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Journal articles on the topic 'Equilibrium constant'

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Published: 4 June 2021
Last updated: 13 June 2025

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1

Gordus, Adon A. "Chemical equilibrium: I. The thermodynamic equilibrium constant." Journal of Chemical Education 68, no. 2 (1991): 138. http://dx.doi.org/10.1021/ed068p138.

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2

Gil, Victor M. S., and Jo�o C. Paiva. "Equilibrium Constant Units Revisited." Chemical Educator 4, no. 4 (1999): 128–30. http://dx.doi.org/10.1007/s00897990312a.

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3

Martin, R. Bruce. "Why Does an Equilibrium Constant Not Appear Constant?" Journal of Chemical Education 75, no. 11 (1998): 1497. http://dx.doi.org/10.1021/ed075p1497.

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4

Martins Ledesma, Cláudia, Jane Mary Lafayette Neves Gelinski, and Endler Marcel Borges. "Equilibrium Constant Determination Using Digital Images." Revista Virtual de Química 11, no. 3 (2019): 555–72. http://dx.doi.org/10.21577/1984-6835.20190043.

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5

Tripathi, Atri D., and Navneet Kumar. "Spectrophotometric determination of equilibrium constant." Bulletin of Pure & Applied Sciences- Chemistry 39c, no. 1 (2020): 14. http://dx.doi.org/10.5958/2320-320x.2020.00002.3.

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6

Laidler, Keith J. "Units of an equilibrium constant." Journal of Chemical Education 67, no. 1 (1990): 88. http://dx.doi.org/10.1021/ed067p88.1.

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7

Vojic, Mirjana, Gordana Popovic, Dusan Sladic, and Lidija Pfendt. "Protolytic equilibria in homogeneous and heterogeneous systems of ketoconazole and its direct spectrophotometric determination in tablets." Journal of the Serbian Chemical Society 70, no. 1 (2005): 67–78. http://dx.doi.org/10.2298/jsc0501067v.

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The acid-base equilibria of a diprotic, slightly hydrosoluble base ketoconazole were studied in homogeneous and heterogeneous water systems. The determinations were performed at 25?C at a constant ionic strength of M(NaCl). The acidity constant Ka1 was determined by potentiometric (pKa1 3.20) and spectrophotometric (pKa1 3.26) methods. A pKa2 constant of 6.10 was obtained based on the equilibrium constants pKs0 4.84 and pKs1 -1.26, determined in a heterogeneous ketoconazole system. The obtained values of the constants served to calculate the solubility and the distribution of the equilibrium forms of ketoconazole as a function of pH. On the basis of the distribution of the equilibrium forms of ketoconazole, a spectrophotometric method for the determination of its content in commercial tablets was developed. The determinations were performed at 225 nm in 0.1 M HCl. The method is simple and rapid and enables the direct spectrophotometric determination of the content of ketoconazole without previous isolation.
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8

Pérez-Chavela, Ernesto, and Juan Manuel Sánchez-Cerritos. "Euler-type Relative Equilibria and their Stability in Spaces of Constant Curvature." Canadian Journal of Mathematics 70, no. 2 (2018): 426–50. http://dx.doi.org/10.4153/cjm-2017-002-7.

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AbstractWe consider three point positivemasses moving onS2andH2. An Eulerian-relative equilibrium is a relative equilibrium where the three masses are on the same geodesic. In this paper we analyze the spectral stability of these kind of orbits where the mass at the middle is arbitrary and the masses at the ends are equal and located at the same distance from the central mass. For the case of S2, we found a positive measure set in the set of parameters where the relative equilibria are spectrally stable, and we give a complete classiûcation of the spectral stability of these solutions, in the sense that, except on an algebraic curve in the space of parameters, we can determine if the corresponding relative equilibriumis spectrally stable or unstable. OnH2, in the elliptic case, we prove that generically all Eulerian-relative equilibria are unstable; in the particular degenerate case when the two equal masses are negligible, we get that the corresponding solutions are spectrally stable. For the hyperbolic case we consider the system where the mass in the middle is negligible; in this case the Eulerian-relative equilibria are unstable.
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9

Guthrie, J. Peter, and Junan Guo. "Acetal formation from methyl formate, pinacolone, and benzophenone: equilibrium constants in methanol and water determined by a chain of transacetalization equilibria." Canadian Journal of Chemistry 72, no. 10 (1994): 2071–76. http://dx.doi.org/10.1139/v94-263.

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Transacetalization equilibrium constants can be measured in methanol solution. This allows a ladder of equilibrium constants to be constructed from acetophenone, for which the equilibrium constant for acetal formation has been measured in methanol, to methyl formate, for which it has not. This is the first direct measurement of an equilibrium constant for formation of an acetal of an acyclic ester. We have also determined equilibrium constants for acetal formation from benzophenone and pinacolone. The value for benzophenone is inconsistent with the value reported for the diethyl acetal by Pfeiffer and Adkins (G.J. Pfeiffer and H. Adkins. J. Am Chem. Soc. 53, 1043 (1931)). We must conclude that their analytical method was subject to systematic errors.
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10

LIU, Xia. "Calculation Method and Application of Multi-Equilibrium Standard Equilibrium Constant." University Chemistry 34, no. 1 (2019): 116–21. http://dx.doi.org/10.3866/pku.dxhx201805033.

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11

Metz, Clyde, and Henry Donato. "Solving equilibrium constant expressions using spreadsheets." Journal of Chemical Education 66, no. 10 (1989): A241. http://dx.doi.org/10.1021/ed066pa241.

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12

Baldwin, W. G., and C. E. Burchill. "The acid equilibrium constant is unity!" Journal of Chemical Education 69, no. 6 (1992): 514. http://dx.doi.org/10.1021/ed069p514.

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13

Silver, G. L. "Equilibrium-constant expressions for aqueous plutonium." Journal of Radioanalytical and Nuclear Chemistry 284, no. 1 (2010): 175–77. http://dx.doi.org/10.1007/s10967-010-0458-z.

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14

Guthrie, J. Peter, and Goonisetty Bhaskar. "The Strecker reaction — an examination in terms of no-barrier theory." Canadian Journal of Chemistry 86, no. 4 (2008): 285–89. http://dx.doi.org/10.1139/v08-014.

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For those examples of the Strecker reaction where information about both rate and equilibrium is available, we have been able to calculate rate constants for the addition of cyanide ion to the iminium ion by the no-barrier theory (NBT) approach. Both experimental and calculated values are for reaction in aqueous solution. Only for the reactions of benzaldehyde with benzyl or allyl amines and HCN are the equilibrium constants and rate constants for the final, rate-determining, step directly available from the literature. For the reactions of acetone with ammonia, methylamine, or dimethylamine and HCN rate constants for the retro-Strecker cleavage and the equilibrium constants for the overall Strecker reaction have been reported. These equilibrium constants, combined with equilibrium constants for iminium ion formation, which can be extracted from information in the literature, allow calculation of the equilibrium constants for the final step of these Strecker reactions. No-barrier theory has already been applied to carbonyl additions, including cyanohydrin formation; this report provides further evidence for the generality of this approach for calculating rate constants without using any kinetic information.Key words: Strecker reaction, rate constant, equilibrium constant, no-barrier theory, computation.
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15

Beattie, JK, and KJ Mcmahon. "Dynamics of the Bis-Tris and High Spin-Low Spin Equilibria of 2-(2′-Pyridyl)imidazoleiron(II) Complexes in Dimethyl Sulfoxide Solutions." Australian Journal of Chemistry 41, no. 9 (1988): 1315. http://dx.doi.org/10.1071/ch9881315.

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Ultrasonic and temperature-jump relaxation kinetics have been used to observe, respectively, the spin equilibrium and tris-bis ligand dissociation equilibrium of the 2-(2′-pyridyl) imidazoleiron (II) complexes in dimethyl sulfoxide solutions. In the ultrasonic experiments a single relaxation curve describes the excess sound absorption with a relaxation time of 73�3 ns. This was identified as perturbation of the singlet-quintet spin equilibrium by comparison with previous laser temperature-jump measurements in other solvents and by the temperature dependence of the relaxation amplitude. The equilibrium constant for the singlet-quintet transition was determined by the Evans n.m.r . method to be 0.48 at 298 K. From the relaxation time and the equilibrium constant the rate constants for the spin-equilibrium transition can be calculated to be k15 of 4.5×106 s-1 and k51 of 9.4×106s-1. In the temperature-jump experiments a millisecond relaxation time was observed. The dependence of the relaxation time on the concentration of the free ligand is of the form kobs = a + b[L]. From the ratio b/a an equilibrium constant for the perturbed process can be calculated. An independent measure of this equilibrium constant was obtained from spectrophotometric measurements. The rate constants for the formation and dissociation of the tris complex are calculated to be 2.8 × 104 dm3 mol-1 s-1 and 2.1 × 102 s-1, respectively, at 298 K.
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16

Harianto, Joko, and Titik Suparwati. "SVIR Epidemic Model with Non Constant Population." CAUCHY 5, no. 3 (2018): 102. http://dx.doi.org/10.18860/ca.v5i3.5511.

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In this article, we present an SVIR epidemic model with deadly deseases and non constant population. We only discuss the local stability analysis of the model. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium point. The local stability of the disease free and endemic equilibrium exists when the basic reproduction number less or greater than unity, respectively. If the value of R0 less than one then the desease free equilibrium point is locally asymptotically stable, and if its exceeds, the endemic equilibrium point is locally asymptotically stable. The numerical results are presented for illustration.
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17

Sarlo, Edward, Paris Svoronos, and Patricia Kulas. "Calculation of equilibrium constant in esterification reactions." Journal of Chemical Education 67, no. 9 (1990): 796. http://dx.doi.org/10.1021/ed067p796.

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18

Castañer, Anna, and M. Mercè Claramunt. "Equilibrium Distributions and Discrete Schur-constant Models." Methodology and Computing in Applied Probability 21, no. 2 (2018): 449–59. http://dx.doi.org/10.1007/s11009-018-9632-5.

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19

Kircher, Raphael, Niklas Schmitz, Jürgen Berje, et al. "Generalized Chemical Equilibrium Constant of Formaldehyde Oligomerization." Industrial & Engineering Chemistry Research 59, no. 25 (2020): 11431–40. http://dx.doi.org/10.1021/acs.iecr.0c00974.

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20

Lysova, S. S., T. A. Starikova, and Yu E. Zevatskii. "Limit of concentration constant of protolytic equilibrium." Russian Journal of General Chemistry 84, no. 8 (2014): 1634–35. http://dx.doi.org/10.1134/s1070363214080325.

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21

Slanina, Zdeněk. "Dimerization equilibrium constant for the ClO radical." Thermochimica Acta 196, no. 2 (1992): 467–75. http://dx.doi.org/10.1016/0040-6031(92)80108-9.

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22

Barth, Johannes, Michael Buback, Wibke Meiser, and Philipp Vana. "Easy Access to the RAFT Equilibrium Constant." Macromolecules 43, no. 1 (2010): 51–54. http://dx.doi.org/10.1021/ma902111z.

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23

Malomuzh, N. P., V. N. Mahlaichuk, and S. V. Khrapatyi. "Water dimer equilibrium constant of saturated vapor." Russian Journal of Physical Chemistry A 88, no. 8 (2014): 1287–92. http://dx.doi.org/10.1134/s003602441406017x.

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24

Cui, Qianqian, Qinghui Du, and Li Wang. "Global Dynamics of a Generalized SIRS Epidemic Model with Constant Immigration." Mathematical Problems in Engineering 2020 (November 20, 2020): 1–9. http://dx.doi.org/10.1155/2020/7845390.

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In this paper, we discuss the global dynamics of a general susceptible-infected-recovered-susceptible (SIRS) epidemic model. By using LaSalle’s invariance principle and Lyapunov direct method, the global stability of equilibria is completely established. If there is no input of infectious individuals, the dynamical behaviors completely depend on the basic reproduction number. If there exists input of infectious individuals, the unique equilibrium of model is endemic equilibrium and is globally asymptotically stable. Once one place has imported a disease case, then it may become outbreak after that. Numerical simulations are presented to expound and complement our theoretical conclusions.
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25

Egorov, S. A., and Eran Rabani. "Chemical equilibrium in supercritical fluids: Solvent effects on the dimerization equilibrium constant." Journal of Chemical Physics 116, no. 19 (2002): 8447. http://dx.doi.org/10.1063/1.1471553.

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26

Crugeiras, Juan, and Howard Maskill. "The 4,4'-dimethoxytrityl carbenium ion by ionization of 4,4'-dimethoxytrityl alcohol in acetonitrile - aqueous perchloric and nitric acids containing electrolytes: kinetics, equilibria, and ion-pair formation." Canadian Journal of Chemistry 77, no. 5-6 (1999): 530–36. http://dx.doi.org/10.1139/v99-003.

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We have studied the equilibration shown in eq. [3] of 4,4prime-dimethoxytrityl alcohol in aqueous perchloric and nitric acids containing low proportions of acetonitrile using stopped-flow kinetics techniques. The rate constants for the overall progress to equilibrium, kobs, have been resolved into forward and reverse components using the equilibrium UV absorbance and a value for the molar absorptivity of the 4,4prime-dimethoxytrityl carbenium ion determined in concentrated aqueous perchloric acid. The forward reaction (rate constant kf) is first order in both the alcohol and the acid concentrations; the reverse reaction (rate constant kr) is pseudo first order with respect to the carbocation. At constant hydronium ion concentration, the forward rate constant increases linearly with the concentration of electrolyte, whereas the reverse rate constant decreases. These effects depend upon the nature of the anion, but not the cation, and are not ionic strength effects. At constant anion concentrations, kf in both acids, and kr in perchloric acid, are independent of hydronium ion concentration; however, kr decreases with increasing hydronium ion concentration at constant nitrate concentration. At nonconstant ionic strength, changes in kf and kr observed in increasing concentrations of perchloric acid are attributable wholly to changes in perchlorate concentration. A mechanism is proposed which involves pre-equilibrium protonation of the alcohol, heterolysis of the protonated alcohol to give a 4,4prime-dimethoxytrityl carbenium ion - water ion-molecule pair, then conversion of this into a dissociated carbenium ion in equilibrium with ion pairs. To account for the strong effects of perchlorate and nitrate upon the forward rate constants, it is proposed that these anions provide additional reaction channels from the ion-molecule pair. However, we find no evidence of acid catalysis in the reaction of the ion-molecule pair (in contrast to our finding for the reaction of the corresponding ion-molecule pair formed from dimethoxytritylamine in acidic media). Some of the elementary rate and equilibrium constants of the proposed mechanism have been evaluated.Key words: trityl, carbenium ion, stopped-flow, ion pair, ion-molecule pair.
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27

KOLPIN, VAN. "SEPARATING EQUILIBRIUM AND PERSISTENT INEFFICIENCY." International Game Theory Review 14, no. 02 (2012): 1250010. http://dx.doi.org/10.1142/s0219198912500107.

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In context of the traditional Spence signaling model, the realization of a separating equilibrium ensures that each worker is allocated to the sector of the economy where they are most productive. Traditional analysis assumes, however, that the incremental returns to labor employment are constant across workers of any given type. This paper demonstrates that the efficiency properties of separating equilibria can be profoundly altered by the presence of nonlinear returns. In particular, we show that separating equilibria fail productive efficiency whenever production satisfies a weak form of diminishing returns. This separating equilibrium efficiency failure persists whether or not equilibrium wages are assumed to depend solely on distributions of worker productivity.
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28

Kumar, Rajnesh, and Sunil Kumar. "A New Fractional Modelling on Susceptible-Infected-Recovered Equations with Constant Vaccination Rate." Nonlinear Engineering 3, no. 1 (2014): 11–19. http://dx.doi.org/10.1515/nleng-2013-0021.

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AbstractIn this article, the authors introduce a fractional order SIR model with constant vaccination rate. The SIR model has been used in the modeling of several epidemiological diseases, biology and medical sciences. Qualitative results show that the model has two equilibria; the disease free equilibrium and the endemic equilibrium points. The local stability of the model for fractional order time derivative is analyzed using fractional Routh-Hurwitz stability criterion. The fractional derivative is described in Caputo sense. The results obtained through numerical procedure show that the method is effective and reliable.
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29

Brittain, T. "Role of dimerization in the control of the functioning of the human haemoglobin mutant haemoglobin Howick (β37 Trp→Gly)". Biochemical Journal 300, № 2 (1994): 553–56. http://dx.doi.org/10.1042/bj3000553.

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Haemoglobin Howick shows a high oxygen affinity (p50 = 1 mmHg) and a low co-operativity (n = 1.3). Equilibrium studies show the protein to be essentially totally dimeric in the oxygenated form. A wide range of rapid kinetic experiments indicate that the deoxygenated form of the protein exists in a tetramer<-->dimer equilibrium with an associated equilibrium constant of 3 microM. These kinetic data also indicate that the oxygenated form of the protein exists in a tetramer<-->dimer equilibrium with an associated equilibrium constant of 35 mM, and furthermore clearly identifies a large increase in the rate of the tetramer-to-dimer dissociation process as the origin of the vastly increased dissociation equilibrium constants. Simulations of the protein-concentration-dependence of the oxygen-binding properties of haemoglobin Howick, based on the measured equilibrium parameters, closely fits the experimental data. The change in dimerization constant for the deoxygenated form of the protein corresponds remarkably well to the free-energy change predicted for the simple transfer of the amino acid side chain at position beta 37 from a hydrophobic to a hydrophilic environment during the dimerization process.
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30

Sharma, Sangita, Mayur C. Shah, Neha Patel, Dipika Dalwadi, and J. J. Vora. "Potentiometric Studies on the Protonation Constants and Protonation Energies of Some Diamines in Methanol + Water Mixtures." E-Journal of Chemistry 4, no. 3 (2007): 313–19. http://dx.doi.org/10.1155/2007/978639.

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The protonation constants of diamines such as ethylenediamine, 1,2-diaminopropane, 1,3-diaminopropane,o-phenylenediamine,m-phenylene-diamine,p-phenylenediamine were determined on the basis of Bjerrum and Calvin method in methanol-water mixtures. A pH metric method was used for calculation of protonation constants. The effects of solvents on protonation constant have been determined at ionic strength 0.2 M dm-3(NaClO4) and temperature 30±0.1oC under nitrogen atmosphere. FORTRAN (IV) programs were used for calculation of protonation constants and distribution of species like H2L, HL, L in equilibrium state. The logarithm of the protonation constants decrease in aliphatic diamines and increase in aromatic diamines with increase in methanol content in mixed equilibria. The verification of constants are explained on the basis of solute-solvent interaction, solvation, proton transfer processes and dielectric constant of equilibria. Protonation energies have been calculated theoretically using computational methods and these protonation energies for aromatic diamines are higher than aliphatic diamines.
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31

Ahn, Jeonghun, and Sung Woon Cha. "Product Development Process Analysis Using Design Equilibrium Constant." Journal of the Korean Society for Precision Engineering 35, no. 9 (2018): 881–85. http://dx.doi.org/10.7736/kspe.2018.35.9.881.

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32

Laibman, David. "Non-constant Returns, Pareto Optimality and Competitive Equilibrium." Review of Political Economy 13, no. 4 (2001): 471–81. http://dx.doi.org/10.1080/09538250120099962.

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33

Schildhauer, T., E. Newson, and St Müller. "The Equilibrium Constant for the Methylcyclohexane–Toluene System." Journal of Catalysis 198, no. 2 (2001): 355–58. http://dx.doi.org/10.1006/jcat.2000.3133.

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34

Hui, Liu, Luo Zanchun, and Zhu Bingchen. "STUDY OF CHEMICAL EQUILIBRIA IN METHANOL SYNTHESIS II. Calculation of Equilibrium Constant Kp." Fuel Science and Technology International 12, no. 6 (1994): 829–43. http://dx.doi.org/10.1080/08843759408916209.

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35

Kasai, Rinshi S., Kenichi G. N. Suzuki, Eric R. Prossnitz, et al. "Full characterization of GPCR monomer–dimer dynamic equilibrium by single molecule imaging." Journal of Cell Biology 192, no. 3 (2011): 463–80. http://dx.doi.org/10.1083/jcb.201009128.

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Receptor dimerization is important for many signaling pathways. However, the monomer–dimer equilibrium has never been fully characterized for any receptor with a 2D equilibrium constant as well as association/dissociation rate constants (termed super-quantification). Here, we determined the dynamic equilibrium for the N-formyl peptide receptor (FPR), a chemoattractant G protein–coupled receptor (GPCR), in live cells at 37°C by developing a single fluorescent-molecule imaging method. Both before and after liganding, the dimer–monomer 2D equilibrium is unchanged, giving an equilibrium constant of 3.6 copies/µm2, with a dissociation and 2D association rate constant of 11.0 s−1 and 3.1 copies/µm2s−1, respectively. At physiological expression levels of ∼2.1 receptor copies/µm2 (∼6,000 copies/cell), monomers continually convert into dimers every 150 ms, dimers dissociate into monomers in 91 ms, and at any moment, 2,500 and 3,500 receptor molecules participate in transient dimers and monomers, respectively. Not only do FPR dimers fall apart rapidly, but FPR monomers also convert into dimers very quickly.
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36

Seki, Ichiro. "Determination of Equilibrium Constant of Calcium Oxidation by Slag-Metal Equilibrium Distribution Method." MATERIALS TRANSACTIONS 61, no. 5 (2020): 985–92. http://dx.doi.org/10.2320/matertrans.mt-mbw2019004.

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37

Malek, A., and S. Farooq. "Determination of Equilibrium Isotherms Using Dynamic Column Breakthrough and Constant Flow Equilibrium Desorption." Journal of Chemical & Engineering Data 41, no. 1 (1996): 25–32. http://dx.doi.org/10.1021/je950178e.

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38

Chakraborty, Uday. "A New Model for Constant Fuel Utilization and Constant Fuel Flow in Fuel Cells." Applied Sciences 9, no. 6 (2019): 1066. http://dx.doi.org/10.3390/app9061066.

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This paper presents a new model of fuel cells for two different modes of operation: constant fuel utilization control (constant stoichiometry condition) and constant fuel flow control (constant flow rate condition). The model solves the long-standing problem of mixing reversible and irreversible potentials (equilibrium and non-equilibrium states) in the Nernst voltage expression. Specifically, a Nernstian gain term is introduced for the constant fuel utilization condition, and it is shown that the Nernstian gain is an irreversibility in the computation of the output voltage of the fuel cell. A Nernstian loss term accounts for an irreversibility for the constant fuel flow operation. Simulation results are presented. The model has been validated against experimental data from the literature.
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39

Kresge, A. Jerry, and Qingshui Meng. "Carboxylic acid amide enols: keto-enol/enolate interconversion of N-methylindoline-2-one and its 2-thione and 2-selone analogs in aqueous solution." Canadian Journal of Chemistry 77, no. 9 (1999): 1528–36. http://dx.doi.org/10.1139/v99-169.

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Carbon-acid ionization constants, QaK (concentration quotient at ionic strength = 0.10 M), were determined by spectrophotometric titration in aqueous solution for N-methylindoline-2-one, pQaK = 15.70, N-methylindoline-2-thione, pQaK = 8.93, and N-methylindoline-2-selone, pQaK = 7.25. Rate profiles were also constructed for the thione and selone. These were interpreted, with support from the form of acid-base catalysis as well as solvent and substrate isotope effects, as representing keto - enol/enolate ion interconversion. That led to the enol acidity constant pQaE = 4.05 and the keto-enol equilibrium constant pKE = 4.88 for the thione and estimates of the limits on these quantities, pQaE< 3 and pKE > 4, for the selone.Key words: lactam, thiolactam, selenolactam, keto-enol equilibria, carbon-acid ionization constants.
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40

Marchi, Giuliano, Cesar Crispim Vilar, George O’Connor, Letuzia Maria de Oliveira, Adriana Reatto, and Thomaz Adolph Rein. "Surface Complexation Modeling in Variable Charge Soils: Prediction of Cadmium Adsorption." Revista Brasileira de Ciência do Solo 39, no. 5 (2015): 1395–405. http://dx.doi.org/10.1590/01000683rbcs20140529.

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ABSTRACT Intrinsic equilibrium constants for 22 representative Brazilian Oxisols were estimated from a cadmium adsorption experiment. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. Intrinsic equilibrium constants were optimized by FITEQL and by hand calculation using Visual MINTEQ in sweep mode, and Excel spreadsheets. Data from both models were incorporated into Visual MINTEQ. Constants estimated by FITEQL and incorporated in Visual MINTEQ software failed to predict observed data accurately. However, FITEQL raw output data rendered good results when predicted values were directly compared with observed values, instead of incorporating the estimated constants into Visual MINTEQ. Intrinsic equilibrium constants optimized by hand calculation and incorporated in Visual MINTEQ reliably predicted Cd adsorption reactions on soil surfaces under changing environmental conditions.
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41

Zhao, Pingping, Kaili Xiang, and Peimin Chen. "Partnerships of Bidders with Constant Relative Risk Aversions." Mathematical Problems in Engineering 2020 (April 7, 2020): 1–7. http://dx.doi.org/10.1155/2020/3925835.

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In this paper, we study a dynamic auction for allocating a single indivisible project while different participants have different bid values for the project. When the price rises continuously, the bidders can retreat the auction and obtain the compensation by the difference between the price at retreating time and the previous bid price. The final successful bidder achieves the project and pays compensations to others. We show that the auction of bidders with constant relative risk aversion (CRRA) has a unique equilibrium. While the relative risk aversion coefficient approaches to zero, the equilibrium with CRRA bidders would approach to the equilibrium with risk-neutral bidders.
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42

Mollin, Jiří, Jitka Dopitová, and Oldřiška Staňková. "Tautomerization of acetylacetone and relation of the tautomerization constant to other equilibrium parameters." Collection of Czechoslovak Chemical Communications 52, no. 12 (1987): 2850–58. http://dx.doi.org/10.1135/cccc19872850.

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The relative partial pressures of acetylacetone above mixed aqueous-organic solutions were measured chromatographically and the Gibbs energies of acetylacetone transfer from water to the mixed solvents were determined and separated into contributions from the keto and enol forms. The tautomerization equilibrium was related to other thermodynamic equilibria and the Gibbs energy of transfer of the keto form was correlated with that of acetone.
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43

Lunn, J. E., and T. ap Rees. "Apparent equilibrium constant and mass-action ratio for sucrose-phosphate synthase in seeds of Pisum sativum." Biochemical Journal 267, no. 3 (1990): 739–43. http://dx.doi.org/10.1042/bj2670739.

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The aim of this work was to use preparations from germinating seeds of Pisum sativum to determine the apparent equilibrium constant of the reaction catalysed by sucrose-phosphate synthase (EC 2.4.1.14) and to compare this with the mass-action ratio of the reaction in the seeds. The apparent equilibrium constant ranged from 5.3 at 0.25 mM-MgCl2, pH 7.0, to 62 at 10 mM-MgCl2, pH 7.5. The sucrose phosphate content of the seeds, 23 nmol/g fresh wt., was determined by separating sucrose phosphate from sucrose by ion-exchange chromatography and then measuring the sucrose released by alkaline phosphatase. Comparison of equilibrium constants and mass-action ratios in the cotyledons of 38 h-germinated seeds showed that the reactions catalysed by glucose-6-phosphate isomerase, phosphoglucomutase and UDP-glucose pyrophosphorylase are close to equilibrium, and those catalysed by sucrose-phosphate synthase and sucrose phosphatase are considerably displaced from equilibrium in vivo.
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44

Povar, Igor. "Détermination de la stabilité du complexonate peu soluble à partir des données pH-métriques." Canadian Journal of Chemistry 79, no. 7 (2001): 1166–72. http://dx.doi.org/10.1139/v01-065.

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A new method has been developed for the determination of the solubility product of complexonate of known composition; because of the initial composition of the heterogeneous mixture (lot a), it uses only the equilibrium values of the pH. For the determination of the stability constant in solution, these data have been completed with information on the solubility of the precipitate. We have shown that, on the basis of lot a and in the absence of reactions of formation of complexes in solution, it is possible to evaluate the equilibrium constants, since they are residuals of the compositions of the precipitate. We conclude on the possibility of applying this method to the test and standardization of ion-selective electrodes. The qualities and defect of the method are discussed. Otherwise, the values for the equilibrium constants and the equilibrium as well as the residual concentrations that we have calculated for a series of real systems from known experimental data are in good accord with those reported in tables under the same conditions.Key words: potentiometric method, heterogeneous system, slightly soluble complexonate, complexone, equilibrium concentration, solubility product, stability constant, hydrolysis reaction.[Journal Translation]
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45

Kudo, Yoshihiro, Tomohiro Amano, and Satoshi Ikeda. "Determination of Distribution Equilibrium-Potential Differences Based on Extraction with Several Crown Ethers by Nitrobenzene, 1,2-Dichloroethane and Dichloromethane." International Journal of Chemistry 9, no. 4 (2017): 110. http://dx.doi.org/10.5539/ijc.v9n4p110.

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Extraction constants (Kex± & Kex) were determined at 298 K for the extraction of sodium picrate (NaPic) by nitrobenzene (NB), 1,2-dichloroethane (DCE) and dichloromethane using 3m-crown-m ethers and their benzo-derivatives (m = 5, 6; abbreviated as L) together with the determination of conditional distribution constants (KD,Pic) of picrate ion, Pic-, into these diluents. The K1,org (= [NaLPic]org/[NaL+]org[Pic-]org) values at the organic (org) phases, such as NB & DCE, were calculated from the relation Kex/Kex± = K1,org. Distribution equilibrium-potential differences (Dfeq) at extraction equilibria were evaluated from the equation Dfeq = -0.05916´(log KD,Pic - constant) at 298 K. Correlations of the above equilibrium constants, particularly Kex±, with Dfeq were examined. Furthermore, the standard formal potentials for Na+ transfers across the interfaces were briefly evaluated from calculated Dfeq, [Na+] and [Pic-]org. The above extraction systems were characterized by K1,org and the complex formation constants of Na+ with L in the org phases.
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46

McClelland, Robert A., Pratima Sukhai, Karen M. Engell, and Poul E. Sorensen. "Hydration equilibria of 9-acridinecarboxaldehyde." Canadian Journal of Chemistry 72, no. 11 (1994): 2333–38. http://dx.doi.org/10.1139/v94-297.

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Hydration rate constants and equilibrium constants have been obtained for 9-acridinecarboxaldehyde in aqueous solution. Under acidic conditions where the acridine is protonated, signals for the hydrate and free aldehyde forms can be observed as separate species in the 1H NMR spectrum. Integration provides the hydration equilibrium constant[Formula: see text] Using an apparent acidity constant obtained from a spectroscopic titration curve, the rate–pH profile was fitted to provide the hydration constant for the equilibration of the neutral acridines, KH = 0.07. This analysis also provides the acidity constants for the two acridinium ions, the aldehyde with pK = 3.78 and the hydrate with pK = 5.36. A comparison with the 4-pyridinecarboxaldehdye system reveals that the [Formula: see text] ratios for the acridine and pyridine are the same within experimental error, but that the acridine and acridinium aldehydes are 20-fold less hydrated than their pyridine analogs. A comparison with benzaldehydes reveals that, in their reactivities, the two heterocyclic aldehydes behave in a similar manner. Thus, for example, plots of log kH for the acid-catalyzed dehydration and hydrations versus log Kh for the equilibrium hydration show single correlation lines including the points for the benzaldehydes and heterocyclic aldehydes (but not the aliphatic aldehydes).
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47

Drazic, Branka, Gordana Popovic, Ratomir Jelic, et al. "Acid-base equilibria of the Zn(II) and Fe(III) complexes with condensation products of 2-acetylpyridine and the dihydrazide of oxalic and malonic acid." Journal of the Serbian Chemical Society 74, no. 3 (2009): 269–77. http://dx.doi.org/10.2298/jsc0903269d.

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Acid-base equilibria of Zn(II) and Fe(III) complexes with N',N'2-bis- [(1E)-1-(2-pyridyl)ethylidene]ethanedihydrazide (ligand L1) and N',N'2-bis[(1E)- -1-(2-pyridyl)ethylidene]propanedihydrazide (ligand L2), i.e., [Fe(L1)Cl2(H2O)], [Fe(L2)Cl(H2O)]2+, [Zn(L1)(H2O)3]+ and [Zn(L2)(H2O)2]2+, which expressed cytotoxic activity, were investigated in aqueous media. The equilibrium constants were determined potentiometrically at 25?C at a constant ionic strength of 0.10 mol/dm3 (Na2SO4). The results showed that at pH < 8 both the Fe(III) complexes studied here have three, while [Zn(L1)(H2O)3]+ and [Zn(L2)(H2O)2]2+ have one and two titratable protons, respectively. Based on the obtained values for the equilibrium constants, protonation schemes of the examined complexes are proposed.
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48

Singare, Pravin U., Akmal L. Khan Mohammed, and N. N. Dixit. "Comparative Study of Uni-Univalent H+/Na+ and Uni-Bivalent H+/Ca2+ Ion Exchange Reactions Using Nuclear Grade Resin Indion-223." International Letters of Chemistry, Physics and Astronomy 33 (May 2014): 127–35. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.33.127.

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The present paper deals with the ion exchange equilibrium studies of uni-univalent and uni-bivalent ion exchange reactions using nuclear grade anion exchange resin Indion-223 in H+ form towards Na+ and Ca2+ ions in the solution. It was observed that with rise in temperature the equilibrium constants K values for H+/Na+ uni-univalet ion exchange reaction increases from 0.01389 to 0.01855. Similarly for H+/Ca2+ uni-bivalet ion exchange reaction the equilibrium constants K values increases from 0.000397 to 0.000639. The increase in equilibrium constant values with rise in temperature indicate endothermic ion exchange reactions having the enthalpy change values of 25.55 and 38.92 kJ/ mol respectively.
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49

Preočanin, Tajana, Željka Majić, Davor Kovačević, and Nikola Kallay. "Adsorption of Oxalic Acid onto Hematite: Application of Surface Potential Measurements." Adsorption Science & Technology 25, no. 6 (2007): 429–37. http://dx.doi.org/10.1260/026361707783908300.

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The surface potential at the hematite/aqueous oxalic acid interface was measured by means of a hematite Single Crystal Electrode. This allowed the simultaneous interpretation of the surface potential, electrokinetic potential and adsorption data for the adsorption of oxalic acid onto a hematite surface. Based on the Surface Complexation Model, this interpretation suggested that the oxalate ion is bound to a metal ion at the solid surface to form a singly-charged oxalate-surface complex, with the charge being exposed to the potential at the outer Helmholtz layer. A number of equilibrium parameters describing the interfacial equilibrium were obtained. Thus, for the two protonation steps of the surface sites, the thermodynamic equilibrium constants were log K1 = 7.1 ± 0.4 and log K2 = 5.2 ± 0.4, respectively. Two assumptions were tested with regard to the adsorption equilibrium constant, i.e. the charge of the surface complex is exposed to the inner surface potential, ψ0, or to the outer surface potential, ψd. The constancy of the interfacial equilibrium constants led to the conclusion the latter assumption was the more appropriate. The observed value of the adsorption equilibrium constant was log Kads = 3.0 ± 0.8. It was shown that measurement of the surface potential by Single Crystal Electrodes is a helpful tool in elucidating the equilibrium behaviour of the complex at the interface.
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50

Baciocchi, R., A. Chiavola, and R. Gavasci. "Ion exchange equilibria of arsenic in the presence of high sulphate and nitrate concentrations." Water Supply 5, no. 5 (2005): 67–74. http://dx.doi.org/10.2166/ws.2005.0040.

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The aim of this work was to develop a quantitative description of the ion exchange equilibria of arsenic on a strong anionic resin, in the presence of nitrates and sulphates. First, the ion exchange equilibrium data of As(V) and NO3− on a strong anionic resin in chloride form were obtained and described with a model based on the mass action law. Namely, assuming ideal behaviour for both solution and resin phase, the thermodynamic constant of the As(V)/Cl− and NO3−/Cl− ion exchange equilibria were estimated by fitting of experimental data. Then, these equilibrium constants were used to predict the ion exchange behaviour of the ternary system As(V)/NO3−/Cl−, providing a rather good agreement with experimental results. The ion exchange equilibria involving sulphate ions were also studied, showing a very high affinity to the resin phase. This behaviour did not allow a quantitative robust modelling of the equilibrium pattern. The results discussed in this paper represent a first step toward the development of a comprehensive modelling of the ion exchange process for the removal of As(V) from surface and groundwater in the presence of competitive, naturally occurring anions.
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