The document discusses criteria for predicting the occurrence of azeotropes in binary systems under isothermal and isobaric conditions.
For isothermal systems, the criteria are expressed in terms of the activity coefficients at infinite dilution (γ∞). For a positive azeotrope, γ∞ of the less volatile component must be greater than or equal to the ratio of the saturation vapor pressures. For a negative azeotrope, γ∞ of the more volatile component must be less than or equal to the inverse of the ratio.
For isobaric systems, the criteria involve γ∞ evaluated at the boiling points. For a minimum-boiling azeotrope
This document discusses the properties and design considerations of continuously stirred tank reactors (CSTRs), also known as back-mixed reactors. It outlines key characteristics of CSTRs such as perfect mixing, uniform conditions throughout the reactor, and identical properties at the inlet and outlet. Advantages include low cost and easy temperature control. Disadvantages are lower reaction rates due to diluted reactant concentrations compared to the inlet. Mass and energy balances are derived and used to determine the reactor volume required for a given conversion based on kinetic data and operating conditions. Examples are provided to demonstrate solving for reactor size and temperature based on specified conversions.
This document proposes a modification to the Redlich-Kwong equation of state by making the temperature-dependent parameter a(T) instead of a constant. This improves the equation's ability to model vapor pressures of pure substances and phase equilibria of mixtures. The modified equation represents vapor pressure data for hydrocarbons more accurately than the original equation. When combined with the original Redlich-Kwong mixing rules, the modified equation can also predict vapor-liquid equilibrium for mixtures of nonpolar fluids like hydrocarbons, with some limitations for hydrogen-containing mixtures.
Liquid-Vapor Equilibria in Binary SystemsKarnav Rana
1) The document discusses liquid-vapor equilibria in binary systems, specifically measuring the compositions of chloroform and acetone mixtures using refractometry.
2) It introduces concepts like Raoult's law and Henry's law to describe ideal and non-ideal behavior in binary solutions, and how vapor pressure varies with composition.
3) Temperature-composition diagrams are used to visualize ideal and non-ideal behavior, including positive and negative deviations from ideality and the possibility of azeotropes.
Liquid liquid equilibrium for the ternary system of isopropyl acetate 2 propa...Josemar Pereira da Silva
The document presents experimental data on liquid-liquid equilibrium for the ternary system of isopropyl acetate, 2-propanol, and glycerol at temperatures of 298.15 K, 308.15 K, and 318.15 K under atmospheric pressure. Triangular phase diagrams were obtained at each temperature showing the two-phase region. Distribution coefficients and selectivity parameters were calculated to evaluate glycerol's capacity as an extractive solvent. The NRTL and UNIQUAC models were applied to correlate the experimental data with low deviations.
This document discusses phase diagrams and the phase rule. It provides definitions of key terms like phase, component, and degree of freedom. The phase rule states that the number of degrees of freedom F equals the number of components C minus the number of phases P plus 2. Examples are given to demonstrate how to count components and phases in different systems. Single and two-component phase diagrams are described, showing how temperature and pressure can be varied. Methods for experimentally measuring phase changes are also mentioned.
1) The isoform of troponin I determines the sensitivity of muscle fibers to low pH conditions. Specifically, slow skeletal troponin I reduces pH sensitivity compared to cardiac troponin I.
2) NMR experiments showed that histidine 130 (H130) in slow skeletal troponin I interacts electrostatically with glutamate 19 (E19) in troponin C, stabilizing the complex under acidic conditions. This interaction reduces muscle deactivation at low pH.
3) Replacing H130 with alanine in slow skeletal troponin I or adding a histidine to cardiac troponin I at the corresponding position reduces/removes the pH sensitivity difference between the troponin isoforms.
This experiment characterized the microenvironment of a gel mixture composed of 50% kappa-carrageenan and 50% type B gelatin at various phases and temperatures using the luminescence probe Ru(bpy)3
2+. Emission spectra and fluorescence decay were measured at 10, 23.5, 30, 37.5, 50, and 60°C to observe changes in maximum emission wavelength and quenching rate constant. The Arrhenius plot showed that the Ru(bpy)3
2+ decay rate increased with temperature. The maximum emission wavelength remained constant within phases but increased slightly between phases, indicating a small decrease in energy emission through phase changes.
Natural Convection and Entropy Generation in Γ-Shaped Enclosure Using Lattice...A Behzadmehr
This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation. A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr = 0.71) and Rayleigh numbers ranging from 103 to 106 at the macroscopic scale (Kn = 10-4). In every case, an appropriate value of the characteristic velocity is chosen using a simple model based on the kinetic theory. By considering the obtained dimensionless velocity and temperature values, the distributions of entropy generation due to heat transfer and fluid friction are determined. It is found that for an enclosure with high value of Rayleigh number (i.e., Ra=105), the total entropy generation due to fluid friction and total Nu number increases with decreasing the aspect ratio.
This document discusses the properties and design considerations of continuously stirred tank reactors (CSTRs), also known as back-mixed reactors. It outlines key characteristics of CSTRs such as perfect mixing, uniform conditions throughout the reactor, and identical properties at the inlet and outlet. Advantages include low cost and easy temperature control. Disadvantages are lower reaction rates due to diluted reactant concentrations compared to the inlet. Mass and energy balances are derived and used to determine the reactor volume required for a given conversion based on kinetic data and operating conditions. Examples are provided to demonstrate solving for reactor size and temperature based on specified conversions.
This document proposes a modification to the Redlich-Kwong equation of state by making the temperature-dependent parameter a(T) instead of a constant. This improves the equation's ability to model vapor pressures of pure substances and phase equilibria of mixtures. The modified equation represents vapor pressure data for hydrocarbons more accurately than the original equation. When combined with the original Redlich-Kwong mixing rules, the modified equation can also predict vapor-liquid equilibrium for mixtures of nonpolar fluids like hydrocarbons, with some limitations for hydrogen-containing mixtures.
Liquid-Vapor Equilibria in Binary SystemsKarnav Rana
1) The document discusses liquid-vapor equilibria in binary systems, specifically measuring the compositions of chloroform and acetone mixtures using refractometry.
2) It introduces concepts like Raoult's law and Henry's law to describe ideal and non-ideal behavior in binary solutions, and how vapor pressure varies with composition.
3) Temperature-composition diagrams are used to visualize ideal and non-ideal behavior, including positive and negative deviations from ideality and the possibility of azeotropes.
Liquid liquid equilibrium for the ternary system of isopropyl acetate 2 propa...Josemar Pereira da Silva
The document presents experimental data on liquid-liquid equilibrium for the ternary system of isopropyl acetate, 2-propanol, and glycerol at temperatures of 298.15 K, 308.15 K, and 318.15 K under atmospheric pressure. Triangular phase diagrams were obtained at each temperature showing the two-phase region. Distribution coefficients and selectivity parameters were calculated to evaluate glycerol's capacity as an extractive solvent. The NRTL and UNIQUAC models were applied to correlate the experimental data with low deviations.
This document discusses phase diagrams and the phase rule. It provides definitions of key terms like phase, component, and degree of freedom. The phase rule states that the number of degrees of freedom F equals the number of components C minus the number of phases P plus 2. Examples are given to demonstrate how to count components and phases in different systems. Single and two-component phase diagrams are described, showing how temperature and pressure can be varied. Methods for experimentally measuring phase changes are also mentioned.
1) The isoform of troponin I determines the sensitivity of muscle fibers to low pH conditions. Specifically, slow skeletal troponin I reduces pH sensitivity compared to cardiac troponin I.
2) NMR experiments showed that histidine 130 (H130) in slow skeletal troponin I interacts electrostatically with glutamate 19 (E19) in troponin C, stabilizing the complex under acidic conditions. This interaction reduces muscle deactivation at low pH.
3) Replacing H130 with alanine in slow skeletal troponin I or adding a histidine to cardiac troponin I at the corresponding position reduces/removes the pH sensitivity difference between the troponin isoforms.
This experiment characterized the microenvironment of a gel mixture composed of 50% kappa-carrageenan and 50% type B gelatin at various phases and temperatures using the luminescence probe Ru(bpy)3
2+. Emission spectra and fluorescence decay were measured at 10, 23.5, 30, 37.5, 50, and 60°C to observe changes in maximum emission wavelength and quenching rate constant. The Arrhenius plot showed that the Ru(bpy)3
2+ decay rate increased with temperature. The maximum emission wavelength remained constant within phases but increased slightly between phases, indicating a small decrease in energy emission through phase changes.
Natural Convection and Entropy Generation in Γ-Shaped Enclosure Using Lattice...A Behzadmehr
This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation. A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr = 0.71) and Rayleigh numbers ranging from 103 to 106 at the macroscopic scale (Kn = 10-4). In every case, an appropriate value of the characteristic velocity is chosen using a simple model based on the kinetic theory. By considering the obtained dimensionless velocity and temperature values, the distributions of entropy generation due to heat transfer and fluid friction are determined. It is found that for an enclosure with high value of Rayleigh number (i.e., Ra=105), the total entropy generation due to fluid friction and total Nu number increases with decreasing the aspect ratio.
- The document discusses isotope fractionation in ozone and its cosmochemical implications. It presents theoretical calculations showing mass-independent isotope effects can arise from scattering processes involving indistinguishable isotopes.
- Numerical simulations of ozone formation reactions reproduce observed fractionation factors without adjustable parameters, supporting this quantum mechanical explanation.
- This process could explain other isotopic anomalies if certain gas-solid reactions are quenched before completion, and warrants further experimental study.
A density correction for the peng robinson equationLuis Follegatti
This document presents a density correction for the Peng-Robinson equation of state. The correction involves adding a simple empirical term that requires one parameter per component. It improves the prediction of liquid densities by 2-4% and vapor densities slightly. The correction retains the internal consistency between vapor and liquid properties predicted by equations of state. It provides a reliable way to enhance density predictions without significantly affecting other properties.
Estudio del efecto de la inversion temportal sobre el campo magnetico - Alber...AlbertoBlancoGarca1
The document analyzes the effect of temporal inversion on the magnetic field B. It demonstrates that B is an odd function of time through the following steps:
1) It is assumed that the electric field E is even under temporal inversion.
2) Using Maxwell's equations, it is shown that the temporal derivative of B (∂B/∂t) is even.
3) By the properties of even functions, the integral of an even function is odd. Therefore, B must be an odd function of time.
Two simulations are presented that experimentally validate the theoretical conclusions - namely that ∂B/∂t is even while B is odd under temporal inversion.
This document discusses multireaction stoichiometry and chemical equilibrium. It contains the following key points:
1) For a system with multiple chemical reactions, the change in moles of a chemical species can be expressed as the sum of the stoichiometric coefficients of that species in each reaction, multiplied by the extent of each reaction.
2) At chemical equilibrium, the total Gibbs free energy of the system is minimized, meaning its differential with respect to the reaction coordinate is zero.
3) The equilibrium constant K for a reaction can be calculated from the standard Gibbs free energy change of the reaction. K is related to the activities of the products over the reactants.
This document discusses biochemistry concepts related to thermodynamics and amino acids. It begins with an overview of the first and second laws of thermodynamics, including definitions of enthalpy, entropy, and free energy. It then describes the standard state conditions used for biological reactions and how coupled reactions can drive unfavorable processes. The document concludes by providing details on the 20 common amino acids found in proteins, including their structures, acid-base properties, and classifications.
This document discusses chemical kinetics, which is the study of reaction rates and how reaction rates change under varying conditions. Chemical kinetics is an empirical and experimental area of study that allows investigation of reaction mechanisms. Kinetic studies involve measuring reaction rates at different reactant concentrations and time intervals to determine the rate law equation and rate constant for a reaction. The rate law relates the reaction rate to the concentrations of reactants in the reaction and can provide information about the reaction mechanism and steps.
This document provides background on analyzing the response of linear systems using modern tools from linear algebra. It introduces a simple spring-mass-damper system as an example and derives the equations of motion. The response depends on the damping ratio ζ. For ζ > 1, the system is overdamped with decaying exponential solutions. For ζ = 1, it is critically damped with a decaying exponential and linear term. For ζ < 1, it is underdamped with decaying sinusoidal oscillations. The document expresses the second-order system as a set of first-order equations and relates the free response to the eigenvalues and eigenvectors of the system matrix A. It then applies this framework to derive the
This document summarizes the results of an experiment measuring the nuclear magnetic resonance (NMR) parameters of chlorine isotopes 35Cl, 36Cl, and 37Cl in molten salt solutions. Key findings include:
1) Spin-lattice relaxation times and NMR spectra were measured for the chloride and perchlorate ions in various solutions.
2) Ratios of relaxation times and linewidths between isotopes were consistent with theoretical predictions based on nuclear quadrupole moments.
3) Measurements of the 36Cl relaxation time allowed estimation of its electric quadrupole moment as -0.023 barn.
This document outlines five common thermodynamic processes - isobaric, isochoric, isothermal, adiabatic, and polytropic - and provides the equations to calculate work, heat, enthalpy change, and entropy change for each process. The equations show that work, heat, and entropy change can be calculated from temperature change, specific heat capacities, gas constant R, and volume or pressure ratios depending on the type of process. Polytropic and adiabatic processes have work terms related to pressure and volume changes.
Systematic Study Multiplicity Production Nucleus – Nucleus Collisions at 4.5 ...IOSRJAP
The correlations between the multiplicity distributions and the projectile fragments, as well as the correlation between the black and grey fragments were given. We observed that the mean number of interacting projectile nucleons increases quickly as the value of heavily ionizing charged particles increase as expected but attains a more or less constant value for extreme central collisions. Finally, there is no distinct correlation between the shower particle production and the target excitation, but the average value of grey particles decreases with the increase of the number of black particles and vice versa. This correlation can also be explained by the fireball model.
The document provides notes on equilibrium chemistry concepts and calculations. It defines equilibrium constants Kc and Kp, and explains how to calculate them using concentration or pressure data for reversible reactions at equilibrium. It also discusses how the reaction quotient Q relates to the direction a reaction will shift to reach equilibrium. Sample equilibrium problems are worked through step-by-step to demonstrate setting up reaction tables and solving for unknown concentrations and constants.
This document defines and describes various types of chemical analysis techniques and concepts. It discusses:
1) Qualitative and quantitative analysis, volumetric analysis, gravimetric analysis, and instrumental analysis.
2) Types of titration including acid-base, redox, precipitation, and complexometric titrations.
3) Key concepts related to titration including indicators, endpoints, equivalence points, and types of reagents.
This document describes a semicontinuous, isothermal reactor used to produce methyl bromide from a reaction between bromocyanide and methylamine. The reactor is fed continuously with a 0.025 M methylamine solution at a flow rate of 0.025 dm3/s into an initially 5 dm3, 0.05 M bromocyanide solution. The document provides the rate equation and material balances to model the reaction and concentration changes over time, which are solved using MATLAB to determine the concentrations of reactants and products as well as the reaction rate as functions of time.
This chapter discusses the concepts of spontaneity, entropy, and free energy in chemical reactions. It introduces three methods to determine the standard free energy change (ΔG°) of a reaction: 1) Using ΔG° = ΔH° - TΔS°, 2) Applying Hess' law, and 3) Summing the standard free energy of formation values. It also describes how free energy depends on temperature, pressure, and can be used to predict spontaneity and equilibrium. Calculating thermodynamic quantities allows prediction of reaction spontaneity based on the signs of ΔH and ΔS.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Production of-n-propyl-acetate-by-reactive-distillation-experimental-and-theo...Josemar Pereira da Silva
This document summarizes the first steps in developing a catalytic reactive distillation process for producing n-propyl acetate. Kinetic experiments were conducted to determine the reaction rates for homogeneous and heterogeneous catalysis. Pilot plant experiments were also performed using a homogeneous strong acid catalyst in a packed column with a top-column decanter. Simulation results matched experimental data well when accounting for non-ideal thermodynamics. Several process configurations were identified that could dramatically increase alcohol conversion and n-propyl acetate purity by adding a stripping section. The best startup strategy was determined to involve an initial charging of the two-phase top product to achieve steady-state conditions most quickly.
This document describes computer simulations of freezing and sublimation processes under various boundary conditions for cylinders and spheres. The simulations solve the moving boundary problem using exact solutions derived for the phase front velocity. Results are presented for cylinders and spheres solidifying or sublimating with and without external heat sources or sinks. Specific solutions are verified for cases such as a sublimating cylinder with a heat sink, a self-freezing cylinder without a heat source, and a self-sublimating sphere. Tables summarizing the results are also presented.
1. Laju reaksi adalah laju pengurangan konsentrasi pereaksi atau penambahan konsentrasi produk per satuan waktu. Laju reaksi dipengaruhi oleh konsentrasi, luas permukaan, suhu, tekanan, dan katalisator.
2. Untuk reaksi 2X → Y + Z, data menunjukkan reaksi berorde 0 karena konsentrasi X berkurang secara linier terhadap waktu. Konsentrasi X pada menit ke-30 adalah 2,
El documento presenta un modelo de enriquecimiento semántico de recursos de información para ampliar el acceso público a la información. Explica que el enriquecimiento semántico identifica detalles en recursos para su extracción y consulta por máquinas, mediante marcaje estructural y semántico. Propone una arquitectura tecnológica de referencia y un esquema XML para el marcaje, y da ejemplos de productos derivados como informes estadísticos y visualizaciones de datos.
Solução da Prova Canguru de Matemática - Nível E - 2016Célio Sousa
Este documento fornece as soluções para problemas de matemática de um exame de nível E. As soluções incluem explicações curtas para cada uma das 23 questões, variando de 3 a 5 pontos cada.
These slides are for a lecture on civil disobedience in an Introduction to Philosophy course at the University of British Columbia in Vancouver, BC, Canada.
- The document discusses isotope fractionation in ozone and its cosmochemical implications. It presents theoretical calculations showing mass-independent isotope effects can arise from scattering processes involving indistinguishable isotopes.
- Numerical simulations of ozone formation reactions reproduce observed fractionation factors without adjustable parameters, supporting this quantum mechanical explanation.
- This process could explain other isotopic anomalies if certain gas-solid reactions are quenched before completion, and warrants further experimental study.
A density correction for the peng robinson equationLuis Follegatti
This document presents a density correction for the Peng-Robinson equation of state. The correction involves adding a simple empirical term that requires one parameter per component. It improves the prediction of liquid densities by 2-4% and vapor densities slightly. The correction retains the internal consistency between vapor and liquid properties predicted by equations of state. It provides a reliable way to enhance density predictions without significantly affecting other properties.
Estudio del efecto de la inversion temportal sobre el campo magnetico - Alber...AlbertoBlancoGarca1
The document analyzes the effect of temporal inversion on the magnetic field B. It demonstrates that B is an odd function of time through the following steps:
1) It is assumed that the electric field E is even under temporal inversion.
2) Using Maxwell's equations, it is shown that the temporal derivative of B (∂B/∂t) is even.
3) By the properties of even functions, the integral of an even function is odd. Therefore, B must be an odd function of time.
Two simulations are presented that experimentally validate the theoretical conclusions - namely that ∂B/∂t is even while B is odd under temporal inversion.
This document discusses multireaction stoichiometry and chemical equilibrium. It contains the following key points:
1) For a system with multiple chemical reactions, the change in moles of a chemical species can be expressed as the sum of the stoichiometric coefficients of that species in each reaction, multiplied by the extent of each reaction.
2) At chemical equilibrium, the total Gibbs free energy of the system is minimized, meaning its differential with respect to the reaction coordinate is zero.
3) The equilibrium constant K for a reaction can be calculated from the standard Gibbs free energy change of the reaction. K is related to the activities of the products over the reactants.
This document discusses biochemistry concepts related to thermodynamics and amino acids. It begins with an overview of the first and second laws of thermodynamics, including definitions of enthalpy, entropy, and free energy. It then describes the standard state conditions used for biological reactions and how coupled reactions can drive unfavorable processes. The document concludes by providing details on the 20 common amino acids found in proteins, including their structures, acid-base properties, and classifications.
This document discusses chemical kinetics, which is the study of reaction rates and how reaction rates change under varying conditions. Chemical kinetics is an empirical and experimental area of study that allows investigation of reaction mechanisms. Kinetic studies involve measuring reaction rates at different reactant concentrations and time intervals to determine the rate law equation and rate constant for a reaction. The rate law relates the reaction rate to the concentrations of reactants in the reaction and can provide information about the reaction mechanism and steps.
This document provides background on analyzing the response of linear systems using modern tools from linear algebra. It introduces a simple spring-mass-damper system as an example and derives the equations of motion. The response depends on the damping ratio ζ. For ζ > 1, the system is overdamped with decaying exponential solutions. For ζ = 1, it is critically damped with a decaying exponential and linear term. For ζ < 1, it is underdamped with decaying sinusoidal oscillations. The document expresses the second-order system as a set of first-order equations and relates the free response to the eigenvalues and eigenvectors of the system matrix A. It then applies this framework to derive the
This document summarizes the results of an experiment measuring the nuclear magnetic resonance (NMR) parameters of chlorine isotopes 35Cl, 36Cl, and 37Cl in molten salt solutions. Key findings include:
1) Spin-lattice relaxation times and NMR spectra were measured for the chloride and perchlorate ions in various solutions.
2) Ratios of relaxation times and linewidths between isotopes were consistent with theoretical predictions based on nuclear quadrupole moments.
3) Measurements of the 36Cl relaxation time allowed estimation of its electric quadrupole moment as -0.023 barn.
This document outlines five common thermodynamic processes - isobaric, isochoric, isothermal, adiabatic, and polytropic - and provides the equations to calculate work, heat, enthalpy change, and entropy change for each process. The equations show that work, heat, and entropy change can be calculated from temperature change, specific heat capacities, gas constant R, and volume or pressure ratios depending on the type of process. Polytropic and adiabatic processes have work terms related to pressure and volume changes.
Systematic Study Multiplicity Production Nucleus – Nucleus Collisions at 4.5 ...IOSRJAP
The correlations between the multiplicity distributions and the projectile fragments, as well as the correlation between the black and grey fragments were given. We observed that the mean number of interacting projectile nucleons increases quickly as the value of heavily ionizing charged particles increase as expected but attains a more or less constant value for extreme central collisions. Finally, there is no distinct correlation between the shower particle production and the target excitation, but the average value of grey particles decreases with the increase of the number of black particles and vice versa. This correlation can also be explained by the fireball model.
The document provides notes on equilibrium chemistry concepts and calculations. It defines equilibrium constants Kc and Kp, and explains how to calculate them using concentration or pressure data for reversible reactions at equilibrium. It also discusses how the reaction quotient Q relates to the direction a reaction will shift to reach equilibrium. Sample equilibrium problems are worked through step-by-step to demonstrate setting up reaction tables and solving for unknown concentrations and constants.
This document defines and describes various types of chemical analysis techniques and concepts. It discusses:
1) Qualitative and quantitative analysis, volumetric analysis, gravimetric analysis, and instrumental analysis.
2) Types of titration including acid-base, redox, precipitation, and complexometric titrations.
3) Key concepts related to titration including indicators, endpoints, equivalence points, and types of reagents.
This document describes a semicontinuous, isothermal reactor used to produce methyl bromide from a reaction between bromocyanide and methylamine. The reactor is fed continuously with a 0.025 M methylamine solution at a flow rate of 0.025 dm3/s into an initially 5 dm3, 0.05 M bromocyanide solution. The document provides the rate equation and material balances to model the reaction and concentration changes over time, which are solved using MATLAB to determine the concentrations of reactants and products as well as the reaction rate as functions of time.
This chapter discusses the concepts of spontaneity, entropy, and free energy in chemical reactions. It introduces three methods to determine the standard free energy change (ΔG°) of a reaction: 1) Using ΔG° = ΔH° - TΔS°, 2) Applying Hess' law, and 3) Summing the standard free energy of formation values. It also describes how free energy depends on temperature, pressure, and can be used to predict spontaneity and equilibrium. Calculating thermodynamic quantities allows prediction of reaction spontaneity based on the signs of ΔH and ΔS.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Production of-n-propyl-acetate-by-reactive-distillation-experimental-and-theo...Josemar Pereira da Silva
This document summarizes the first steps in developing a catalytic reactive distillation process for producing n-propyl acetate. Kinetic experiments were conducted to determine the reaction rates for homogeneous and heterogeneous catalysis. Pilot plant experiments were also performed using a homogeneous strong acid catalyst in a packed column with a top-column decanter. Simulation results matched experimental data well when accounting for non-ideal thermodynamics. Several process configurations were identified that could dramatically increase alcohol conversion and n-propyl acetate purity by adding a stripping section. The best startup strategy was determined to involve an initial charging of the two-phase top product to achieve steady-state conditions most quickly.
This document describes computer simulations of freezing and sublimation processes under various boundary conditions for cylinders and spheres. The simulations solve the moving boundary problem using exact solutions derived for the phase front velocity. Results are presented for cylinders and spheres solidifying or sublimating with and without external heat sources or sinks. Specific solutions are verified for cases such as a sublimating cylinder with a heat sink, a self-freezing cylinder without a heat source, and a self-sublimating sphere. Tables summarizing the results are also presented.
1. Laju reaksi adalah laju pengurangan konsentrasi pereaksi atau penambahan konsentrasi produk per satuan waktu. Laju reaksi dipengaruhi oleh konsentrasi, luas permukaan, suhu, tekanan, dan katalisator.
2. Untuk reaksi 2X → Y + Z, data menunjukkan reaksi berorde 0 karena konsentrasi X berkurang secara linier terhadap waktu. Konsentrasi X pada menit ke-30 adalah 2,
El documento presenta un modelo de enriquecimiento semántico de recursos de información para ampliar el acceso público a la información. Explica que el enriquecimiento semántico identifica detalles en recursos para su extracción y consulta por máquinas, mediante marcaje estructural y semántico. Propone una arquitectura tecnológica de referencia y un esquema XML para el marcaje, y da ejemplos de productos derivados como informes estadísticos y visualizaciones de datos.
Solução da Prova Canguru de Matemática - Nível E - 2016Célio Sousa
Este documento fornece as soluções para problemas de matemática de um exame de nível E. As soluções incluem explicações curtas para cada uma das 23 questões, variando de 3 a 5 pontos cada.
These slides are for a lecture on civil disobedience in an Introduction to Philosophy course at the University of British Columbia in Vancouver, BC, Canada.
Neanderthal Subsistence Strategies and Implications of Cognition Complexity -...Jaclyn Janero
A presentation that was given in 6 minutes on Neanderthal Cognition. Some of the slides are just photos - feel free to contact me for the notes on the slides if you're interested in what I had to say.
Here are notes from a few slides:
Slide 6: Jonzac has a prevalent reindeer bone bed, as you can see in the image of the excavation. When these bones were analyzed, researchers found that 22% of them had butchery marks that were in the correct location to indicate skinning, dismembering, and defleshing, as well as marrow extraction. The age analysis of the skeletal remains show that it was mostly prime-age reindeer, which is an important distinction for cognition implication, since animals in their prime are harder to exploit than the juveniles or seniors. These reindeer seasonally migrated past the Jonzac rock shelter where the processed remains were found, but the remains show multiple years’ worth of use or multiple hunting trips for the site.
Slide 7: It’s hard to document human interaction with cave bears, as most of the remains are found in caves which matches the hibernation pattern of cave bears. However, there are cave bear remains in open air Paleolithic occupation sites, showing evidence of deliberate hunting. Some of the remains in the open air sites are missing the associated fauna with natural cave taphonomy, implying the remains were not scavenged from an already dead bear. Cut marks were identified on the remains and one cave bear had an embedded flint projectile in its vertebrae. These animals were massive, and would have taken a lot of individuals and communication in order to successfully utilize. In some of these sites, there is evidence of art objects, such as pendants, and bone tools made from the bones of the cave bear.
Slide 8: Using two forms of mass spectrometry, combined with morphological analysis of plant microfossils, researchers were able to identify materials trapped inside the dental calculus of five Neanderthal individuals from El Sidron, Spain. This analysis revealed the first molecular evidence of inhalation of wood-fire smoke, bitumen or oil shale, and ingestion of a range of cooked foods, specifically plants. They also found evidence of ingestion of two plants known today for their medicinal qualities. The medicinal plants discovered were bitter-tasting plants with no nutritional value. The authors also point out that the evidence for complex use of medicinal plants by primates is well-documented, so it is not unreasonable to extrapolate medicinal use of plants by Neanderthals. Bitumen was used as a hafting material by Neanderthals, and the nearest oil shale source is 15 km away from the site of Sidron.
This document contains worksheets on prisms with multiple problems involving calculating surface areas and volumes of triangular, square, and cylindrical prisms. There are 4 problems in each of 3 activities - calculating surface area of triangular prisms with given dimensions, volume of triangular and trapezoidal prisms, and volumes of cylinders that can be carved from prisms or formed by rolling rectangular sheets. The document provides the questions and spaces for answers but no solutions shown.
This document is a doctoral thesis submitted by Efstathios Skouras-Iliopoulos for the degree of Doctor of Engineering at the Norwegian University of Science and Technology. The thesis focuses on feasibility and operation aspects of heterogeneous azeotropic (heteroazeotropic) distillation in batch distillation columns. Both conventional batch columns (rectifiers) and novel multivessel column configurations are considered for separating azeotropic mixtures. Dynamic simulations are used to analyze time requirements and separation performance of different column configurations for various mixture types. The thesis aims to provide a deeper understanding of heteroazeotropic batch distillation and develop guidelines for assessing feasibility and practical operation of such processes.
This focus group document contains 10 questions to ask participants about a music magazine, including whether the front cover, contents page, and spreads seem cohesive; what information on the front cover looks interesting; who the magazine seems targeted towards in terms of gender or ethnicity; what language is interesting to read; what aspects catch the eye on the front cover; opinions on the color scheme; what music genre the magazine represents; whether the magazine appeals to the participant; and whether they would want to read the next issue.
Legionnaires' disease was first recognized in 1976 after an outbreak in Philadelphia. It is caused by Legionella bacteria found in water sources, with L. pneumophila being the most common cause. Symptoms include pneumonia and fever. Risk factors include older age, smoking, and weakened immunity. Diagnosis involves urine antigen testing or culture from respiratory samples. Treatment involves antibiotics like fluoroquinolones or azithromycin. Prevention focuses on disinfecting water systems in buildings where outbreaks occur.
The photographer chose a photography studio as the location for their shoot because studios are commonly used in magazines and provide a professional look. Shooting in a studio also allows for easier editing and manipulation of images compared to outdoor locations. Most magazines use plain backgrounds in the studio so the subject is the main focus of the photo.
Eva was interviewed about her career in rock music. She grew up surrounded by rock music like AC/DC and Queen, which inspired her to pursue a career in rock. Over the past year, she has had a hectic schedule but is grateful for her success. When she was nominated for 3 Brit Awards and won Best New Artist, she was shocked and felt overwhelmed with love and gratitude. She is happy that rock music is being appreciated by more people today. Fans can look forward to seeing Eva and her band very soon as they have exciting new things planned.
The document discusses different types of music magazine articles - free flowing articles and Q&A style articles. Free flowing articles require the writer to describe scenes and express opinions to set an atmosphere, while Q&As are easier to create by simply writing questions and answers. After analyzing examples of each style, the conclusion is that a free flowing article would allow more creative expression, but a Q&A is good for getting specific information from an artist and is interesting for readers. The decision is made to produce a free flowing article to take advantage of the more open format.
Evaluación en el marco de la lomce. presentación de María Luisa Suárez ÁlvarezCPR Oviedo
Este documento proporciona información sobre la evaluación en el marco de la LOMCE en España. Explica que la evaluación debe centrarse en los aprendizajes del alumnado con el fin de mejorar al alumno, el aula, el centro y el entorno. Además, detalla que la evaluación puede ser formativa, sumativa o por cursos y debe realizarse de forma continua e interna y externa considerando el currículo y el contexto del alumnado.
The document discusses phases and solutions in chemical systems. It defines a phase as a homogeneous portion of matter that can consist of multiple disconnected pieces. The phase rule relates the degrees of freedom (f), number of chemical species (c), and number of phases (p) in a system. It also describes ideal solutions, which obey Raoult's and Dalton's laws. Vapour pressure is defined as the pressure of a gas in equilibrium with its condensed phases. Boiling and melting points depend on temperature and pressure based on phase diagrams.
Introduction
Concepts of Fugacity
Effect of Temperature & pressure on Fugacity
Important relation of Fugacity Coefficient
Vapour Liquid Equilibrium for pure species
Fugacity & Fugacity coefficient: Species in solution
Reference
The document discusses several concepts related to non-ideal gases and solutions, including:
1) Fugacity is introduced as a concept to represent the behavior of real gases, which differs from ideal gases. Fugacity takes the place of pressure in equations relating to free energy.
2) At low pressures, fugacity approximates pressure as real gases behave more ideally. Equations are provided to calculate fugacity at low pressures.
3) Excess functions quantify the non-ideal behavior of real mixtures and are defined as the difference between properties of real and ideal mixtures under the same conditions. Excess properties include volume, enthalpy, and chemical potential.
This document discusses the concept of fugacity, which is a property that accounts for the non-ideal behavior of real gases. It introduces fugacity and explains that fugacity can be used to represent real gases in thermodynamic equations in place of pressure. The document then discusses methods for determining fugacity, including calculating fugacity at low pressures. It also covers the fugacity of gas mixtures and the physical significance of fugacity. Finally, it defines excess functions which quantify the non-ideal behavior of solutions and provides expressions for excess chemical potential, Gibbs free energy, entropy and enthalpy.
This document discusses vapor/liquid equilibrium (VLE) and provides models for predicting VLE using simple models like Raoult's law and Henry's law. It defines key terms like mass fraction, mole fraction, molar concentration. Duhem's theorem is introduced which states that the equilibrium state is determined by fixing any two independent variables for a closed system. Simple calculations are shown for using Raoult's law to determine the bubble point and dew point temperatures and pressures of a binary system from its phase compositions or known temperature. P-x-y and T-x-y diagrams are used to illustrate the VLE behavior between the phases.
This lecture introduces concepts of thermodynamics and how they relate to living systems. It discusses how living systems maintain order far from equilibrium and uses energy and molecular interactions. Key concepts covered include entropy, Gibbs free energy, and how biological systems can direct spontaneous reactions through non-equilibrium conditions and concentration control. Thermodynamic equilibrium is defined and how the sign of change in Gibbs free energy determines reaction direction.
This document contains information about an equilibrium liquid-vapor project conducted by students at the Universidad Nacional de Piura in Peru. It includes the names of the students, their professor, and introduces the topic of equilibrium between liquid and vapor phases for miscible liquids. It provides theoretical background on how temperature, pressure, and composition influence the vapor pressure of mixtures. It defines key concepts like boiling point, condensation point, and volatility. Diagrams are presented to illustrate liquid-vapor equilibrium relationships. Calculations of equilibrium using volatility are described.
This document contains information about an equilibrium liquid-vapor project conducted by students at the Universidad Nacional de Piura in Peru. It includes the names of the students, their professor, and introduces the topic of equilibrium between liquid and vapor phases for miscible liquids. It provides theoretical background on how temperature, pressure, and composition influence vapor pressure and phase equilibria. It defines key concepts like boiling point, condensation point, and volatility. Diagrams are presented to illustrate liquid-vapor equilibrium relationships. Methods for calculating phase equilibria using volatility are also summarized.
1) The document discusses selection rules for electronic transitions in molecules, which are used to predict transition intensities. Transitions are allowed if the electronic, spin, and nuclear transition moments are non-zero, and forbidden if any are zero.
2) Symmetry selection rules are described, where the symmetry of molecular orbitals and selection of dipole moment components determine if transitions are allowed. Center of symmetry also influences selection rules.
3) Spin selection rules indicate that transitions between states of the same multiplicity are allowed, while different multiplicity transitions are spin-forbidden, but can occur through spin-orbit coupling.
1) Thermodynamics describes how changes in temperature, pressure, and composition affect equilibrium in rock systems. It allows prediction of mineral stability and interpretation of mineral compositions.
2) Thermodynamic models use concepts like internal energy, enthalpy, entropy, and Gibbs free energy to describe equilibrium and the direction of spontaneous processes.
3) Phase diagrams visualize thermodynamic stability by showing pressure-temperature-composition conditions where minerals are stable. However, kinetic effects can cause disequilibrium.
1. The document discusses spontaneity, entropy, and free energy in chemical reactions. It defines spontaneity as a reaction that will occur without outside intervention and explains that both thermodynamics and kinetics are needed to fully describe a reaction.
2. Entropy is defined in terms of the number of possible arrangements of particles. The second law of thermodynamics states that the entropy of the universe increases. Whether a reaction is spontaneous depends on the change in entropy of the surroundings and system.
3. The free energy change (ΔG) of a reaction can be calculated from the enthalpy and entropy changes and can be used to predict spontaneity - a negative ΔG means the reaction is spontaneous.
This document discusses thermodynamic properties of fluids and covers several key topics:
1) It outlines the objectives of studying thermodynamic properties, including developing property relations from the first and second laws of thermodynamics.
2) Fundamental thermodynamic properties like pressure, volume, temperature, and entropy are defined.
3) The first and second laws of thermodynamics are summarized, including equations for closed systems and ideal gases.
4) Methods for determining thermodynamic properties from tables or correlations are introduced.
This document defines key terms used to explain phase equilibria and the phase rule. It discusses:
- A system, phase, components, number of phases (P), and number of components (C)
- The phase rule relationship that the degree of freedom (F) of a system equals the number of components (C) minus the number of phases (P) plus two.
- Examples of applying the phase rule to systems with different numbers of phases and components, such as a one-component system with ice, liquid water, and water vapor having three phases and zero degrees of freedom.
This document discusses thermodynamics concepts including entropy, spontaneity, Gibbs free energy, and how to use thermodynamic data to determine if chemical reactions are spontaneous. It provides examples of calculating entropy changes, Gibbs free energy changes, and using these values along with enthalpy changes to predict spontaneity. Standard enthalpy and entropy values are used from data tables to perform sample calculations for reactions.
The document discusses using enthalpy vs composition plots, also known as Ponchon-Savarit plots, to obtain information about separation problems involving energy balances based on enthalpy. It explains that these plots show three phases - solid, liquid, and vapor - with temperature represented by tie lines. Points between saturated lines represent two-phase systems, and azeotropes are indicated by vertical isotherms.
This document discusses thermodynamic properties and relationships for homogeneous phases. It defines key concepts like internal energy, enthalpy, entropy, and Gibbs free energy. Equations are derived relating these properties to temperature and pressure. The relationships show that entropy decreases with increasing pressure as particles are confined to a smaller space, reducing disorder. Gibbs free energy can be used to predict spontaneity of reactions according to the second law of thermodynamics.
This document discusses thermodynamic properties and relationships for homogeneous phases. It defines key concepts like internal energy, enthalpy, entropy, and Gibbs free energy. Equations are derived relating these properties to temperature and pressure. The relationships show that entropy decreases with increasing pressure as particles are confined to a smaller space, reducing disorder. Gibbs free energy can be used to predict spontaneity of reactions according to the second law of thermodynamics.
Chemical equilibrium is briefly discussed with following topics:
Free energy change in a chemical reaction. Thermodynamic derivation of the law of chemical equilibrium.
Definition of ΔG and ΔG◦
Le Chatelier’s principle.
Relationships between Kp, Kc and Kx
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The document contains critical data for various compounds including their molecular weights, freezing points, boiling points, critical temperatures, pressures, volumes, compressibility factors, and acentric factors. The data is presented in a table with 27 compounds listed along with their properties. This table provides physical property data for analysis of these compounds and calculations involving their critical points and states.
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This document summarizes the topological structure of ternary residue curve maps, which describe the dynamics of ternary distillation processes. It introduces differential equations that model ternary distillation and place a meaningful structure on ternary phase diagrams. By recognizing this structure is subject to the Poincaré-Hopf index theorem, the authors obtained a topological relationship between azeotropes and pure components in ternary mixtures. This relationship provides useful information about ternary mixture distillation behavior and predicts situations where ternary azeotropes cannot occur.
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CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
On criteria for occurence of azeotropes in isothermal and isobraric binary systems
1. VOLUME 83, AUGUST 2005 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING 667
F
rom the point of view of separation processes involving
vapour-liquid systems (e.g. fractional distillation), it is
important to know if an azeotrope exists in a particular
system. If complete experimental vapour-liquid equilibrium data
are available, this information is known explicitly. If, however,
the data are embedded in a correlation for liquid-phase activity
coefficients (γi) (or, equivalently, for the excess molar Gibbs
function (gE)), or if the data come from a model for γi or gE, this
information is only known implicitly. Models may include a
solution model such as a regular solution (Hildebrand et al.,
1970), or a group-contribution method based on molecular
structure, such as UNIFAC (Fredenslund et al., 1975), for use
when no experimental or model parameters are available.
The possible existence of an azeotrope may be considered for
a system either at constant temperature (T) or at constant
pressure (P). The former may be more important from a theoretical
On Criteria for Occurrence of Azeotropes
in Isothermal and Isobaric Binary Systems
Ronald W. Missen
Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street,
Toronto, ON, Canada M5S 3E5
point of view, but since separation processes involving vapour-
liquid systems operate essentially at constant pressure, this
situation is more important from this practical point of view.
Attention has been paid in the literature to the isothermal case,
but we address both situations here.
These considerations lead to the question of obtaining criteria
for the occurrence of azeotropes in general. Some guidance in
the literature for isothermal systems comes from the “Bancroft
rule” (King, 1969) and from criteria developed by Prigogine and
Defay (1954) for regular solutions. The former, which states, in
effect, that if two species have the same saturation vapour
pressure p* (at T′, say), then there is an azeotrope at T′, is
self-evident, since any departure from ideality in such a case
leads to an azeotrope. Comprehensive criteria for isothermal
systems are given by Brandini (1974) in terms of activity coeffi-
cients at infinite dilution (γ∞). We include here a different
Criteria are developed for the occurrence of azeotropes in binary nonelectrolyte systems for both isothermal and isobaric situations in terms of
liquid-phase activity coefficients at infinite dilution (γ∞). In the case of isothermal systems at temperature T, for a positive azeotrope, γ∞
lvc ≥ p*mvc/
p*lvc, where lvc refers to the less volatile component, mvc to the more volatile component, and p* to saturation vapour pressure at T; for a
negative azeotrope, γ∞
mvc ≤ p*lvc/p*mvc. In the case of isobaric systems at pressure P, for a minimum-boiling azeotrope, γ∞
lvc(TBmvc) ≥ P/p*lvc(TBmvc),
where TB refers to the boiling point at P; for a maximum-boiling azeotrope, γ∞
mvc(TBlvc) ≤ P/p*mvc(TBlvc). The criteria are also given in terms of the
parameters of selected correlations for the excess molar Gibbs function (gE). Examples of the use of the criteria are provided. Various methods
that generate values of γ∞ can be used in conjunction with the criteria, for example, in screening procedures.
Des critères basés sur les coefficients d’activité en phase liquide pour une dilution infinie (γ∞) ont été mis au point pour prédire l’apparition des
azéotropes dans les systèmes non électrolytiques binaires dans des conditions isothermes et isobares. Dans le cas des systèmes isothermes à la
température T, pour une azéotrope positive, γ∞
lvc ≥ p*mvc/p*lvc , où lvc réfère au composant moins volatil, mvc au composant plus volatil et p* à la
pression de vapeur saturante à T; pour une azéotrope négative, γ∞
mvc ≤ p*lvc/p*mvc . Dans le cas de systèmes isobares à la pression P, pour une
azéotrope d’ébullition minimum, γ∞
lvc(TBmvc) ≥ P/p*lvc(TBmvc) , où TB réfère au point d’ébullition à P; pour une azéotrope d’ébullition maximum,
γ∞
mvc(TBlvc) ≤ P/p*mvc(TBlvc). On donne également les critères pour les paramètres de corrélations sélectionnées pour la fonction molaire d’excès de
Gibbs (gE). Des exemples d’utilisation des critères sont donnés. Diverses méthodes donnant des valeurs de γ∞ peuvent être utilisées avec ces
critères, par exemple dans les méthodes de tamisage.
Keywords: isothermal azeotrope criteria; isobaric azeotrope criteria; binary systems
2. 668 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 83, AUGUST 2005
development of these together with a graphical interpretation.
We also give a corresponding new treatment for isobaric systems.
Examples to illustrate application of the criteria developed are
provided.
ISOTHERMAL CRITERIA FOR OCCURRENCE
OF AZEOTROPES
Qualitative Considerations
Figure 1 illustrates schematically P(x1) relationships for a fixed-
T plane intersecting a P-T-x1 saturated-liquid surface, where x1is
mole fraction of component 1. It shows P(x1) for various degrees
of departure from Raoult’s law (A, for an ideal system) in both
positive and negative directions. Curves B, C, and D show
increasing degrees of positive deviation: B for no azeotrope and
D for a positive azeotrope (at the maximum, where x1 = y1 (not
shown, the mole fraction in the coexisting vapour phase,
whether actual or virtual)); C represents the boundary between
these two types of behaviour, as the indication of incipient
occurrence of a positive azeotrope with respect to increasing
extent of nonideality. (For still greater positive deviation than in
D, single liquid-phase stability eventually breaks down, and
increasing degrees of partial miscibility set in, leading ultimately
to complete immiscibility, the greatest degree of positive
deviation from Raoult’s law.). Correspondingly, curves E and G
(negative azeotrope at the minimum) illustrate increasing
degrees of negative deviation, with F representing incipient
negative azeotrope formation with respect to increasing nonide-
ality. (There is no corresponding single-phase stability breakdown
in this direction.)
Assumptions
We assume the following:
(A1) The system is a binary nonelectrolyte system of
components 1 and 2 that are completely miscible in the
liquid phase.
(A2) Information for γi or gE is for a saturated liquid phase,
actually or potentially in equilibrium with a vapour
phase.
(A3) The γi or gE data refer to Raoult’s law ideality; that is, γi
→ 1 as xi → 1.
(A4) The γi or gE data refer either to isothermal or to isobaric
(case to follow) conditions.
(A5) The dependence of γi or gE on P is negligible, but the
dependence on T must be allowed for.
(A6) The pressure is sufficiently low that the Poynting correc-
tion (Sandler, 1999) is equal to one.
Criteria in Terms of Activity Coefficients at Infinite
Dilution
The activity coefficients at infinite dilution are designated γ1
∞ (at
x1 = 0) and γ2
∞ (at x2 = 0) for components 1 and 2, respectively.
Our goal is to obtain criteria in terms of these quantities.
In the absence of any fugacity corrections at low pressure
(assumption (A6)), the total pressure at T is given by
P = γ1(T,x1)x1p1* (T) + γ2(T,x1)x2p2* (T) (1)
From Equation (1), on differentiation at constant T, we obtain
∂
∂
= +
∂
∂
− +
∂
∂
P
x
p x p
x
p x p
x1
1 1 1 1
1
1
2 2 2 2
2
1
* * * *γ
γ
γ
γ
(2)
= 0 (at an azeotrope) (3)
Consider incipient positive azeotrope formation with component
1 as the more volatile component (p1* > p2* at T). This occurs
as x1 → 1 at C in Figure 1. In such a case, x2 → 0, γ1 → 1, γ2 →
γ2
∞, x1p1* ∂γ1/∂x1 = x1p1*γ1 ∂lnγ1/∂x1 → p1* ∂lnγ1/∂x1 → 0, and
x2p2* ∂γ2/∂x1 → 0. From Equations (2) and (3), we conclude that
a criterion for incipient formation of a positive azeotrope is
γ2
∞ = p1*/p2* ( > 1). Instead of component 1 being the more
volatile component, an arbitrary designation may have component
2 in this role. The situation depicted in Figure 1 is then reversed
(although not shown). Incipient azeotrope formation occurs as
x1 → 0 or x2 → 1, in which case, γ1 → γ1
∞ and γ2 → 1. From
Equations (2) and (3), the criterion for an incipient azeotrope is
γ1
∞ = p2*/p1* ( > 1). In either case, if the component designa-
tions are changed to more volatile component (mvc) and less
volatile component (lvc), instead of components 1 and 2, the
criterion for an incipient positive azeotrope can be written as
one equation:
p*2
P
X1
F
T CONSTANTT CONSTANTT CONST
p*1
0 1
G
E
A
B
D
C
Figure 1. Schematic representation of P(x1) at fixed T showing positive
and negative deviations from Raoult’s law.
A Raoult’s law
B Positive deviation, no azeotrope
C Positive deviation, incipient positive azeotrope
D Positive deviation, positive azeotrope at maximum
E Negative deviation, no azeotrope
F Negative deviation, incipient negative azeotrope
G Negative deviation, negative azeotrope at minimum
3. VOLUME 83, AUGUST 2005 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING 669
γlvc
mvc
lvc
p
p
∞
=
*
*
criterion for
incipient positive
azeotrope formaation
(4)
As the degree of positive departure from ideality increases, in
the sense of curve D in Figure 1, azeotrope formation occurs. In
every case, γ∞
lvc increases relative to the value in Equation (4).
Thus, a criterion for the existence of a positive azeotrope is
γlvc
mvc
lvc
p
p
∞
≥
*
*
criterion for
positive azeotrope (5)
If γ∞
lvc < p*mvc/p*lvc, no azeotrope exists.
Similarly, consider incipient negative azeotrope formation as
x1 → 0 at F in Figure 1, with component 1 as the mvc (or the
reverse as x1 → 1, if component 2 is the mvc). Considerations
based on Equations (2) and (3) corresponding to those above
lead to the following criterion for an incipient negative
azeotrope:
γmvc
lvc
mvc
p
p
∞
=
*
*
criterion for
incipient negative
azeotrope formaation
(6)
As the degree of negative departure from ideality increases in
the sense of curve G in Figure 1, azeotrope formation occurs. In
every case, γ∞
mvc decreases relative to the value in Equation (6).
Table 1. Expressions for γ1
∞ and γ2
∞ from selected gE equations
gE equation γ1
∞ γ2
∞
Redlich-Kister, Equation (8)
Van Laar
Wilson
NRTL
exp ( ) exp
exp exp
1
1
1
1
0 0
1
RT
g
RT
g
A B
k
K
k
k
k
K
k
= =
∑ ∑−
Λ 22
21
21
12
21 12 12 12 1
1
1
1exp( ) exp( )
exp exp - exp
− −
+ ( )
Λ
Λ
Λ
τ τ α τ τ 2
2 21 12 2
1+ ( ) τ α τexp -
Table 2. Examples of use of criteria (5) and (7) for positive and negative azeotropes
System T/ºC mvc dev. gE criterion (5) criterion (7) ref.
corr.a γ∞
lvc P*mvc pos. γ∞
lvc P*lvc neg.
P*lvc azeo. P*mvc azeo.
n-C5H12 (1) 40 (1) + VL 4.07 1.52 Y ← N/A → (a)
+ 40 (1) + W 4.02 1.52 Y ← N/A → (a)
propionaldehyde (2) 40 (1) + NRTL 3.85 1.52 Y ← N/A → (a)
n-butyraldehyde (1) 45 (1) + VL 3.05 2.30 Y ← N/A → (a)
+ 45 (1) + W 3.12 2.30 Y ← N/A → (a)
n-C7H16 (2) 45 (1) + NRTL 3.04 2.30 Y ← N/A → (a)
isobutyraldehyde (1) 45 (1) + VL 2.72 3.41 N ← N/A → (a)
+ 45 (1) + W 2.76 3.41 N ← N/A → (a)
n-C7H16 (2) 45 (1) + NRTL 2.73 3.41 N ← N/A → (a)
DMA (1) + CH3OH (2) 40 (2) – RK ← N/A → 0.406 0.019 N (b)
CH3F (1) + HCl (2) –90.8 (2) – RK ← N/A → 0.267 0.668 Y (c)
C6F6(1) + C6H6(2) 60 (2) ± RK 1.20 1.04 Y 0.898 0.979 Y (d)
(a) Eng and Sandler (1984); (b) Zielkiewicz (2003); (c) Senra et al. (2002); (d) Gaw and Swinton (1968)
aRK (Redlich-Kister); VL (van Laar); W (Wilson)
Figure 2. Regions of occurrence of positive and negative azeotropes in
binary systems at fixed T according to criteria (5) and (7).
(note change of variables in lower left and upper right fields)
4. 670 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 83, AUGUST 2005
a gE expression is available, but is outside the scope of this
paper.
As noted above, Brandini (1974) presents essentially the same
criteria as (5) and (7) for isothermal systems, but expresses them
in terms of components 1 and 2, and provides no graphical
interpretation corresponding to Figure 2. The designation as
components 1 and 2 requires four statements rather than the two
in criteria (5) and (7).
Criteria in Terms of Parameters of gE Correlations
As noted above, the information required to apply the criteria for
existence of azeotropes may be embedded in equations for the
excess molar Gibbs function (gE). In Table 1, expressions are
provided for γ1
∞ and γ2
∞ from four such equations: Redlich-Kister
(1948), van Laar (Carlson and Colburn, 1942), Wilson (1964),
and NRTL (Renon and Prausnitz, 1968). The van Laar results are
readily apparent from the Carlson-Colburn forms of the activity
coefficients. The Redlich-Kister equation is an expansion in
terms of composition that can be represented by:
g x x g x xE
k
K
k
k
= −
=
∑1 2
0
1 2( ) (8)
The results in Table 1 can be derived from Equation (8).
Examples of Use of Criteria
Table 2 shows randomly selected examples of the use of criteria
(5) and (7) to indicate presence or absence of an azeotrope. The
first nine entries come from the work of Eng and Sandler (1984)
on three aldehyde systems (column 1) at the T given in column
2. In each of these cases, component (1) is the more volatile
component (mvc), and the deviation from ideality is positive.
For each system, they compared the fitting of several gE correla-
tions (corr.), including van Laar (VL), Wilson (W) and NRTL
equations. The use of criterion (5) is applicable here, and
columns 6 to 8 give the results – azeotropes in the first two
systems, but no azeotrope in the third, as consistently shown by
each gE correlation. The next two entries (Zielkiewicz, 2003;
Senra et al., 2002) refer to negative deviation and the use of
criterion (7) in conjunction with the RK equation. The last entry
in Table 2 is for the rare case of a double azeotrope, in the
hexafluorobenzene + benzene system at 60°C (Gaw and
Swinton, 1968). This is the situation in which both a positive
and a negative azeotrope occur at a particular T. In this case,
both criteria (5) and (7) are required, and they indicate the
existence of the two azeotropes observed. In all 12 cases in
Table 2, the results of application of criterion (5) or (7) agree
with experimental results.
ISOBARIC CRITERIA FOR OCCURRENCE
OF AZEOTROPES
Qualitative Considerations
Figure 3 illustrates schematically T(x1) relationships for fixed-P
planes intersecting a P-T-x1 saturated-liquid surface. The
behaviour labelled by C′, D′, F′, and G′ corresponds to that
labelled by C, D, F, and G in Figure 1. Thus, D′ represents a
minimum-boiling azeotrope at fixed P, which corresponds to a
positive azeotrope at fixed T. Similarly, G′ represents a maximum-
boiling azeotrope, which corresponds to a negative azeotrope.
The behaviour indicated at C′ and F′ represents incipient
formation (with respect to increasing extent of nonideality) of
Thus, a criterion for the existence of a negative azeotrope is
γmvc
lvc
mvc
p
p
∞
≤
*
*
criterion for
negative azeotrope
(7)
If γ∞
mvc > p*lvc/p*mvc, no azeotrope exists.
Figure 2 shows the results expressed by the criteria of (5) and
(7) in graphical form. In the lower left (closed) field, the
diagonal line representing incipient azeotrope formation divides
the regions of negative azeotrope occurrence and no azeotrope
according to (7). Similarly, the continuation of the diagonal line
through the upper right (open-ended) field divides the regions of
positive azeotrope occurrence and no azeotrope according to (5).
The horizontal axis at γ = 1 represents ideal (Raoult’s law)
behaviour, and forms one border of each “no azeotrope” field.
The vertical axis at a pressure ratio = 1 represents the Bancroft
rule, and forms one border of each azeotrope field. In a model
sense, Figure 2 indicates the extent of nonideality, in terms of γ∞
lvc
or γ∞
mvc that can be tolerated to avoid the occurrence of an
azeotrope for a given ratio of vapour pressures.
In Figure 2, the indefinite extension of criterion (5) for a
positive azeotrope can be deceiving. Assumption (A1) notwith-
standing, increasing nonideality, represented by increasing γ∞
lvc,
leads eventually to a miscibility gap in the liquid phase. This
cannot be predicted by criterion (5), and, if suspected, must be
tested independently by a stability analysis. This is facilitated if
TB1
C'
D'
X1
G'
F'
T
P CONSTANTP CONSTANTP CONST
TB2
0 1
Figure 3. Schematic representation of T(x1) at fixed P for various
situations:
D′ minimum-boiling azeotrope
C′ incipient formation of minimum-boiling azeotrope
G′ maximum-boiling azeotrope
F′ incipient formation of maximum-boiling azeotrope
5. VOLUME 83, AUGUST 2005 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING 671
minimum-boiling and maximum-boiling azeotropes, respec-
tively. TB1 and TB2 are the boiling points of components 1 and 2,
respectively, at P. The more volatile component (mvc) has the
lower boiling point: TB1 < TB2.
Criteria in Terms of Activity Coefficients at Infinite
Dilution
The activity coefficient intercepts at x1 = 0 and x1 = 1, γ1
∞ and
γ2
∞, respectively, again represent the activity coefficients at
infinite dilution. Our goal is to obtain criteria for the occurrence
of azeotropes in terms of these quantities.
From Equation (1), which represents P(T,x1), with dP = 0, we
form the derivative
∂
∂
= −
+
∂
∂
− +
∂
∂
∂
T
x
p x p
x
p x p
x
x p1
1 1 1 1 1
1
1
2 2 2 2 2
2
1
1 1 1
γ γ
γ
γ γ
γ
γ
* *
ln
* *
ln
*
lln *
*
ln *γ
γ γ
γ
γ1
1 1
1
2 2 2
2
2 2
2
∂
+ +
∂
∂
+
T
x
dp
dT
x p
T
x
dp
dT
(9)
= 0 (at an azeotrope) (10)
where (Smith and Missen, 1991)
∂
∂
= −
l
T
h
RT
i i
E
2
nγ
(11)
where
–
hi
E is the excess partial molar enthalpy of species i, and R
is the gas constant.
Corresponding to the isothermal case, consider first incipient
formation of a minimum-boiling azeotrope as x1 → 1 at C′ in
Figure 3. Then, x2 → 0, T → TB1, γ1 → 1, γ2 → γ2
∞ (TB1),
–
hi
E →
0, and Equations (9) and (10) reduce to
−
−
=
∞
p T T p T
dp
dT
B1 B1 2 B1 2 1
1
*( ) ( ) *( )
*
γ
0 (12)
From Equation (12), since dp1*/dT ≠ 0, we obtain the following
criterion for incipient formation of a minimum-boiling azeotrope
with component 1 as the mvc:
γ2 1
1 1
2 1 2 1
∞
= =( )
*( )
*( ) *( )
T
p T
p T
P
p T
B
B
B B
(13)
If component 2 is arbitrarily designated as the mvc, then the
criterion for incipient formation becomes
γ1 2
2 B2
1 B2 1 B2
∞
= =( )
*( )
*( ) *( )
T
p T
p T
P
p T
B (14)
Equations (13) and (14) can be combined into one criterion by
using designations mvc and lvc instead of 1 and 2:
Table 4. Examples of use of criterion (18) for maximum-boiling azeotropes
System P/ TB1 (P)/ TB2 (P)/ mvc gE γ∞
mvc P
kPa ºC ºC corr.a (TBlvc) P*mvc(TBlvc) azeo ref.
1-butanol (1) 101.3 117.7 77.1 (2) VL 0.44 0.31 N (a)
+ 101.3 117.7 77.1 (2) W 0.40 0.31 N (a)
1-butylamine (2) 101.3 117.7 77.1 (2) NRTL 0.43 0.31 N (a)
2-butanol (1) 101.3 99.6 77.1 (2) VL 0.41 0.51 Y (b)
+ 101.3 99.6 77.1 (2) W 0.35 0.51 Y (b)
1-butylamine (2) 101.3 99.6 77.1 (2) NRTL 0.42 0.51 Y (b)
CH3OH (1) + diethylamine (2) 97.3 63.5 53.8 (2) M3 0.37 0.72 Y (c)
CH3OH (1) + 1-butylamine (2) 97.3 63.5 76.6 (1) M2 0.79 0.61 N (c)
(a) Dominguez et al. (1997); (b) Dominguez et al. (2002); (c) Nakanishi et al. (1967)
aVL (van Laar); W (Wilson); M2, M3 (two-constant, three-constant Margules)
Table 3. Examples of use of criterion (16) for minimum-boiling azeotropes
System P/ TB1 (P)/ TB2 (P)/ mvc gE γ∞
lvc P azeo ref.
kPa ºC ºC corr.a (TBmvc) P*lvc(TBmvc)
1-butanol (1) 101.3 117.7 68.8 (2) VL 8.6 7.9 Y (a)
+ 101.3 117.7 68.8 (2) W 12.4 7.9 Y (a)
n-hexane (2) 101.3 117.7 68.8 (2) NRTL 6.7 7.9 Nb (a)
2-butanol (1) 101.3 99.6 68.8 (2) VL 6.8 3.6 Y (b)
+ 101.3 99.6 68.8 (2) W 8.3 3.6 Y (b)
n-hexane (2) 101.3 99.6 68.8 (2) NRTL 5.8 3.6 Y (b)
n-hexane (1) 101.3 68.8 77.1 (1) VL 1.83 1.36 Y (a)
+ 101.3 68.8 77.1 (1) W 1.83 1.36 Y (a)
1-butylamine (2) 101.3 68.8 77.1 (1) NRTL 1.82 1.36 Y (a)
CH3OH (1) + triethylamine (2) 97.3 63.5 88.3 (1) M2 2.09 2.37 N (c)
C3H7OH (1) + H2O (2) 101.3 87.8 100.0 (1) VL 3.10 1.57 Y (d)
(a) Dominguez et al. (1997); (b) Dominguez et al. (2002); (c) Nakanishi et al. (1967); (d) Carlson and Colburn (1942)
aVL (van Laar); W (Wilson); M2 (two-constant Margules)
bsee text
6. 672 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 83, AUGUST 2005
γlvc B mvc
lvc B mvc
T
P
p T
∞
=( )
( )*
criterion for
incipient formation of
mminimum boiling azeotrope−
(15)
Since the actual occurrence of a minimum-boiling azeotrope,
as in curve D′ in Figure 3, results from a greater positive
departure from ideality (that is, a greater value of γ∞
lvc) than
represented in Equation (15), a criterion for this is
γlvc B mvc
lvc B mvc
T
P
p T
∞
≥( )
( )*
criterion for
minimum - boiling
azeotrrope
(16)
If γ∞
lvc(TBmvc) < P/p*lvc(TBmvc), there is no azeotrope.
Next, consider incipient formation of a maximum-boiling
azeotrope as x1 → 0 at F′ in Figure 3. Or, conversely, if component
2 is arbitrarily designated as the mvc, incipient formation occurs
as x2 → 0 (not shown in Figure 3). In either case, it occurs as
xmvc → 0. Arguments similar to those above for a minimum-
boiling azeotrope lead to the following criterion for incipient
formation:
γ∞
mvc B lvc
mvc B lvc
T
P
p T
( )
( )*
=
criterion for incipient
formation off
maximum - boiling azeotrope
(17)
Since the actual occurrence of a maximum-boiling azeotrope, as
in curve G′ in Figure 3, results from a greater negative departure
from ideality (that is, a smaller value of γ∞
mvc)than represented in
Equation (17), a criterion for this is
γmvc B lvc
mvc B lvc
T
P
p T
∞
≤( )
( )*
criterion for
maximum - boiling
azeotrrope
(18)
If γ∞
mvc(TBlvc) > P/p*mvc(TBlvc), there is no azeotrope.
Figure 4 shows the results expressed by criteria (16) and (18)
in graphical form. In the lower left (closed) field, the diagonal
line representing incipient azeotrope formation divides the
regions of maximum-boiling azeotrope occurrence and no
azeotrope according to (18). Similarly, the continuation of the
diagonal line through the upper right (open-ended) field divides
the regions of minimum-boiling azeotrope occurrence and no
azeotrope according to (16). Figure 4 is similar to Figure 2, but
the variables and azeotrope fields have different significance.
In the use of Figure 4 or criterion (16) for a minimum-boiling
azeotrope, the possible occurrence of a liquid-phase miscibility
gap for sufficiently large values of γ∞
lvc(TBmvc) must be consid-
ered, as discussed above for a positive azeotrope. Criterion (16)
cannot predict this.
In the use of criteria (16) and (18), values of γ∞
lvc(TBmvc) and
γ∞
lvc(TBlvc) are the ones naturally obtained from experimental
vapour-liquid equilibrium data at P. If, however, γ∞
lvc and γ∞
mvc are
obtained otherwise, for example, from gE(T′), their values,
γ∞
lvc(T′) and γ∞
lvc(T′) must be adjusted to give the values required
for criteria (16) and (18). This temperature adjustment is done
by means of Equation (11). Thus, for γ∞
lvc
ln
γ
γ
lvc B mvc
lvc
T
T
lvc
ET
T
h T
T
dT
B mvc
∞
∞ ′
∞
′
= − ∫
( )
( )
( )1
R 2 (19)
and for γ∞
mvc
ln
γmvc B lvc
mvc
T
T
mvc
ET
T
h T
T
dT
B lvc
∞
∞ ′
∞
′
= − ∫
( )
( )
( )
³
1
R 2 (20)
where
–
hlvc
E∞
and
–
hE∞
mvc are the excess partial molar enthalpies at
infinite dilution of lvc and mvc, respectively. The excess enthalpy
(heat of mixing) compilations of Christensen et al. (1982, 1988)
and of Christensen et al. (1984) and Gmehling and Holderbaum
(1989,1991) are useful for this purpose.
Criteria in Terms of Parameters of gE Correlations
As noted for isothermal systems, since γi
∞ can be obtained from
gE correlations, the criteria for the occurrence of azeotropes in
isobaric systems can be applied using the parameters of the gE
correlations, as given in Table 1. The last three of these are used
in the examples of applications of the criteria in the following
section.
Examples of Use of Criteria
Tables 3 and 4 show randomly selected examples of the use of
criteria (16) and (18), respectively, to indicate presence or
absence of azeotropes. In these tables, vapour pressures required
were calculated from Antoine constants provided by Boublík et
al. (1984) for the butanols, and by Nakanishi et al. (1967) for
methanol and the amines.
In Table 3, the first nine entries for three systems come from
the work of Dominguez et al. (1997, 2002) for positive deviations
from ideality for systems involving butanols, n-hexane, and
1-butylamine (column 1) at 101.3 kPa (column 2). The boiling
points (TB) of the components are listed in columns 3 and 4. The
MINIMUM - BOILING
AZEOTROPE
NO
AZEOTROPE
P CONSTANT
γlvcγlvcγ∞(TBmvc)
P/plvc*(TBmvc)
MAXIMUM -
BOILING
AZEOTROPE
NO
AZEOTROPE
γmvγmvγc∞(TBlvc)
P/pmvc (TBlvc)0 1P/p0 1P/p *0 1*(T0 1(TBlvc
0 1
Blvc)0 1)
1
Figure 4. Regions of occurrence of minimum-boiling and maximum-
boiling azeotropes in binary systems at fixed P, according to criteria
(16) and (18).
(note change of variables in lower left and upper right fields)
7. VOLUME 83, AUGUST 2005 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING 673
mvc is indicated next, followed, in order, by the gE (or γ) correla-
tion (corr.) used to fit experimental equilibrium data, the value
of γ∞
lvc at TBmvc, the value of the ratio P/p*lvc(TBmvc), and the
conclusion as to whether an azeotrope occurs. For each of these
three systems (nine entries), the authors fitted the van Laar
(VL), Wilson (W), and NRTL equations, among others, to the
experimental data, and provided resulting values of γ∞
lvc(TBmvc)
In each case except one, the existence of a minimum-boiling
azeotrope is indicated, in agreement with experimental results.
The one apparent exception is for the third entry. In this case,
however, the NRTL estimate of γ∞
lvc(TBmvc) (together with two
others not listed here) is low in comparison with the estimates
from the van Laar and Wilson equations (graphical extrapolation
indicates a value ≥ 9, in line with these last two). (This example
shows that the experimental data from VLE measurements
across the composition range do not always provide for a good
statistical fit at the extremes for γ1
∞ and γ2
∞ for a given correla-
tion.) The last two entries (Nakanishi et al., 1967; Carlson and
Colburn, 1942) similarly illustrate situations in which no
azeotrope and an azeotrope, respectively, occur.
In Table 4, the first six entries for two systems come from the
work of Dominguez et al. (1997, 2002) for negative deviations
from ideality. For the system 1-butanol (1) + 1-butylamine (2),
the conclusion is that there is no azeotrope. For the system 2-
butanol (1) + 1-butylamine (2), the conclusion is the opposite
– there is a maximum-boiling azeotrope. Both of these conclu-
sions agree with the experimental result. The last two entries,
from the work of Nakanishi et al. (1967), also provide one
example in which an azeotrope occurs and one in which there
is no azeotrope.
CONCLUSION
Any method that generates values of activity coefficients at
infinite dilution, γ1
∞ and γ2
∞, in a binary system can be used to
determine whether an azeotrope exists in the system at a
specified (constant) T, in accordance with Figure 2 (based on
criteria (5) and (7)); or in the system at a specified (constant) P
in accordance with Figure 4 (based on criteria (16) and (18)).
(For isothermal systems, the criteria are essentially the same as
those given by Brandini (1974).) In a model sense, Figure 2 or
Figure 4 shows the extent of nonideality that can be tolerated to
avoid an azeotrope for a given pressure ratio; the greater the
ratio, the greater the extent of nonideality allowable, consistent
with qualitative considerations.
Gmehling et al. (1994) have described various experimental
methods for determining γ∞, including the use of gas-liquid
chromatography and ebulliometry (as well as from VLE measure-
ments). Malanowski and Anderko (1992) note these and
describe two estimation methods. Applications should prove
useful for screening for various purposes.
ACKNOWLEDGEMENT
Financial assistance has been received from the Natural Sciences
and Engineering Research Council of Canada.
NOMENCATURE
A,B parameters in Van Laar equation
gE excess Gibbs function (J mol-1)
gk parameter in Redlich-Kister equation (8)
–
hi
E excess partial molar enthalpy of component i (J mol-1)
p* saturation vapour pressure (kPa)
P pressure (kPa)
R gas constant, 8.3145 (J mol-1 K-1)
T temperature (K or °C)
y mole fraction in vapour phase
x mole fraction in liquid phase
Greek Symbols
γ activity coefficient
Λ12, Λ21 parameters in Wilson equation
τ12, τ21 parameters in NRTL equation
Superscripts
∞ at infinite dilution
Subscripts
B boiling point
i component i
lvc less volatile component
mvc more volatile component
1, 2 component 1, 2
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Manuscript received February 17, 2005; revised manuscript received
June 22, 2005; accepted for publication July 27, 2005.