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Equilibrium constant

About: Equilibrium constant is a(n) research topic. Over the lifetime, 11920 publication(s) have been published within this topic receiving 297117 citation(s).
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Journal ArticleDOI
Zhenyu Shen1, Yanjun Li1, Nan Xu1, Sun Baozhi1  +3 moreInstitutions (1)
15 Feb 2022-Fuel
Abstract: As international concern that regards N O x emissions from the shipping industry increases, it is challenging and urgent to reduce ships’ N O x emissions. According to the extended Zeldovich, the determination of the equilibrium concentration of combustion products is crucial for the prediction of N O formation in internal combustion engines. In the present work, an equilibrium constants database of related chemical reactions is established based on the theory that the total Gibbs energy reaches its minimum when a reaction achieves equilibrium. Afterward, a combustion product equilibrium model with twelve species considered is established based on the equilibrium constants database. The accuracy of the model is significantly improved compared with the commonly used ones which calculate the equilibrium constants through fitting function. The errors of the model are within 2% compared with STANJAN which is widely used for chemical equilibrium analysis. The model results are comparable to STANJAN. Afterward, the effects of the temperature, pressure, fuel–air equivalence ratio, O 2 concentration, N 2 concentration, A r concentration and fuel type on the equilibrium mole fractions of the combustion products are investigated. The equilibrium concentration of combustion products is significantly affected by the temperature, O 2 concentration and fuel–air equivalence ratio, but slightly influenced by the pressure and A r concentration. The existence of O and N in the fuel slightly reduces the N O equilibrium mole fraction of the combustion products at the same temperature, pressure and fuel–air equivalence ratio. However, the ratio of molar carbon hydrogen in the fuel and the existence of O and N in the fuel have a significant impact on the C O 2 mole fraction of the combustion products.

Journal ArticleDOI
Wei Meng1, Fenggui Sui1, Xuefeng Hao1, Shoupeng Zhang1  +4 moreInstitutions (1)
15 Jan 2022-Fuel
Abstract: Diagenesis controls the formation, evolution, and distribution of deep-buried sandstone reservoirs in sedimentary basins. The essence of diagenesis is the transformation of substances between different phases (solid, gas and liquid phases) and the migration of materials transported by formation water. Fluids transport in deep-buried formations in sedimentary basins is generally slow, which lead the reaction system is in a near-equilibrium-to-equilibrium state. In this context, thermodynamics can be employed to calculate the solubility and characterize the occurrences of various minerals in different states, which can help reveal the genetic mechanism of secondary pores in the deep-buried rocks of sedimentary basins. In this study, we investigate the types and contents of particles in the aqueous solutions in the H2O-CO2-CaCO3-Albite-SiO2 system under different temperature and pressure conditions. Specifically, the Gibbs free energy of formation of minerals and gases are calculated based on the constant-pressure specific heat model; the apparent standard molal Gibbs free energy of different ions in fluids are computed using the HKF model; the equilibrium constants of different reactions are calculated according to the Gibbs function; the contents of different types of particles are computed based on the charge balance principle in the aqueous solution. The results show that the contents of various particles in the aqueous solution are mainly controlled by temperature and CO2 partial pressure, while they are rarely impacted by the total pressure. Different ions are demonstrated to have different responses to temperature changes. Specifically, types of Ca- and C-containing particles in the aqueous solution are closely related to temperature, while those of Al- and Si-rich particles are rarely changed as temperature varies. The CO2-rich fluid migration environment that results from hydrocarbon generation can be regarded as an open system for the dissolution of calcite, while it is a closed-to-semi-closed system for the dissolution of quartz and feldspar. The content of secondary pores is demonstrated to be determined by the solubility of various particles in the aqueous solution as well as the rate and duration of fluid migration, while the distribution patterns and ranges of secondary pores are controlled by responses of various particles in the solution to temperature and pressure changes.

2 citations

Journal ArticleDOI
Allan N. Hayhurst1Institutions (1)
Abstract: Continuously sampling a flame, burning at 1 atm., for mass spectrometry at ≈ 10–8 atm. seriously disturbs the flame. Not only are a flame's temperature and velocity altered, often the composition of a sample is falsified. Thus, “fake” ions appear, even when sampling as quickly as possible, i.e. supersonically, to quench chemical reactions. However, studying these spurious ions is fruitful. They arise, because a sample is unavoidably cooled; the drop in temperature causes a rapid chemical equilibrium to shift position and change the sample's composition. That ions react faster than neutrals (to perturb a sample) magnifies the problem for ions. When continuously sampling a flame, burning at 1 atm., through an inlet at the tip of a hollow, metallic nozzle, cooling can occur in three ways during the formation of a beam for mass spectrometry. Firstly, before a sample passes through the inlet hole to enter the supersonic expansion into the first vacuum chamber of the mass spectrometer, it loses heat to the cooler, sampling nozzle, usually conical in shape. By detecting spurious ions from a flame, this drop in temperature has been measured to be greatest (≈ 400 K) for the smallest orifices. This cooling becomes smaller for larger holes and is trivial for diameters above 150 µm. Secondly, a sample cools (by maybe ≈ 300 K), whatever the orifice's size, on being accelerated to the local speed of sound in the narrowest part, i.e. the throat of the inlet orifice. Thirdly, the drop in temperature in the subsequent, near-adiabatic expansion inside the nozzle is greatest (≈ 1000 K) and most prolonged for the largest inlet holes (diam. > 150 µm). The upshot is that with a small hole (diam. 150 µm), cooling happens in the acceleration to a Mach number of unity and the following supersonic expansion. Analysis shows that, if a positive ion reacts exothermally in a reversible reaction with a time constant briefer than ≈ 0.5 µs, that reaction will be equilibrated early in the flame. In addition, if the orifice is small, the equilibrium will be just fast enough to shift position to that for a temperature reduced in both the thermal boundary layer around the inlet, and in accelerating to the speed of sound. Consequently, the sample begins the expansion with new species. When using a big orifice, the reaction's time constant (in the flame) must be less than ≈ 0.05 µs (depending on the flame) to generate new ions in the supersonic expansion. It follows that, if there is not an exothermic chemical reaction with a time constant less than ≈ 0.5 µs, sampling is most probably genuine. A similar criterion usually means that no fake neutral species are observed in a low-pressure flame. Negative ions are complicated by their reactions often involving free electrons. Being mobile, they often leave a sample to attach to the metallic sampling nozzle. This loss of free electrons changes the ionic composition, because rapid, steady-state relationships for individual negative ions are thereby shifted, with the change in composition depending on the orifice's size. A theme of this review is that these problems can be identified and resolved by repeating observations using sampling orifices with a range of different diameters. The resulting measurements are then extrapolated to a hole size of either zero or infinity, when there is no effect of a perturbation in either the expansion or the boundary layer; this yields a measurement, e.g. of an equilibrium constant, for the known conditions in the neck of the orifice. In addition, applying a voltage between the burner and the sampling nozzle considerably improves the accuracy, with which ionic concentrations are measured. Consequently, many rapid reactions have had their equilibrium constants measured, yielding the proton affinities of e.g. H2O, CO, CO2 and NH3, the hydration energies of many ions, the stability of ions like MnOH+ (resulting from seeding a flame with Mn) and also the standard changes of enthalpy and entropy for e.g. OH– + CO2 + M = HCO3– + M and HCO3– + OH = CO3– + H2O. In addition, rate constants have been deduced for reactions like the mono-hydration of H3O+, for LiOH + H3O+ → Li+ + H2O and Li+ + CO + M → Li+.CO + M, as well as those for the forward and reverse steps in: e– + O2 + M ⇄ O2– + M, Cl– + H ⇄ HCl + e–, O2– + H ← → HO2 + e– and O2– + OH ← → OH– + O2. The design of mass spectrometers was discussed, as well as the sampling of neutral species.

Journal ArticleDOI
Yingzhen Chen1, Yingzhen Chen2, Manuel B. Endres1, Jürgen Giffin1  +2 moreInstitutions (2)
Abstract: Protic ionic liquids (PILs) are promising candidates as non-aqueous proton-conducting electrolytes for use in polymer electrolyte membrane fuel cells with operating temperatures over 100 °C. 2-sulfoethylammonium triflate [2-Sea][TfO] is one such PIL electrolyte, in which the highly Bronsted acidic sulfoalkylammonium cations act as mobile protonic charge carriers and proton donors. In order to gain a molecular-level understanding of proton transfer in a PIL electrolyte containing a small amount of residual water from fuel cell operation, the protolytic equilibrium of the highly acidic cation was investigated by means of Raman spectroscopy. Density functional theory (DFT) calculations were conducted to identify the vibration modes sensitive to protonation and to gain information on the possible conformation of the cation. The deprotonation of the 2-sulfoethylammonium cation resulted in a characteristic upward frequency shift in the ν(SC) stretching vibration. An equilibrium constant of 0.23 ± 0.09 was calculated for the protolytic reaction, indicating [2-Sea][TfO] as a promising proton donor for the fuel cell application.

Journal ArticleDOI
Abstract: An original method for direct synthesis of tetramethyl orthosilicate from SiO2 raw minerals and supercritical methanol was developed for the first time in a flow mode. The process promoted by KOH was performed at 270 °C and 100 atm using 3 A zeolite molecular sieves to shift the reversible reaction toward TMOS formation by removing released water. The equilibrium constant Keq of the reaction was determined as 0.839E-08. Silica gel (100 wt% SiO2), quartz sand (97 wt% SiO2), expanded perlite (73 wt% SiO2) and vermiculite (38 wt% SiO2) were tested as SiO2 minerals. The highest equilibrium concentration of TMOS equal to 20.4 g/L was achieved for silica gel that can be increased using larger amount of water adsorbent.

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