had a ratio that was equal to the activity coefficient ratio for the product and reactant species. This surprising result, never formally incorporated in elementary rate expressions over approximately one and a half centuries of quantitative chemical kinetics measurement and calculation is accepted axiomatically and leads to an outline of a theory for the form of the rate constant, in any one given substrate—here the vacuum state. A major deduction is that the long-standing definition of the rate constant for elementary reactions is not complete and is nonlinear, where previous works almost always implicitly refer to the zero density limit for strictly irreducible elementary reactions without any attending concatenation of side-reactions. This is shown directly from MD simulation, where for specially designed elementary reactions without any transition states, density dependence of reactants and products always feature, in contrast to current practice of writing rate equations. It is argued that the rate constant expression without reactant and product dependence is due to historical conventions used for strictly elementary reactions. From the above observations, a theory is developed with the aid of some proven elementary theorems in thermodynamics, and expressions under different state conditions are derived whereby a feasible experimental and computational method for determining the activity coefficients from the rate constants may be obtained under various approximations and conditions. Elementary relations for subspecies equilibria and its relation to the bulk activity coefficient are discussed. From one choice of reaction conditions, estimates of activity coefficients are given which are in at least semi-quantitative agreement with the data for non-reacting Lennard-Jones (LJ) particles for the atomic component. The theory developed is applied to ionic reactions where the standard Brönsted-Bjerrum rate equation and exceptions to this are rationalized.

Application of a generalized model to the estimation of physical properties and description of the aromatic extraction from a highly paraffinic lubricating oil

In the lubricating oil manufacturing process, the aromatic content of vacuum distillates is reduced by solvent extraction, frequently with furfural. In this work, a generalized model (based on a reduced number of pseudo-components and the NRTL model) for estimation of activity coefficients is applied to the simulation of the extraction process of aromatics by furfural from a highly paraffinic Argentinian lubricating oil. Such model proposes a linear dependence between the pseudo-component properties and the NRTL parameters with the average boiling point of the distillate used as feed. Physical properties of the mixtures are calculated using the calculated pseudo-component properties. Obtained values are compared to those calculated by other methods reported in the literature, obtaining no remarkable deviations, but showing the influence of the paraffinic content on the accuracy of the predictions. The extraction process is simulated using the calculated pseudo-component properties and the NRTL parameters by means of Aspen Plus ® commercial software. Good agreement was found between predicted and experimental values of yield, furfural content and composition.

Self-diffusion coefficients and structure of the trivalent f-element ions, Eu, Gd, Am, Bk, Cf and Es in aqueous diluted and concentrated solutions

Self-diffusion coefficients D of the trivalent ions in aqueous solutions of Eu and Gd have been determined in electrolyte support Gd(NO 3) 3, and of Am, Bk, Cf and Es in electrolyte support Nd(ClO 4) 3, in concentrated solutions at (pH = 2.5) HNO 3, HClO 4 and at 25 °C using the open end capillary method (O.E.C.M.). This method measures the transportation time of ions across a fixed distance. In this paper we complete a measurement of self-diffusion coefficient at concentrated solution (1.5 M). We optimized the pH in order to avoid the hydrolysis, pairing and complexing trivalent 4f and 5f ions. The behavior of D and Dη are plotted versus √ C. The similarities observed of self-diffusion coefficients of trivalent f-elements ions can be explained by a similar electronic configuration and same hydration number. The variation of D versus the square root of the concentration of the solution was found to be quasi-linear in the studied concentration range ( C ≤ 1.5 M). Results of the diffusion for the two couples (Am–Eu) and (Bk–Gd) show us that 4f and 5f elements, having similar electronic configuration and/or sub shell half-filled configuration of trivalent ions, have the same behavior. We compared variation of D/ D° versus √ C for all studied 4f and 5f elements from concentration 0 to 1.5 M and we obtained the same variation with √ C for all studied elements. We have estimated activity coefficients for both 4f and 5f trivalent ion elements using Nernst–Hartley expression. We deduced that we can achieve self-diffusion experience using 4f support electrolyte as Nd(ClO 4) 3 in acid medium and needing only some 5f element tracer element. This method is adequate for the study of 5f element which is not available as a macro element such as heavy 5f elements fermium Fm 3+ and mendelevium Md 3+.

A proposal for the estimation of binary mixture activity coefficients from surface tension measurements throughout the entire concentration range

A method to estimate the concentration dependence of the bulk activity coefficients of both binary mixture components from experimental surface tension data covering the whole concentration range is presented. To this end, high-quality experimental surface tension data as a function of the concentration, paying special attention to the diluted regions, are needed. The method is based on the application of equilibrium conditions to the surface chemical potential arisen from the Volmer equation (the simplest non-ideal surface EOS) and to the bulk chemical potential coming from the three-suffix Margules equation for activity coefficients. It can be applied provided that positive aneotropy is not present and the second derivative of the surface pressure as a function of the mole fraction is not positive in any composition region, which means rather unrestrictive conditions. In order to test the method, a compilation of 25 systems for which surface tension and activity coefficient data are simultaneously available in the literature was performed, turning out that most of them involved water. It was found that surface tension data with enough concentration coverage and good quality are really scarce, which makes the development of this kind of methods difficult.

Binary Mutual Diffusion Coefficients of Aqueous Solutions of α-Cyclodextrin, 2-Hydroxypropyl-α-cyclodextrin, and 2-Hydroxypropyl-β-cyclodextrin at Temperatures from (298.15 to 312.15) K

Binary mutual diffusion coefficients measured by the Taylor dispersion method are reported for aqueous solutions of α-cyclodextrin (α-CD), 2-hydroxypropyl-α-cyclodextrin (HP-α-CD), and 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) at concentrations from (0.002 to 0.010) mol·dm-3 at temperatures from (298.15 to 312.15) K. The hydrodynamic radius and activation energy for the diffusion of aqueous α-CD, HP-α-CD, and HP-β-CD are calculated from the experimental results. In addition, the Hartley equation and the measured diffusion coefficients are used to estimate activity coefficients for aqueous α-CD, HP-α-CD, and HP-β-CD.

Struvite precipitation thermodynamics in source-separated urine

Struvite (MgNH 4PO 4·6H 2O) precipitation eliminates phosphate efficiently from urine, a small but highly concentrated stream in the total flux of domestic wastewater. Precipitation experiments with hydrolysed urine evaluated the solubility product of struvite. The stored and fully hydrolysed urine had an ionic strength of between 0.33 and 0.56 M and required the estimation of activity coefficients. From our data, we identified the Davies approximation with the two constants A=0.509 and B=0.3 as agreeing best with our laboratory results. The standard solubility product K s 0= f 1[NH 4 +] f 2[Mg 2+] f 3[PO 4 3−] ([ ]=concentration of the species; f x =corresponding activity coefficient) of struvite in urine was found to be 10 −13.26±0.057 at 25 °C and the enthalpy of struvite formation Δ H was 22.6(±1.1) kJ mol −1. The equilibrium calculations required the following dissolved complexes: [MgCO 3] aq, [MgHCO 3] +, [MgPO 4] −, [NH 4HPO 4] −, and [NaHPO 4] − and to a lesser extent [MgSO 4] aq and [NH 4SO 4] −. Organic complexes do not seem to influence the solubility product substantially. For practical purposes, a conditional solubility product K s cond=[Mg aq]·[NH 4 ++NH 3]·[P ortho]=10 −7.57 M 3 was derived to calculate struvite solubility in urine at 25 °C, pH=9.0 and ionic strength I=0.4 M directly from measured concentrations.

Design of Industrial Reactive Absorption Processes in Sour Gas Treatment Using Rigorous Modelling and Accurate Experimentation

In this paper a rigorous rate-based model for the selective absorption and desorption of sour gases in packed towers within a coke oven gas purification process (VACASULF ®-process) is presented. It considers multi-component mass transfer of CO 2, H 2S, NH 3 and HCN in aqueous potassium hydroxide (KOH) or potash (K 2CO 3) solutions and the influence of chemical reactions on mass transfer using enhancement factors. A modified Pitzer model is used to estimate activity coefficients in the electrolyte solution for the calculation of the chemical and the phase equilibria as well as the reaction kinetics (Brönsted-Bjerrum equation). Using data from the literature this thermodynamically consistent approach was successfully validated for the phase equilibria and the reaction kinetic calculation. Since no experimental data for the above-mentioned chemical system in packed towers is available in the literature, own experiments were carried out in a pilot plant packed tower. A newly developed experimental method using redundant measurements and a Data Reconciliation procedure improved the accuracy of concentration profiles for the gas and the liquid phase. Using eight absorption and eight desorption experiments, as well as industrial on-site measurements of the entire plant, the model was successfully validated. In addition, the model was used for global optimization using evolutionary algorithms, revealing an optimization potential of 30% in operating costs.

Prediction of activities of three components in the ternary molten slag CaO-FeO-SiO2 by the molecular interaction volume model

In this article, a novel thermodynamic model—the molecular interaction volume model (MIVM)—was employed to predict the activities of three components in the ternary molten slag CaO-FeO-SiO2 at different temperatures. The results show that the predicted values of activity of CaO and SiO2 are in reasonable agreement with the experimental data in a range of lower concentrations, which are about xCaO<0.2 for CaO and about xSiO2=0.15 to 0.50 for SiO2 at 1823 K, respectively, and that the predicted values of activity of FeO are in good agreement with the experimental data in a range of entire concentrations at 1623, 1823, and 1873 K. This shows that MIVM is an alternative for the estimation of activity coefficients of all components in a ternary molten slag, where its activity data are absent or their accuracies are questionable only when its sub-binary activities are known and reasonably reliable.

Binary Mutual Diffusion Coefficients of Aqueous Solutions of Sucrose, Lactose, Glucose, and Fructose in the Temperature Range from (298.15 to 328.15) K

Binary mutual diffusion coefficients measured by the Taylor dispersion method in two different laboratories (University of Naples, Federico II, Italy, and University of Coimbra, Portugal) are reported for aqueous solutions of lactose, sucrose, glucose, and fructose at various concentrations (0.001 to 0.1) mol·dm-3 and temperatures (298.15 to 328.15) K. The hydrodynamic radius and activation energy for the diffusion of aqueous sugars are calculated from those results. In addition, the measured diffusion coefficients are used with the Hartley equation to estimate activity coefficients for aqueous lactose, sucrose, glucose, and fructose.

Prediction of activity coefficients in liquid aerosol particles containing organic compounds, dissolved inorganic salts, and water—Part 2: Consideration of phase separation effects by an X-UNIFAC model

A thermodynamic model is presented for predicting the formation of particulate matter (PM) within an aerosol that contains organic compounds, inorganic salts, and water. Neutral components are allowed to partition from the gas phase to the PM, with the latter potentially composed of both a primarily aqueous ( α) liquid phase and a primarily organic ( β) liquid phase. Partitioning is allowed to occur without any artificial restraints: when both α and β PM phases are present, ionic constituents are allowed to partition to both. X-UNIFAC.2, an extended UNIFAC method based on Yan et al. (1999. Prediction of vapor–liquid equilibria in mixed-solvent electrolyte systems using the group contribution concept. Fluid Phase Equilibria 162, 97–113), was developed for activity coefficient estimation. X-UNIFAC.2 utilizes the standard UNIFAC terms, a Debye–Hückel term, and a virial equation term that represents the middle-range (MR) contribution to activity coefficient effects. A large number (234) of MR parameters are already available from Yan et al. (1999). Six additional MR parameters were optimized here to enable X-UNIFAC.2 to account for interactions between the carboxylic acid group and Na +, Cl −, and Ca 2+. Predictions of PM formation were made for a hypothetical sabinene/O 3 system with varying amounts of NaCl in the PM. Predictions were also made for the chamber experiments with α-pinene/O 3 (and CaCl 2 seed) carried out by Cocker et al. (2001. The effect of water on gas-particle partitioning of secondary organic aerosol. Part I. α-pinene/ozone system. Atmospheric Environment 35, 6049–6072); good agreement between the predicted and chamber-measured PM mass concentrations was achieved.

Prediction of activity coefficients in liquid aerosol particles containing organic compounds, dissolved inorganic salts, and water—Part 3: Organic compounds, water, and ionic constituents by consideration of short-, mid-, and long-range effects using X-UNIFAC.3

X-UNIFAC.3, a group contribution method for estimating activity coefficients of neutral and ionic components in liquid mixtures of organic compounds, inorganic salts, and water, is presented here. It is an extended UNIFAC method, in that traditional UNIFAC terms for short-range energetic interaction effects are extended to include ions as mixture components, and are combined with a Debye–Hückel long-range effect term and a second virial coefficient-type mid-range effect term. The method is formulated for application in modeling the formation of liquid aerosol particles consisting of general organic+inorganic salt+water solutions in which phase separation is likely to occur. Existing extended UNIFAC activity coefficient estimation methods can be problematic in modeling phase separation, since they require independent reference state corrections that may introduce significant errors. In X-UNIFAC.3, this problem is avoided by selecting appropriate reference states for all solution components, and imposing additional constraints on method parameters, when necessary, by inclusion of reference state correction terms within the activity coefficient expressions. Interaction parameters in the X-UNIFAC.3 equations are optimized for 12 different chemical groups (CH 3–, –CH 2–, - C | H - , - C | | - , −OH, −COOH, H 2O, NH 4 +, Na +, Cl −, NO 3 - , and SO 4 2 - ) using available data for systems containing multi-functional oxygenated organic compounds and/or inorganic salts that are relevant to atmospheric aerosol applications. Estimations of water activities and mean ionic activity coefficients using X-UNIFAC.3 are compared with those of other extended UNIFAC methods. To demonstrate the use of X-UNIFAC.3 in predicting phase separation, the method is also applied to the butanoic acid+NaCl+water system, for which experimental liquid–liquid equilibrium data is available. The method performs well for aqueous salt solutions with salt concentrations within 30 mol kg −1 and for organic+inorganic salt+water solutions with salt concentrations less than or equal to 10 mol kg −1. Suggestions are proposed for improving the predictive capabilities of the method in future work.

Electrochemical behaviour of americium ions in LiCl–KCl eutectic melt

This work presents a study on the electrochemical properties of AmCl 3 in a molten LiCl–KCl eutectic, at a temperature range of 733–833 K. Transient electrochemical techniques, such as cyclic voltammetry and chronopotentiometry, on inert metallic tungsten working electrode have been used to investigate the reduction mechanism of Am 3+ ions. The results show that Am 3+ is reduced to Am metal by a two-step mechanism corresponding to the Am 3+/Am 2+ and Am 2+/Am 0 transitions. Formal standard potentials of Am 3+/Am 2+ ( E A m 3 + / A m 2 + 0 ′ = − 2.695 V versus Cl 2/Cl − at 733 K) and Am 2+/Am 0 ( E A m 2 + / A m 0 0 ′ = − 2.911 V versus Cl 2/Cl − at 733 K) redox couples as well as diffusion coefficients of Am 3+ and Am 2+ (2.4 × 10 −5 and 1.15 × 10 −5 cm 2 s −1 at 733 K, respectively) have been calculated at three different temperatures. In the studied range of temperature, the D A m 3 + / D A m 2 + ratio was found to be around 2. In addition, thermodynamic properties have been calculated for Am 3+ ( Δ G AmC l 3 ∞ = − 933.7 + 0.152 T ) and Am 2+ ( Δ G AmC l 2 ∞ = − 623.9 + 0.085 T ) and compared to thermodynamic reference data in order to estimate activity coefficients (Am 3+ = 4.7 × 10 −3 and Am 2+ = 2.7 × 10 −2 at 733 K) in the molten LiCl–KCl eutectic.

New free‐volume‐related activity model for polymer solutions

AbstractA new activity model was developed with the use of the Gibbs–Helmholtz relation at constant pressure and composition. This model consists of combinatorial and residual terms. The residual term is the same as that in the UNIQUAC method, but the total area fraction of molecules is introduced on account of the hole effect. The combinatorial part takes into account the free volume (FV) effect, which plays a significant role in polymer systems. The validity of this model is demonstrated by calculating the solvent activities in 36 polymer solutions in comparison with Entropic‐FV (EFV) and UNIFAC‐FV methods. The total average absolute deviations (AAD) from the experimental observations are 8.27, 6.38, and 1.64 for EFV, UNIFAC‐FV, and the present method, respectively. It is found that the fit to these experimental data by the present model is quite good over a wide range of concentration. An estimation of the infinite dilution activity coefficients also proves the validity of the new method. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3299–3307, 2005