• 제목/요약/키워드: Redlich-Kister polynomial

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양친매성 2-butoxyethanol과 물 혼합계에서의 과잉 엔탈피 및 활동도 계수 (Excess Enthalpies and Activity Coefficients for the Binary Nonionic Amphiphile 2-Butoxyethanol/Water System)

  • 임경희
    • 한국응용과학기술학회지
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    • 제17권2호
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    • pp.132-138
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    • 2000
  • Excess enthalpies ($H^{E}$) were measured by isothermal flow calorimetry for the nonionic amphiphile 2-butoxyethanol/water mixtures at 10 different temperatures (48.5 to $70^{\circ}C$) around and above the lower consolute solution temperature, $T_{lc}$. $H^{E}$ exhibits U-shape for the binary mixtures, and is large and negative which reflects substantial interaction between two chemical species. When the commonly used, semi-empirical Redlich-Kister (RK) polynomials were fitted to the measured $H^{E}$, plots of $H^{E}$ vs. weight fraction provided more accurate fitting with fewer parameters than conventionally drawn $H^{E}$ vs. mole fraction plots. This was due to the enhanced symmetry of $H^{E}$ vs. weight fraction plots. Using the fitted Redlich-Kister polynomials and the Gibbs-Helmholtz relation, temperature dependence of the activity coefficients were found and compared to the values determined from vapor-liquid equilibria. The activity coefficients were in the range of one to three, indicating that the binary system deviates from ideality but not substantially. They slightly depended on temperature and the temperature effect was equivalent to 10 % change in the activity coefficients.

톨루엔-크레졸의 정압 기-액 평형 (Isobaric Vapor-Liquid Equilibrium of Toluene and Cresol Systems)

  • 강동육;장회구;한창남;노선균;조동련;강춘형
    • Korean Chemical Engineering Research
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    • 제47권6호
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    • pp.755-761
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    • 2009
  • 일반적으로 비등점의 차이가 큰 물질들은 그 물리적 성질의 차이로 인해 혼합물에서 비이상적인 상거동을 보이며, 이러한 혼합물의 상거동 특성을 이해하기 위해서는 정확한 실험적 데이터가 필요하다. 본 연구에서는 재순환 평형조가 포함된 기-액 상평형 장치를 사용하여 10, 30, 60 kPa에서 톨루엔과 크레졸 혼합물에 대한 정압 기-액 평형 실험을 행하였다. 측정한 기-액 평형 데이터는 NRTL과 UNIQUAC 모델식을 이용하여 잘 적합할 수 있었으며 Gibbs/Duhem 식에 근거한 열역학적 건전성 테스트를 수행하여 실험결과의 건전성을 확인하였다. 한편, 혼합물의 과잉몰부피를 측정하여 Redlich-Kister 다항식으로 나타내었다.

감압하에서 1-propanol과 Bromochloromethane의 정압 기-액 평형 (Isobaric Vapor-Liquid Equilibrium of 1-propanol and Bromochloromethane System at Subatmospheric Pressures)

  • 장회구;강춘형
    • 공업화학
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    • 제21권3호
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    • pp.295-300
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    • 2010
  • 1-propanol과 bromochloromethane 혼합물은 공비점의 형성이나 큰 휘발성 차이 때문에 실제 증류탑이나 흡수탑 등의 단위 공정에서 효율적이고 경제적인 운전이 쉽지 않다. 이처럼 비이상성이 큰 혼합물을 효과적으로 다루기 위해서는 혼합물에 대한 기-액 평형 등의 열역학적인 정보가 필수적이다. 본 연구에서는 재순환 기-액 평형장치를 이용하여 일정 압력 하에서 30 kPa에서 70 kPa까지 1-propanol과 bromochloromethane 혼합물의 기-액 평형을 측정하였으며 얻어진 실험 데이터를 UNIQUAC과 NRTL 모델식을 이용하여 상관하였고 과잉 Gibbs 에너지와 활동도 계수를 추산하였다. 또한 Gibbs/Duhem식에 근거한 열역학적 건전성 테스트를 수행하였고 진동 밀도계를 사용하여 이성분계의 과잉 몰부피를 측정하였으며 그 결과를 Redlich-Kister다항식으로 상관하였다.

298.15~318.15 K 에서 2-브로모프로판-메탄올 이성분 혼합물의 밀도, 점성도, 여분 성질 (Densities, Viscosities and Excess Properties of 2-Bromopropane - Methanol Binary Mixtures at Temperature from (298.15 to 318.15) K)

  • Li, Hua;Zhang, Zhen;Zhao, Lei
    • 대한화학회지
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    • 제54권1호
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    • pp.71-76
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    • 2010
  • 298.15~318.15 K 온도에서 디지탈 진동 U-tube densimeter 와 Ubbelohde 모세관 점성계을 사용하여 2-브로모프로판/메탄올 이성분 혼합물의 밀도와 점성도를 측정하였다. 온도와 농도에 대한 밀도와 점성도 상호 의존 관계를 조사하였다. 이성분 혼합물의 여분 몰부피와 여분 점성도를 실험으로 얻어진 밀도와 점성돌로부터 계산하여 구하였다. 모델이 실험치와 잘부합됨을 발견하였다.

Excess Volumes, Speeds of Sound, Isentropic Compressibilities and Viscosities of Binary Mixtures of N-Ethyl Aniline with Some Aromatic Ketones at 303.15 K

  • Gowrisankar, M.;Sivarambabu, S.;Venkateswarlu, P.;Kumar, K. Siva
    • Bulletin of the Korean Chemical Society
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    • 제33권5호
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    • pp.1686-1692
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    • 2012
  • Densities (${\rho}$), Viscosities (${\eta}$) and ultrasonic speeds (u) of pure acetophenone (AP), propiophenone (PP), $p$-methyl acetophenone ($p$-MeAP), $p$-chloroacetophenone ($p$-ClAP) and those of their binary mixtures with $N$-ethyl aniline ($N$-EA) as a common component, were measured at 303.15 K over the entire composition range. These experimental data were used to calculate the excess volume $V^E$, deviation in ultrasonic speeds ${\Delta}u$, isentropic compressibility $K_s$, intermolecular free length $L_f$, acoustic impedance Z, deviations in isentropic compressibility ${\Delta}K_s$, deviation in viscosity ${\Delta}{\eta}$ and excess Gibbs free energy of activation of viscous flow ($G^{*E}$) at all mole fractions of $N$-ethyl aniline. These parameters, especially excess functions, are found to be quite sensitive towards the intermolecular interactions between component molecules. Theoretical values of viscosity of the binary mixtures were calculated using different empirical relations and theories. The relative merits of these relations and theories were discussed. The experimental results were correlated by using the polynomial proposed by Redlich-Kister equation.

Application of Flory-Treszczanowicz-Benson model and Prigogine-Flory-Patterson theory to Excess Molar Volumes of Isomers of Propanol with Cyclohexane or n-Hexane

  • Gahlyan, Suman;Verma, Sweety;Rani, Manju;Maken, Sanjeev
    • Korean Chemical Engineering Research
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    • 제56권4호
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    • pp.536-541
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    • 2018
  • Excess molar volumes ($V_m^E$) of binary mixtures of 1-propanol or 2-propanol (1) + cyclohexane or n-hexane (2) were measured with V-shaped dilatometer at 303.15 K. The $V_m^E$ data for these mixtures varied as: 2-propanol > 1-propanol and were higher for cyclohexane than n-hexane for both propanol systems. The experimental data were correlated with Redlich-Kister polynomial. The $V_m^E$ data were interpreted qualitatively as well as quantitatively in terms of Flory-Treszczanowicz-Benson model and Prigogine-Flory-Patterson theory. Both models correctly described the sign and shape of $V_m^E$ vs $x_1$ curves. The values calculated by both the models agree well with the experimental data.

Thermophysical Properties of Acetophenone with Ethylchloroacetate at Temperatures of 303.15, 313.15 and 323.15 K

  • Saravanakumar, K.;Baskaran, R.;Kubendran, T.R.
    • 대한화학회지
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    • 제56권4호
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    • pp.424-430
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    • 2012
  • Densities, viscosities, refractive indices and speed of sounds of the binary mixtures of Acetophenone with Ethylchloroacetate were measured over the entire mole fractions at (303.15, 313.15 and 323.15) K. From these experimental results, excess molar volume $V^E$, viscosity deviation ${\Delta}{\eta}$, refractive index deviation ${\Delta}n_D$, deviations in speed of sound ${\Delta}u$, deviations in isentropic compressibility ${\Delta}k_s$ and excess intermolecular free length ${\Delta}L_f$ were calculated. The viscosity data have been correlated with the equations of Grunberg and Nissan, Hind et al., Tamura and Kurata, Katti and Chaudri, Sedgwick, Krishnan-Laddha and McAllister. The thermo physical properties under study were fit to the Jouyban-Acree model. The excess values were correlated using Redlich-Kister polynomial equation to obtain their coefficients and standard deviations. It was found that in all cases, the data obtained fitted with the values correlated by the corresponding models very well. The results are interpreted in terms of molecular interactions occurring in the solution.

Carboxylic acid 이성분계의 고-액 상평형과 과잉물성, 굴절률 및 점도 편차 (Solid-Liquid Equilibria and Excess Molar Volumes, Refractive Indices and Deviation in Viscosity for Binary Systems of C3-C6 Carboxylic Acids)

  • 구지은;오하영;박소진
    • Korean Chemical Engineering Research
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    • 제57권1호
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    • pp.78-84
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    • 2019
  • 최근 지속 가능형 에너지로 바이오 부탄올(bio-butanol)에 관한 연구가 활발히 진행되고 있으나, 이의 상업화에는 저렴한 바이오메스 개발 및 경제적 분리 방법 등 선결해야 할 문제들이 있다. 전통적인 ABE 바이오부탄올 발효공정은 아세톤, 부탄올, 에탄올과 함께 유기산(organic acid)과 같은 부산물을 생성한다. 따라서 이들의 상호분리를 위해 아세톤, 부탄올, 에탄올 및 아세틱 산에 대한 상평형 데이터 등은 많이 발표되었으나, 탄소수가 큰 유기산에 대한 상평형 및 혼합물성 데이터는 매우 부족한 실정이다. 따라서 본 연구는 $C_3-C_6$ 유기산 조합의 이성분계 혼합물에 대한 고-액 상평형과 혼합물성으로 과잉부피($V^E$), 굴절율 편차(${\Delta}R$) 그리고 점도 편차(${\Delta}v$)를 298.15 K에서 실험적으로 측정하였다. 측정된 고-액 상평형 데이터는 NRTL, UNIQUAC식을 이용하여 상관시켰으며 RMSD, 0.5 K이하로 잘 상관되었다. 또한 동일 이성분계 혼합물에 대한 $V^E$, ${\Delta}R$${\Delta}v$의 혼합물성 데이터는 Redlich-Kister 다항식을 이용해 매개변수를 상관하였으며 약 0.004 이하의 표준편차로 잘 상관됨을 확인하였다.

Viscometric Studies of Molecular Interactions in Binary Mixtures of Formamide with Alkanol at 298.15 and 308.15 K

  • Gahlyan, Suman;Verma, Sweety;Rani, Manju;Maken, Sanjeev
    • Korean Chemical Engineering Research
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    • 제55권4호
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    • pp.520-529
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    • 2017
  • Viscosity data were measured at 298.15 K and 308.15 K for formamide + 1-propanol, 2-propanol, 1-butanol, 2-methyl-1-propanol or 2-methyl-2-propanol mixtures. For an equimolar mixture, deviation in viscosity follows the sequence: 2-methyl-2-propanol >2-methyl-1-propanol>1-butanol>2-propanol>1-propanol. The viscosity data were further analyzed in terms of graph theory. Free energy of activation was also calculated from experimental viscosity data along with previously reported excess volume data. The deviation in viscosity and free energy of activation were fitted to Redlich-Kister polynomial equation. The viscosity data were also correlated by correlations like Grunberg-Nissan, Tamura-Kurata, HindMcLaughlin-Ubbelohde, and Katti-Chaudhari relation. Various adjustable parameters, $G_{12}$, $T_{12}$, $H_{12}$, and $W_{vis}/RT$, of various correlations were used to predict viscosity deviation of binary mixtures. Positive value of $G_{12}$ indicates strong interaction in the studied systems. Grunberg-Nissan relation has lowest deviation among the four correlations for formamide + 1-propanol or 2-propanol mixtures; and for mixtures of formamide with 1-butanol or 2-methyl-1-propanol, TamuraKurata has lowest deviation. Grunberg-Nissan gives lowest deviation for formamide + 2-methyl-2-propanol mixtures.

Application of Flory-Treszczanowicz-Benson model and Prigogine-Flory-Patterson theory to Excess Molar Volume of Binary Mixtures of Ethanol with Diisopropyl Ether, Cyclohexane and Alkanes (C6-C9)

  • Kashyap, Pinki;Rani, Manju;Tiwari, Dinesh Pratap;Park, So-Jin
    • Korean Chemical Engineering Research
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    • 제58권2호
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    • pp.257-265
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    • 2020
  • Densities (ρ) for binary mixtures of ethanol (1) + diisopropyl ether (DIPE) or cyclohexane or alkane (C6-C9) (2) were measured at 298.15 K, 308.15 K and 318.15 K. The excess molar volume (VEm) of binary mixtures was calculated using ρ data and correlated with Redlich-Kister polynomial equation. The VEm values for binary mixtures of ethanol (1) + cyclohexane or n-alkane (C6-C9) (2) were positive, whereas for ethanol (1) + DIPE (2) these were negative. The magnitude of VEm values follows the order: cyclohexane > n-nonane > n-octane > n-heptane > n-hexane > DIPE. The VEm values have been interpreted qualitatively and also quantitatively in terms of Flory-Treszczanowicz-Benson (FTB) model and Prigogine-Flory-Patterson (PFP) theory. The values VEm predicted using FTB model agree well with experimental VEm values at all mole fractions. But the PFP theory describes well VEm data in ethanol-rich region (x1 > 0.5) for all binary mixtures and is able to predict the sign of VEm vs x1 curve for ethanol-lean region (x1 < 0.5) except for ethanol (1) + nonane (2) mixtures.