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At least 19 records

Classical calculation of the equilibrium constants for true bound dimers using complete potential energy surface

The present paper aims at deriving classical expressions which permit calculation of the equilibrium constant for weakly interacting molecular pairs using a complete multidimensional potential energy surface. The latter is often available nowadays as a result of the more and more sophisticated and accurate ab initio calculations. The water dimer formation is considered as an example. It is shown that even in case of a rather strongly bound dimer the suggested expression permits obtaining quite reliable estimate for the equilibrium constant. The reliability of our obtained water dimer equilibrium constant is briefly discussed by comparison with the available data based on experimental observations, quantum calculations, and the use of RRHO approximation, provided the latter is restricted to formation of true bound states only.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Isotopic equilibrium constants for very low-density and low-temperature nuclear matter

Yields of equatorially emitted light isotopes, 1 ≤ Z ≤ 14, observed in ternary fission in the reaction 241 Pu(n th, f) are employed to determine apparent chemical equilibrium constants for low-temperature and low-density nuclear matter. The degree of equilibration and role of medium modifications are probed through a comparison of experimentally derived reaction quotients with equilibrium constants calculated using a relativistic mean-field model employing a universal medium modification correction for the attractive σ meson coupling. The results of these comparisons indicate that equilibrium is achieved for the lighter ternary fission isotopes. For the heavier isotopes experimental reaction quotients are well below calculated equilibrium constants. This is attributed to a dynamical limitation reflecting insufficient time for full equilibrium to develop. The role of medium effects leading to yield reductions is discussed as is the apparent enhancement of yields for 8 He and other very neutron rich exotic nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Thermodynamic Modeling and Optimization of the Copper Flash Converting Process Using the Equilibrium Constant Method

Based on the principle of multiphase equilibrium, a mathematical model of the copper flash converting process was established by the equilibrium constant method, and a computational system was developed with the use of MetCal software platform. The mathematical model was validated by comparing simulated outputs, industrial data, and published data. To obtain high-quality blister copper, a low copper content in slag, and increased impurity removal rate, the model was then applied to investigate the effects of the operational parameters [oxygen/feed ratio (R{sub OF}), flux rate (R{sub F}), and converting temperature (T)] on the product weights, compositions, and the distribution behaviors of impurity elements. The optimized results showed that R{sub OF}, R{sub F}, and T should be controlled at approximately 156 Nm{sup 3}/t, within 3.0 pct, and at approximately 1523 K (1250 °C), respectively.

36 MATERIALS SCIENCE↗

Comment on “Equilibrium constants and rate constants for adsorbates: Two-dimensional (2D) ideal gas, 2D ideal lattice gas, and ideal hindered translator models”

The paper by Campbell et al. was recently brought to my attention. This comment is written to provide greater clarity to the community to prevent misconceptions regarding the entropies being discussed in that work and to clarify the differences between the adsorbate standard states suggested by Campbell and by Savara.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Correction to “Comment on ‘Equilibrium Constants and Rate Constants for Adsorbates: 2D Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models’”

There was an error in the original Comment. The entropy term arising from 1/N! should be free from dimensional dependence, but also negative. In the original Comment, the nN A arising from 1/N! was inadvertently moved into the dimensional dependent term of Eqs. 2 and 3. To avoid confusion and to keep the same numbering as before, the equations should be as follows.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimental determination of the solubility constant of kurnakovite, MgB3O3(OH)5·5H2O

In this study, I present experimental results on the equilibrium between boracite [Mg 3 B 7 O 13 C1(cr)] and kurnakovite [chemical formula, Mg 2 B 6 O 11 ·15H 2 O(cr); structural formula, MgB 3 O 3 (OH) 5 ·5H 2 O(cr)] at 22.5 ± 0.5 °C from a long-term experiment up to 1629 days, approaching equilibrium from the direction of supersaturation, Mg 3 B 7 O 13 C1(cr) + H + + 2B(OH)$^-_4$ + 18H 2 O(1) ⇌ 3MgB 3 O 3 (OH) 5 ·5H 2 O(cr) + C1 - . Based on solubility measurements, the 10-based logarithm of the equilibrium constant for the above reaction at 25 °C is determined to be 12.83 ± 0.08 (2σ). Based on the equilibrium constant for dissolution of boracite, Mg 3 B 7 O 13 C1(cr) + 15H 2 O(1) = 3Mg 2+ + 7B(OH)$^-_4$ + C1 - + 2H + at 25 °C measured previously (Xiong et al. 2018) and that for the reaction between boracite and kurnakovite determined here, the equilibrium constant for dissolution of kurnakovite, MgB 3 O 3 (OH) 5 ·5H 2 O(cr) = Mg 2+ + 3B(OH)$^-_4$ + H + + H 2 O(1) is derived as -14.11 ± 0.40 (2σ). Using the equilibrium constant for dissolution of kurnakovite obtained in this study and the experimental enthalpy of formation for kurnakovite from the literature, a set of thermodynamic properties for kurnakovite at 25 °C and 1 bar is recommended as follows: Δ H $^0_f$ = -4813.24 ± 4.92 kJ/mol, Δ G$^0_f$ = -4232.0 ± 2.3 kJ/mol, and S 0 = 414.3 ± 0.9 J/(mol·K). Among them, the Gibbs energy of formation is based on the equilibrium constant for kurnakovite determined in this study; the enthalpy of formation is from the literature (Li et al. 1997), and the standard entropy is calculated internally with the Gibbs-Helmholtz equation in this work. The thermodynamic properties of kurnakovite estimated using the group contribution method for borate minerals based on the sums of contributions from the cations, borate polyanions, and structural water to the thermodynamic properties from the literature (Li et al. 2000) are consistent, within their uncertainties, with the values listed above. Since kurnakovite usually forms in salt lakes rich in sulfate, studying the interactions of borate with sulfate is important to modeling kurnakovite in salt lakes. Finally, for this purpose, I have re-calibrated our previous model (Xiong et al. 2013) describing the interactions of borate with sulfate based on the new solubility data for borax in Na 2 SO 4 solutions presented here.

36 MATERIALS SCIENCE↗

Generalized adsorption isotherms for molecular and dissociative adsorption of a polar molecular species on two polar surface geometries: Perovskite (100) (Pm-3m) and fluorite (111) (Fm-3m)

Lattice based kinetic Monte Carlo simulations have been used to determine a functional form for the second order adsorption isotherms on two commonly investigated crystal surfaces: the (111) fluorite surface and the (100) perovskite surface which has the same geometric symmetry as the NaCl (100) surface. The functional form is generalized to be applicable to all values of the equilibrium constant by a shift along the pressure axis. Functions have been determined for estimating the pressure at which a desired coverage would be achieved and, conversely, for estimating the coverage at a certain pressure. The generalized form has been calculated by investigating the surface adsorbate coverage across a range of thermodynamic equilibrium constants that span the range 10{sup −26} to 10{sup 13}. The equations have been shown to be general for any value of the adsorption equilibrium constant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Heterolytic Hydrogen Activation: Understanding Support Effects in Water–Gas Shift, Hydrodeoxygenation, and CO Oxidation Catalysis

Identifying the role of oxide supports in transition metal catalysis is critical toward our understanding of heterogeneous catalysis. The water-gas shift (WGS) reaction is a prototypical example where oxide support dictates catalytic activity, yet the cause for this remains uncertain. Herein, we show that a single descriptor—the equilibrium constant for hydroxyl formation—relates the WGS turnover frequency across disparate oxide supports. The dissimilar equilibrium constant, or oxophilicity, between early and late transition metals exemplify the utility of metal-support interfacial sites to circumvent adsorption-energy scaling restrictions, thereby providing bifunctional gains for the WGS reaction class. In relation, the equilibrium constant for hydroxyl formation is equivalent to the equilibrium constant for the formal heterolytic dissociation of hydrogen, and therefore, reflects the ability of the metal-support interface to participate in hydrogen heterolysis. The ubiquitous coexistence, yet divergent chemical behavior of homo- and heterolytically activated hydrogen renders oxide support identity central toward our understanding of hydrogenation catalysis. This work was supported by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences and performed at the Environmental Molecular Sciences Laboratory in (EMSL), which is a DOE Office of Science User Facility located at the Pacific Northwest National Laboratory (PNNL). PNNL is a multiprogram national laboratory operated for DOE by Battelle. Computational resources were provided by a user proposal at the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility. N.N. would like to thank Oliver Y. Gutierrez for critical feedback during the final stage of manuscript preparation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories

Here, the accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH 3 ) molecule and the nucleophilic substitution (S N 2) reaction F – + CH 3 F → FCH 3 + F – . We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Iyer, Gopal R.↗

Experimental determination of solubilities of magnesium borates: Solubility constants of boracite [Mg 3 B 7 O 13 Cl(cr)] and aksaite [MgB 6 O 7 (OH) 6 ·2H 2 O(cr)]

In this work, solubility measurements regarding boracite [Mg 3 B 7 O 13 Cl(cr)] and aksaite [MgB 6 O 7 (OH) 6 ·2H 2 O(cr)] from the direction of supersaturation were conducted at 22.5 ± 0.5 °C. The equilibrium constant (log 10 K 0 ) for boracite in terms of the following reaction, Mg 3 B 7 O 13 Cl(cr) + 15H 2 O(l) ⇌ 3Mg 2+ + 7B(OH) 4 – + Cl – + 2H + is determined as -29.49 ± 0.39 (2σ) in this study. The equilibrium constant for aksaite according to the following reaction, MgB 6 O 7 (OH) 6 •2H 2 O(cr) + 9H 2 O(l) ⇌ Mg 2+ + 6B(OH) 4 – + 4H + is determined as -44.41 ± 0.41 (2σ) in this work. This work recommends a set of thermodynamic properties for aksaite at 25 °C and 1 bar as follows: ΔH$0\atop{f}$ =-6063.70 ± 4.85 kJ·mol -1 , ΔG =-5492.55 ± 2.32 kJ·mol -1 , and S 0 = 344.62 ± 1.85 J·mol -1 ·K -1 . Among them, ΔG$0\atop{f}$ is derived from the equilibrium constant for aksaite determined by this study; ΔH$0\atop{f}$ is from the literature, determined by calorimetry; and S 0 is computed in the present work from ΔG$0\atop{f}$ and ΔH$0\atop{f}$. This investigation also recommends a set of thermodynamic properties for boracite at 25 °C and 1 bar as follows: ΔH$0\atop{f}$ =-6575.02 ± 2.25 kJ·mol -1 , ΔG$0\atop{f}$ =-6178.35 ± 2.25 kJ·mol -1 , and S 0 = 253.6 ± 0.5 J·mol -1 ·K -1 . Among them, ΔG$0\atop{f}$ is derived from the equilibrium constant for boracite determined by this study; S 0 is from the literature, determined by calorimetry; and ΔH$0\atop{f}$ is computed in this work from ΔG$0\atop{f}$ and S 0 . The thermodynamic properties determined in this study can find applications in many fields. For instance, in the field of material science, boracite has many useful properties including ferroelectric and ferroelastic properties. The equilibrium constant of boracite determined in this work will provide guidance for economic synthesis of boracite in an aqueous medium. Similarly, in the field of nuclear waste management, iodide boracite [Mg 3 B 7 O 13 I(cr)] is proposed as a waste form for radioactive 129 I. Therefore, the solubility constant for chloride boracite [Mg 3 B 7 O 13 Cl(cr)] will provide the guidance for the performance of iodide boracite in geological repositories. Boracite/aksaite themselves in geological repositories in salt formations may be solubility-controlling phase(s) for borate. Finally, solubility constants of boracite and aksaite will enable researchers to predict borate concentrations in equilibrium with boracite/aksaite in salt formations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Statistical effects related to low numbers of reacting molecules analyzed for a reversible association reaction A + B = C in ideally dispersed systems: An apparent violation of the law of mass action

Theoretical analysis and computer simulations (Monte Carlo and numerical integration of differential equations) show that the statistical effect of a small number of reacting molecules depends on a way the molecules are distributed among the small volume nano-reactors (droplets in this study). A simple reversible association A + B = C was chosen as a model reaction, enabling to observe both thermodynamic (apparent equilibrium constant) and kinetic effects of a small number of reactant molecules. When substrates are distributed uniformly among droplets, all containing the same equal number of substrate molecules, the apparent equilibrium constant of the association is higher than the chemical one (observed in a macroscopic—large volume system). The average rate of the association, being initially independent of the numbers of molecules, becomes (at higher conversions) higher than that in a macroscopic system: the lower the number of substrate molecules in a droplet, the higher is the rate. This results in the correspondingly higher apparent equilibrium constant. A quite opposite behavior is observed when reactant molecules are distributed randomly among droplets: the apparent association rate and equilibrium constants are lower than those observed in large volume systems, being the lower, the lower is the average number of reacting molecules in a droplet. The random distribution of reactant molecules corresponds to ideal (equal sizes of droplets) dispersing of a reaction mixture. Our simulations have shown that when the equilibrated large volume system is dispersed, the resulting droplet system is already at equilibrium and no changes of proportions of droplets differing in reactant compositions can be observed upon prolongation of the reaction time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theoretical Study of C-H Bond Cleavage via Concerted Proton-Coupled Electron Transfer in Fluorenyl-Benzoates

Developing new strategies to activate and cleave C-H bonds is important for a broad range of applications. Recently a new approach for C-H bond activation using multi-site concerted proton-coupled electron transfer (PCET) involving intermolecular electron transfer to an oxidant coupled to intramolecular proton transfer was reported. For a series of oxidants reacting with 2-(9H-fluoren-9-yl)benzoate, experimental studies revealed an atypical Brønsted a, defined as the slope of the logarithm of the PCET rate constant versus the logarithm of the equilibrium constant or the scaled driving force. Herein this reaction is modeled with a vibronically nonadiabatic PCET theory. Hydrogen tunneling, thermal sampling of the proton donor-acceptor mode, solute and solvent reorganization, and contributions from excited vibronic states are found to play important roles. The calculations qualitatively reproduce the experimental observation of a Brønsted a significantly less than 0.5 and explain this shallow slope in terms of exoergic processes between pairs of electron-proton vibronic states. These fundamental mechanistic insights may guide the design of more effective strategies for C-H bond activation and cleavage.

Sayfutyarova, Elvira R.↗

Experimental Determination of Solubilities of Sodium Polyborates In MgCl 2 Solutions: Solubility Constant of Di-Sodium Hexaborate Tetrahydrate, and Implications For the Diagenetic Formation of Ameghinite

In this paper, solubility measurements were conducted for sodium polyborates in MgCl 2 solutions at 22.5 ± 0.5 °C. According to solution chemistry and XRD patterns, di-sodium tetraborate decahydrate (borax) dissolves congruently, and is the sole solubility-controlling phase, in a 0.01 mol/kg MgCl 2 solution: Na 2 B 4 O 7 •10H 2 O(cr) ⇌ 2Na + + 4B(OH) 4 + 2H + + H 2 O(l). However, in a 0.1 mol/kg MgCl 2 solution borax dissolves incongruently and is in equilibrium with di-sodium hexaborate tetrahydrate: 2Na 2 B 6 O 10 •4H 2 O(cr) + 2Na + + 23H 2 O(l) ⇌ 3Na 2 B 4 O 7 •10H 2 O(cr) + 2H + . In this study, the equilibrium constant (log K 0 ) for Reaction 2 at 25 °C and infinite dilution was determined to be –16.44 ± 0.13 (2σ) based on the experimental data and the Pitzer model for calculations of activity coefficients of aqueous species. In accordance with the log K 0 for Reaction 1 from a previous publication from this research group, and log K 0 for Reaction 2 from this study, the equilibrium constant for dissolution of di-sodium hexaborate tetrahydrate at 25 °C and at infinite dilution, Na 2 B 6 O 10 •4H 2 O(cr) + 10H 2 O(l) ⇌ 2Na + + 6B(OH) 4 - + 4H + was derived to be –45.42 ± 0.16 (2σ). The equilibrium constants determined in this study can find applications in many fields. For example, in the field of nuclear waste management, the formation of di-sodium hexaborate tetrahydrate in brines containing magnesium will decrease borate concentrations, making less borate available for interactions with Am(III). In the field of experimental investigations, based on the equilibrium constant for Reaction 2, the experimental systems can be controlled in terms of acidity around neutral pH by using the equilibrium assemblage of borax and di-sodium hexaborate tetrahydrate at 25 °C. As salt lakes and natural brines contain both borate and magnesium as well as sodium, the formation of sodium hexaborate tetrahydrate may influence the chemical evolution of salt lakes and natural brines. Di-sodium hexaborate tetrahydrate is a polymorph of the mineral ameghinite [chemical formula Na 2 B 6 O 10 •4H 2 O; structural formula NaB 3 O 3 (OH) 4 or Na 2 B 6 O 6 (OH) 8 ]. Finally, di-sodium hexaborate tetrahydrate could be a precursor of ameghinite and could be transformed when borate deposits are subject to diagenesis.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Inositol Hexakisphosphate Increases The Transition Constant And The Affinity Of Horse Aquomethemoglobin for 5,5′‐dithiobis(2‐nitrobenzoate)

CysF9[93]β exists in two tertiary conformations, r and t , which are in dynamic equilibrium. The equilibrium constant, K equ , for the reaction of 5,5′‐dithiobis(2‐nitrobenzoate) — DTNB — with the CysF9[93]β sulfhydryl group of each hemoglobin was determined at 25°C as a function of pH. The reactivity of CysF9[93]β is affected by allosteric effectors such as the proton (H + ) and inositol hexakisphosphate (inositol‐P 6 ). The major and minor haemoglobins in horse haemolysate were separated using a column of Whatman's carboxymethylcellulose (CMC 52). The absorbance of the product of DTNB reaction, 5‐thio‐2‐nitrobenzoate, at different concentrations of DTNB and 50 μmol (haem) dm −3 was read at 412 nm. The absorbance was then substituted into an appropriate equation derived for the determination of the equilibrium constant, K equ , for the reaction. K equ decreased the orders of magnitude between pH 5.6 and 9.0 in the absence and presence of inositol‐P 6 . Inositol‐P 6 increased the affinity of the major and minor Hb for DTNB but decreased the affinity of the minor aquomet‐Hb. The results show that inositol‐P 6 increases the relative population of the t tertiary conformation. So, it increases the affinity of CysF9[93]β by changing the relative distribution of two protein conformations. Study objective The study also seeks to find the equilibrium between the r and t isomers in the reaction of DTNB with CysF9[93]β sulphydryl group of the horse aquomethemoglobins. The relative populations of these two conformations from the pH dependence of equilibrium and kinetic parameters and the effect of inositol‐P 6 on these relative populations were determined. Methods Preparation and separation of horse hemoglobin had been described in Omotosho et al ., 2017. Preparation and determination of aquomethemoglobin concentration: Aquomethemoglobin was prepared by the addition of a two‐fold excess of potassium ferricyanide, K 3 Fe(CN) 6 , to oxyhemoglobin of a known concentration. An approximately 1 mol dm −3 K 3 Fe(CN) 6 solution was prepared by dissolving 0.33 g of the reagent in 1 cm 3 of distilled water. The volume of the K 3 Fe(CN) 6 , v cm 3 , added to V cm 3 of hemoglobin to give a two‐fold excess is related to the concentration of the hemoglobin solution. Results Domestic horse contains two hemoglobin types: A, the fast hemoglobin, and B, the slow hemoglobin. The two haemoglobins have identical α chains. Horse hemoglobin consists of two electrophoretically distinct components. From Figs. 1 and 2 it is seen that inositol‐P6 increases the affinity of CysF9[93]β of each haemoglobin for DTNB by about three orders of magnitude throughout the pH range 5.6 to 9.2. Conclusion Figs. 1 and 2 report the dependence of K equ, the equilibrium constant of the reaction of DTNB with CysF9[93]β, on pH. The values of K equ decrease by about two orders of magnitude for slow aquomet hemoglobin over the range 5.6 ≥ pH ≤ 9.0 whereas there in the fast hemoglobin, the values of K equ increases by about six orders of magnitude and there is an increase in the affinity for the aquomet derivative. This shows that there is more insight on the nature of the tertiary structure transition in both T and R state hemoglobin. Support or Funding Information We appreciate Covenant University Centre for Research, Innovation and Development for the financial support.

Omotosho, Omolola E.↗