• Title/Summary/Keyword: kinetic equation

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The Grunwald-Winstein Relationship in the Solvolysis of β-Substituted Chloroformate Ester Derivatives: The Solvolysis of 2-Phenylethyl and 2,2-Diphenylethyl Chloroformates

  • Park, Kyoung-Ho;Yang, Gi-Hoon;Kyong, Jin Burm
    • Bulletin of the Korean Chemical Society
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    • v.35 no.8
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    • pp.2263-2270
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    • 2014
  • Solvolysis rate constants of 2-phenylethyl-(2-$PhCH_2CH_2OCOCl$, 1) and 2,2-diphenylethyl chloroformate (2,2-$Ph_2CHCH_2OCOCl$, 2), together with the previously studied solvolyses of ${\alpha}$- and ${\beta}$-substituted chloroformate ester derivatives, are reported in pure and binary solvents at $40.0^{\circ}C$. The linear free energy relationship (LFER) and sensitivities (l and m) to changes in solvent nucleophilicity ($N_T$) and solvent ionizing power ($Y_{Cl}$) of the solvolytic reactions are analyzed using the Grunwald-Winstein equation. The kinetic solvent isotope effects (KSIEs) in methanol and activation parameter values in various solvents are investigated for 1 and 2. These results support well the bimolecular pathway with same aspects. Furthermore, the small negative values of the entropies of activation of solvolysis of 1 and 2 in the highly ionizing aqueous fluoroalcohols are consistent with the ionization character of the rate-determining step, and the KSIE values of 1.78 and 2.10 in methanol-d indicate that one molecule of solvent acts as a nucleophile and the other acts as a general-base catalyst. It is found that the ${\beta}$-substituents in alkyl chloroformate are not the important factor to decide the solvolysis reaction pathway.

Biosorption of Lead $(Pb^{2+})$ from Aqueous Solution by Rhodotorula aurantiaca

  • Cho, Dae-Haeng;Yoo, Man-Hyong;Kim, Eui-Yong
    • Journal of Microbiology and Biotechnology
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    • v.14 no.2
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    • pp.250-255
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    • 2004
  • The aim of this work was to investigate the adsorption isotherm and kinetic model for the biosorption of lead $(Pb^{2+})$ by Rhodotorula aurantiaca and to examine the environmental factors for this metal removal. Within five minutes of contact, $Pb^{2+}$ sorption reached nearly 86% of the total $Pb^{2+}$ sorption. The optimum initial pH value for removal of $Pb^{2+}$ was 5.0. The percentage sorption increased steeply with the biomass concentration up to 2 g/l and thereafter remained more or less constant. The Langmuir sorption model provided a good fit throughout the concentration range. The conformity of these data to the Langmuir model indicated that biosorption of $Pb^{2+}$ by R. aurantiaca could be characterized as a monolayer, single-site type phenomenon with no interaction between ions adsorbed in neighboring sites. The maximum $Pb^{2+}$ sorption capacity $(q_{max})$ and Langmuir constant (b) were 46.08 mg/g of biomass and 0.04 l/mg, respectively. The pseudo second-order equation was well fitted to the experimental data. The correlation coefficients for the linear plots of t/q against t for the second-order equation were 0.999 for all the initial concentrations of biosorbent for contact times of 180 min. The theoretical $q_{eq}$ value was very close to the experimental $q_{eq}$ value.

Performance Estimation of SBR Aerobic Digestion Combined with Ultrasonication by Numerical Experiment (수치실험을 통한 초음파 결합형 SBR 호기성 소화의 거동 예측)

  • Kim, Sunghong;Kim, Donghan;Lee, Dongwoo
    • Journal of Korean Society of Water and Wastewater
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    • v.27 no.6
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    • pp.815-826
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    • 2013
  • Using a developed mathematical model and calibrated kinetic constants, numerical experiments for a aerobic digestion of wastewater sludge by SBR aerobic digestion process combined with ultrasonication (USSBR) were performed in this study. It simulated well the phenomena of the decomposition of particulate organics and the release of organic nitrogen and transformation. To achieve 40 % of particulate organics removal, USSBR process requires only 6 days of SRT and 14 W/L of ultrasonic power whereas SBR aerobic digestion process requires 12 days of SRT. Based on the model simulation results, an empirical equation was presented here. This equation will be used to predict digestion efficiency for the given variables of SRT and ultrasonic power dose. USSBR aerobic digestion process can reduce the nitrogen concentration. The optimal operation strategy for the simultaneous removal of solids and soluble nitrogen in this process is estimated to 7 days of SRT with 14 W/L of ultrasonic power dose while anoxic period was 6 hours out of 24 hours of cycle time. In this condition, 40 % of particulate organics as well as 36 % of total nitrogen will be removed and the soluble nitrogen concentration of the centrate will be lower less then 40 mg/L.

Effect of Propene($C_3H_6$) ON NO-$NO_2$ Conversion Process in a Pulsed Corona Discharge (펄스코로나 방전에서 프로핀($C_3H_6$)이 NO-$NO_2$ 변환에 미치는 영향에 관한 연구)

  • 박광서;전배혁;전광민
    • Transactions of the Korean Society of Automotive Engineers
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    • v.8 no.5
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    • pp.67-77
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    • 2000
  • Investigated was the effect of propene(C3H6) on the NO-NO2 conversion in dry exhaust gases from lean burn engine using a pulsed corona discharge. A kinetic model was developed to characterize the plasma chemistry in simulated exhausts containing propene. The model uses ELENDIF program to solve Boltzmann equation for electron energy distribution function, and CHEMKIN-II program to solve stiff ODE(ordinary differential equation) problems for species concentrations. The corona discharge energy per pulse and the time-space averaged E/N were obtained by fitting the model to experimental data. The model calculation shows good agreement for NO and NO2 concentrations with the experimental data, and predicts the formation of byproducts such as CH2O, CH3HCO, CO AND CH3NO2 Propene enhances the NOx conversion enormously at lower energy density and the NOx conversion increases with the increase of initial propene and oxygen concentration, and temperature.

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Kinetic Studies on the Nucleophilic Addition of Cysteine to 3,4-Methylenedioxyphenylmethylene Malononitrile (3,4-Methylenedioxyphenylmethylene Malononitrile에 대한 Cysteine의 친핵성 첨가반응에 관한 반응속도론적 연구)

  • Tae-Rin Kim;Dong-Suk Rho;Young-Haeng Lee
    • Journal of the Korean Chemical Society
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    • v.26 no.6
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    • pp.407-413
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    • 1982
  • The rate constants of the nucleophilic addition of cysteine to 3,4-methylenedioxyphenylmethylene malononitrile were determined by UV Spectrophotometry and a rate equation which can be applied over wide pH range was obtained. On the basis of rate equation, it may be concluded that the rate constants were dependent upon only the concentration of hydroxide ion above pH 9.0, however, below pH 6.0, the reaction were initiated by the addition of neutral cysteine molecule to carbon-carbon double bond and at pH 7.0~9.0, the addition of a neutral cysteine molecule and it's anion occurred competitively.

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Kinetics of water vapor adsorption by vacuum-dried jujube powder

  • Lee, Jun Ho;Zuo, Li
    • Food Science and Preservation
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    • v.24 no.4
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    • pp.505-509
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    • 2017
  • Water vapor adsorption kinetics of vacuum-dried jujube powder were investigated in temperature and relative humidity ranges of 10 to $40^{\circ}C$ and 32 to 75%, respectively. Water vapor was initially adsorbed rapidly and then reached equilibrium condition slowly. Reaction rate constant for water vapor adsorption of vacuum-dried jujube powder increased with an increase in temperature. The temperature dependency of water activity followed the Clausius-Clapeyron equation. The net isosteric heat of sorption increased with an increase in water activity. Good straight lines were obtained with plotting of $1/(m-m_0)$ vs. 1/t. It was found that water vapor adsorption kinetics of vacuum-dried jujube powder was accurately described by a simple empirical model, and temperature dependency of the reaction rate constant followed the Arrhenius-type equation. The activation energy ranged from 50.90 to 56.00 kJ/mol depending on relative humidity. Arrhenius kinetic parameters ($E_a$ and $k_0$) for water vapor adsorption by vacuum-dried jujube powder showed an effect between the parameters with the isokinetic temperature of 302.51 K. The information on water vapor adsorption kinetics of vacuum-dried jujube powder can be used to establish the optimum condition for storage and processing of jujube.

Rate and Product Studies of 1-Adamantylmethyl Haloformates Under Solvolytic Conditions

  • Park, Kyoung-Ho;Lee, Yelin;Lee, Yong-Woo;Kyong, Jin Burm;Kevill, Dennis N.
    • Bulletin of the Korean Chemical Society
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    • v.33 no.11
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    • pp.3657-3664
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    • 2012
  • Reactions of 1-adamantylmethyl chloroformate ($1-AdCH_2OCOCl$, 1) and 1-adamantylmethyl fluoroformate ($1-AdCH_2OCOF$, 2) in hydroxylic solvents have been studied. Application of the extended Grunwald-Winstein (G-W) equation to solvolyses of 1 in a variety of pure and binary solvents indicates an addition-elimination pathway in the majority of the solvents except an ionization pathway in the solvents of relatively low nucleophilcity and high ionizing power. The solvolyses of 2 show an addition-elimination pathway in all of the mixed solvents. The leaving group effects ($k_F/k_{Cl}$), the kinetic solvent isotope effects (KSIEs, $k_{MeOH}/k_{MeOD}$), and the enthalpy and entropy of activation for the solvolyses of 1 and 2 were also calculated. The selectivity values (S) for each solvent composition are reported and discussed. These observations are compared with those previously reported for other alkyl haloformate esters.

Design and Dynamic Analysis of Air-core Coil type Linear DC Motor (공심 코일형 리니어 DC 모터의 설계 및 동특성 해석)

  • Gang, Gyu-Hong;Hong, Jeong-Pyo;Kim, Gyu-Tak;Ha, Geun-Su;Jeong, Jung-Gi;Im, Tae-Bin
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.49 no.3
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    • pp.165-171
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    • 2000
  • This paper proposes a technique to design of air-core type Linear DC Motor(LDM) by using Equivalent Magnetizing Current(EMC) method and has performed its dynamic analysis. The magnetic flux density differ in accordance with airgap position due to difference of mechanical and magnetic air gap length and the coil shape has an influence on the thrust. Therefore, the analysis of magnetic field due to the magnets is carried out by EMC. The phenomena according to the various coil various coil shape under the same Magneto Motive Force(MMF) has been analyzed and its result is applied to the design process. The appropriateness of the proposed technique is confirmed by Finite Element Method(FEM) and its dynamic analysis is carried out from the coupling of the electrical circuit equation and mechanical kinetic equation.

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Study on Solvent Mediated Phase Transformation Kinetics of Hexanitrohexaazaisowurtzitane(HNIW) (용매를 매체로 한 Hexanitrohexaazaisowurtzitane(HNIW)의 상전이 속도에 관한 연구)

  • 김준형;임유진
    • Journal of the Korean Society of Propulsion Engineers
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    • v.4 no.4
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    • pp.9-17
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    • 2000
  • The crystal growth and dissolution rates were calculated by solving a model equation, which involved the dissolution of the metastable phase($\beta$-HNIW) and growth of the stable phase($\varepsilon$-HNIW), together with the mass balance equation. The model has been successfully used to simulate available kinetic data for the $\beta$$\longrightarrow$$\varepsilon$ polymorphic transformation via a solution phase. From the effectiveness factor based on the two-step model, it was found that the surface integration contribution to the process was comparatively small, and a diffusion dependency decreased with an increase of the mass fraction of chloroform in the mixed solvents of ethyl acetate and chloroform. Appling these kinetics in process simulation allowed for the prediction of the product size of $\varepsilon$-HNIW.

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Simulation of Capacitively Coupled RF Plasma; Effect of Secondary Electron Emission - Formation of Electron Shock Wave

  • Park, Seung-Kyu;Kim, Heon-Chang
    • Journal of the Semiconductor & Display Technology
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    • v.8 no.3
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    • pp.31-37
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    • 2009
  • This paper presents one and two dimensional simulation results with discontinuous features (shocks) of capacitively coupled rf plasmas. The model consists of the first two and three moments of the Boltzmann equation for the ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The local field and drift-diffusion approximations are not employed, and as a result the charged species conservation equations are hyperbolic in nature. Hyperbolic equations may develop discontinuous solutions even if their initial conditions are smooth. Indeed, in this work, secondary electron emission is shown to produce transient electron shock waves. These shocks form at the boundary between the cathodic sheath (CS) and the quasi-neutral (QN) bulk region. In the CS, the electrons emitted from the electrode are accelerated to supersonic velocities due to the large electric field. On the other hand, in the QN the electric field is not significant and electrons have small directed velocities. Therefore, at the transition between these regions, the electron fluid decelerates from a supersonic to a subsonic velocity in the direction of flow and a jump in the electron velocity develops. The presented numerical results are consistent with both experimental observations and kinetic simulations.

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