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Henry’s law constants (IUPAC Recommendations 2021)

Henry’s law states that the abundance of a volatile solute dissolved in a liquid is proportional to its abundance in the gas phase. It applies at equilibrium and in the limit of infinite dilution of the solute. For historical reasons, numerous different definitions, names, and symbols are used in the literature to express the proportionality coefficient, denoted the “Henry’s law constant”. Furthermore, a consistent set of recommendations is presented. An important distinction is made between two new recommended reciprocal quantities: “Henry’s law solubility constant” (H s ) and “Henry’s law volatility constant” (H v ). Eight recommended variants of H s and H v are described and relations among them presented.

54 ENVIRONMENTAL SCIENCES↗

Semi-empirical model for Henry’s law constant of noble gases in molten salts

Henry’s law constant, which describes the proportionality of dissolved gas to partial pressure of free gas in liquid–gas equilibrium systems, can also be applied to mass transport applications. In this work, we investigated an approach for determining the solubility of noble gases in a molten salt liquid utilizing the equilibrium concept of Henry’s gas constant. Henry’s gas constant is described as a mathematical function dependent on the van der Waals radius of the noble gas and the temperature of the molten salt. The alteration in Gibbs free energy encompasses contributions from both surface and volume energies. Enthalpy and entropy are deduced from these surface and volume energies in the Gibbs free energy formulation. A comparative analysis was conducted between the conventional method and our proposed model. Moreover, useful chemical properties can be determined from examination of surface and volume energies. Our findings provide an accurate and general theory of Gibbs free energy that can be validated experimentally based on the model proposed herein. This work unifies the prediction of Henry gas constant and subsequently the entropy and enthalpy calculation for noble gases in a molten salt solution to a single functional form using van der Waals radius of the gas and temperature of the system. This functional form is then used to perform a multiple regression method to find two parameters corresponding to the surface energy and volume energy. These two parameters are consistent between all combinations of noble gas and molten salt.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling Henry's law and phase separations of water–NaCl–organic mixtures with solvation and ion-pairing

Empirical measurements of solution vapor pressure of ternary acetonitrile (MeCN) H 2 O–NaCl–MeCN mixtures were recorded, with NaCl concentrations ranging from zero to the saturation limit, and MeCN concentrations ranging from zero to an absolute mole fraction of 0.64. After accounting for speciation, the variability of the Henry's law coefficient at vapor–liquid equilibrium (VLE) of MeCN ternary mixtures decreased from 107% to 5.1%. Solute speciation was modeled using a mass action solution model that incorporates solute solvation and ion-pairing phenomena. Two empirically determined equilibrium constants corresponding to solute dissociation and ion pairing were utilized for each solute. When speciation effects were considered, the solid–liquid equilibrium of H 2 O–NaCl–MeCN mixtures appear to be governed by a simple saturation equilibrium constant that is consistent with the binary H 2 O–NaCl saturation coefficient. Further, our results indicate that the precipitation of NaCl in the MeCN ternary mixtures was not governed by changes in the dielectric constant. Our model indicates that the compositions of the salt-induced liquid–liquid equilibrium (LLE) boundary of the H 2 O–NaCl–MeCN mixture correspond to the binary plateau activity of MeCN, a range of concentrations over which the activity remains largely invariant in the binary water–MeCN system. Broader comparisons with other ternary miscible organic solvent (MOS) mixtures suggest that salt-induced liquid–liquid equilibrium exists if: (1) the solution displays a positive deviation from the ideal limits governed by Raoult's law; and (2) the minimum of the mixing free energy profile for the binary water-MOS system is organic-rich. Finally, this work is one of the first applications of speciation-based solution models to a ternary system, and the first that includes an organic solute.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Estimated timescales for wet deposition of organic compounds as a function of Henry's law constants

Atmospheric organic compounds may deposit to Earth's surfaces via dry deposition, driven by concentration gradients, and wet deposition, driven by the scavenging of compounds by precipitation. Their removal by deposition has downstream impacts on concentrations of secondary organic aerosol by removing potential aerosol precursors that would otherwise oxidize to form particulate matter. The impact of deposition processes can consequently be considered as competition between rates of oxidation and deposition, but timescales for deposition are not well constrained. While timescales for dry deposition have been estimated and experimentally validated in the past, understanding of wet deposition of organics is still very limited. In this work, we estimate the wet deposition timescale for gas-phase organic compounds in the atmosphere as a function of Henry's law constants, H, using real-world precipitation frequency and size distributions at five globally-distributed sites. The wet deposition timescale decreases significantly with the increase of H until reaching a stable minimum for compounds with H > 10 5 M per atm. We estimate that the median wet deposition timescale for highly soluble gases is approximately 5 hours during a continuous rain event for all sites. However, median estimated timescales ranged from 80 to 200 hours, depending on location. Timescales are found to depend primarily on the frequency and duration of precipitation events rather than their intensity or size characteristics. Based on these data, we demonstrate that timescales for wet deposition of gases can be estimated at any given location using only basic precipitation information, without detailed or high-precision measurements.

54 ENVIRONMENTAL SCIENCES↗

Vapor-Liquid Partitioning of Methylmercury Compounds: Fundamental Data to Support the Savannah River Site Liquid Waste System: Henry's Law, Solubility and Vapor Pressure Determination for Representative Methylmercury Compounds

The Savannah River Site (SRS) Liquid Waste System (LWS) contains approximately 66 tons of mercury within the liquids, salts, and sludges that are currently being processed into final wasteforms for disposal. Mercury concentrations within the system exceed those typically experienced in environmental or industrial systems; thus, management of mercury compounds continues to be a priority for SRS. In the LWS, waste is vitrified into a borosilicate glass wasteform that contains most of the radioactivity, while the lower activity solutions are dispositioned in a low-level grout wasteform, or “saltstone”. The alkaline, high ionic strength caustic wastes are pumped, evaporated, and otherwise managed throughout the LWS and Defense Waste Processing Facility (DWPF) as they are stored and prepared for conversion to the final wasteforms. Because of the complexity of this system, a key component of effective mercury management in the LWS requires analysis of mercury in various physical phases. The high concentration of mercury within the SRS LWS has the potential to generate vapor-phase contamination. Elemental mercury (Hg 0 ), dimethylmercury ((CH 3 ) 2 Hg), and methylmercury (CH 3 Hg + ) are among species known or suspected to contribute to the flux of mercury from liquid to vapor phase (Iverfeldt and Lindquist, 1982). Chemical speciation affects not only mercury behavior in LWS operations but may also affect the performance of mercury treatment and removal technologies in the LWS.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Quantifying fission gas adsorption onto natural clinoptilolite in the presence of environmental air and water

Adsorption of noble gas fission products onto naturally occurring minerals is of interest for its potential to retain or retard emissions from nuclear fuel reprocessing operations or underground nuclear explosions. However, experimental studies of trace noble gas adsorption in the presence of air and water have largely focused on synthetic materials, such as activated carbon or metal-organic frameworks. Here, in this study, adsorption of Kr and Xe onto the naturally occurring zeolitic mineral clinoptilolite is studied in the presence of nitrogen and water. By varying the composition of the gas phase and monitoring the change in the combined adsorbate mass, the adsorbed concentration of noble gas is calculated gravimetrically. For dry clinoptilolite, the concentration of adsorbed Kr and Xe is linearly correlated with noble gas pressure and Henry's Law appears satisfactory, despite the presence of nitrogen at atmospheric pressures. However, the presence of water significantly reduces the adsorbed concentration of both Kr and Xe, which is typical in nanoporous sorbents. Here, an empirical bivariate model is presented, combining the Henry's Law adsorption model for a dry adsorbent with the exponential reduction in the presence of water, as reported by Lungu and Underhill in 1999. This model provides a means to estimate the adsorbate concentration at the trace partial pressures and higher water contents relevant to field-scale modeling of fission gas transport through the vadose zone.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Computing the solubility of argon and xenon in molten sodium chloride and potassium chloride salts

Molten salt reactors (MSRs) offer significant advancements in nuclear reactor safety and efficiency by operating at higher temperatures and lower pressures compared to traditional reactors. A critical aspect of MSR operation involves understanding the solubility of fission byproducts, particularly noble gases, in the molten salts used. This study employs molecular dynamics (MD) simulations to compute Henry’s law constants and enthalpies of solvation for argon and xenon in molten sodium chloride (NaCl) and potassium chloride (KCl). We developed a new pairwise potential for the noble gas and salt interactions based on first principles calculations. We then used this potential to calculate Henry’s law constants of the two gases in the molten salts, which were modeled using both a rigid ion model (RIM) and a polarizable ion model (PIM). The solubility calculations, performed using the Widom insertion method, show qualitative agreement with limited experimental data, highlighting the temperature dependence and greater solubility of both gases in KCl compared to NaCl. Additionally, free volume analysis elucidated the role of available space within the molten salts in governing solubility trends. Our findings suggest that PIM trajectories provide more reliable predictions for noble gas solubility than RIM due to their accurate density representation. Furthermore, these results enhance understanding of gas solubility in MSR environments, and the methods can be readily extended to other systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Investigating the Role of Silver Oxidation State on the Thermodynamic Interactions between Xenon and Silver-Functionalized Zeolites

The molecular level understanding of the strong adsorption of Xe to silver-modified zeolites remains elusive. Here, we probe the effect of silver oxidation state on the thermodynamics of Xe sorption in silver-functionalized zeolites by measuring the enthalpies of adsorption after various treatments using inverse gas chromatography (IGC). The enthalpy of adsorption was measured for silver-functionalized chabazites (AgCHA) before and after hydrogen reduction and subsequent reoxidation. The sorption enthalpy (ΔH) for AgCHA was 35.2 kJ/mol, which decreased to 25.8 kJ/mol with hydrogen reduction. After reoxidation (O 2 -AgCHA), 95% of the binding strength was restored. Hydrogen reduction of the base chabazite (CHA) did not influence Xe adsorption. Henry’s law constant for Xe adsorption increased in the order AgCHA > O 2 -AgCHA > H 2 -AgCHA > CHA. A decrease in enthalpy and Henry’s constant with silver reduction and increase with reoxidation suggest that ionic silver is playing a role in Xe binding. The effect of reduction and reoxidation on the zeolite microstructure was analyzed using surface area analysis, powder X-ray diffraction (p-XRD), scanning electron microscopy/energy-dispersive X-ray spectroscopy (SEM/EDS), and X-ray photoelectron spectroscopy (XPS). Finally, these results lay the groundwork for better material design of strong noble gas adsorbents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

UNESE Data Analysis-Disko Elm Gas Transport Characteristics (NA-22 Quarterly Report)

Recently published papers have demonstrated the impact of sorption mechanisms on gas transport in the subsurface following an underground nuclear explosion. To include sorption processes in the multi-physics models of noble gas production and transport, researchers have conducted experiments of gas sorption in geologic materials and calibrated a linear (Henry’s law) sorption model for all gases in various geologic materials. As a part of Task #4, we requested the experimental data from Sandia Laboratories and derived a dual-mode (Henry’s absorption and Langmuir adsorption) sorption model. The derived model better describes the nonlinear sorption mechanism with much higher fitness with the experimental data. When gas concentrations are relatively low (in the conditions of field experiments or underground nuclear explosions) compared to those used sorption experiments, the nonlinear sorption model can be approximated as a linear sorption model. The equivalent Henry’s constant, which equals the product of Langmuir capacity and affinity, is systematically higher than the literature values. Further analyses and comparison of sorption models are planned in FY2020 Q4 and the sorption model will be coupled in models of nonisothermal multiphase transport for studying noble gas detectability.

58 GEOSCIENCES↗

Organic Evaporation and Oxidation Testing in Support of Hanford Sample-and-Send

The Hanford site has approximately 56 million gallons of radioactive mixed waste stored in 177 underground storage tanks. The Hanford Waste Treatment and Immobilization Plant (WTP) is being built to treat and immobilize the tank waste. The baseline method for immobilization of Low Activity Waste (LAW) through the WTP is vitrification, but additional immobilization capacity is needed to supplement the initial LAW melters. An alternative cementitious waste form is being investigated for that future immobilization method to supplement vitrification. However, one impediment to a cementitious waste form is the presence of Land Disposal Restricted (LDR) organic chemicals in tank waste. This work evaluates potential avenues to eliminate that impediment to permit possible use of a cementitious waste form and work towards a decision whether additional LDR organic pretreatment would be required. Savannah River National Laboratory (SRNL) performed testing using simulants to examine evaporation as a method to remove some prevalent organics from LAW. Spiking the caustic LAW simulant with selected regulated organic chemicals found one that clearly decomposes because of caustic instability. Oxidation testing of other organic chemicals found some LDR organics degrade as desired and others are stable in the presence of peroxide and permanganate. In addition to studies with simulants, a literature review was performed to evaluate radiological stability of LDR organics. Descriptions of the experimental details, equipment, and results are included in this report. Evaporation testing consisted of preparing the LAW simulant, spiking that simulant with organic chemicals, and evaporating the mixture via differential distillation. The apparatus was a laboratory-scale vacuum evaporator operated at 60 ±5 torr absolute (vacuum evaporation) and also at atmospheric pressure. The LAW simulant represented the liquid expected to be retrieved from the Hanford tank farms at approximately 4.0 M [Na + ] total sodium ion concentration. The concentration of the organic chemicals added was significantly higher than typically found in the tank waste samples since the higher levels were necessary to assist in analytical measurement and tracking of the spiked species. Organic chemicals were chosen for the work with a consideration of how their volatility compares with that of methanol. This was done by comparing the ratio of the pure water Henry’s law coefficient (K h ) of methanol to that of the compound in question (hereafter termed the K h ratio), where ratios above unity indicated less volatility than methanol. Methanol was chosen because it is a common regulated chemical with relatively low volatility but which has been removed by evaporation in previous laboratory work. While organic separation results depend on evaporator design, laboratory experiments verified that organic partitioning to the overhead condensate stream by evaporation is a practical process. The work reported here found difficulties in quantitative analysis of the organic chemicals in aqueous samples. Most of the time there was insufficient analysis to close a mass balance for evaporator runs, but qualitative evidence of carryover was obtained. The methods were also able to show whether organic chemicals were susceptible or resistant to solution oxidation in permanganate or hydrogen peroxide tests.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A Self‐Consistent Model for Sorption and Transport in Polyimide‐Derived Carbon Molecular Sieve Gas Separation Membranes

Abstract Demand for energy‐efficient gas separations exists across many industrial processes, and membranes can aid in meeting this demand. Carbon molecular sieve (CMS) membranes show exceptional separation performance and scalable processing attributes attractive for important, similar‐sized gas pairs. Herein, we outline a mathematical and physical framework to understand these attributes. This framework shares features with dual‐mode transport theory for glassy polymers; however, physical connections to CMS model parameters differ from glassy polymer cases. We present evidence in CMS membranes for a large volume fraction of microporous domains characterized by Langmuir sorption in local equilibrium with a minority continuous phase described by Henry's law sorption. Using this framework, expressions are provided to relate measurable parameters for sorption and transport in CMS materials. We also outline a mechanism for formation of these environments and suggest future model refinements.

Sanyal, Oishi↗

Comparing and contrasting In-Vial and full-scale systems for sparging volatile analytes

Here, in-vial sparging was demonstrated as an effective, practical alternative to a full-scale sparging system for supporting the analysis of volatile constituents. Using elemental mercury (Hg 0 ) and toluene as representative purgeable analytes, the mass removal for various sparge configurations was measured and a reduced order model was developed and validated. In the primary experiments, Hg 0 in the sparge gas was trapped on activated carbon or gold, thermally desorbed, and quantified using atomic absorption or atomic fluorescence spectroscopy. Toluene experiments using the same in-vial sparge apparatus and sparge parameters were performed to demonstrate the applicability of the reduced order model to a broad range of compounds. Toluene removal was tracked by measuring the remaining toluene in sparged aliquots using Ultraviolet-visible (UV–Vis) spectroscopy. For the sparging, flow rates varied from 25 to 75 mL/min for periods from 0 to 30 min. Sparge performance, mass removal as a function of time, and sparge gas volume were measured for both in-vial and full-scale systems. A model based on dimensionless Henry's Law coefficient, normalized sparge gas volume, and fractional extent of equilibrium matched the experimental data for both compounds and provides a practical tool for future applications. For the conditions tested in this study, the calibrated model indicated that the sparge gas in the in-vial system reached approximately 33% of its equilibrium value before exiting the water surface, while a full-scale system reached approximately 100%. The tests validated the quality, reproducibility, and predictability of sparging performance for both full scale and in-vial sparge systems. Related factors such as waste generation, worker risk, and labor were also assessed. Full scale sparge systems provide the advantage of lower detection levels due to larger sample volume, while the in-vial sparge systems provide advantages for most other factors; including automatability, reducing secondary wastes, lessening the need to clean and check the sparge apparatus, and lowering labor and costs. The data and associated reduced order model support continued development and deployment of in-vial sparge platforms as a practical option for analysis of purgeable analytes such as volatile organic compounds and volatile metals/organometallics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solute- and solvent-based electromotive force cells for activity measurements of electroactive species in molten salts

A novel combination of solute- and solvent-based electrodes was used to determine the activities of NdCl 3 and GdCl 3 in molten LiCI-KCI eutectic using electromotive force measurements across a broad concentration range of dissolved electroactive species. First, an electrochemical cell using solute-based electrodes was used to define the relative activity of each species as a function of concentration and the concentration region in which Henry's law was applicable. Next, the electromotive force between a solute-based electrode with a known NdCl 3 or GdCl 3 concentration and a solvent-based electrode with a known electromotive force was measured. The solvent-based electrode potential was converted to the Lithium Eutectic Electrode (LEE) potential, which allowed the activity of dissolved NdCl 3 and GdCl 3 to be calculated at the concentrations measured using the solute-based electrodes. The described two-cell method uses electromotive force measurements to accurately determine the activity of electroactive species over a wide concentration range and provides a simple approach to closing the knowledge gap of thermochemical properties of molten salts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermochemical measurements of FeCl 2 in LiCl via electromotive force, coulometric titration, and cyclic voltammetry

The thermochemical properties of FeCl 2 in the LiCl-FeCl 2 binary system were determined at 913 K using electromotive force (emf) cells containing pre-made and coulometrically titrated molten salt compositions. Coulometric titration to in-situ change the salt composition utilizes the multiple valences of Fe ions and the tendency of Fe 3+ ions to comproportionate with Fe metal, forming additional Fe 2+ . The emf results were used to define the compositions in which Henry’s law is applicable, up to approximately 2 mol% FeCl 2 . Thermochemical quantities were determined from emf using a Standard Lithium Chloride Electrode (SLiCE) which defines 0 V as the reduction of Li + in pure LiCl at all temperatures. Validation of emf measurements was performed by comparing the formal potential measured by using cyclic voltammetry (2.224 ± 0.013 V vs SLiCE) and emf measurements (2.236 ± 0.004 V). In conclusion, this work shows that coulometric titration of an electroactive species that undergoes comproportionation can be used to rapidly obtain granular emf data in molten salt systems.

Coulometric titration↗

Noble gas adsorption to tuff

For this report a method was developed to measure trace noble gas element adsorption to the surfaces of geologic materials in the presence of a background gas that could potentially compete for surface adsorption sites. Adsorption of four noble gas elements (Ne, Ar, Kr, and Xe) at a concentration of 100 ppm in helium and nitrogen were measured on a sample of crushed tuff at 0, 15, 30, and 45°C. In addition, Ne, Ar, Kr, and Xe at 250 ppm and 500 ppm in nitrogen at 15°C were measured. Noble gas adsorption was found to increase with increasing atomic mass and decreasing temperature. It was also observed that the relative increase in noble gas element adsorption with decreasing temperature tends to increase with increasing atomic mass. Noble gas adsorption from nitrogen was approximately an order of magnitude greater than for the noble gases in helium. As the noble gas concentrations in nitrogen increased, adsorption increased in a slightly non-linear fashion which could be modeled using a Freundlich isotherm. For noble gas concentrations that were ≤100 ppm Henry's Law constant were calculated.

58 GEOSCIENCES↗

Coupled Interfacial and Bulk Kinetics Govern the Timescales of Multiphase Ozonolysis Reactions

Chemical transformations in aerosols impact the lifetime of particle phase species, the fate of atmospheric pollutants, and both climate- and health-relevant aerosol properties. Timescales for multiphase reactions of ozone in atmospheric aqueous phases are governed by coupled kinetic processes between the gas phase, the particle interface, and its bulk, which respond dynamically to reactive consumption of O 3 . However, models of atmospheric aerosol reactivity often do not account for the coupled nature of multiphase processes. Herein, to examine these dynamics, we use new and prior experimental observations of aqueous droplet reaction kinetics, including three systems with a range of surface affinities and ozonolysis rate coefficients ( trans -aconitic acid (C 6 H 6 O 6 ), maleic acid (C 4 H 4 O 4 ), and sodium nitrite (NaNO 2 )). Using literature rate coefficients and thermodynamic properties, we constrain a simple two-compartment stochastic kinetic model which resolves the interface from the particle bulk and represents O 3 partitioning, diffusion, and reaction as a coupled kinetic system. Our kinetic model accurately predicts decay kinetics across all three systems, demonstrating that both the thermodynamic properties of O 3 and the coupled kinetic and diffusion processes are key to making accurate predictions. An enhanced concentration of adsorbed O 3 , compared to gas and bulk phases is rapidly maintained and remains constant even as O 3 is consumed by reaction. Multiphase systems dynamically seek to achieve equilibrium in response to reactive O 3 loss, but this is hampered at solute concentrations relevant to aqueous aerosol by the rate of O 3 arrival in the bulk by diffusion. As a result, bulk-phase O 3 becomes depleted from its Henry's law solubility. This bulk-phase O 3 depletion limits reaction timescales for relatively slow-reacting organic solutes with low interfacial affinity (i.e., trans-aconitic and maleic acids, with k rxn ≈ 10 3 -10 4 M -1 s -1 ), which is in contrast to fast-reacting solutes with higher surface affinity (i.e., nitrite, with k rxn ≈ 10 5 M -1 s -1 ) where surface reactions strongly impact the observed decay kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ultrasound-Assisted Nonthermal, Nonequilibrium Separation of Organic Molecules from Their Binary Aqueous Solutions: Effect of Solute Properties on Separation

The separation of organic molecules in downstream processes, such as distillation, plays a vital role in biobased chemical production. A comprehensive study was performed here using ultrasonic energy to separate 11 organic molecules from their binary aqueous solutions under nonthermal, nonequilibrium, and phase-change free conditions. A batch sonoseparator with a three-stage mist collection unit allowed direct analysis of ultrasound-generated mist with an HPLC/GC and differentiation and quantification of the vapor and mist. The results showed that the alcohols (1-butanol, ethanol, 1-propanol, and methanol) and acetone were enriched in the ultrasound-generated mist with enrichment ratios of 3.2–5. On the other hand, ethylene glycol, glycerol, γ-valerolactone (GVL), glucose, and sucrose were diluted with dilution ratios in the range of 2.04–15.7 in the mist and vapor generated by ultrasound (or concentrated in the bulk solution). No enrichment nor dilution of acetic acid was observed. The role of various physicochemical parameters such as dynamic viscosity, surface tension, Henry’s law of solubility constant, vapor pressure, and octanol–water partition coefficient in the enrichment was examined. Furthermore, the hydrophobicity of the organic molecules represented by the octanol–water partition coefficient was found to play a crucial role in determining the separation characteristics of the molecules in ultrasound-generated mist and vapor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗