Phase Diagrams & Thermodynamics

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Phase Diagrams & Thermodynamics"

Transcription

1 Phase Diagrams & Thermodynamics A phase diagram is a graphical representation of the equilibrium state of a system using the intensive variables T and i while p is kept constant. The equilibrium may be calculated from thermodynamic data using G for all relevant phases G Solubility of B in pure A Line Compound p const. T const. Solution (e.g. Liquid) Solution with miscibility gap A B B 1 Modeling

2 The Tangent Method Graphical evaluation of equilibria from the G() curves G T, p const. Local equilibrium conditions: phase μ A phase μ A μ B μ B μ A μ A : G ' ' G ' ( ) μ B μ B : G '' '' G ( ) '' G ' ' G + (1 ) ( ) and: T T ; p p ' G '' '' G + (1 ) ( ) '' A B 2 Modeling

3 What do we need for the Calculation? For each phase relevant in the system we need the Gibbs Energy G as a function of the intensive variables p, T, i (analytical epression) The combination of these Gibbs energies defines our thermodynamic model. The minimum of G for the system, and thus the phase equilibria, can be calculated by minimization procedures. Phases: pure condensed substances (elements, compounds) solutions (liquid and solid solutions) nonstoichiometric compounds gas phase (consisting of different gas species i with partial pressure p i ) 3 Modeling

4 Thermodynamic Modeling Literature M. Hillert: Phase Equilibria, Phase Diagrams and Phase Transformations Their Thermodynamic Basis, Cambridge University Press 1998 M Hillert: By modeling we shall understand the selection of some assumptions from which it is possible to calculate the properties of a system 1) Physical models: hypothesis mathematical epression 2) Empirical models: eperimental data mathematical epression 4 Modeling

5 Eample: Simple Empirical Model Consider the representation of G as a power series in T c p But: G G H a + bt + dt c p SER 2 G T ( ) 2dT 2 T Usual course of c p at high temperature T / K This means we need a constant term in c p for a proper description! c p c 2dT... G a + bt + ct lnt + dt Representation generally used in SGTE format. Only valid for high temperatures! 5 Modeling

6 Simple Physical Model: Thermal acancies Consider a pure crystalline solid ( N + N element. The number of possible W arrangements is: N! Nv! )! N: number of atoms N : number of vacancies According to Boltzmann this gives a change in entropy: ΔS k lnw k [( N + N )ln( N + N ) N lnn N lnn ] This may be introduced into the Gibbs Energy: ΔG N N g TΔS g + knt[ln N N + N + N N N ln N + N ] g: energy of formation for one vacancy 6 Modeling

7 Thermal acancies (2) Regard N as internal variable for a Gibbs energy minimization: D G 0 ( ) T, p, N N g + N kt ln N + N Equilibrium fraction of vacancies (for D 0) y D: thermodynamic driving force eq N N + N ep( g kt ) At equilibrium the internal variable (N ) can now be eliminated: ΔG N N g g + knt[ln(1 y knt ln(1 y + knt[ln N eq ) N + N eq ) + N + N N N ln y RT ln[1 ep( 7 Modeling N ln N + N eq g kt ] )] ]

8 Solution Phases Thermodynamic properties have to be modeled as a function of composition ΔG solution phase T, p const. line compound e.g. NaCl, GaAs In fact also shows homogeneity range Depends on the scale! line compound AB 2 solution phase Most liquids Solid solutions nonstoichiometric compounds A B B Two component system (binary) 8 Modeling

9 Ideal Solution G G( p, T, N1, N2,...) G G( p, T, ) (binary system) No difference in the interaction between like and unlike atoms is assumed for the ideal solution : ΔH Δ id id 0 0 A - A A - B B B ΔS id 0 ΔG id 0 ΔS ΔG id id R RT c i 1 c i 1 i ln i i ln i R[ ln + (1 )ln(1 )] RT[ ln + (1 )ln(1 )] As < 1 ln < 0 always stabilizing! 9 Modeling

10 Ideal Solution (2) 0.5 ln + (1 )ln(1 ) lim a0 Δ S id lim Δ a1 lim a0 S id Δ G id lim Δ a1 G id Modeling

11 Regular Solution [Hildebrand 1929]: Interaction between unlike atoms contributes to ΔH. ΔG ε ( 1 ) + RT[ ln + (1 )ln(1 )] Ecess term Ideal term Define Ecess functions of the form Y Y E + Y IDEAL ε < 0 : Additional stabilization from H E ε 0 : Ideal Solution ε > 0 : Interplay between S (stabilization) and H (destabilization) 11 Modeling

12 Regular Solution - Eample ε 12.5 kjmol -1 Critical point [Y.A. Chang, University of Wisconsin] 12 Modeling

13 Regular Solution Eample (2) ε 12.5 kjmol Modeling

14 Regular Solution Eample (3) Resulting phase diagram obtained by the calculation with our regular solution model (ε 12.5 kjmol -1 ) single phase field spinodal curve two phase field 14 Modeling

15 Redlich-Kister Polynoms Common standard model for solution modeling. Etension of the regular solution model for the modeling of all kinds of asymmetric shapes. I I G B A E Δ ) 1 ( General epression for the binary Redlich-Kister:... ) ( ) ( B A B A L L L I Δ n k k B A k B A E L G 0 ) ( L is modeled as a function of T e.g.: or higher powers of T bt a L k + 15 Modeling

16 Sublattice Models Nonstoichiometric compounds require composition dependent modeling. Usually they have more than one sublattice. No adequate representation by conventional Redlich-Kister models! Usual case for crystalline phases: acancies Interstitials Substitutions Occur on different sublattices! Crystal structure and defect mechanisms must be known! X-ray diffraction investigations Spectroscopy Diffusion studies, etc 16 Modeling

17 Eample: TiO 2- Sublattice Model Rutile structure type Tetragonal P4 2 /mnm Ti 4+ : 2a (0,0,0) O 2-, a 2-4f (0.3,0.3,0) Sublattice notation: (Ti 4+ ) 1 (O 2-,a 2- ) 2 ΔG + y 0 2 y y O 2 a G 2 0 TiO n 2 k 0 k + y a 2 L( T )( y G O 0 Tia 2 2 y + a 2RT ( y 2 ) k O 2 ln y O 2 + y a 2 ln y a 2 ) (y Site fraction) [Waldner and Eriksson, CALPHAD 1999] 17 Modeling

18 Etension to higher order Systems 1) Solutions: The thermodynamic properties of the solution are etrapolated from the thermodynamic properties of the subsystems using different geometrical models. e.g.: - Kohler Model (symmetric) - Muggianu Model (symmetric) - Toop Model (asymmetric) Etrapolation with or without additional interaction parameters 2) Compounds: Up to now it is not possible to predict compound formation Eperiments necessary! Higher order compounds are modeled as line compounds (only temperature dependence) or with suitable sublattice models according to the crystal structure. 18 Modeling

19 Kohler Model A B(AB) C(AC) ΔG + + E ABC A A( AB) A A( AC) B B( BC) B B( AB) C C( AC) C G C( BC) E AB G G E AC E BC A(AC) A(AB) C B Symmetric Etrapolation B(BC) C(BC) 19 Modeling

20 Muggianu Model A B(AB) C(AC) ΔG + + E ABC A A( AB) A A( AC) B B( BC) B B( AB) C C( AC) C G C( BC) E AB G G E AC E BC A(AC) A(AB) C B Symmetric Etrapolation B(BC) C(BC) 20 Modeling

21 Toop Model A(AC) C C(AC) A Asymmetric Component 0.8 B(AB) A(AB) B ΔG + + E ABC A A( AB) A A( AC) B B( BC) B B( AB) C C( AC) C G C( BC) E AB G G E AC E BC Asymmetric Etrapolation B(BC) C(BC) 21 Modeling

22 The CALPHAD Method CALPHAD Calculation of Phase Diagrams Critical assessment and thermodynamic optimization of binary and higher order systems 1) Literature Assessment: evaluation of all available literature sources 2) Modeling of the Gibbs energies G(p,T, i ) for all phases in the system. 3) Optimization of model parameters for best representation of the eperimental data interconsistency of data! Data Sources: Thermodynamics (Calorimetry, EMF, vapor pressure) Phase Diagram Studies (DTA/DSC, X-ray diffraction, optical microscopy, SEM/EPMA, ) Other Methods (Diffusion studies, magnetic investigations, ) 22 Modeling

23 Evaluation and selection of input data Thermodynamic modeling of the phases The CALPHAD approach [G. Cacciamani, Genova University] Optimization of model parameters (by error minimization procedures) Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Applications (databases, predictions, simulations, etc.) 23 Modeling

24 The CALPHAD Approach (1) Evaluation and selection of input data Optimisation of model parameters (by error minimisation procedures) Thermodynamic modeling of the phases Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Stoichiometric compounds Ordered solutions Disordered solid solutions Liquids etc. Applications (databases, predictions, simulations, etc.) 24 Modeling

25 The CALPHAD Approach (2) Evaluation and selection of input data Optimisation of model parameters (by error minimisation procedures) Thermodynamic modeling of the phases Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Eperiments (DTA, DSC, calorimetry, EMF, vapor pressure, LOM, SEM, X-ray diffraction, etc.) Estimates (periodic properties, chemical criteria, etc.) Theory (ab-initio, semi-empirical, etc.) Applications (databases, predictions, simulations, etc.) 25 Modeling

26 The CALPHAD Approach (3) Evaluation and selection of input data Thermodynamic modeling of the phases Optimisation of model parameters (by error minimisation procedures) Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Applications (databases, predictions, simulations, etc.) G(P,T, 1,..., i,) Data selection and input Weight assignment Parameter evaluation by non-linear least squares regression 26 Modeling

27 The CALPHAD Approach (4) Evaluation and selection of input data Thermodynamic modeling of the phases Optimisation of model parameters (by error minimisation procedures) Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Applications (databases, predictions, simulations, etc.) Comparison with input and derived data Compatibility with similar and higher order systems 27 Modeling

28 The CALPHAD Approach (5) Evaluation and selection of input data Thermodynamic modeling of the phases Optimisation of model parameters (by error minimisation procedures) Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Applications (databases, predictions, simulations, etc.) Database implementation Etrapolation to higher order Materials simulation etc. 28 Modeling

29 The CALPHAD Approach (6) optimized A-B optimized A-C optimized B-C etrapolated A-B-C a few key data optimized A-B-C 29 Modeling

30 The CALPHAD Approach (7) optimized A-B-C optimized A-B-D optimized A-C-D optimized B-C-D etrapolated A-B-C-D a few key data optimized A-B-C-D 30 Modeling

31 Eample: Hypothetical Binaries, Ideal Solution SGTE parameter representation for pure elements (stable and metastable phases) in combination with the ideal solution model. Calculation of hypothetical binary phase diagrams. Program: FazDiaGr by G. Garzeł Data base: 4d and 5d elements of Group 4-8: Zr, Hf, Nb, Ta, Mo, W, Re, Rh, Ir, Pd, Pt, Ru, Os Phases: Liquid (λ), fcc (α), bcc (β), hcp (ε) 31 Modeling

32 Hypothetical Binaries, Ideal Solution (1) λ β ε α 32 Modeling

33 Hypothetical Binaries, Ideal Solution (2) λ β ε α 33 Modeling

34 Hypothetical Binaries, Ideal Solution (3) λ β ε α 34 Modeling

35 Eample: Modeling using Regular Solutions Binary Phase diagram features modeled with use of the regular solution model Cigar shape of the solid/liquid phase boundaries Maimum congruent melting of the solid phase Minimum congruent melting of the solid phase Peritectic phase diagram Eutectic phase diagram T S m A m A 800 S m B K, 20 T m B J / 1000 K mol K Regular solution parameters ε l and ε s are varied 35 Modeling

36 1 - Liquidus and Solidus Curves 1000 ε l ε s T(K) 900 ε l s ε 5kJ Solid Liquid 850 ε l s ε 15kJ Mole Fraction of B 36 Modeling

37 2 - Maimum and Minimum 1100 ε l s ε 0 10kJ / mol Liquid 1000 T(K) 900 ε l s ε 0 0 ε l s ε 12kJ / mol 700 Solid 10kJ / mol Mole Fraction of B ε l s ε 37 Modeling

38 3 - Peritectic Phase Diagram ε l ε s 15 kj Liquid 900 T(K) Solid ε l s ε 12kJ / mol Solid+Solid Mole fraction of B 38 Modeling

39 4 - Eutectic Phase Diagram ε l s ε 0 15kJ / mol Liquid T(K) Solid ε l s ε 20kJ / mol 25kJ / mol ε l s ε 0 10kJ / mol Solid+Solid Mole fraction of B 39 Modeling

40 5 - Monotectic Phase Diagram ε l s ε 17.5kJ 13.5kJ / mol / mol Liquid 1000 Liq+liq T(K) Liquid+Solid Solid Solid+Solid Mole fraction of B 40 Modeling

41 6 - Syntectic Phase Diagram ε l s ε 25kJ / mol 10kJ / mol Liquid 1200 Liquid+liquid T(K) 900 Liquid+Solid Solid 600 Solid+Solid Mole fraction of B 41 Modeling

42 7 Monotectic + Peritectic Phase Diagram 1500 ε l s ε 20kJ 20kJ / mol / mol Liquid 1200 Liquid+liquid T(K) 900 Liquid+Solid Solid 600 Solid Solid+Solid Mole fraction of B 42 Modeling

43 Models: Eample: Modeling of binary In-Ni CALPHAD assessment by Waldner and Ipser L, (Ni): Redlich-Kister solution models δ: (Ni,a) 1 (In,Ni) 1 sublattice model ξ, ξ : (Ni,a) 1 (Ni) 1 (In,Ni) 1 sublattice models Ni 3 In, Ni 2 In, NiIn, Ni 2 In 3, Ni 3 In 7 : Stoichiometric [Massalski s Phase Diagram Compilation] 43 Modeling

44 Modeling of binary In-Ni (1) Data Sources: Phase diagram: mainly 2 papers ( + older literature) apor pressure data: 3 papers EMF measurements: 5 papers Calorimetry: 3 papers Crystal structure: various literature on defect mechanisms of the structure type Used as input for the optimization procedure 44 Modeling

45 Modeling of binary In-Ni (2) Calorimetric data 45 Modeling

46 Modeling of binary In-Ni (3) apor pressure data 46 Modeling

47 Modeling of binary In-Ni (4) Pressures over Ni 2 In from EMF and Knudsen sources 47 Modeling

48 Modeling of binary In-Ni (5) Enthalpies from EMF and Calorimetric sources 48 Modeling

49 Modeling of binary In-Ni (6) Fit with phase diagram data 49 Modeling

Chapter 8. Phase Diagrams

Chapter 8. Phase Diagrams Phase Diagrams A phase in a material is a region that differ in its microstructure and or composition from another region Al Al 2 CuMg H 2 O(solid, ice) in H 2 O (liquid) 2 phases homogeneous in crystal

More information

ELEC-D Principles of materials science- Thermodynamics and diffusion. ELEC-D Principles of materials science

ELEC-D Principles of materials science- Thermodynamics and diffusion. ELEC-D Principles of materials science Thu 3.3 Mon 7.3 ELEC-D8710 - Principles of materials science- Thermodynamics and diffusion Thu 10.3 Exercise 5 Mon 14.3 Thu 17.3 Exercise 6 Mon 21.3 Thermodynamics - Principles (T,xi) equilibrium diagrams

More information

Phase Equilibria & Phase Diagrams

Phase Equilibria & Phase Diagrams Phase Equilibria & Phase Diagrams Week7 Material Sciences and Engineering MatE271 1 Motivation Phase diagram (Ch 9) Temperature Time Kinematics (Ch 10) New structure, concentration (mixing level) (at what

More information

The Clausius-Clapeyron Equation:

The Clausius-Clapeyron Equation: Chapter 10 Solid Solutions and Phase Equilibrium What is a phase? Phase Diagram Basics A phase diagram represents what phases are present at a given pressure, temperature and composition. Virtual maps

More information

μ α =μ β = μ γ = =μ ω μ α =μ β =μ γ = =μ ω Thus for c components, the number of additional constraints is c(p 1) ( ) ( )

μ α =μ β = μ γ = =μ ω μ α =μ β =μ γ = =μ ω Thus for c components, the number of additional constraints is c(p 1) ( ) ( ) Phase Diagrams 1 Gibbs Phase Rule The Gibbs phase rule describes the degrees of freedom available to describe a particular system with various phases and substances. To derive the phase rule, let us begin

More information

AP CHEMISTRY 2007 SCORING GUIDELINES. Question 2

AP CHEMISTRY 2007 SCORING GUIDELINES. Question 2 AP CHEMISTRY 2007 SCORING GUIDELINES Question 2 N 2 (g) + 3 F 2 (g) 2 NF 3 (g) ΔH 298 = 264 kj mol 1 ; ΔS 298 = 278 J K 1 mol 1 The following questions relate to the synthesis reaction represented by the

More information

BINARY SYSTEMS. Definition of Composition: Atomic (molar) fraction. Atomic percent. Mass fraction. Mass percent (weight percent)

BINARY SYSTEMS. Definition of Composition: Atomic (molar) fraction. Atomic percent. Mass fraction. Mass percent (weight percent) BINARY SYSTEMS Definition of Composition: Atomic (molar) fraction Atomic percent Mass fraction Mass percent (weight percent) na =, x i n = A i i i Weight percent mainly in industry! x at % A = x 100 A

More information

Final Exam CHM 3410, Dr. Mebel, Fall 2005

Final Exam CHM 3410, Dr. Mebel, Fall 2005 Final Exam CHM 3410, Dr. Mebel, Fall 2005 1. At -31.2 C, pure propane and n-butane have vapor pressures of 1200 and 200 Torr, respectively. (a) Calculate the mole fraction of propane in the liquid mixture

More information

1 Exercise 5.33b pg 204

1 Exercise 5.33b pg 204 In this solution set, an underline is used to show the last significant digit of numbers. For instance in x = 2.51693 the 2,5,1, and 6 are all significant. Digits to the right of the underlined digit,

More information

Mean Field Flory Huggins Lattice Theory

Mean Field Flory Huggins Lattice Theory Mean Field Flory Huggins Lattice Theory Mean field: the interactions between molecules are assumed to be due to the interaction of a given molecule and an average field due to all the other molecules in

More information

LN 10. 3.091 Introduction to Solid State Chemistry. Lecture Notes No. 10 PHASE EQUILIBRIA AND PHASE DIAGRAMS

LN 10. 3.091 Introduction to Solid State Chemistry. Lecture Notes No. 10 PHASE EQUILIBRIA AND PHASE DIAGRAMS 3.091 Introduction to Solid State Chemistry Lecture Notes No. 10 PHASE EQUILIBRIA AND PHASE DIAGRAMS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Sources

More information

Chapter 5: Diffusion. 5.1 Steady-State Diffusion

Chapter 5: Diffusion. 5.1 Steady-State Diffusion : Diffusion Diffusion: the movement of particles in a solid from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance Diffusion is process

More information

Thermodynamics. Chapter 13 Phase Diagrams. NC State University

Thermodynamics. Chapter 13 Phase Diagrams. NC State University Thermodynamics Chapter 13 Phase Diagrams NC State University Pressure (atm) Definition of a phase diagram A phase diagram is a representation of the states of matter, solid, liquid, or gas as a function

More information

Thermodynamics of Mixing

Thermodynamics of Mixing Thermodynamics of Mixing Dependence of Gibbs energy on mixture composition is G = n A µ A + n B µ B and at constant T and p, systems tend towards a lower Gibbs energy The simplest example of mixing: What

More information

VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICAL UNIVERSITY OF OSTRAVA COMPUTER SIMULATION AND MODELLING IN MATERIALS ENGINEERING. Study Support

VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICAL UNIVERSITY OF OSTRAVA COMPUTER SIMULATION AND MODELLING IN MATERIALS ENGINEERING. Study Support VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF METALLURGY AND MATERIALS ENGINEERING COMPUTER SIMULATION AND MODELLING IN MATERIALS ENGINEERING Study Support Jaromír Drápala, Vlastimil Vodárek,

More information

Gibbs Free Energy and Chemical Potential. NC State University

Gibbs Free Energy and Chemical Potential. NC State University Chemistry 433 Lecture 14 Gibbs Free Energy and Chemical Potential NC State University The internal energy expressed in terms of its natural variables We can use the combination of the first and second

More information

Lecture 6 Application of Thermodynamics in Phase Diagrams. Today s Topics

Lecture 6 Application of Thermodynamics in Phase Diagrams. Today s Topics Lecture 6 Application of Thermodynamics in Phase Diagrams A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics The phase diagrams and its applications The structure of phase diagrams

More information

Binary Solutions. Reading: Chapter 1.3 of Porter and Easterling, Chapters 9.5, 9.6, 9.9, 9.10 of Gaskell

Binary Solutions. Reading: Chapter 1.3 of Porter and Easterling, Chapters 9.5, 9.6, 9.9, 9.10 of Gaskell inary Solutions Composition as a thermodynamic variable ibbs free energy of binary solutions Entropy of formation and ibbs free energy of an ideal solution Regular solutions: Heat of formation of a solution

More information

Thermodynamic database of the phase diagrams in copper base alloy systems

Thermodynamic database of the phase diagrams in copper base alloy systems Journal of Physics and Chemistry of Solids 66 (2005) 256 260 www.elsevier.com/locate/jpcs Thermodynamic database of the phase diagrams in copper base alloy systems C.P. Wang a, X.J. Liu b, M. Jiang b,

More information

Phase Transformations

Phase Transformations Vysoká škola báňská Technická univerzita Ostrava Phase Transformations Didactic Text Vlastimil Vodárek Ostrava 2013 Review: Prof. Dr. Ing. Jaroslav Sojka Description: Phase Transformations Author: Vlastimil

More information

Introduction to Materials Science, Chapter 9, Phase Diagrams. Phase Diagrams. University of Tennessee, Dept. of Materials Science and Engineering 1

Introduction to Materials Science, Chapter 9, Phase Diagrams. Phase Diagrams. University of Tennessee, Dept. of Materials Science and Engineering 1 Phase Diagrams University of Tennessee, Dept. of Materials Science and Engineering 1 Chapter Outline: Phase Diagrams Microstructure and Phase Transformations in Multicomponent Systems Definitions and basic

More information

The first law: transformation of energy into heat and work. Chemical reactions can be used to provide heat and for doing work.

The first law: transformation of energy into heat and work. Chemical reactions can be used to provide heat and for doing work. The first law: transformation of energy into heat and work Chemical reactions can be used to provide heat and for doing work. Compare fuel value of different compounds. What drives these reactions to proceed

More information

Lecture 3: Models of Solutions

Lecture 3: Models of Solutions Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP4, Thermodynamics and Phase Diagrams, H. K. D. H. Bhadeshia Lecture 3: Models of Solutions List of Symbols Symbol G M

More information

Pressure/composition phase diagram There are 2 main types of composition diagrams pressure and temperature. This is an example of how the total vapor

Pressure/composition phase diagram There are 2 main types of composition diagrams pressure and temperature. This is an example of how the total vapor Pressure/composition phase diagram There are 2 main types of composition diagrams pressure and temperature. This is an example of how the total vapor pressure changes for an ideal solution. Pressure/composition

More information

Simple Mixtures. Atkins 7th: Sections ; Atkins 8th: The Properties of Solutions. Liquid Mixtures

Simple Mixtures. Atkins 7th: Sections ; Atkins 8th: The Properties of Solutions. Liquid Mixtures The Properties of Solutions Simple Mixtures Atkins 7th: Sections 7.4-7.5; Atkins 8th: 5.4-5.5 Liquid Mixtures Colligative Properties Boiling point elevation Freezing point depression Solubility Osmosis

More information

Thermodynamics: First Law, Calorimetry, Enthalpy. Calorimetry. Calorimetry: constant volume. Monday, January 23 CHEM 102H T.

Thermodynamics: First Law, Calorimetry, Enthalpy. Calorimetry. Calorimetry: constant volume. Monday, January 23 CHEM 102H T. Thermodynamics: First Law, Calorimetry, Enthalpy Monday, January 23 CHEM 102H T. Hughbanks Calorimetry Reactions are usually done at either constant V (in a closed container) or constant P (open to the

More information

TERNARY SYSTEMS. x 1 + x 2 + x 3 = 1 in the same way: h 1 + h 2 + h 3 = h triangle. Concentration given in Gibbs Triangle. h triangle. h 2. h 3.

TERNARY SYSTEMS. x 1 + x 2 + x 3 = 1 in the same way: h 1 + h 2 + h 3 = h triangle. Concentration given in Gibbs Triangle. h triangle. h 2. h 3. TERNARY SYSTEMS Concentration given in Gibbs Triangle x 1 h triangle h 2 h 1 x 3 h 3 x 2 x 3 x 1 x 1 + x 2 + x 3 = 1 in the same way: h 1 + h 2 + h 3 = h triangle 270121 VO Phasendiagramme Ternäre Systeme

More information

Thermo-Calc Software. Data Organization and Knowledge Discovery. Paul Mason Thermo-Calc Software, Inc. Thermo-Chemistry to Phase Diagrams and More

Thermo-Calc Software. Data Organization and Knowledge Discovery. Paul Mason Thermo-Calc Software, Inc. Thermo-Chemistry to Phase Diagrams and More Thermo-Calc Software Data Organization and Knowledge Discovery Thermo-Chemistry to Phase Diagrams and More Paul Mason Thermo-Calc Software, Inc. http://www.thermocalc.com Tel: (724) 731 0074 E-mail: paul@thermo-calc.com

More information

H 2 (g) + ½ O 2 (g) H 2 O(l) H o f [NO(g)] = 90.2 kj/mol; H o f [H 2 O(g)] = kj/mol H o f [NH 3 (g)] = kj/mol; H o f [O 2 (g)] =?

H 2 (g) + ½ O 2 (g) H 2 O(l) H o f [NO(g)] = 90.2 kj/mol; H o f [H 2 O(g)] = kj/mol H o f [NH 3 (g)] = kj/mol; H o f [O 2 (g)] =? Chapter 16 Thermodynamics GCC CHM152 Thermodynamics You are responsible for Thermo concepts from CHM 151. You may want to review Chapter 8, specifically sections 2, 5, 6, 7, 9, and 10 (except work ). Thermodynamics:

More information

Reading: Moore chapter 18, sections 18.6-18.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102.

Reading: Moore chapter 18, sections 18.6-18.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102. Thermodynamics 2: Gibbs Free Energy and Equilibrium Reading: Moore chapter 18, sections 18.6-18.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102. Key Concepts and skills: definitions

More information

Phase. Gibbs Phase rule

Phase. Gibbs Phase rule Phase diagrams Phase A phase can be defined as a physically distinct and chemically homogeneous portion of a system that has a particular chemical composition and structure. Water in liquid or vapor state

More information

AP Practice Questions

AP Practice Questions 1) AP Practice Questions The tables above contain information for determining thermodynamic properties of the reaction below. C 2 H 5 Cl(g) + Cl 2 (g) C 2 H 4 Cl 2 (g) + HCl(g) (a) Calculate ΔH for

More information

4. Thermodynamics of Polymer Blends

4. Thermodynamics of Polymer Blends 4. Thermodynamics of Polymer Blends Polymeric materials find growing applications in various fields of everyday life because they offer a wide range of application relevant properties. Blending of polymers

More information

Lecture 1: Physical Equilibria The Temperature Dependence of Vapor Pressure

Lecture 1: Physical Equilibria The Temperature Dependence of Vapor Pressure Lecture 1: Physical Equilibria The Temperature Dependence of Vapor Pressure Our first foray into equilibria is to examine phenomena associated with two phases of matter achieving equilibrium in which the

More information

Thermodynamics explores the connection between energy and the EXTENT of a reaction but does not give information about reaction rates (Kinetics).

Thermodynamics explores the connection between energy and the EXTENT of a reaction but does not give information about reaction rates (Kinetics). Thermodynamics explores the connection between energy and the EXTENT of a reaction but does not give information about reaction rates (Kinetics). Rates of chemical reactions are controlled by activation

More information

Each grain is a single crystal with a specific orientation. Imperfections

Each grain is a single crystal with a specific orientation. Imperfections Crystal Structure / Imperfections Almost all materials crystallize when they solidify; i.e., the atoms are arranged in an ordered, repeating, 3-dimensional pattern. These structures are called crystals

More information

Lecture 5: Diffusion Coefficient (Diffusivity)

Lecture 5: Diffusion Coefficient (Diffusivity) Lecture 5: Diffusion Coefficient (Diffusivity) Today s topics Understand the general physical meaning of diffusion coefficient. What is chemical diffusion coefficient (D C ) and tracer diffusion coefficient

More information

Lecture 19: Eutectoid Transformation in Steels: a typical case of Cellular

Lecture 19: Eutectoid Transformation in Steels: a typical case of Cellular Lecture 19: Eutectoid Transformation in Steels: a typical case of Cellular Precipitation Today s topics Understanding of Cellular transformation (or precipitation): when applied to phase transformation

More information

SOLIDIFICATION. (a)formation of stable nuclei. Growth of a stable nucleus. (c) Grain structure

SOLIDIFICATION. (a)formation of stable nuclei. Growth of a stable nucleus. (c) Grain structure SOLIDIFICATION Most metals are melted and then cast into semifinished or finished shape. Solidification of a metal can be divided into the following steps: Formation of a stable nucleus Growth of a stable

More information

Thermal Analysis TGA / DTA. Linda Fröberg

Thermal Analysis TGA / DTA. Linda Fröberg Thermal Analysis TGA / DTA Linda Fröberg Outline Definitions What is thermal analysis? Instrumentation & origin of the TGA-DTA signal. TGA DTA Basics and applications Phase diagrams & Thermal analysis

More information

Phase Transformations in Metals and Alloys

Phase Transformations in Metals and Alloys Phase Transformations in Metals and Alloys THIRD EDITION DAVID A. PORTER, KENNETH E. EASTERLING, and MOHAMED Y. SHERIF ( г йс) CRC Press ^ ^ ) Taylor & Francis Group Boca Raton London New York CRC Press

More information

Review of Chemical Equilibrium Introduction

Review of Chemical Equilibrium Introduction Review of Chemical Equilibrium Introduction Copyright c 2016 by Nob Hill Publishing, LLC This chapter is a review of the equilibrium state of a system that can undergo chemical reaction Operating reactors

More information

Rate of Reaction and the Collision Theory. Factors that Affect the Rate of a Chemical Reaction

Rate of Reaction and the Collision Theory. Factors that Affect the Rate of a Chemical Reaction Chemical Kinetics and Thermodynamics Chemical Kinetics- concerned with: 1. Rates of Chemical Reactions- # of moles of reactant used up or product formed Unit time Or 2. Reaction Mechanisms- Rate of Reaction

More information

1 Phase Equilibria [1]

1 Phase Equilibria [1] 1 Phase Equilibria [1] Vapor-liquid equilibrium VLE) is the state of coexistence between liquid and vapor phases. For a one component system, this is easily visualized, as shown in Figure 1. As the number

More information

Imperfections in atomic arrangements

Imperfections in atomic arrangements MME131: Lecture 8 Imperfections in atomic arrangements Part 1: 0D Defects A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Occurrence and importance of crystal defects Classification

More information

Thermodynamics and Kinetics. Lecture 14 Properties of Mixtures Raoult s Law Henry s Law Activity NC State University

Thermodynamics and Kinetics. Lecture 14 Properties of Mixtures Raoult s Law Henry s Law Activity NC State University Thermodynamics and Kinetics Lecture 14 Properties of Mixtures Raoult s Law Henry s Law Activity NC State University Measures of concentration There are three measures of concentration: molar concentration

More information

Statistical Physics Exam

Statistical Physics Exam Statistical Physics Exam 23rd April 24 Name Student Number Problem Problem 2 Problem 3 Problem 4 Total Percentage Mark Useful constants gas constant R Boltzmann constant k B Avogadro number N A speed of

More information

Chapter 20. Thermodynamics p. 811 842. Spontaneity. What have we learned about spontaneity during this course?

Chapter 20. Thermodynamics p. 811 842. Spontaneity. What have we learned about spontaneity during this course? Chapter 20 p. 811 842 Spontaneous process: Ex. Nonspontaneous process: Ex. Spontaneity What have we learned about spontaneity during this course? 1) Q vs. K? 2) So.. Spontaneous process occurs when a system

More information

Kinetics of Phase Transformations: Nucleation & Growth

Kinetics of Phase Transformations: Nucleation & Growth Kinetics of Phase Transformations: Nucleation & Growth Radhika Barua Department of Chemical Engineering Northeastern University Boston, MA USA Thermodynamics of Phase Transformation Northeastern University

More information

Bomb Calorimetry. Example 4. Energy and Enthalpy

Bomb Calorimetry. Example 4. Energy and Enthalpy Bomb Calorimetry constant volume often used for combustion reactions heat released by reaction is absorbed by calorimeter contents need heat capacity of calorimeter q cal = q rxn = q bomb + q water Example

More information

Chapter 17 Thermodynamics: Directionality of Chemical Reactions

Chapter 17 Thermodynamics: Directionality of Chemical Reactions Reactant- & Product-Favored Processes John W. Moore Conrad L. Stanitski Peter C. Jurs http://academic.cengage.com/chemistry/moore Chapter 17 hermodynamics: Directionality of Chemical Reactions Why are

More information

Materials Science and Engineering Department MSE , Sample Test #1, Spring 2010

Materials Science and Engineering Department MSE , Sample Test #1, Spring 2010 Materials Science and Engineering Department MSE 200-001, Sample Test #1, Spring 2010 ID number First letter of your last name: Name: No notes, books, or information stored in calculator memories may be

More information

Lecture 4: Thermodynamics of Diffusion: Spinodals

Lecture 4: Thermodynamics of Diffusion: Spinodals Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP6, Kinetics and Microstructure Modelling, H. K. D. H. Bhadeshia Lecture 4: Thermodynamics of Diffusion: Spinodals Fick

More information

Expt. 5: Binary Phase Diagram CHEM 366 V-1. Binary Solid-Liquid Phase Diagram

Expt. 5: Binary Phase Diagram CHEM 366 V-1. Binary Solid-Liquid Phase Diagram Expt. 5: Binary Phase Diagram CHEM 366 V-1 Introduction Binary Solid-Liquid Phase Diagram The substances that we encounter in the material world are hardly ever pure chemical compounds but rather mixtures

More information

Chemistry 433. The Third Law of Thermodynamics. Residual Entropy. CO: an Imperfect Crystal. Question. Question. Lecture 12 The Third Law

Chemistry 433. The Third Law of Thermodynamics. Residual Entropy. CO: an Imperfect Crystal. Question. Question. Lecture 12 The Third Law Chemistry 433 Lecture 12 he hird Law he hird Law of hermodynamics he third law of thermodynamics states that every substance has a positive entropy, but at zero Kelvin the entropy is zero for a perfectly

More information

The Equipartition Theorem

The Equipartition Theorem The Equipartition Theorem Degrees of freedom are associated with the kinetic energy of translations, rotation, vibration and the potential energy of vibrations. A result from classical statistical mechanics

More information

Reading. Spontaneity. Monday, January 30 CHEM 102H T. Hughbanks

Reading. Spontaneity. Monday, January 30 CHEM 102H T. Hughbanks Thermo Notes #3 Entropy and 2nd Law of Thermodynamics Monday, January 30 CHEM 102H T. Hughbanks Reading You should reading Chapter 7. Some of this material is quite challenging, be sure to read this material

More information

a mixture each Processing methods 1. Single-stage process (batchwise or continuously) 2. Multiple-stage process (batchwise or continuously) process.

a mixture each Processing methods 1. Single-stage process (batchwise or continuously) 2. Multiple-stage process (batchwise or continuously) process. Introduction to Separation Processes What are separation processes? those operations which transform a mixture of substances into two or more products which differ from each other in composition. Two important

More information

Chapter 12 Solutions

Chapter 12 Solutions Chapter 12 Solutions 12.1 Ideal solutions Solutions are arguably the most important kind of system studied by chemical engineers, whether in large chemical processing or cellular-level molecular phenomena.

More information

Ch. 4: Imperfections in Solids Part 1. Dr. Feras Fraige

Ch. 4: Imperfections in Solids Part 1. Dr. Feras Fraige Ch. 4: Imperfections in Solids Part 1 Dr. Feras Fraige Outline Defects in Solids 0D, Point defects vacancies Interstitials impurities, weight and atomic composition 1D, Dislocations edge screw 2D, Grain

More information

Chapter 15 Chemical Equilibrium

Chapter 15 Chemical Equilibrium Chapter 15 Chemical Equilibrium Chemical reactions can reach a state of dynamic equilibrium. Similar to the equilibrium states reached in evaporation of a liquid in a closed container or the dissolution

More information

Advanced Higher Chemistry. THERMODYNAMICS (Reaction Feasibility) Learning Outcomes Questions & Answers

Advanced Higher Chemistry. THERMODYNAMICS (Reaction Feasibility) Learning Outcomes Questions & Answers Advanced Higher Chemistry Unit 2 - Chemical Reactions THERMODYNAMICS (Reaction Feasibility) Learning Outcomes Questions & Answers KHS Chemistry Nov 2006 page 1 4. THERMODYNAMICS (Reaction Feasibility)

More information

Module 5 : Electrochemistry Lecture 22 : Free energy and EMF

Module 5 : Electrochemistry Lecture 22 : Free energy and EMF Module 5 : Electrochemistry Lecture 22 : Free energy and EMF Objectives After studying this Lecture you will be able to Distinguish between electrolytic cells and galvanic cells. Write the cell representation

More information

Crystal Structures of Interest

Crystal Structures of Interest rystal Structures of Interest Elemental solids: Face-centered cubic (fcc) Hexagonal close-packed (hcp) ody-centered cubic (bcc) Diamond cubic (dc) inary compounds Fcc-based (u 3 u,nal, ß-ZnS) Hcp-based

More information

vap H = RT 1T 2 = 30.850 kj mol 1 100 kpa = 341 K

vap H = RT 1T 2 = 30.850 kj mol 1 100 kpa = 341 K Thermodynamics: Examples for chapter 6. 1. The boiling point of hexane at 1 atm is 68.7 C. What is the boiling point at 1 bar? The vapor pressure of hexane at 49.6 C is 53.32 kpa. Assume that the vapor

More information

1. the same as E. correct. 2. less than E. 3. unrelated to E.

1. the same as E. correct. 2. less than E. 3. unrelated to E. Version PREVIEW Exam 3 JONSON (53140) 1 This print-out should have 40 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. LDE Carbon Allotropes

More information

Periodic Table of the Elements

Periodic Table of the Elements Periodic Table of the Elements 1A 8A 1 18 1 2 H 2A 3A 4A 5A 6A 7A He 1.0079 2 13 14 15 16 17 4.0026 3 4 5 6 7 8 9 10 Li Be B C N O F Ne 6.941 9.0122 10.811 12.011 14.0067 15.9994 18.9984 20.1797 11 12

More information

Chapter 14. CHEMICAL EQUILIBRIUM

Chapter 14. CHEMICAL EQUILIBRIUM Chapter 14. CHEMICAL EQUILIBRIUM 14.1 THE CONCEPT OF EQUILIBRIUM AND THE EQUILIBRIUM CONSTANT Many chemical reactions do not go to completion but instead attain a state of chemical equilibrium. Chemical

More information

Test Review # 9. Chemistry R: Form TR9.13A

Test Review # 9. Chemistry R: Form TR9.13A Chemistry R: Form TR9.13A TEST 9 REVIEW Name Date Period Test Review # 9 Collision theory. In order for a reaction to occur, particles of the reactant must collide. Not all collisions cause reactions.

More information

Thermodynamics and Equilibrium

Thermodynamics and Equilibrium Chapter 19 Thermodynamics and Equilibrium Concept Check 19.1 You have a sample of 1.0 mg of solid iodine at room temperature. Later, you notice that the iodine has sublimed (passed into the vapor state).

More information

1 Exercise 5.5b pg 201

1 Exercise 5.5b pg 201 In this solution set, an underline is used to show the last significant digit of numbers. For instance in x 2.51693 the 2,5,1, and 6 are all significant. Digits to the right of the underlined digit, the

More information

Chemical Vapor Deposition

Chemical Vapor Deposition Chemical Vapor Deposition Physical Vapor Deposition (PVD) So far we have seen deposition techniques that physically transport material from a condensed phase source to a substrate. The material to be deposited

More information

Determination of Molecular Weight by Freezing Point Depression

Determination of Molecular Weight by Freezing Point Depression Determination of Molecular Weight by Freezing Point Depression Freezing point depression is a kind of colligative properties as treated in high school chemistry course. Normally used alcohol or mercury

More information

Chapter 5. Thermochemistry

Chapter 5. Thermochemistry Chapter 5. Thermochemistry THERMODYNAMICS - study of energy and its transformations Thermochemistry - study of energy changes associated with chemical reactions Energy - capacity to do work or to transfer

More information

Thermodynamics Answers to Tutorial # 1

Thermodynamics Answers to Tutorial # 1 Thermodynamics Answers to Tutorial # 1 1. (I) Work done in free expansion is Zero as P ex = 0 (II) Irreversible expansion against constant external pressure w = P ex (V 2 V 1 ) V 2 = nrt P 2 V 1 = nrt

More information

6. 2. Unit 6: Physical chemistry of spectroscopy, surfaces and chemical and phase equilibria

6. 2. Unit 6: Physical chemistry of spectroscopy, surfaces and chemical and phase equilibria 6. 2 Phase equilibria Many industrial processes involve several phases in equilibrium gases, liquids, solids and even different crystalline forms of the solid state. Predicting the number of phases present

More information

Lecture 3: Introduction to Diffusion

Lecture 3: Introduction to Diffusion Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP6, Kinetics and Microstructure Modelling, H. K. D. H. Bhadeshia Lecture 3: Introduction to Diffusion Mass transport in

More information

Mineral Stability Diagrams and Chemical Weathering of Feldspars

Mineral Stability Diagrams and Chemical Weathering of Feldspars Mineral Stability Diagrams and Chemical Weathering of Feldspars Albite Jadeite Quartz dδg = ΔVdP - ΔSdT and G, S, V values for albite, jadeite and quartz to calculate the conditions for which ΔG of the

More information

Answers: Given: No. [COCl 2 ] = K c [CO][Cl 2 ], but there are many possible values for [CO]=[Cl 2 ]

Answers: Given: No. [COCl 2 ] = K c [CO][Cl 2 ], but there are many possible values for [CO]=[Cl 2 ] Chemical Equilibrium What are the concentrations of reactants and products at equilibrium? How do changes in pressure, volume, temperature, concentration and the use of catalysts affect the equilibrium

More information

Gas phase transport reactions. Transport reaction A(s) + B(g) = AB(g)

Gas phase transport reactions. Transport reaction A(s) + B(g) = AB(g) Gas phase transport reactions CT CVT CTR Chemical Transport Chemical Vapour Transport Chemical Transport Reaction Fast stoff A Gassfase Fast stoff A Used to: Purify materials Grow single crystals Increase

More information

Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry

Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Why? Chemists are concerned with mass relationships in chemical reactions, usually run on a macroscopic scale (grams, kilograms, etc.). To deal with

More information

Thermochemistry. Thermochemistry 1/25/2010. Reading: Chapter 5 (omit 5.8) As you read ask yourself

Thermochemistry. Thermochemistry 1/25/2010. Reading: Chapter 5 (omit 5.8) As you read ask yourself Thermochemistry Reading: Chapter 5 (omit 5.8) As you read ask yourself What is meant by the terms system and surroundings? How are they related to each other? How does energy get transferred between them?

More information

In order to solve this problem it is first necessary to use Equation 5.5: x 2 Dt. = 1 erf. = 1.30, and x = 2 mm = 2 10-3 m. Thus,

In order to solve this problem it is first necessary to use Equation 5.5: x 2 Dt. = 1 erf. = 1.30, and x = 2 mm = 2 10-3 m. Thus, 5.3 (a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion. Solution (a) With vacancy diffusion,

More information

Defects Introduction. Bonding + Structure + Defects. Properties

Defects Introduction. Bonding + Structure + Defects. Properties Defects Introduction Bonding + Structure + Defects Properties The processing determines the defects Composition Bonding type Structure of Crystalline Processing factors Defects Microstructure Types of

More information

Chem 420/523 Chemical Thermodynamics Homework Assignment # 6

Chem 420/523 Chemical Thermodynamics Homework Assignment # 6 Chem 420/523 Chemical hermodynamics Homework Assignment # 6 1. * Solid monoclinic sulfur (S α ) spontaneously converts to solid rhombic sulfur (S β ) at 298.15 K and 0.101 MPa pressure. For the conversion

More information

Thermochemistry. r2 d:\files\courses\1110-20\99heat&thermorans.doc. Ron Robertson

Thermochemistry. r2 d:\files\courses\1110-20\99heat&thermorans.doc. Ron Robertson Thermochemistry r2 d:\files\courses\1110-20\99heat&thermorans.doc Ron Robertson I. What is Energy? A. Energy is a property of matter that allows work to be done B. Potential and Kinetic Potential energy

More information

Major chemistry laws. Mole and Avogadro s number. Calculating concentrations.

Major chemistry laws. Mole and Avogadro s number. Calculating concentrations. Major chemistry laws. Mole and Avogadro s number. Calculating concentrations. Major chemistry laws Avogadro's Law Equal volumes of gases under identical temperature and pressure conditions will contain

More information

Vapor-Liquid Equilibria

Vapor-Liquid Equilibria 31 Introduction to Chemical Engineering Calculations Lecture 7. Vapor-Liquid Equilibria Vapor and Gas Vapor A substance that is below its critical temperature. Gas A substance that is above its critical

More information

Range of Competencies

Range of Competencies CHEMISTRY Content Domain Range of Competencies l. Nature of Science 0001 0003 18% ll. Matter and Atomic Structure 0004 0006 18% lll. Energy and Chemical Bonding 0007 0010 23% lv. Chemical Reactions 0011

More information

3.091 OCW Scholar Fall 2010 Final Exam - Solutions Key. Prof. Donald R. Sadoway, Instructor

3.091 OCW Scholar Fall 2010 Final Exam - Solutions Key. Prof. Donald R. Sadoway, Instructor .091 OCW Scholar Fall 2010 Final Exam - Solutions Key Prof. Donald R. Sadoway, Instructor .091 Fall Term 2010 Final Exam page 2 Problem #1 (20 points) Answer the following questions about the hydrogen

More information

Gibbs Energy Modeling of Binary and Ternary Molten Nitrate Salt Systems

Gibbs Energy Modeling of Binary and Ternary Molten Nitrate Salt Systems Lehigh University Lehigh Preserve Theses and Dissertations 2012 Gibbs Energy Modeling of Binary and Ternary Molten Nitrate Salt Systems Tucker Elliott Lehigh University Follow this and additional works

More information

Standard Free Energies of Formation at 298 K. Average Bond Dissociation Energies at 298 K

Standard Free Energies of Formation at 298 K. Average Bond Dissociation Energies at 298 K 1 Thermodynamics There always seems to be at least one free response question that involves thermodynamics. These types of question also show up in the multiple choice questions. G, S, and H. Know what

More information

Crystallization and energy relations between states of matter

Crystallization and energy relations between states of matter Crystallization and energy relations between states of matter This text is meant as background information about how undercooling happens, and how the latent heat of crystallization has to be released

More information

k 2f, k 2r C 2 H 5 + H C 2 H 6

k 2f, k 2r C 2 H 5 + H C 2 H 6 hemical Engineering HE 33 F pplied Reaction Kinetics Fall 04 Problem Set 4 Solution Problem. The following elementary steps are proposed for a gas phase reaction: Elementary Steps Rate constants H H f,

More information

Chapter 7: Stoichiometry - Mass Relations in Chemical Reactions

Chapter 7: Stoichiometry - Mass Relations in Chemical Reactions Chapter 7: Stoichiometry - Mass Relations in Chemical Reactions How do we balance chemical equations? How can we used balanced chemical equations to relate the quantities of substances consumed and produced

More information

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS FUNDAMENTALS OF ENGINEERING THERMODYNAMICS System: Quantity of matter (constant mass) or region in space (constant volume) chosen for study. Closed system: Can exchange energy but not mass; mass is constant

More information

Exploring Creation With Chemistry Table of Contents

Exploring Creation With Chemistry Table of Contents Exploring Creation With Chemistry Table of Contents MODULE #1: Measurement and Units...1 Introduction... 1 Experiment 1.1: Air Has Mass... 1 Experiment 1.2: Air Takes Up Space... 2 Units of Measurement...

More information

Chapter 16 Review Packet

Chapter 16 Review Packet Chapter 16 Review Packet AP Chemistry Chapter 16 Practice Multiple Choice Portion 1. For which process is ΔS negative? Note: ΔS = S final S initial therefore, if ΔS is positive, S final > S initial if

More information

FORMA is EXAM I, VERSION 1 (v1) Name

FORMA is EXAM I, VERSION 1 (v1) Name FORMA is EXAM I, VERSION 1 (v1) Name 1. DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO. 2. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets. 3.

More information

Mr. Bracken. Multiple Choice Review: Thermochemistry

Mr. Bracken. Multiple Choice Review: Thermochemistry Mr. Bracken AP Chemistry Name Period Multiple Choice Review: Thermochemistry 1. If this has a negative value for a process, then the process occurs spontaneously. 2. This is a measure of how the disorder

More information