The Mixture Fraction
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Ideal-Gas Mixtures and Real-Gas Mixtures
Thermodynamics: An Engineering Approach, 6th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 Chapter 13 GAS MIXTURES Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Objectives • Develop rules for determining nonreacting gas mixture properties from knowledge of mixture composition and the properties of the individual components. • Define the quantities used to describe the composition of a mixture, such as mass fraction, mole fraction, and volume fraction. • Apply the rules for determining mixture properties to ideal-gas mixtures and real-gas mixtures. • Predict the P-v-T behavior of gas mixtures based on Dalton’s law of additive pressures and Amagat’s law of additive volumes. • Perform energy and exergy analysis of mixing processes. 2 COMPOSITION OF A GAS MIXTURE: MASS AND MOLE FRACTIONS To determine the properties of a mixture, we need to know the composition of the mixture as well as the properties of the individual components. There are two ways to describe the composition of a mixture: Molar analysis: specifying the number of moles of each component Gravimetric analysis: specifying the mass of each component The mass of a mixture is equal to the sum of the masses of its components. Mass fraction Mole The number of moles of a nonreacting mixture fraction is equal to the sum of the number of moles of its components. 3 Apparent (or average) molar mass The sum of the mass and mole fractions of a mixture is equal to 1. Gas constant The molar mass of a mixture Mass and mole fractions of a mixture are related by The sum of the mole fractions of a mixture is equal to 1. -
Page 1 of 6 This Is Henry's Law. It Says That at Equilibrium the Ratio of Dissolved NH3 to the Partial Pressure of NH3 Gas In
CHMY 361 HANDOUT#6 October 28, 2012 HOMEWORK #4 Key Was due Friday, Oct. 26 1. Using only data from Table A5, what is the boiling point of water deep in a mine that is so far below sea level that the atmospheric pressure is 1.17 atm? 0 ΔH vap = +44.02 kJ/mol H20(l) --> H2O(g) Q= PH2O /XH2O = K, at ⎛ P2 ⎞ ⎛ K 2 ⎞ ΔH vap ⎛ 1 1 ⎞ ln⎜ ⎟ = ln⎜ ⎟ − ⎜ − ⎟ equilibrium, i.e., the Vapor Pressure ⎝ P1 ⎠ ⎝ K1 ⎠ R ⎝ T2 T1 ⎠ for the pure liquid. ⎛1.17 ⎞ 44,020 ⎛ 1 1 ⎞ ln⎜ ⎟ = − ⎜ − ⎟ = 1 8.3145 ⎜ T 373 ⎟ ⎝ ⎠ ⎝ 2 ⎠ ⎡1.17⎤ − 8.3145ln 1 ⎢ 1 ⎥ 1 = ⎣ ⎦ + = .002651 T2 44,020 373 T2 = 377 2. From table A5, calculate the Henry’s Law constant (i.e., equilibrium constant) for dissolving of NH3(g) in water at 298 K and 340 K. It should have units of Matm-1;What would it be in atm per mole fraction, as in Table 5.1 at 298 K? o For NH3(g) ----> NH3(aq) ΔG = -26.5 - (-16.45) = -10.05 kJ/mol ΔG0 − [NH (aq)] K = e RT = 0.0173 = 3 This is Henry’s Law. It says that at equilibrium the ratio of dissolved P NH3 NH3 to the partial pressure of NH3 gas in contact with the liquid is a constant = 0.0173 (Henry’s Law Constant). This also says [NH3(aq)] =0.0173PNH3 or -1 PNH3 = 0.0173 [NH3(aq)] = 57.8 atm/M x [NH3(aq)] The latter form is like Table 5.1 except it has NH3 concentration in M instead of XNH3. -
On the Multi-Physics of Mass-Transfer Across Fluid Interfaces
On the multi-physics of mass-transfer across fluid interfaces Dieter Bothe Center of Smart Interfaces TU Darmstadt [email protected] Abstract Mass transfer of gaseous components from rising bubbles to the ambient liquid can be described based on continuum mechanical sharp-interface balances of mass, momentum and species mass. In this context, the stan- dard model consists of the two-phase Navier-Stokes equations for incom- pressible fluids with constant surface tension, complemented by reaction- advection-diffusion equations for all constituents, employing Fick’s law. This standard model is inconsistent with the continuity equation, the mo- mentum balance and the second law of thermodynamics. The present paper reports on the details of these severe shortcomings and provides thermodynamically consistent model extensions which are required to cap- ture various phenomena which occur due to the multi-physics of interfacial mass transfer. In particular, we provide a simple derivation of the interface Maxwell-Stefan equations which does not require a time scale separation, while the main contribution is to show how interface concentrations and interface chemical potentials mediate the influence on mass transfer of a transfer component exerted by the change in interface energy due to an adsorbing surfactant. Keywords: Soluble surfactant, interface chemical potentials, interfacial en- tropy production, interface Maxwell-Stefan equations, jump conditions, surface tension effects, high Schmidt number problem, artificial boundary conditions. Introduction The standard model for the continuum mechanical description of mass transfer across fluid interfaces is based on the incompressible two-phase Navier-Stokes equations for fluid systems without phase change. To be more precise, inside the fluid phases the governing equations are arXiv:1501.05610v1 [physics.flu-dyn] 22 Jan 2015 ∇ · v =0, (1) visc ∂t(ρv)+ ∇ · (ρv ⊗ v)+ ∇p = ∇ · S + ρg (2) with the viscous stress tensor T Svisc = η(∇v + ∇v ), (3) 1 where the material parameters depend on the respective phase. -
An Empirical Model Predicting the Viscosity of Highly Concentrated
Rheol Acta &2001) 40: 434±440 Ó Springer-Verlag 2001 ORIGINAL CONTRIBUTION Burkhardt Dames An empirical model predicting the viscosity Bradley Ron Morrison Norbert Willenbacher of highly concentrated, bimodal dispersions with colloidal interactions Abstract The relationship between the particles. Starting from a limiting Received: 7 June 2000 Accepted: 12 February 2001 particle size distribution and viscos- value of 2 for non-interacting either ity of concentrated dispersions is of colloidal or non-colloidal particles, great industrial importance, since it e generally increases strongly with is the key to get high solids disper- decreasing particle size. For a given sions or suspensions. The problem is particle system it then can be treated here experimentally as well expressed as a function of the num- as theoretically for the special case ber average particle diameter. As a of strongly interacting colloidal consequence, the viscosity of bimo- particles. An empirical model based dal dispersions varies not only with on a generalized Quemada equation the size ratio of large to small ~ / Àe g g 1 À / is used to describe particles, but also depends on the g as a functionmax of volume fraction absolute particle size going through for mono- as well as multimodal a minimum as the size ratio increas- dispersions. The pre-factor g~ ac- es. Furthermore, the well-known counts for the shear rate dependence viscosity minimum for bimodal dis- of g and does not aect the shape of persions with volumetric mixing the g vs / curves. It is shown here ratios of around 30/70 of small to for the ®rst time that colloidal large particles is shown to vanish if interactions do not show up in the colloidal interactions contribute maximum packing parameter and signi®cantly. -
THE SOLUBILITY of GASES in LIQUIDS Introductory Information C
THE SOLUBILITY OF GASES IN LIQUIDS Introductory Information C. L. Young, R. Battino, and H. L. Clever INTRODUCTION The Solubility Data Project aims to make a comprehensive search of the literature for data on the solubility of gases, liquids and solids in liquids. Data of suitable accuracy are compiled into data sheets set out in a uniform format. The data for each system are evaluated and where data of sufficient accuracy are available values are recommended and in some cases a smoothing equation is given to represent the variation of solubility with pressure and/or temperature. A text giving an evaluation and recommended values and the compiled data sheets are published on consecutive pages. The following paper by E. Wilhelm gives a rigorous thermodynamic treatment on the solubility of gases in liquids. DEFINITION OF GAS SOLUBILITY The distinction between vapor-liquid equilibria and the solubility of gases in liquids is arbitrary. It is generally accepted that the equilibrium set up at 300K between a typical gas such as argon and a liquid such as water is gas-liquid solubility whereas the equilibrium set up between hexane and cyclohexane at 350K is an example of vapor-liquid equilibrium. However, the distinction between gas-liquid solubility and vapor-liquid equilibrium is often not so clear. The equilibria set up between methane and propane above the critical temperature of methane and below the criti cal temperature of propane may be classed as vapor-liquid equilibrium or as gas-liquid solubility depending on the particular range of pressure considered and the particular worker concerned. -
Colloidal Suspensions
Chapter 9 Colloidal suspensions 9.1 Introduction So far we have discussed the motion of one single Brownian particle in a surrounding fluid and eventually in an extaernal potential. There are many practical applications of colloidal suspensions where several interacting Brownian particles are dissolved in a fluid. Colloid science has a long history startying with the observations by Robert Brown in 1828. The colloidal state was identified by Thomas Graham in 1861. In the first decade of last century studies of colloids played a central role in the development of statistical physics. The experiments of Perrin 1910, combined with Einstein's theory of Brownian motion from 1905, not only provided a determination of Avogadro's number but also laid to rest remaining doubts about the molecular composition of matter. An important event in the development of a quantitative description of colloidal systems was the derivation of effective pair potentials of charged colloidal particles. Much subsequent work, largely in the domain of chemistry, dealt with the stability of charged colloids and their aggregation under the influence of van der Waals attractions when the Coulombic repulsion is screened strongly by the addition of electrolyte. Synthetic colloidal spheres were first made in the 1940's. In the last twenty years the availability of several such reasonably well characterised "model" colloidal systems has attracted physicists to the field once more. The study, both theoretical and experimental, of the structure and dynamics of colloidal suspensions is now a vigorous and growing subject which spans chemistry, chemical engineering and physics. A colloidal dispersion is a heterogeneous system in which particles of solid or droplets of liquid are dispersed in a liquid medium. -
MATERIAL BALANCE NOTES Revision 3 Irven Rinard Department
MATERIAL BALANCE NOTES Revision 3 Irven Rinard Department of Chemical Engineering City College of CUNY and Project ECSEL October 1999 © 1999 Irven Rinard CONTENTS INTRODUCTION 1 A. Types of Material Balance Problems B. Historical Perspective I. CONSERVATION OF MASS 5 A. Control Volumes B. Holdup or Inventory C. Material Balance Basis D. Material Balances II. PROCESSES 13 A. The Concept of a Process B. Basic Processing Functions C. Unit Operations D. Modes of Process Operations III. PROCESS MATERIAL BALANCES 21 A. The Stream Summary B. Equipment Characterization IV. STEADY-STATE PROCESS MODELING 29 A. Linear Input-Output Models B. Rigorous Models V. STEADY-STATE MATERIAL BALANCE CALCULATIONS 33 A. Sequential Modular B. Simultaneous C. Design Specifications D. Optimization E. Ad Hoc Methods VI. RECYCLE STREAMS AND TEAR SETS 37 A. The Node Incidence Matrix B. Enumeration of Tear Sets VII. SOLUTION OF LINEAR MATERIAL BALANCE MODELS 45 A. Use of Linear Equation Solvers B. Reduction to the Tear Set Variables C. Design Specifications i VIII. SEQUENTIAL MODULAR SOLUTION OF NONLINEAR 53 MATERIAL BALANCE MODELS A. Convergence by Direct Iteration B. Convergence Acceleration C. The Method of Wegstein IX. MIXING AND BLENDING PROBLEMS 61 A. Mixing B. Blending X. PLANT DATA ANALYSIS AND RECONCILIATION 67 A. Plant Data B. Data Reconciliation XI. THE ELEMENTS OF DYNAMIC PROCESS MODELING 75 A. Conservation of Mass for Dynamic Systems B. Surge and Mixing Tanks C. Gas Holders XII. PROCESS SIMULATORS 87 A. Steady State B. Dynamic BILIOGRAPHY 89 APPENDICES A. Reaction Stoichiometry 91 B. Evaluation of Equipment Model Parameters 93 C. Complex Equipment Models 96 D. -
Introduction to the Solubility of Liquids in Liquids
INTRODUCTION TO THE SOLUBILITY OF LIQUIDS IN LIQUIDS The Solubility Data Series is made up of volumes of comprehensive and critically evaluated solubility data on chemical systems in clearly defined areas. Data of suitable precision are presented on data sheets in a uniform format, preceded for each system by a critical evaluation if more than one set of data is available. In those systems where data from different sources agree sufficiently, recommended values are pro posed. In other cases, values may be described as "tentative", "doubtful" or "rejected". This volume is primarily concerned with liquid-liquid systems, but related gas-liquid and solid-liquid systems are included when it is logical and convenient to do so. Solubilities at elevated and low 'temperatures and at elevated pressures may be included, as it is considered inappropriate to establish artificial limits on the data presented. For some systems the two components are miscible in all proportions at certain temperatures or pressures, and data on miscibility gap regions and upper and lower critical solution temperatures are included where appropriate and if available. TERMINOLOGY In this volume a mixture (1,2) or a solution (1,2) refers to a single liquid phase containing components 1 and 2, with no distinction being made between solvent and solute. The solubility of a substance 1 is the relative proportion of 1 in a mixture which is saturated with respect to component 1 at a specified temperature and pressure. (The term "saturated" implies the existence of equilibrium with respect to the processes of mass transfer between phases) • QUANTITIES USED AS MEASURES OF SOLUBILITY Mole fraction of component 1, Xl or x(l): ml/Ml nl/~ni = r(m.IM.) '/. -
Chapter 15: Solutions
452-487_Ch15-866418 5/10/06 10:51 AM Page 452 CHAPTER 15 Solutions Chemistry 6.b, 6.c, 6.d, 6.e, 7.b I&E 1.a, 1.b, 1.c, 1.d, 1.j, 1.m What You’ll Learn ▲ You will describe and cate- gorize solutions. ▲ You will calculate concen- trations of solutions. ▲ You will analyze the colliga- tive properties of solutions. ▲ You will compare and con- trast heterogeneous mixtures. Why It’s Important The air you breathe, the fluids in your body, and some of the foods you ingest are solu- tions. Because solutions are so common, learning about their behavior is fundamental to understanding chemistry. Visit the Chemistry Web site at chemistrymc.com to find links about solutions. Though it isn’t apparent, there are at least three different solu- tions in this photo; the air, the lake in the foreground, and the steel used in the construction of the buildings are all solutions. 452 Chapter 15 452-487_Ch15-866418 5/10/06 10:52 AM Page 453 DISCOVERY LAB Solution Formation Chemistry 6.b, 7.b I&E 1.d he intermolecular forces among dissolving particles and the Tattractive forces between solute and solvent particles result in an overall energy change. Can this change be observed? Safety Precautions Dispose of solutions by flushing them down a drain with excess water. Procedure 1. Measure 10 g of ammonium chloride (NH4Cl) and place it in a Materials 100-mL beaker. balance 2. Add 30 mL of water to the NH4Cl, stirring with your stirring rod. -
Phase Transitions in Multicomponent Systems
Physics 127b: Statistical Mechanics Phase Transitions in Multicomponent Systems The Gibbs Phase Rule Consider a system with n components (different types of molecules) with r phases in equilibrium. The state of each phase is defined by P,T and then (n − 1) concentration variables in each phase. The phase equilibrium at given P,T is defined by the equality of n chemical potentials between the r phases. Thus there are n(r − 1) constraints on (n − 1)r + 2 variables. This gives the Gibbs phase rule for the number of degrees of freedom f f = 2 + n − r A Simple Model of a Binary Mixture Consider a condensed phase (liquid or solid). As an estimate of the coordination number (number of nearest neighbors) think of a cubic arrangement in d dimensions giving a coordination number 2d. Suppose there are a total of N molecules, with fraction xB of type B and xA = 1 − xB of type A. In the mixture we assume a completely random arrangement of A and B. We just consider “bond” contributions to the internal energy U, given by εAA for A − A nearest neighbors, εBB for B − B nearest neighbors, and εAB for A − B nearest neighbors. We neglect other contributions to the internal energy (or suppose them unchanged between phases, etc.). Simple counting gives the internal energy of the mixture 2 2 U = Nd(xAεAA + 2xAxBεAB + xBεBB) = Nd{εAA(1 − xB) + εBBxB + [εAB − (εAA + εBB)/2]2xB(1 − xB)} The first two terms in the second expression are just the internal energy of the unmixed A and B, and so the second term, depending on εmix = εAB − (εAA + εBB)/2 can be though of as the energy of mixing. -
Lecture 3. the Basic Properties of the Natural Atmosphere 1. Composition
Lecture 3. The basic properties of the natural atmosphere Objectives: 1. Composition of air. 2. Pressure. 3. Temperature. 4. Density. 5. Concentration. Mole. Mixing ratio. 6. Gas laws. 7. Dry air and moist air. Readings: Turco: p.11-27, 38-43, 366-367, 490-492; Brimblecombe: p. 1-5 1. Composition of air. The word atmosphere derives from the Greek atmo (vapor) and spherios (sphere). The Earth’s atmosphere is a mixture of gases that we call air. Air usually contains a number of small particles (atmospheric aerosols), clouds of condensed water, and ice cloud. NOTE : The atmosphere is a thin veil of gases; if our planet were the size of an apple, its atmosphere would be thick as the apple peel. Some 80% of the mass of the atmosphere is within 10 km of the surface of the Earth, which has a diameter of about 12,742 km. The Earth’s atmosphere as a mixture of gases is characterized by pressure, temperature, and density which vary with altitude (will be discussed in Lecture 4). The atmosphere below about 100 km is called Homosphere. This part of the atmosphere consists of uniform mixtures of gases as illustrated in Table 3.1. 1 Table 3.1. The composition of air. Gases Fraction of air Constant gases Nitrogen, N2 78.08% Oxygen, O2 20.95% Argon, Ar 0.93% Neon, Ne 0.0018% Helium, He 0.0005% Krypton, Kr 0.00011% Xenon, Xe 0.000009% Variable gases Water vapor, H2O 4.0% (maximum, in the tropics) 0.00001% (minimum, at the South Pole) Carbon dioxide, CO2 0.0365% (increasing ~0.4% per year) Methane, CH4 ~0.00018% (increases due to agriculture) Hydrogen, H2 ~0.00006% Nitrous oxide, N2O ~0.00003% Carbon monoxide, CO ~0.000009% Ozone, O3 ~0.000001% - 0.0004% Fluorocarbon 12, CF2Cl2 ~0.00000005% Other gases 1% Oxygen 21% Nitrogen 78% 2 • Some gases in Table 3.1 are called constant gases because the ratio of the number of molecules for each gas and the total number of molecules of air do not change substantially from time to time or place to place. -
Grade 6 Science Mechanical Mixtures Suspensions
Grade 6 Science Week of November 16 – November 20 Heterogeneous Mixtures Mechanical Mixtures Mechanical mixtures have two or more particle types that are not mixed evenly and can be seen as different kinds of matter in the mixture. Obvious examples of mechanical mixtures are chocolate chip cookies, granola and pepperoni pizza. Less obvious examples might be beach sand (various minerals, shells, bacteria, plankton, seaweed and much more) or concrete (sand gravel, cement, water). Mechanical mixtures are all around you all the time. Can you identify any more right now? Suspensions Suspensions are mixtures that have solid or liquid particles scattered around in a liquid or gas. Common examples of suspensions are raw milk, salad dressing, fresh squeezed orange juice and muddy water. If left undisturbed the solids or liquids that are in the suspension may settle out and form layers. You may have seen this layering in salad dressing that you need to shake up before using them. After a rain fall the more dense particles in a mud puddle may settle to the bottom. Milk that is fresh from the cow will naturally separate with the cream rising to the top. Homogenization breaks up the fat molecules of the cream into particles small enough to stay suspended and this stable mixture is now a colloid. We will look at colloids next. Solution, Suspension, and Colloid: https://youtu.be/XEAiLm2zuvc Colloids Colloids: https://youtu.be/MPortFIqgbo Colloids are two phase mixtures. Having two phases means colloids have particles of a solid, liquid or gas dispersed in a continuous phase of another solid, liquid, or gas.