Hydration Equilibrium Constants Research Articles

Step-wise ion hydration modeling of aqueous solutions of 1:1 acid neutral electrolytes at different temperatures

In a previous work, we showed that the current stepwise ion hydration framework was promising for modeling electrolyte activities at 298.15 K. Briefly, the model assumes that (1) ions are hydrated in solution and this hydration is governed by an equilibrium between the bound and free water, (2) the mean spherical approximation (MSA) models the long range electrostatic interactions in the solution sufficiently well, and (3) this solution behaves ideally. In this work, we continue developing this model by exploring its temperature dependence. MSA has no temperature-dependent adjustable parameters. The hydration equilibrium constants are temperature dependent due to non-zero enthalpy and specific heat of the hydration equilibrium. Their values were adjusted. The calculated osmotic coefficients from the model are in good agreement with measured values.

Mass action model of solution activity via speciation by solvation and ion pairing equilibria

Solutes and their concentrations influence many natural and anthropogenic solution processes. Electrolyte and solution models are used to quantify and predict such behavior. Here we present a mechanistic solution model based on mass action equilibria. Solvation and ion pairing are used to model speciated solute and solvent concentrations such that they correlate to a solution’s vapor pressure (solvent activity) according to Raoult’s law from dilute conditions to saturation. This model introduces a hydration equilibrium constant (Kha) that is used with either an ion dissociation constant (Kid) or a hydration modifier (m) with an experimentally determined ion dissociation constant, as adjustable parameters to fit vapor–liquid equilibrium data. The modeled solvation equilibria are accompanied by molecular dynamics (MD) studies that support a decline in the observed degree of solvation with increased concentration. MD calculations indicate this finding is a combination of a solvent that solvates multiple solutes, and changes in a solute’s solvation sphere, with the dominant factor changing with concentration. This speciation-based solution model is lateral to established electrostatics-based electrolyte theories. With its basis in mass action, the model can directly relate experimental data to the modeled solute and solvent speciated concentrations and structures.

Henry’s law constants and hydration equilibrium constants of n-hexanal and their temperature dependence as determined by the rectangular pulse method

The Henry’s law constants of n-hexanal are needed to predict its rate of mass transfer between gas and aqueous phases. However, information on these constants is limited because the mass transfer of n-hexanal involves a reversible hydration reaction in water; therefore, Henry’s law constants are difficult to obtain experimentally and cannot be deduced only from the gas-to-water equilibrium. Here, we conducted stimulus–response experiments using a rectangular input pulse and a double-mixing gas–liquid contactor to simultaneously determine Henry’s law constants and hydration equilibrium constants for n-hexanal in deionized water, aqueous sodium chloride, or aqueous sodium sulfate in the temperature range of 5.3–22.5 °C. The change in the concentration of a mixture of n-hexanal in nitrogen gas after passing through the contactor was examined, and simulation-based optimization was conducted to optimize parameters that included Henry’s law constants and hydration rate constants. In the simulation, convolution using the rectangular input pulse was used to determine the input signal, and perfect gas-phase mixing and two-film layer mass transfer were assumed. This approach, which we called the rectangular pulse method, was validated by performing similar investigations for toluene, ethyl acetate, and ethyl trifluoroacetate. As a result, Henry’s law constants and rate constants for the reversible hydration reactions of n-hexanal and their temperature dependence were obtained, and the calculated effective Henry’s law constant agreed with some, but not all, of the values reported in the literature. A potential reason for the disagreement was discussed from the viewpoint of long time-constants used for the hydration equilibrium. In addition, a salting effect by the aqueous salt solutions was found to affect the Henry’s law constants, but not the hydration equilibrium constants. The overall liquid‐side mass‐transfer coefficient was found to be correlated with the diffusion coefficient, based on the Higbie penetration theory.

Grape pectic polysaccharides stabilization of anthocyanins red colour: Mechanistic insights

Grape pectic polysaccharides-malvidin-3-O- β -d-glucoside binding was studied, aiming to unveil the impact of structural diversity of polysaccharides on anthocyanins-polysaccharides interactions. Polysaccharides were extracted with solutions of imidazole (ISP) and carbonate at 4 °C (CSP-4 °C) and room temperature (CSP-RT) and also recovered from the dialysis supernatant of the remaining cellulosic residue after the aqueous NAOH extraction of hemicellulosic polysaccharides (Sn-CR). Polysaccharides richer in homogalacturonan domains, like those present in the CSP-4 °C fraction had approximately 50–fold higher binding affinity to malvidin-3-O- β-d-glucoside, than polysaccharides with side chains (as ISP and CSP-RT extractable polysaccharides). CSP-4 °C polysaccharides showed a positive effect on malvidin-3-O- β-d-glucoside colour fading. Hydration equilibrium constant of malvidin-3-O- β-d-glucoside in the presence of CSP-4 °C polysaccharides was higher, showing the preferential stabilization of the flavylium cation. The results showed that anthocyanins colour stabilization can be promoted by pectic polysaccharide structures such as those extracted by cold carbonate.

Predicting reactive sites with quantum chemical topology: carbonyl additions in multicomponent reactions.

Quantum Chemical Topology (QCT) is a well established structural theoretical approach, but the development of its reactivity component is still a challenge. The hypothesis of this work is that the reactivity of an atom within a molecule is a function of its electronic population, its delocalization in the rest of the molecule, and the way it polarizes within an atomic domain. In this paper, we present a topological reactivity predictor for cabonyl additions, κ. It is a measure of the polarization of the electron density with the carbonyl functional group. κ is a model obtained from a QSAR procedure, using quantum-topological atomic descriptors and reported hydration equilibrium constants of carbonyl compounds. To validate the predictive capability of κ, we applied it to organic reactions, including a multicomponent reaction. κ was the only property that predicts the reactivity in each reaction step. The shape of κ can be interpreted as the change between two electrophilic states of a functional group, reactive and non-reactive.

Cationic Copolymerization of o-Phthalaldehyde and Functional Aliphatic Aldehydes

There has been a resurgence of research related to poly(phthalaldehyde) (PPHA) in the past several years because of the demonstration of long room-temperature lifetime and its low ceiling temperature facilitating the ability to rapidly depolymerize the polymer at ambient conditions. This rapid depolymerization upon triggering of PPHA mixtures makes them well suited for fabricating transient devices or stimuli-responsive materials. The copolymerization of phthalaldehyde (PHA) with other aldehydes provides a route to incorporate chemical or physical functionality into PHA-based polymers while still maintaining the favorable degradation properties. Although the anionic copolymerization of PHA with benzaldehydes has been described, only a limited number of examples have been reported on the cationic copolymerization of PHA with other aldehydes. In this study, the synthesis and reactivity behavior of PHA copolymers is reported. Aliphatic aldehydes were chosen for their prevalence and favorable degradation properties. Dichloromethane solvent and the boron trifluoride diethyl etherate Lewis acid catalyst showed the best monomer conversions and highest polymer molecular weights. It was found that the aliphatic aldehyde reactivity for copolymerization increased with the electron-withdrawing nature of the aldehyde, which correlates with the aldehyde hydration equilibrium constant. The molecular weight and copolymer yield decrease with an increase in the aliphatic aldehyde feed concentration. Results indicate that the polymerization conditions used in this study (ca. −78 °C) are above the ceiling temperature of the aliphatic aldehyde comonomers, but this does not prevent copolymerization of the comonomer with PHA. Postpolymerization modifications were performed to introduce functional groups into the PHA-based copolymer that are incompatible with the polymerization chemistry. PPHA copolymers were cross-linked using a radiation-induced thiol–ene click chemistry to show that the mechanical properties can be improved even though the copolymer has a lower molecular weight.

Experiment-based physicochemical aspects for the coulombic hydration kinetics and thermodynamics of a pyrimidine and thiopyrimidine

The hydration, solvation kinetics and thermodynamics of recently synthesized 5-benzoyl-1-(methylphenylmethyleneamino)-4-phenyl-1H-pyrimidine-2-one (I) and 5-benzoyl-1-(methylphenylmethyleneamino)-4-phenyl-1H-pyrimidine-2-thione (II) are studied in due to course of time at pH values from 1.0 to 13.0 using UV/vis spectroscopic analysis of their aged solutions for the first time, at a temperature of 25 ± 0.1 °C. In this sense, a time dependent intersection point was discovered in the UV/vis spectra obtained. The time dependent intersection point method is thus improved for the first time in this study. The improved method is found to be more useful in the determination of the existence of a time dependent equilibrium and the time to reach the equilibrium at a constant pH. Methanol solvation property of the compounds is also investigated only at pH values of ca. 1.13 and ca. 13.0. Pseudo-first-order hydration kinetics and thermodynamics data comprising rate constants, hydration equilibrium constants, and the corresponding Gibbs free energy changes are calculated for water molecules which are in direct contact with the molecules of I and II. A remarkable result is discovered with II for which the hydration Gibbs energy change was calculated to be −422.64 J/mol at a pH of ca. 12, indicating the hydration is exothermic, energetically downhill and weakly in forward direction. Plausible hydration mechanisms are suggested for the compounds based on the extensive experimental UV/vis data presented.

Rationalizing the Color in Heavenly Blue Anthocyanin: A Complete Kinetic and Thermodynamic Study.

All equilibrium and rate constants of heavenly blue anthocyanin (HBA 1) as well as the derivatives with two (HBA 2) or none (HBA 3) acylated units were determined. The three acylated units of the sugar in position 3 of the peonidin chromophore of HBA 1 are essential to confer the peculiar stability of its purple and blue colors. The sugars generate an efficient protective environment around position 2 (and 4) of the flavylium cation, through an intramolecular sandwich-type stacking that retards 35-fold the hydration reaction ( kh) and increases 8.8-fold the dehydration reaction ( k-h), when compared with the peonidin chromophore HBA 3. The conjugation of these two rates lowers 308-fold the hydration equilibrium constant ( Kh), corresponding to a raise of the energy level of the hemiketal by 14.2 kJ mol-1. Conversely, the p Ka of the quinoidal base in HBA 1 is only slightly stabilized in comparison with that of HBA 2 and HBA 3. The energy level of hemiketal increases with the number of acylated units, but the inversion of energies between hemiketal and quinoidal base takes place exclusively for HBA 1 (three acylated units), permitting in moderately acidic solutions the stabilization of the purple quinoidal base. Identical inversion of energy was observed for the corresponding ionized species, allowing the stabilization of the blue ionized quinoidal base in slightly basic solutions. At pH values higher than 8, the hydroxyl groups of the hydroxycinnamic acid units start to deprotonate disrupting the intramolecular sandwich-type stacking and the more or less slow degradation of the anthocyanin is observed.

Effect of Temperature on Acidity and Hydration Equilibrium Constants of Delphinidin-3-O- and Cyanidin-3-O-sambubioside Calculated from Uni- and Multiwavelength Spectroscopic Data.

Delphinidin-3-O-sambubioside and cyanidin-3-O-sambubioside are the main anthocyanins of Hibiscus sabdariffa calyces, traditionally used to make a bright red beverage by decoction in water. At natural pH, these anthocyanins are mainly in their flavylium form (red) in equilibrium with the quinonoid base (purple) and the hemiketal (colorless). For the first time, their acidity and hydration equilibrium constants were obtained from a pH-jump method followed by UV-vis spectroscopy as a function of temperature from 4 to 37 °C. Equilibrium constant determination was also performed by multivariate curve resolution (MCR). Acidity and hydration constants of cyanidin-3-O-sambubioside at 25 °C were 4.12 × 10(-5) and 7.74 × 10(-4), respectively, and were significantly higher for delphinidin-3-O-sambubioside (4.95 × 10(-5) and 1.21 × 10(-3), respectively). MCR enabled the obtaining of concentration and spectrum of each form but led to overestimated values for the equilibrium constants. However, both methods showed that formations of the quinonoid base and hemiketal were endothermic reactions. Equilibrium constants of anthocyanins in the hibiscus extract showed comparable values as for the isolated anthocyanins.

Aqueous phase hydration and hydrate acidity of perfluoroalkyl and n:2 fluorotelomer aldehydes

ABSTRACTThe SPARC software program and comparative density functional theory (DFT) calculations were used to investigate the aqueous phase hydration equilibrium constants (Khyd) of perfluoroalkyl aldehydes (PFAlds) and n:2 fluorotelomer aldehydes (FTAlds). Both classes are degradation products of known industrial compounds and environmental contaminants such as fluorotelomer alcohols, iodides, acrylates, phosphate esters, and other derivatives, as well as hydrofluorocarbons and hydrochlorofluorocarbons. Prior studies have generally failed to consider the hydration, and subsequent potential hydrate acidity, of these compounds, resulting in incomplete and erroneous predictions as to their environmental behavior. In the current work, DFT calculations suggest that all PFAlds will be dominantly present as the hydrated form in aqueous solution. Both SPARC and DFT calculations suggest that FTAlds will not likely be substantially hydrated in aquatic systems or in vivo. PFAld hydrates are expected to have pKa values in the range of phenols (ca. 9 to 10), whereas n:2 FTAld hydrates are expected to have pKa values ca. 2 to 3 units higher (ca. 12 to 13). In order to avoid spurious modeling predictions and a fundamental misunderstanding of their fate, the molecular and/or dissociated hydrate forms of PFAlds and FTAlds need to be explicitly considered in environmental, toxicological, and waste treatment investigations. The results of the current study will facilitate a more complete examination of the environmental fate of PFAlds and FTAlds.

A high‐level theoretical study into the atmospheric phase hydration, bond dissociation enthalpies, and acidity of aldehydes

CBS‐Q//B3, G4(MP2), and G4 composite method calculations were used to estimate atmospheric phase standard state (298.15 K, 1 atm) free energies of hydration (ΔhydrG°(g)), hydration equilibrium constants (log Khydr,(g)), bond dissociation enthalpies (BDEs), and enthalpies (ΔdH°(g)) and free energies (ΔdG°(g)) of aldehydic proton acid dissociation for various substituted aldehydes with electron withdrawing and electron releasing groups. Good quality log Khydr,(g) correlations with the Swain–Lupton resonance effect parameters R and R+ were found, allowing extension of the model to predict log Khydr,(g) values for 487 substituted aldehydes having available R‐values and 108 substituted aldehydes having available R+ values. Good correlations were also found between experimental aqueous phase hydration equilibrium constants (log Khydr,(aq)) and summative R/R+ values for peripheral substituents on a range of carbonyl derivatives (aldehydes, ketones, esters, and amides), suggesting that the structure–reactivity modeling approach can be extended to include all possible combinations of R1C(O)R2 carbonyl substitution in both gas and aqueous systems. Computationally derived BDEs and ΔdH°(g)/ΔdG°(g) were in good agreement with the limited experimental and theoretical datasets. BDEs did not generally correlate with any of the Hammett substituent constants or Swain–Lupton parameters considered. Gas phase acidities exhibited high correlation coefficients with Hammett inductive substituent constants (σI) and field effect parameters (F), allowing these to be employed as surrogates for estimating the gas phase aldehydic proton acidities of a larger potential compound range. The resulting models will be of use in predicting the environmental behavior for a broad range of environmentally relevant compounds containing carbonyl functionalities. Copyright © 2016 John Wiley & Sons, Ltd.

Predicting hydration propensities of biologically relevant α-ketoamides.

Quantum chemical calculations coupled to experiments were used to predict covalent hydration propensities of biologically relevant α-ketoamides. Experimentally determined hydration equilibrium constants for related ketones and aldehydes were compared to computationally determined values to develop a method for predicting hydration equilibrium constants. This method was used on six newly synthesized α-ketoamides to experimentally verify computational predictions. A correlation between calculation and experiment was observed and applied to models of several pertinent APIs. Our results indicate that the keto form is favored for practically all α-ketoamides in biological environs.

A new approach to determination of hydration equilibria constants for the case of [Er(EDTA)(H2O)(n)](-) complexes.

Two anionic complexes [Er(EDTA)(H2O)2](-) and [Er(EDTA)(H2O)3](-) were obtained in the form of the following compounds: [C(NH2)3]2[Er(EDTA)(H2O)2]ClO4·6H2O () and Na[Er(EDTA)(H2O)3]·5H2O (), respectively. The UV-vis-NIR absorption spectra of both monocrystals were measured at room temperature and at 4.2 K. The influence of the coordination number changes on intensities of the f-f transitions and the crystal field splitting of (2S+1)LJ multiplets are discussed. The weighted sum of molar absorption coefficients of f-f transitions in the spectra of and was used to reproduce the absorption bands of the Er(3+)-EDTA complex in aqueous solution. This approach allowed us to estimate that the complex in solution exists in 95% as the 8-coordinate [Er(EDTA)(H2O)2](-) species and in 5% as the 9-coordinate [Er(EDTA)(H2O)3](-) ones as well as to calculate the conditional hydration equilibrium constant (Kaqua) of the reaction: [Er(EDTA)(H2O)3](-) ↔ [Er(EDTA)(H2O)2](-) + H2O which is rather difficult to determine by using other methods. The Kaqua value was found to be 19 ± 1.

Two-fold -to-single-fold transition of the conductivity relaxation patterns of proton-conducting oxides upon hydration/dehydration

Hydration/dehydration kinetics of proton conducting oxides has long been believed to be due to the chemical diffusion of H2O (or ambipolar diffusion of H+ and O2 −), causing defect-structure-sensitive properties, e.g., electrical conductivity and mass, of the oxides to relax single-fold. Thus, a mass relaxation with a change of water activity used to be regarded as a measure of the equilibrium water solubility. It has recently been observed, however, that the conductivity and mass relax are not single-fold, but two-fold upon hydration or dehydration in usual oxidizing atmospheres, indicating that the above does not proceed via single-fold chemical diffusion of H2O, but via decoupled two-fold chemical diffusion of H (or ambipolar diffusion of H+ − h+) and O (or ambipolar diffusion of O2 − + 2 h+). In this paper, we will show theoretically and demonstrate experimentally that the two-fold kinetics asymptotically converges to the single-fold as the hole transference number diminishes to zero with decreasing oxygen activity in the ambient. Its implications are discussed particularly concerning the hydration equilibrium constant or equilibrium water solubility as determined from the mass relaxation.

Outer‐sphere reduction of hexacyanoferrate(III) by enolizable and nonenolizable aldehydes in alkaline medium

AbstractOuter‐sphere reduction of hexacyanoferrate(III) by some enolizable/nonenolizable aldehydes (viz., aliphatic, heterocyclic, and aromatic aldehydes) in alkaline medium has been studied spectrophotometrically at λmax = 420 nm. The reactions are first order each in [aldehyde] and [Fe(CN)63−]. The rate increases with an increase in [OH−] in the oxidation of aliphatic and heterocyclic aldehydes, whereas it is independent of [OH−] in the reaction with aromatic aldehydes. The intervention of free radicals in the reaction mixture was carried out using both acrylonitrile and acrylamide scavenger in two different experiments. The kinetic results indicate that the oxidation of benzaldehyde in aqueous medium proceeds at a slower rate than the aliphatic aldehydes (other than formaldehyde) and furfural. The values of third‐order rate constant (k3) at 308 K in the oxidations of some aliphatic aldehydes and furfural follow the order (CH3)2CH > CH3CH2 > CH3 > C4H3O > H. The rate constants correlate with Taft's σ* value, the reaction constant being negative (–9.8). The pseudo–first‐order rate constants in the oxidations of benzaldehyde and substituted benzaldehydes follow the order NO2 > H > Cl > OCH3. The Hammett plot is also linear with a ρ value (0.6488) for meta‐ and para‐substituted benzaldehydes. The kinetic isotope effect for benzaldehyde (kH/kD = 1.93 at 303 K) was obtained. The rate‐determining step is the outer‐sphere formation of Fe(CN)64− and free radicals, which is followed by the rapid oxidation of free radicals by Fe(CN)63− to give products. The kinetic data and hence thermodynamic parameters have been used to distinguish enolizable and nonenolizable aldehydes. An attempt has also been made to correlate kinetic data with hydration equilibrium constants of some aliphatic aldehydes. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 494–505, 2012

Gas phase hydration, bond dissociation enthalpies, and acidity of aldehydes: A CBS-Q//B3, G4MP2, and G4 theoretical study of substituent effects

AbstractCBS-Q//B3, G4MP2, and G4 composite method calculations were used to estimate gas phase standard state (298.15 K, 1 atm) free energies of hydration (Δ~hydr~G°~(g)~), hydration equilibrium constants (log K~hydr,(g)~), bond dissociation enthalpies (BDEs), and enthalpies (Δ~d~H°~(g)~) and free energies (Δ~d~G°~(g)~) of aldehydic proton acid dissociation for various substituted aldehydes with electron withdrawing and electron releasing groups. Good quality log K~hydr,(g)~ correlations with the Swain-Lupton resonance effect parameters R and R^+^ were found, allowing extension of the model to predict log K~hydr,(g)~ values for 487 substituted aldehydes having available R-values and 108 substituted aldehydes having available R^+^-values. Good correlations were also found between experimental aqueous phase hydration equilibrium constants (log K~hydr,(aq)~) and summative R/R^+^-values for peripheral substituents on a range of carbonyl derivatives (aldehydes, ketones, esters, and amides), suggesting the structure-reactivity modeling approach can be extended to include all possible combinations of R~1~C(O)R~2~ carbonyl substitution in both gas and aqueous systems. Computationally derived BDEs and Δ~d~H°~(g)~ / Δ~d~G°~(g)~ were in good agreement with the limited experimental and theoretical datasets. BDEs did not generally correlate with any of the Hammett substituent constants or Swain-Lupton parameters considered. Gas phase acidities exhibited high correlation coefficients with Hammett inductive substituent constants (σ~I~) and field effect parameters (F), allowing these to be employed as surrogates for estimating the gas phase aldehydic proton acidities of a larger potential compound range.

Aqueous phase hydration and hydrate acidity of perfluoroalkyl and n:2 fluorotelomer aldehydes

AbstractPerfluoroalkyl aldehydes (PFAlds) and n:2 fluorotelomer aldehydes (FTAlds) are degradation products of precursor compounds that include fluorotelomer alcohols, iodides, acrylates, phosphate esters, and other derivatives, as well as hydrofluorocarbons and hydrochlorofluorocarbons. The SPARC software program and comparative density functional theory (DFT) calculations were used to investigate the aqueous phase hydration equilibrium constants (K~hyd~) of PFAlds and FTAlds. DFT studies suggest that all PFAlds will be dominantly present as the hydrated form in aqueous solution. While SPARC correctly estimates the K~hyd~ for the C~1~ PFAld, it appears to incorrectly predict a large decline in K~hyd~ (particularly between C~1~ and C~2~) with increasing perfluoroalkyl chain length for this class of compounds. Both SPARC and DFT investigations suggest that FTAlds will not likely be substantially hydrated in aquatic systems or in vivo. Using corrected SPARC estimates, PFAld hydrates are expected to have pK~a~ values in the range of phenols (ca. 9 to 10), whereas n:2 FTAld hydrates are expected to have pK~a~ values ca. 2 to 3 units higher (ca. 12 to 13). Where relevant, the molecular and/or dissociated hydrate forms of PFAlds and FTAlds need to be explicitly considered in environmental, toxicological, and waste treatment investigations.

Computational Calculation of Equilibrium Constants: Addition to Carbonyl Compounds

Hydration reactions are relevant for understanding many organic mechanisms. Since the experimental determination of hydration and hemiacetalization equilibrium constants is fairly complex, computational calculations now offer a useful alternative to experimental measurements. In this work, carbonyl hydration and hemiacetalization constants were calculated from the free energy differences between compounds in solution, using absolute and relative approaches. The following conclusions can be drawn: (i) The use of a relative approach in the calculation of hydration and hemiacetalization constants allows compensation of systematic errors in the solvation energies. (ii) On average, the methodology proposed here can predict hydration constants within +/- 0.5 log K(hyd) units for aldehydes. (iii) Hydration constants can be calculated for ketones and carboxylic acid derivatives within less than +/- 1.0 log K(hyd), on average, at the CBS-Q level of theory. (iv) The proposed methodology can predict hemiacetal formation constants accurately at the MP2 6-31++G(d,p) level using a common reference. If group references are used, the results obtained using the much cheaper DFT-B3LYP 6-31++G(d,p) level are almost as accurate. (v) In general, the best results are obtained if a common reference for all compounds is used. The use of group references improves the results at the lower levels of theory, but at higher levels, this becomes unnecessary.

Updated H2SO4‐H2O binary homogeneous nucleation look‐up tables

The calculated rates of H2SO4‐H2O binary homogeneous nucleation (BHN), which is the only nucleation mechanism currently widely used in global aerosol models, are well known to have large uncertainties. Recently, we have reduced the uncertainties in the BHN rates on the basis of a kinetic quasi‐unary nucleation (KQUN) model, by taking into account the measured bonding energetics of H2SO4 monomers with hydrated sulfuric acid dimers and trimers. The uncertainties were further reduced by using two independent measurements to constrain the equilibrium constants for monomer hydration. In this paper, we present updated BHN rate look‐up tables derived from the improved KQUN model which can be used by anyone to obtain the BHN rates under given conditions. The look‐up tables cover a wide range of key parameters that can be found in the atmosphere and laboratory studies, and their usage significantly reduces the computational costs of the BHN rate calculations, which is critical for multidimensional modeling. The look‐up tables can also be used by those involved in experiments and field measurements to quickly assess the likeliness of BHN. For quick application, one can obtain the BHN rates and properties of critical clusters by browsing through the tables. A comparison of results based on the look‐up tables with those from widely used classical BHN model indicates that, in addition to several orders of magnitude difference in nucleation rates, there also exists substantial difference in the predicted numbers of sulfuric acid molecules in the critical clusters and their dependence on key parameters.

Variable hydration of small carbohydrates for predicting equilibrium properties in diluted and concentrated solutions

A physical–chemical model is proposed to describe the equilibrium properties of binary and multicomponent water–carbohydrate mixtures. The chemical part of the model accounts for the hydration equilibrium of carbohydrate with the formation of carbohydrate n-water molecules in a single stage process; n, the hydration number, and K, the hydration equilibrium constant, are the two independent parameters in this part. The physical part of the model is the UNIFAC group-contribution model as modified by Larsen et al. (I.E.C. Research, 26 (1987) 2274–2286). The original functional groups and the structural and interaction parameter values are maintained and introducing new groups such as pyranose rings, furanose rings and osidic bonds was not necessary. The model is compared to experimental data including water activity, osmotic coefficients, activity coefficients, freezing and boiling point temperatures and solubility for binary systems containing xylose, glucose, mannose, galactose, fructose, sucrose, maltose, lactose and trehalose and for food products containing sugars.