Chapter 5: the Thermodynamic Description of Mixtures
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Chapter 4 Calculation of Standard Thermodynamic Properties of Aqueous Electrolytes and Non-Electrolytes
Chapter 4 Calculation of Standard Thermodynamic Properties of Aqueous Electrolytes and Non-Electrolytes Vladimir Majer Laboratoire de Thermodynamique des Solutions et des Polymères Université Blaise Pascal Clermont II / CNRS 63177 Aubière, France Josef Sedlbauer Department of Chemistry Technical University Liberec 46117 Liberec, Czech Republic Robert H. Wood Department of Chemistry and Biochemistry University of Delaware Newark, DE 19716, USA 4.1 Introduction Thermodynamic modeling is important for understanding and predicting phase and chemical equilibria in industrial and natural aqueous systems at elevated temperatures and pressures. Such systems contain a variety of organic and inorganic solutes ranging from apolar nonelectrolytes to strong electrolytes; temperature and pressure strongly affect speciation of solutes that are encountered in molecular or ionic forms, or as ion pairs or complexes. Properties related to the Gibbs energy, such as thermodynamic equilibrium constants of hydrothermal reactions and activity coefficients of aqueous species, are required for practical use by geologists, power-cycle chemists and process engineers. Derivative properties (enthalpy, heat capacity and volume), which can be obtained from calorimetric and volumetric experiments, are useful in extrapolations when calculating the Gibbs energy at conditions remote from ambient. They also sensitively indicate evolution in molecular interactions with changing temperature and pressure. In this context, models with a sound theoretical basis are indispensable, describing with a limited number of adjustable parameters all thermodynamic functions of an aqueous system over a wide range of temperature and pressure. In thermodynamics of hydrothermal solutions, the unsymmetric standard-state convention is generally used; in this case, the standard thermodynamic properties (STP) of a solute reflect its interaction with the solvent (water), and the excess properties, related to activity coefficients, correspond to solute-solute interactions. -
Chapter 3. Second and Third Law of Thermodynamics
Chapter 3. Second and third law of thermodynamics Important Concepts Review Entropy; Gibbs Free Energy • Entropy (S) – definitions Law of Corresponding States (ch 1 notes) • Entropy changes in reversible and Reduced pressure, temperatures, volumes irreversible processes • Entropy of mixing of ideal gases • 2nd law of thermodynamics • 3rd law of thermodynamics Math • Free energy Numerical integration by computer • Maxwell relations (Trapezoidal integration • Dependence of free energy on P, V, T https://en.wikipedia.org/wiki/Trapezoidal_rule) • Thermodynamic functions of mixtures Properties of partial differential equations • Partial molar quantities and chemical Rules for inequalities potential Major Concept Review • Adiabats vs. isotherms p1V1 p2V2 • Sign convention for work and heat w done on c=C /R vm system, q supplied to system : + p1V1 p2V2 =Cp/CV w done by system, q removed from system : c c V1T1 V2T2 - • Joule-Thomson expansion (DH=0); • State variables depend on final & initial state; not Joule-Thomson coefficient, inversion path. temperature • Reversible change occurs in series of equilibrium V states T TT V P p • Adiabatic q = 0; Isothermal DT = 0 H CP • Equations of state for enthalpy, H and internal • Formation reaction; enthalpies of energy, U reaction, Hess’s Law; other changes D rxn H iD f Hi i T D rxn H Drxn Href DrxnCpdT Tref • Calorimetry Spontaneous and Nonspontaneous Changes First Law: when one form of energy is converted to another, the total energy in universe is conserved. • Does not give any other restriction on a process • But many processes have a natural direction Examples • gas expands into a vacuum; not the reverse • can burn paper; can't unburn paper • heat never flows spontaneously from cold to hot These changes are called nonspontaneous changes. -
Thermodynamics, Flame Temperature and Equilibrium
Thermodynamics, Flame Temperature and Equilibrium Combustion Summer School 2018 Prof. Dr.-Ing. Heinz Pitsch Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass balances of combustion systems • Thermodynamic quantities • Thermodynamics, flame • Flame temperature at complete temperature, and equilibrium conversion • Governing equations • Chemical equilibrium • Laminar premixed flames: Kinematics and burning velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames • FlameMaster flame calculator 2 Thermodynamic Quantities First law of thermodynamics - balance between different forms of energy • Change of specific internal energy: du specific work due to volumetric changes: δw = -pdv , v=1/ρ specific heat transfer from the surroundings: δq • Related quantities specific enthalpy (general definition): specific enthalpy for an ideal gas: • Energy balance for a closed system: 3 Multicomponent system • Specific internal energy and specific enthalpy of mixtures • Relation between internal energy and enthalpy of single species 4 Multicomponent system • Ideal gas u and h only function of temperature • If cpi is specific heat at constant pressure and hi,ref is reference enthalpy at reference temperature Tref , temperature dependence of partial specific enthalpy is given by • Reference temperature may be arbitrarily chosen, most frequently used: Tref = 0 K or Tref = 298.15 K 5 Multicomponent system • Partial molar enthalpy hi,m is and its temperature dependence is where the molar specific -
Chapter 8 Thermodynamic Properties of Mixtures
Chapter 8 Thermodynamic Properties of Mixtures 2012/3/29 1 Abstract The thermodynamic description of mixtures, extended from pure fluids. The equations of change, i.e., energy and entropy balance, for mixtures are developed. The criteria for phase and chemical equilibrium in mixtures 2012/3/29 2 8.1 THE THERMODYNAMIC DESCRIPTION OF MIXTURES Thermodynamic property for pure fluids, θθ=()TPN , , where N is the number of moles. θθ=()TP , where the number of mole equals to 1. Thermodynamic property for mixtures, θθ=()TPN , ,12 , N ,L , Nc where Ni is the number of moles of the ith component. θθ=()TPx , ,12 , x ,L , xci where x is the mole fraction of the ith component. For example UUTPNN=() , ,12 , ,LL , Ncc or UUTPxx=() , , 12 , , , x VVTPNN=() , ,12 , ,L , Nc or VVTPxx=() , ,12 , ,L , xc 2012/3/29 3 Summation of the properties of pure fluids (before mixing at TP and ) C UTPxx(), ,12 , ,L , xci− 1= ∑ xUTPi () , (8.1-1) i=1 where UU is the molar internal energy, i is the internal energy of the pure i-th component at TP and . C ˆˆ UTPww()(), ,12 , ,L , wcii− 1= ∑ wUTP , (8.1-2) i=1 where wi is the mass fraction of component i. 2012/3/29 4 At the same T and P 50 cc 25 cc + 25 cc H2O H2O or 52 cc 25 cc + 25 cc 48 cc + 2 cc A B -2 cc Attractive Repulsive 2012/3/29 5 Property change upon mixing (at constantTP and ) C Δ=mixθθ()TPx,,ii −∑ x θi () TP , i=1 Volume change upon mixing C Δ=mixVTP(),,,, VTPx()ii −∑ xVTPi () i=1 Enthalpy change upon mixing C Δ=mix HTP(),,,, HTPx()ii −∑ xHTPi () i=1 2012/3/29 6 Experimental data : properties changes upon mixing (H and V) Figure 8.1-1 Enthalpy-concentration diagram for aqueous sulfuric acid at 0.1 MPa. -
Calculating the Configurational Entropy of a Landscape Mosaic
Landscape Ecol (2016) 31:481–489 DOI 10.1007/s10980-015-0305-2 PERSPECTIVE Calculating the configurational entropy of a landscape mosaic Samuel A. Cushman Received: 15 August 2014 / Accepted: 29 October 2015 / Published online: 7 November 2015 Ó Springer Science+Business Media Dordrecht (outside the USA) 2015 Abstract of classes and proportionality can be arranged (mi- Background Applications of entropy and the second crostates) that produce the observed amount of total law of thermodynamics in landscape ecology are rare edge (macrostate). and poorly developed. This is a fundamental limitation given the centrally important role the second law plays Keywords Entropy Á Landscape Á Configuration Á in all physical and biological processes. A critical first Composition Á Thermodynamics step to exploring the utility of thermodynamics in landscape ecology is to define the configurational entropy of a landscape mosaic. In this paper I attempt to link landscape ecology to the second law of Introduction thermodynamics and the entropy concept by showing how the configurational entropy of a landscape mosaic Entropy and the second law of thermodynamics are may be calculated. central organizing principles of nature, but are poorly Result I begin by drawing parallels between the developed and integrated in the landscape ecology configuration of a categorical landscape mosaic and literature (but see Li 2000, 2002; Vranken et al. 2014). the mixing of ideal gases. I propose that the idea of the Descriptions of landscape patterns, processes of thermodynamic microstate can be expressed as unique landscape change, and propagation of pattern-process configurations of a landscape mosaic, and posit that relationships across scale and through time are all the landscape metric Total Edge length is an effective governed and constrained by the second law of measure of configuration for purposes of calculating thermodynamics (Cushman 2015). -
Homework 5 Solutions
SCI 1410: materials science & solid state chemistry HOMEWORK 5. solutions Textbook Problems: Imperfections in Solids 1. Askeland 4-67. Why is most “gold” or “silver” jewelry made out of gold or silver alloyed with copper, i.e, what advantages does copper offer? We have two major considerations in jewelry alloying: strength and cost. Copper additions obviously lower the cost of gold or silver (Note that 14K gold is actually only about 50% gold). Copper and other alloy additions also strengthen pure gold and pure silver. In both gold and silver, copper will strengthen the material by either solid solution strengthening (substitutional Cu atoms in the Au or Ag crystal), or by formation of second phase in the microstructure. 2. Solid state solubility. Of the elements in the chart below, name those that would form each of the following relationships with copper (non-metals only have atomic radii listed): a. Substitutional solid solution with complete solubility o Ni and possibly Ag, Pd, and Pt b. Substitutional solid solution of incomplete solubility o Ag, Pd, and Pt (if you didn’t include these in part (a); Al, Co, Cr, Fe, Zn c. An interstitial solid solution o C, H, O (small atomic radii) Element Atomic Radius (nm) Crystal Structure Electronegativity Valence Cu 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Pt 0.1387 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2 3. -
Lecture 15: 11.02.05 Phase Changes and Phase Diagrams of Single- Component Materials
3.012 Fundamentals of Materials Science Fall 2005 Lecture 15: 11.02.05 Phase changes and phase diagrams of single- component materials Figure removed for copyright reasons. Source: Abstract of Wang, Xiaofei, Sandro Scandolo, and Roberto Car. "Carbon Phase Diagram from Ab Initio Molecular Dynamics." Physical Review Letters 95 (2005): 185701. Today: LAST TIME .........................................................................................................................................................................................2� BEHAVIOR OF THE CHEMICAL POTENTIAL/MOLAR FREE ENERGY IN SINGLE-COMPONENT MATERIALS........................................4� The free energy at phase transitions...........................................................................................................................................4� PHASES AND PHASE DIAGRAMS SINGLE-COMPONENT MATERIALS .................................................................................................6� Phases of single-component materials .......................................................................................................................................6� Phase diagrams of single-component materials ........................................................................................................................6� The Gibbs Phase Rule..................................................................................................................................................................7� Constraints on the shape of -
Solution Is a Homogeneous Mixture of Two Or More Substances in Same Or Different Physical Phases. the Substances Forming The
CLASS NOTES Class:12 Topic: Solutions Subject: Chemistry Solution is a homogeneous mixture of two or more substances in same or different physical phases. The substances forming the solution are called components of the solution. On the basis of number of components a solution of two components is called binary solution. Solute and Solvent In a binary solution, solvent is the component which is present in large quantity while the other component is known as solute. Classification of Solutions Solubility The maximum amount of a solute that can be dissolved in a given amount of solvent (generally 100 g) at a given temperature is termed as its solubility at that temperature. The solubility of a solute in a liquid depends upon the following factors: (i) Nature of the solute (ii) Nature of the solvent (iii) Temperature of the solution (iv) Pressure (in case of gases) Henry’s Law The most commonly used form of Henry’s law states “the partial pressure (P) of the gas in vapour phase is proportional to the mole fraction (x) of the gas in the solution” and is expressed as p = KH . x Greater the value of KH, higher the solubility of the gas. The value of KH decreases with increase in the temperature. Thus, aquatic species are more comfortable in cold water [more dissolved O2] rather than Warm water. Applications 1. In manufacture of soft drinks and soda water, CO2 is passed at high pressure to increase its solubility. 2. To minimise the painful effects (bends) accompanying the decompression of deep sea divers. O2 diluted with less soluble. -
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. -
Self-Assembly of a Colloidal Interstitial Solid Solution with Tunable Sublattice Doping: Supplementary Information
Self-assembly of a colloidal interstitial solid solution with tunable sublattice doping: Supplementary information L. Filion,∗ M. Hermes, R. Ni, E. C. M. Vermolen,† A. Kuijk, C. G. Christova,‡ J. C. P. Stiefelhagen, T. Vissers, A. van Blaaderen, and M. Dijkstra Soft Condensed Matter, Debye Institute for NanoMaterials Science, Utrecht University, Princetonplein 1, NL-3584 CC Utrecht, the Netherlands I. CRYSTAL STRUCTURE LS6 In the main paper we use full free-energy calculations to determine the phase diagram for binary mixtures of hard spheres with size ratio σS/σL = 0.3 where σS(L) is the diameter of the small (large) particles. The phases we considered included a structure with LS6 stoichiometry for which we could not identify an atomic analogue. Snapshots of this structure from various perspectives are shown in Fig. S1. FIG. S1: Unit cell of the binary LS6 superlattice structure described in this paper. Note that both species exhibit long-range crystalline order. The unit cell is based on a body-centered-cubic cell of the large particles in contrast to the face-centered-cubic cell associated with the interstitial solid solution covering most of the phase diagram (Fig. 1). II. PHASE DIAGRAM AT CONSTANT VOLUME 3 In the main paper, we present the xS − p representation of the phase diagram where p = βPσL is the reduced pressure, xS = NS/(NS + NL), NS(L) is the number of small (large) hard spheres, β = 1/kBT , kB is the Boltzmann constant, and T is the absolute temperature. This is the natural representation arising from common tangent construc- tions at constant pressure and the representation required for further simulation studies such as nucleation studies. -
Phase Diagrams
Module-07 Phase Diagrams Contents 1) Equilibrium phase diagrams, Particle strengthening by precipitation and precipitation reactions 2) Kinetics of nucleation and growth 3) The iron-carbon system, phase transformations 4) Transformation rate effects and TTT diagrams, Microstructure and property changes in iron- carbon system Mixtures – Solutions – Phases Almost all materials have more than one phase in them. Thus engineering materials attain their special properties. Macroscopic basic unit of a material is called component. It refers to a independent chemical species. The components of a system may be elements, ions or compounds. A phase can be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics i.e. it is a physically distinct from other phases, chemically homogeneous and mechanically separable portion of a system. A component can exist in many phases. E.g.: Water exists as ice, liquid water, and water vapor. Carbon exists as graphite and diamond. Mixtures – Solutions – Phases (contd…) When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties; a disparity in one or the other set of properties is sufficient. A solution (liquid or solid) is phase with more than one component; a mixture is a material with more than one phase. Solute (minor component of two in a solution) does not change the structural pattern of the solvent, and the composition of any solution can be varied. In mixtures, there are different phases, each with its own atomic arrangement. It is possible to have a mixture of two different solutions! Gibbs phase rule In a system under a set of conditions, number of phases (P) exist can be related to the number of components (C) and degrees of freedom (F) by Gibbs phase rule. -
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.