• Title/Summary/Keyword: Equation of a first-order chemical reaction

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A Study of Transonic Premixed Combustion in a Diverging Channel Using Asymptotic Analysis (점근해석을 이용한 확대형 채널 내의 천음속 예혼합 연소에 관한 연구)

  • Lee, Jang-Chang
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.8
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    • pp.75-83
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    • 2005
  • A steady transonic dilute premixed combustion in a diverging channel is investigated by using asymptotic analysis. This model explores the nonlinear interactions between the near-sonic speed of the flow, the small changes in geometry from a straight channel, and the small heat release due to the one-step first-order Arrhenius chemical reaction. The reactive flow is described by a nonhomogeneous transonic small-disturbance (TSD) equation coupled with an ordinary differential equation for the calculation of the reactant mass fraction in the combustible gas. Also the asymptotic analysis reveals the similarity parameters that govern the reacting flow problem. The results show the complicated nonlinear interaction between the convection, reaction, and geometry effects and its effect on the flow behavior.

Kinetic Study for Aquation of $cis-[Co(en)_2(NH_3)Cl]^{2+}$ in $Hg^{2+}$ Aqueous Solution ($Hg^{2+}$수용액에서 $cis-[Co(en)_2(NH_3)Cl]^{2+}$의 아쿠아반응에 대한 속도론적 연구)

  • Byung-Kak Park;Gil-Jun Lee;Jae-Weon Lee;Joo-Sang Lim
    • Journal of the Korean Chemical Society
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    • v.32 no.3
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    • pp.227-232
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    • 1988
  • A kinetic study was made to determine the mechanism of the aquation of $cis-[Co(en)_2(NH_3)Cl]^{2+}\;in\;Hg^{2+}$ aqueous solution. The progress of reaction was followed UV/vis-spectrophotometrically by a measurement of the absorbance at a specific wave length (530nm) of $cis-[Co(en)_2(NH_3)Cl]^{2+}$ as a function of time. The experimental results have shown that the reaction rate is dependent upon the concentration of $Hg^{2+}$ that act as a catalyst. And it was found that the overall reaction proceed with second order, first order with respect to Co(III) complex and $Hg^{2+}$. Activation parameters, ${\Delta}H^{\neq}\;and\;{\Delta}S^{\neq}$, were obtained as 12.9 kcal/mol and -19.3 e.u., respectively. We have proposed a plausible reaction mechanism which is consistent with the observed rate equation.

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Study of Kinetics for Removal H2S by Natural Manganese ore Sorbent (황화수소 제거를 위한 천연망간광석 탈황제의 반응 속도 연구)

  • Yoon, Yeo Il;Kim, Myung Wook;Kim, Sung Hyun
    • Clean Technology
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    • v.7 no.3
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    • pp.187-194
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    • 2001
  • The desulfurization process which belongs to the gas refining part is the unit process that eliminates $H_2S$ and COS in the coal gas formed by the coal gasification part in the integrated gasification combined cycle(IGCC). In this study, natural manganese ores were selected as the raw material of the desulfurization sorbent due to economical efficiency. Initial rates for the reactions between $H_2S$ and desulfurization sorbent using natural manganese ores were determined in a temperature range of $400{\sim}800^{\circ}C$ using a thermobalance reactor. All reactions were first order with respect to $H_2S$ and were in accord with the Arrhenius equations. When sulfidation reaction was controlled by diffusion, the temperature dependence of the effective diffusivity was given by the Arrhenius equation. Activation energies and frequency factors were obtained from the product layer diffusion coefficient of various sorbents by plotting as Arrhenius equation form.

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Limitations of the Transition State Variation Model. Part 8. Dual Reaction Channels for Solvolyses of 3,4-Dimethoxybenzenesulfonyl Chloride

  • Koo, In-Sun;Kwon, Eun-Ju;Choi, Ho-June;Yang, Ki-Yull;Park, Jong-Keun;Lee, Jong-Pal;Lee, Ikc-Hoon;Bentley, T. William
    • Bulletin of the Korean Chemical Society
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    • v.28 no.12
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    • pp.2377-2381
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    • 2007
  • Solvolyses of 3,4-dimethoxybenzenesulfonyl chloride (DSC) in water, D2O, CH3OD, and in aqueous binary mixtures of acetone, acetonitrile, 1,4-dioxane, ethanol, methanol, and 2,2,2-trifluoroethanol (TFE) have been investigated at 25.0 oC. Kinetic solvent isotope effects (KSIE) in water and in methanol and product selectivities in alcohol-water mixtures are also reported. The Grunwald-Winstein plot of first-order rate constants for the solvolyic reaction of DSC with YCl shows marked dispersions into separated lines for various aqueous mixtures. With use of the extended Grunwald-Winstein equation, the l and m values obtained are 1.12 and 0.58 respectively for the solvolyses of DSC. The relatively large magnitude of l is consistent with substantial nucleophilic solvent assistance. From Grunwald-Winstein plots the rate data are dissected approximately into contributions from two competing reaction channels. This interpretation is supported for alcohol-water mixtures by the trends of product selectivities, which show a maximum for ethanol-water mixtures. From the KSIE of 1.45 in methanol, it is proposed that the reaction channel favored in methanolwater mixtures and in all less polar media is general-base catalysed and/or is possibly (but less likely) an addition-elimination pathway. Also, the KISE value of 1.35 for DSC in water is expected for SN2-SN1 processes, with minimal general base catalysis, and this mechanism is proposed for solvolyses in the most polar media.

Transition-State Variation in the Solvolyses of para-Substiuted Phenyl Chloroformates in Alcohol-Water Mixtures

  • 구인선;양기율;강금덕;이익춘
    • Bulletin of the Korean Chemical Society
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    • v.19 no.9
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    • pp.968-973
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    • 1998
  • Solvolyses of para-substituted phenyl chloroformates in water, $D_2O,\;CH_3OD$, 50% $D_2O-CH_3OD$, and in aqueous binary mixtures of acetone, ethanol, methanol are investigated at 25.0 ℃. Product selectivities are reported for a wide range of ethanol-water and methanol-water solvent compositions. These data are interpreted using the Grunwald-Winstein relationship, Hammett equation, and quantum mechanical model. Grunwald-Winstein plots of the first-order rate constants for phenyl chloroformates with $Y_{Cl}$ (based on 1-adamantyl chloride) show marked dispersions into three separate curves for the three aqueous mixtures with a small m value and a rate maximum for aqueous alcohol solvents. To account for these results, third-order rate constants, $k_{ww},\;k_{aw},\;k_{wa}$, and $k_{aa}$ were calculated from the observed $k_{ww}\;and\;k_{aa}$ values together with $k_{aw}\;and\;k_{wa}$ calculated from the computer fit. The kinetic solvent isotope effects determined in water and methanol are consistent with the proposed mechanism of the general base catalyzed carbonyl addition-elimination for para-substituted phenyl chloroformates solvolyses based on mass law and stoichiometric salvation effect studies. This study has shown that the quantum mechanical model predicts transition state variation correctly for $S_N2\;like\;S_AN$ reaction mechanism of para-substituted phenyl chloroformates.

Synthesis of Tetrafluoroethylene from the Pyrolysis of Chlorodifluoromethane in the Presence of Steam (과열 수증기를 이용한 클로로디플루오르메탄 열분해 반응에 의한 테트라플루오르에틸렌의 합성)

  • Han, Myungwan;Kim, Beom-Sik;Kim, Chul-Ung;Lee, Jung-Min
    • Applied Chemistry for Engineering
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    • v.10 no.2
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    • pp.190-195
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    • 1999
  • The thermal pyrolysis of chlorodifluoromethane (R22) for producting tetrafluoroethylene (TFE) has been studied using the tubular reactor designed by the authors. The reaction temperature over $600{\sim}850^{\circ}C$, residence time over 0.005~0.6 sec, and steam/R22 ratio 3 to 30 were varied through experiments to analyze the effect of these variables on the conversion of R22 and selectivity for TFE. We have provided the guidelines for the optimal operation and design for the pyrolysis reactor. With increasing the dilution ratio, not only the conversion of R22 but also the selectivity for TFE increase. The optimum range of reaction temperature was $700{\sim}750^{\circ}C$ and the residence time 0.07~0.1 sec. In the kinetic study, first order rate equation was fitted well with the experimental data. This indicates that the main reaction step is a $CF_2$ generation from R22 pyrolysis. The range of activation energy for the rate constant was obtained 44.7~48 kcal/mol.

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The Kinetics and Activation Energy for the Mutarotation or Optically Active Poly(trans-5-methyl-L-proline (광활성 Poly(trans-5-methyl-L-proline)의 변광회전에 대한 반응속도와 활성화에너지)

  • Han Man Jung
    • Journal of the Korean Chemical Society
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    • v.22 no.6
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    • pp.386-395
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    • 1978
  • The rates of the forward mutarotation of poly(trans-5-methyl-L-proline) in trifluoro-ethanol and of the reverse mutarotation in trifluoroethanol-n-butanol (1:4 v/v) have been measured at a number of temperatures and polymer concentrations. It was found that both mutarotations are of first-order with respect to the polymer concentration. A modified Arrhenius equation to evalute the activation energy was derived for the reaction kinetics, in which the relation between the measured physical properties and concentration, and the order of tle reaction are uncertain. The activation energies for the forward and reverse mutarotation were found to be 32.5 and 33.5 kcal per residue mole, respectively, which are about 10 kcal per residue mole higher than the $E_a$ for the mutarotation of polyproline (the resonance energy of amide bonds). The excessive quantity of the activation energy was attributed to the steric barrier between carbonyl and methyl groups during the cis-trans isomerization of amide bonds in the polymer.

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A Study on the Solvent Extraction Mechanism of Nickel(Ⅱ) with N-Benzylisonitrosoacetylacetone Imine by Spectrophotometry (분광광도법에 의한 Ni(Ⅱ)-N-Benzylisonitrosoacetylacetone Imine착물의 용매추출 반응메카니즘)

  • Heung Lark Lee;Zun Ung Bae;Dong-Gyu Kim
    • Journal of the Korean Chemical Society
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    • v.36 no.4
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    • pp.546-551
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    • 1992
  • Reaction mechanism on the solvent extraction of nickel(Ⅱ) with N-benzylisonitrosoacetylacetone imine(HIAANB) was studied spectrophotometrically. Absorbance was measured by changing the ligand HIAANB concentration in the chloroform organic phase and the pH values in the agueous solution phase. From the absorbance data, the reaction rate was found to be the first order for HIAANB concentration and the inverse first one for [$H^+$]. The rate determining step of the extraction reaction and the rate equation are as follows; $Ni^{2+}$+HIAANB ${\to}$ Ni-IAANB$^+$$H^+$ -d[Ni$^{2+}$] / dt = K'[Ni$^{2+}$][HIAANB]$_0$ / [H$^+$] Calibration curve for the spectrophotometric determination of nickel(Ⅱ) ion in the aqueous solution was linear below the concentration of 1.17 ppm at the optimum experimental condition. And the ligand-to-metal ratio, the relationship between extractability and pH of the aqueous phase, and the effect of diverse ion on the determination of nickel(Ⅱ) ion were examined.

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Effect of Alkali Metal Ions on Nucleophilic Substitution Reactions of 4-Nitrophenyl X-Substituted Benzoates with Alkali Metal Ethoxides in Anhydrous Ethanol

  • Seo, Jin-A;Kim, Song-I;Hong, Yeon-Ju;Um, Ik-Hwan
    • Bulletin of the Korean Chemical Society
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    • v.31 no.2
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    • pp.303-308
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    • 2010
  • Pseudo-first-order rate constants ($k_{obsd}$) have been measured spectrophotometrically for nucleophilic substitution reactions of 4-nitrophenyl benzoate (5a), 4-nitrophenyl 4-methoxybenzoate (5b), and 4-nitrophenyl 4-hydroxybenzoate (5c) with alkali metal ethoxides, $EtO^-M^+$ ($M^+=Li^+$, $Na^+$ and $K^+$) in anhydrous ethanol (EtOH) at $25.0{\pm}0.1^{\circ}C$. The plots of $k_{obsd}$ vs. [$EtO^-M^+$] exhibit upward curvatures in all cases, indicating that $M^+$ ions catalyze the reactions and ionpaired $EtO^-M^+$ species are more reactive than dissociated $EtO^-$. Second-order rate constants for reactions with dissociated $EtO^-$ and ion-paired $EtO^-M^+$ (i.e., $k_{EtO^-}$ and $k_{EtO^-M^+}$, respectively) have been calculated from ion-pair treatment for the reactions of 5a and 5b. However, such ion-pair treatment has failed to determine $k_{EtO^-}$ and $k_{EtO^-M^+}$ values for the reactions of 5c. It has been concluded that reactions of 5a and 5b are catalyzed by one metal ion, which increases electrophilicity of the reaction center through coordination on the carbonyl oxygen. In contrast, reactions of 5c have been suggested to involve two metal ions, i.e., the one coordinated on the carbonyl oxygen increases the electrophilicity of the reaction center while the other one associated on the phenoxy oxygen decreases the charge repulsion between the anionic reagents (i.e., $EtO^-$ and deprotonated 5c). It has been found that the rate equation derived from the mechanism involving two metal ions fits nicely to the kinetic results obtained for the reactions of 5c.

Kinetic Studies on Solvolyses of Substituted Cinnamoyl Chlorides in Alcohol-Water Mixture (알코올-물 혼합 용매계에서 치환된 염화신남오일의 가용매분해반응에 관한 속도론적 연구)

  • Koo, In Sun;Kim, Jung Soon;An, Sun Kyoung;Yang, Kyu Il;Lee, Ic Hoon
    • Journal of the Korean Chemical Society
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    • v.43 no.5
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    • pp.527-534
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    • 1999
  • Solvolyses of para-substituted cinnamoyl chlorides in aqueous binary mixtures of acetone, ethanol, methanol were investigated at 25.0$^{\circ}C$. These data were interpreted using the Grunwald-Winstein relationship, Hammett equation, and quantum mechanical model. Grunwald-Winstein plots of the first-order rate constants for para-substituted cinnamoyl chlorides with $Y_{CI}$ showed marked dispersions into three separate curves for the three aqueous mixtures with a large m vaIue for aqueous alcohol solvents. This study has shown that the potential energy surface and quanturm mechanical model predict transition state variation correctly for $S_N1$ like $S_N2$ reaction mechanism of para-substituted cinnamoyl chlorides.

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