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Approximate formulas for calculating thermodynamic characteristics and equilibrium constants of chemical reactions
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.
Results are presented from a study of the equilibria, kinetic rates, and the aggregation pathway which leads from a lysozyme monomer crystal to a tetragonal crystal, using dialyzed and recrystallized commercial hen eggwhite lysozyme. Relative light scattering intensity measurements were used to estimate the initial equilibrium constants for undersaturated lysozyme solutions in the tetragonal regime. The K1 value was estimated to be (1-3) x 10 exp 4 L/mol. Estimates of subsequent equilibrium constants depend on the crystal aggregation model chosen or determined. Experimental data suggest that tetragonal lysozyme crystal grows by addition of aggregates preformed in the bulk solution, rather than by monomer addition.
It is shown here that the equilibrium constant for the reversible reaction ClO + O2 - ClO-O2 at stratospheric temperatures must be at least three orders of magnitude less than the current NASA upper limit. The new upper limit greatly diminishes the possible role of ClO-O2 in the chlorine-photosensitized decomposition of O3. Nevertheless, it does not preclude the possibility that it is a significant reservoir of ClO, as well as a possible reactant, at low temperatures characteristic of polar vortices.
Direct determinations of the equilibrium constant for the reaction N2O5 = NO2 + NO3 were carried out by measuring NO2, NO3, and N2O5 using long-path visible and infrared absorption spectroscopy as a function of temperature from 243 to 397 K. The first-order decay rate constant of N2O5 was experimentally measured as a function of temperature. These results are in turn used to derive a value for the rate coefficient for the NO-forming channel in the reaction of NO3 with NO2. The implications of the results for atmospheric chemistry, the thermodynamics of NO3, and for laboratory kinetics studies are discussed.
The computer codes developed provide data to 30000 K for the thermodynamic and transport properties of individual species and reaction rates for the prominent reactions occurring in an 11-species nonequilibrium air model. These properties and the reaction-rate data are computed through the use of curve-fit relations which are functions of temperature (and number density for the equilibrium constant). The curve fits were made using the most accurate data believed available. A detailed review and discussion of the sources and accuracy of the curve-fitted data used herein are given in NASA RP 1232.
Abstract not provided.
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.
A basic, experimental study on the hydrochlorination of silicon tetrachloride and metallurgical grade silicon with hydrogen gas to form trichlorosilane was carried out to greatly expand the range of reaction conditions. The equilibrium constant, K sub p, for the hydrochlorination reaction was measured as a function of temperature, pressure and concentration. The variation of the equilibrium constant as a function of temperature provided the measurement on the heat of reaction, delta H, by the Second Law Method. The value of delta H was measured to give 10.6 Kcal/mole. The equilibrium constant was also studied as a function of concentration. In agreement with the theory, the equilibrium constant remained constant with respect to the varying H2/SiCl4 feed ratios. On the other hand, the effect of pressure on the equilibrium constant was found to be more complex.
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.
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.
Purpose of research on rough-to-smooth transition of an equilibrium neutral constant stress layer is to develop a model for low-level atmospheric flow over terrains of abruptly changing roughness, such as those occurring near the windward end of a landing strip, and to use the model to derive functions which define the extent of the region affected by the roughness change and allow adequate prediction of wind and shear stress profiles at all points within the region. A model consisting of two bounding logarithmic layers and an intermediate velocity defect layer is assumed, and dimensionless velocity and stress distribution functions which meet all boundary and matching conditions are hypothesized. The functions are used in an asymptotic form of the equation of motion to derive a relation which governs the growth of the internal boundary layer. The growth relation is used to predict variation of surface shear stress.
The entropy of a gas system with the number of particles subject to external control is maximized to derive relations between the thermodynamic variables that obtain at equilibrium. These relations are described in terms of the chemical potential, defined as equivalent partial derivatives of entropy, energy, enthalpy, free energy, or free enthalpy. At equilibrium, the change in total chemical potential must vanish. This fact is used to derive the equilibrium constants for chemical reactions in terms of the partition functions of the species involved in the reaction. Thus the equilibrium constants can be determined accurately, just as other thermodynamic properties, from a knowledge of the energy levels and degeneracies for the gas species involved. These equilibrium constants permit one to calculate the equilibrium concentrations or partial pressures of chemically reacting species that occur in gas mixtures at any given condition of pressure and temperature or volume and temperature.
Light-scattering intensity measurements are a sensitive method for following changes in the hydrodynamic radius of particles in solution. The approach used in this report utilizes the light-scattering intensity ratios of a polydisperse to a monodisperse system. By numerically modeling the process, and fitting the model curves to the data, estimates have been obtained for the dimerization equilibrium constant, the dimer + dimer yields tetramer equilibrium constant, and the association rate constant for the dimerization process.
Thin, ~1-nm films of CaTiO3, SrTiO3, and BaTiO3 were deposited onto MgAl2O4 by Atomic Layer Deposition (ALD) and then studied as catalyst supports for ~5 wt % of Ni that was added to the perovskite thin films by Atomic Layer Deposition. Scanning Transmission Electron Microscopy demonstrated that both the Ni and the perovskites uniformly covered the surface of the support following oxidation at 1073 K, even after redox cycling, but large Ni particles formed following a reduction at 1073 K. When compared to Ni/MgAl2O4, the perovskite-containing catalysts required significantly higher temperatures for Ni reduction. Equilibrium constants for Ni oxidation, as determined from Coulometric Titration, indicated that the oxidation of Ni shifted to lower PO2 on the perovskite-containing materials. Based on Ni equilibrium constants, Ni interactions are strongest with CaTiO3, followed by SrTiO3 and BaTiO3. The shift in the equilibrium constant was shown to cause reversible deactivation of the Ni/CaTiO3/MgAl2O4 catalyst for CO2 reforming of CH4 at high CO2 pressures, due to the oxidation of the Ni.
We developed a first-principles machine learning model for the reactive vapor–liquid phase behavior of molten Li 2 CO 3 . The model was trained on ab initio electronic density functional theory data using the Deep Potential (DP) methodology, and its accuracy was evaluated by comparing model predictions of density and viscosity to experimental measurements. Direct coexistence simulations with the DP model over time scales of tens of nanoseconds were used to observe equilibrium dissociation of Li 2 CO 3 into CO 2 residing primarily in the vapor phase and Li 2 O which remains dissolved in the liquid. The simulations covered a range of temperatures, overall system sizes, and vapor-to-liquid volume ratios. Results were analyzed in terms of the observed chemical composition of the liquid and vapor phases, product structure, and CO 2 partial pressures. In addition, we calculated equilibrium constants for the dissociation reaction by assuming ideal-solution behavior for the liquid. As expected on the basis of thermodynamic arguments and prior experiments for this system, the observed partial pressure of CO 2 in the gas phase depends on both the temperature and the ratio of vapor to liquid volumes, while the calculated equilibrium constants only depend on temperature. DP model predictions for the equilibrium constant of the reaction are generally consistent with the available experimental measurements. Furthermore, the present study establishes the validity of the DP methodology for the description of reactive, multiphase equilibria from first principles, with possible applications to many other systems of scientific and technological interest even in the absence of relevant experimental measurements.
A novel method to determine redox potentials without electrolyte is presented here. The method is based on a new ability to determine the dissociation constant, $K°_d$, for ion pairs formed between any radical anion and any inert electrolyte counterion. These dissociation constants can be used to determine relative shifts of redox potential as a function of electrolyte concentration, connecting referenced potentials determined with electrochemistry (with 0.1 M electrolyte) to electrolyte-free values. Pulse radiolysis created radical anions enabling determination of equilibrium constants for electron transfer between anions of donor and acceptor molecules as a function of electrolyte concentration in THF. The measurements determined “composite equilibrium constants”, $K_{eqC}$, which contain information about the dissociation constant for the electrolyte cations, X + , with the radical anions of both the donor, $K°_d$(D –• ,X + ) and the acceptor, $K°_d$(A –• ,X + ). Dissociation constants were obtained for a selection of radical anions with tetrabutylammonium (TBA + ). The electrolyte was found to shift the reduction potentials of small molecules 1-methylpyrene and trans-stilbene by close to +130 mV whereas oligo-fluorenes and polyfluorenes experienced shifts of only (+25 ± 6) mV due to charge delocalization weakening the ion pair. These shifts for reduction of aromatic hydrocarbon molecules are smaller than shifts of +232 and +451 mV seen previously for benzophenone radical anion with TBA + and Na + respectively where the charge on the radical anion is localized largely on one C=O bond, thus forming a more tightly bound ion pair.
Hydrogen bonding in deuterochloroform studied using IR spectra and dielectric constant methods, calculating equilibrium constants and heat of formation