# Thermodynamics. Chapter 13 Phase Diagrams. NC State University

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Thermodynamics Chapter 13 Phase Diagrams NC State University

2 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 of temperature and pressure. In the Figure shown below the regions of space indicate the three phases of carbon dioxide. The curved lines indicate the coexistence curves. Note there is a unique triple point.

3 Degrees of freedom Within any one of the single-phase regions both temperature and pressure must be specified. Because two thermodynamic variables can be changed independently we say that the system has two degrees of freedom. Along any of the coexistence curves the pressure and temperature are coupled, i.e. any change in the temperature implies a change in pressure to remain on the line. Thus, along the curves there is only one degree of freedom. The triple point is a unique point in phase space and there is only one set of values of pressure and temperature consistent with the triple point. Thus, we say that at the triple point the system has zero degrees of freedom. If we follow the liquid-vapor coexistence curve towards higher temperature we find that it ends at the critical point. Above the critical point there is no distinction between liquid and vapor and there is a single fluid phase.

4 Free energy dependence along the coexistence curve In a system where two phases (e.g. liquid and gas) are in equilibrium the Gibbs energy is G = G l + G g, where G l and G g are the Gibbs energies of the liquid phase and the gas phase, respectively. If dn modes (a differential amount of n the number of moles) are transferred from one phase to another at constant temperature and pressure, the differential Gibbs energy for the process is: dg = Gg ng dng + Gl P,T nl dnl P,T The rate of change of free energy with number of moles is called the chemical potential.

5 The significance of chemical potential of coexisting phases We can write the Gibbs free energy change using the following notation: dg = m g dng + m l dnl Note that if the system is entirely composed of gas molecules the chemical potential m g will be large and m l will be zero. Under these conditions the number of moles of gas will decrease dn g < 0 and the number of moles of liquid will increase dn l > 0. Since every mole of gas molecules converted results in a mole of liquid molecules we have that: dn g = -dn l

6 Coexistence criterion In terms of chemical potential, the Gibbs energy for the phase equilibrium is: dg = m g m l dng Since the two phases are in equilibrium dg = 0 and since dn g 0 we have m g = m l. In plain language, if two phases of a single substance are in equilibrium their chemical potentials are equal. If the two phases are not in equilibrium a spontaneous transfer of matter from one phase to the other will occur in the direction that minimizes dg. Matter is transferred from a phase with higher chemical potential to a phase with lower chemical potential consistent with the negative sign of Gibb's free energy for a spontaneous process.

7 Solid-liquid coexistence curve To derive expressions for the coexistence curves on the phase diagram we use the fact that the chemical potential is equivalent in the two phases. We consider two phases a and b and write m a (T,P) = m b (T,P) Now we take the total derivative of both sides m a dp + ma P T T dt = mb dp + mb P P T T P dt The appearance of this equation is quite different from previous equations and yet you have seen this equation before. The reason for the apparent difference is the symbol m. Remember that m for a single substance is just the molar free energy.

8 The Clapeyron equation Substituting these factors into the total derivative above we have V a m dp S a m dt = V b m dp S b m dt Solving for dp/dt gives dp dt = S b a m S m V b a m V m = D trss m D trs V m = D trsh m TD trs V m This equation is known as the Clapeyron equation. It gives the two-phase boundary curve in a phase diagram with D trs H and D trs V between them. The Clapeyron equation can be used to determine the solid-liquid curve by integration. P 1 P 2 dp = D trsh m D trs V m Starting with a known point along the curve (e.g. the triple point or the melting temperature at one bar) we can calculate the rest of the curve referenced to this point. T 2 T 1 dt T

9 The liquid-vapor and solidvapor coexistence curves The Clapeyron equation cannot be applied to a phase transition to the gas phase since the molar volume of a gas is a function of the pressure. Making the assumption that V m g >> V m l we can use the ideal gas law to obtain a new expression for dp/dt. dp dt = D trsh m TV m g The integrated form of this equation P 1 dp P P 2 = T 1 T 2 = PD trsh m RT 2 D trs H m RT dt 2 yields the Clausius-Clapeyron equation. ln P 2 P 1 = D trsh m R 1 T 1 1 T 2 = D trsh m R T 2 T 1 T 1 T 2

10 Applying the Clausius- Clapeyron equation If we use DH of evaporation the C-C equation can be used to describe the liquid-vapor coexistence curve and if we use DH of sublimation this equation can be used to describe the solid-vapor curve. The pressure derived from the C-C equation is the vapor pressure at the given temperature. Applications also include determining the pressure in a high temperature vessel containing a liquid (e.g. a pressure cooker). If you are given an initial set of parameters such as the normal boiling point, for example you may use these as T 1 and P 1. Then if you are given a new temperature T 2 you can use the C-C to calculate P 2.

11 Constructing the phase diagram for CO 2 We can use the Clapeyron and Clausius-Clapeyron equations to calculate a phase diagram. For example, we can begin with the CO 2 diagram shown above. The triple point for CO 2 is 5.11 atm and K. The critical point for for CO 2 is atm and K. We also have the following data Transition D trs H o (kj/mol) T trs (K) Fusion Sublimation Note that we can calculate the enthalpy of sublimation from D vap H o = D sub H o - D fus H o = 16.9 kj/mol. r solid = 1.53 g/cm 3 and r liquid = 0.78 g/cm 3, respectively. The density r = m/v = nm/v so the molar volume is V m = V/n = M/r where M is the molar mass. In units of L/mole we have V s m = 44 g/mole/[1530 g/l] = V l m = 44 g/mole/[780 g/l] = D fus V = V l m - V s m = = L/mole

12 Constructing the phase diagram for CO 2 Starting with the triple point we use the Clausius-Clapeyron equation to calculate the liquid-vapor coexistence curve. P = 5.11exp{D vap H/R[T ]/216.15T} P = 5.11exp{2,032[T ]/216.15T} Notice that if we were to calculate the critical pressure using this formula we would obtain 77.3 atm which is about 5 atm larger than the experimental number. There are several sources of inaccuracy including mainly our neglect of the temperature dependence of the enthalpy. We can also begin a the critical point P = 72.8 exp{d vap H/R[T 304.2]/304.2T} P = 72.8 exp{2,032[t 304.2]/304.2T}

13 Pressure (atm) Constructing the liquid-vapor curve P = 5.11exp{2032[T ]/216.15T} Liquid-vapor P (atm) T (K)

14 Pressure (atm) Constructing the liquid-vapor curve P = 5.11exp{2032[T ]/216.15T} Liquid-vapor P (atm) T (K)

15 Pressure (atm) Constructing the liquid-vapor curve P = 5.11exp{2032[T ]/216.15T} Liquid-vapor P (atm) T (K)

16 Pressure (atm) Constructing the liquid-vapor curve P = 5.11exp{2032[T ]/216.15T} Liquid-vapor P (atm) T (K)

17 Pressure (atm) Constructing the liquid-vapor curve P = 5.11exp{2032[T ]/216.15T} Liquid-vapor P (atm) T (K)

18 Pressure (atm) Constructing the liquid-vapor curve P = 5.11exp{2032[T ]/216.15T} Liquid-vapor P (atm) T (K)

19 Pressure (atm) Constructing the solid-vapor curve Starting again at the triple point P = 5.11exp{D sub H/R[T ]/216.15T} P = 5.11exp{3034[T ]/216.15T} Solid-vapor P (atm) T (K)

20 Pressure (atm) Constructing the solid-vapor curve Starting again at the triple point P = 5.11exp{D sub H/R[T ]/216.15T} P = 5.11exp{3034[T ]/216.15T} Solid-vapor P (atm) T (K)

21 Pressure (atm) Constructing the solid-vapor curve Starting again at the triple point P = 5.11exp{D sub H/R[T ]/216.15T} P = 5.11exp{3034[T ]/216.15T} Solid-vapor P (atm) T (K)

22 Pressure (atm) Constructing the solid-vapor curve Starting again at the triple point P = 5.11exp{D sub H/R[T ]/216.15T} P = 5.11exp{3034[T ]/216.15T} Solid-vapor P (atm) T (K)

23 Pressure (atm) Constructing the solid-liquid curve Using the Clapeyron equation we calculate: P = [D fus H/D fus V] ln{t/216.15} P = ,967 ln{t/216.15} Solid-liquid P (atm) T (K)

24 Pressure (atm) Constructing the solid-liquid curve Using the Clapeyron equation we calculate: P = [D fus H/D fus V] ln{t/216.15} P = ,967 ln{t/216.15} Solid-liquid P (atm) T (K)

25 Pressure (atm) Constructing the solid-liquid curve Using the Clapeyron equation we calculate: P = [D fus H/D fus V] ln{t/216.15} P = ,967 ln{t/216.15} Solid-liquid P (atm) T (K)

26 Constructing the solid-liquid curve Using the Clapeyron equation we calculate: P = [D fus H/D fus V] ln{t/216.15} P = ,967 ln{t/216.15} Solid-liquid P (atm) T (K)

27 Solving Problems What is the vapor pressure of water above a lake on a day When the temperature of both water and air is 32 o C?

28 Solving Problems What is the melting point of ice underneath an ice skater Who has a mass of 100 kg assuming that the area of the Skate blades is 10-7 m 2.

### 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

### Chem 338 Homework Set #5 solutions October 10, 2001 From Atkins: 5.2, 5.9, 5.12, 5.13, 5.15, 5.17, 5.21

Chem 8 Homework Set #5 solutions October 10, 2001 From Atkins: 5.2, 5.9, 5.12, 5.1, 5.15, 5.17, 5.21 5.2) The density of rhombic sulfur is 2.070 g cm - and that of monoclinic sulfur is 1.957 g cm -. Can

### So T decreases. 1.- Does the temperature increase or decrease? For 1 mole of the vdw N2 gas:

1.- One mole of Nitrogen (N2) has been compressed at T0=273 K to the volume V0=1liter. The gas goes through the free expansion process (Q = 0, W = 0), in which the pressure drops down to the atmospheric

roblem Set 4 Answers rofessor: C. E. Loader. At 5.0 ºC, the vapor pressure of ice is 3.03 mm and that of liquid water is 3.63 mm. Calculate G for the change of one mole of liquid water at 5.0 ºC to solid

### 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

### 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

### Thermodynamics [ENGR 251] [Lyes KADEM 2007]

CHAPTER II Properties of Pure Substances II.1. What is a pure substance? A pure substance is defined as a substance that has a fixed chemical composition (example: water; Co 2 ; nitrogen; ). A mixture

### PROPERTIES OF PURE SUBSTANCES

Thermodynamics: An Engineering Approach Seventh Edition in SI Units Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2011 Chapter 3 PROPERTIES OF PURE SUBSTANCES Mehmet Kanoglu University of Gaziantep Copyright

### 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

### Assigned questions for Lecture 14 are listed below. The questions occur in the following editions of Physical Chemistry by P.W.

Assigned questions for Lecture 14 are listed below. The questions occur in the following editions of Physical Chemistry by P.W. Atkins: 10th edition 9th edition 8th edition Note: The letter P in front

### CHAPTER 14 THE CLAUSIUS-CLAPEYRON EQUATION

CHAPTER 4 THE CAUIU-CAPEYRON EQUATION Before starting this chapter, it would probably be a good idea to re-read ections 9. and 9.3 of Chapter 9. The Clausius-Clapeyron equation relates the latent heat

### Chapter 3 Properties of A Pure Substance

Chapter 3 Properties of A Pure Substance Pure substance: A pure substance is one that has a homogeneous and invariable chemical composition. Air is a mixture of several gases, but it is considered to be

### 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

### THERMODYNAMICS / CHPTER 4 Lec. Saleh Hasson

2 - The P-v Diagram The general shape of the P-v diagram of a pure substance is very much like the T-v diagram, but the T = constant lines on this diagram have a downward trend, as shown in the following

### Example: orange juice from frozen concentrate.

Dilution: a process in which the concentration (molarity) of a solution is lowered. The amount of solute (atoms, moles, grams, etc.) remains the same, but the volume is increased by adding more solvent.

### Name Date Class THERMOCHEMISTRY. SECTION 17.1 THE FLOW OF ENERGY HEAT AND WORK (pages 505 510)

17 THERMOCHEMISTRY SECTION 17.1 THE FLOW OF ENERGY HEAT AND WORK (pages 505 510) This section explains the relationship between energy and heat, and distinguishes between heat capacity and specific heat.

### 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

### 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

### 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

### Physical Transformations of Pure Substances

Physical Transformations of Pure Substances Chapter 6 of Atkins Sections 6.1-6.6 (6th, 7th Eds.), Sections 4.1-4.6 (8th Ed.) Phase Diagrams Stabilities of Phases Phase Boundaries Three Typical Phase Diagrams

### 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

### ( )( L L)

Chemistry 360 Dr. Jean M. Standard Problem Set 5 Solutions 1. Determine the amount of pressure-volume work performed by 1 mole of water freezing to ice at 0 C and 1 atm pressure. The density of liquid

### Name Class Date. In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question.

Assessment Chapter Test A Chapter: States of Matter In the space provided, write the letter of the term or phrase that best completes each statement or best answers each question. 1. The kinetic-molecular

### Chapter 6 Multiphase Systems

Chapter 6 Multiphase Systems Single-Component Systems Phase Diagram: a plot that shows conditions under which a pure substance exists in a particular phase e.g. a liquid, a solid, or a gas. Often, the

### Chapter 13 The Chemistry of Solids

Chapter 13 The Chemistry of Solids Jeffrey Mack California State University, Sacramento Metallic & Ionic Solids Crystal Lattices Regular 3-D arrangements of equivalent LATTICE POINTS in space. Lattice

### Colligative properties. Chemistry 433. Freezing point depression. Freezing point depression. Freezing point depression 10/28/2008

Chemistry 433 Lecture 20 Colligative Properties Freezing Point Depression Boiling Point Elevation Osmosis NC State University Colligative properties There are a number of properties of a dilute solution

### 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).

### The Chemical Potential and Phase Equilibria

Chapter 7 The Chemical Potential and Phase Equilibria c 2009 by Harvey Gould and Jan Tobochnik 6 July 2009 We discuss the nature of the chemical potential by considering some simple models and simulations.

### CHEM 36 General Chemistry EXAM #1 February 13, 2002

CHEM 36 General Chemistry EXAM #1 February 13, 2002 Name: Serkey, Anne INSTRUCTIONS: Read through the entire exam before you begin. Answer all of the questions. For questions involving calculations, show

### Thermodynamics of Moist Air

Thermodynamics of Moist Air Phase transitions: what are the equilibrium conditions for a mixed-phase system, e.g. a mixture of water and water vapor? Consider a system consisting of liquid water and H

### The First Law of Thermodynamics: Closed Systems. Heat Transfer

The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained

### 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

### 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

### CHAPTER. Properties of Pure Substances

CHAPTER 2 Properties of Pure Substances A Pure Substance Is a substance that is chemically homogenous and fixed in chemical composition.(e.g. water, nitrogen, air & etc.) mixture of oil and water is not

### 1/7/2013. Chapter 12. Chemistry: Atoms First Julia Burdge & Jason Overby. Intermolecular Forces and the Physical properties of Liquids and Solids

/7/203 Chemistry: Atoms First Julia Burdge & Jason Overby Chapter 2 Intermolecular Forces and the Physical Properties of Liquids and Solids Kent L. McCorkle Cosumnes River College Sacramento, CA Copyright

### Chemical Process calculation III

Chapter 7 Ideal and Real Gases Gas, Liquid, and Solid Chemical Process calculation III Gas: a substance in a form like air, relatively low in density and viscosity Liquid: a substance that flows freely

### 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

### Chapter 19. Chemical Thermodynamics. The reverse reaction (two eggs leaping into your hand with their shells back intact) is not spontaneous.

Chapter 19. Chemical Thermodynamics SOURCE: Chemistry the Central Science: Prentice hall I. Spontaneous Processes Thermodynamics is concerned with the question: will a reaction occur? First Law of Thermodynamics:

### 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

### Ch. 11: Liquids and Intermolecular Forces

Ch. 11: Liquids and Intermolecular Forces Learning goals and key skills: Identify the intermolecular attractive interactions (dispersion, dipole-dipole, hydrogen bonding, ion-dipole) that exist between

### Chapter 12 - Liquids and Solids

Chapter 12 - Liquids and Solids 12-1 Liquids I. Properties of Liquids and the Kinetic Molecular Theory A. Fluids 1. Substances that can flow and therefore take the shape of their container B. Relative

### The International Association for the Properties of Water and Steam

The International Association for the Properties of Water and Steam Plzeň, Czech Republic September 011 Revised Release on the Pressure along the Melting and Sublimation Curves of Ordinary Water Substance

### KINETIC THEORY OF MATTER - molecules in matter are always in motion - speed of molecules is proportional to the temperature

1 KINETIC TERY F MATTER - molecules in matter are always in motion - speed of molecules is proportional to the temperature TE STATES F MATTER 1. Gas a) ideal gas - molecules move freely - molecules have

### Reservoir Fluids PETE 310

Reservoir Fluids PETE 31 Lab 2: Determination of the Vapor Pressure of Propane Learning Objectives When you complete this laboratory, you should be able to: Use closed-cell and sight-glass methods for

### Problem # 2 Determine the kinds of intermolecular forces present in each element or compound:

Chapter 11 Homework solutions Problem # 2 Determine the kinds of intermolecular forces present in each element or compound: A. Kr B. NCl 3 C. SiH 4 D. HF SOLUTION: Kr is a single atom, hence it can have

### Chemical Thermodynamics

Chemical Thermodynamics David A. Katz Department of Chemistry Pima Community College Tucson, AZ 85709, USA First Law of Thermodynamics The First Law of Thermodynamics was expressed in the study of thermochemistry.

### We will study the temperature-pressure diagram of nitrogen, in particular the triple point.

K4. Triple Point of Nitrogen I. OBJECTIVE OF THE EXPERIMENT We will study the temperature-pressure diagram of nitrogen, in particular the triple point. II. BAKGROUND THOERY States of matter Matter is made

### 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

### Energy Changes in Chemical Reactions. System loses heat (negative); gains heat (positive) Describe the difference between the two.

Energy Changes in Chemical Reactions Most reactions give off or absorb energy Energy is the capacity to do work or supply heat. Heat: transfer of thermal (kinetic) energy between two systems at different

### 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

### Thermochemistry. Chapter 6. Concept Check 6.1. Concept Check 6.2. Solution

Chapter 6 Thermochemistry Concept Check 6.1 A solar-powered water pump has photovoltaic cells on protruding top panels. These cells collect energy from sunlight, storing it momentarily in a battery, which

### EXERCISES. 16. What is the ionic strength in a solution containing NaCl in c=0.14 mol/dm 3 concentration and Na 3 PO 4 in 0.21 mol/dm 3 concentration?

EXERISES 1. The standard enthalpy of reaction is 512 kj/mol and the standard entropy of reaction is 1.60 kj/(k mol) for the denaturalization of a certain protein. Determine the temperature range where

### = T T V V T = V. By using the relation given in the problem, we can write this as: ( P + T ( P/ T)V ) = T

hermodynamics: Examples for chapter 3. 1. Show that C / = 0 for a an ideal gas, b a van der Waals gas and c a gas following P = nr. Assume that the following result nb holds: U = P P Hint: In b and c,

### Physical and chemical properties of water Gas Laws Chemical Potential of Water Rainfall/Drought

Lecture 14, Water, Humidity, Pressure and Trace Gases, Part 1 Physical and chemical properties of water Gas Laws Chemical Potential of Water Rainfall/Drought Atmospheric Gas Composition constitue nt percent

### 3A Energy. What is chemical energy?

3A Energy What is chemical energy? Chemical energy is a form of potential energy which is stored in chemical bonds. Chemical bonds are the attractive forces that bind atoms together. As a reaction takes

### Thermodynamics I Spring 1432/1433H (2011/2012H) Saturday, Wednesday 8:00am - 10:00am & Monday 8:00am - 9:00am MEP 261 Class ZA

Thermodynamics I Spring 1432/1433H (2011/2012H) Saturday, Wednesday 8:00am - 10:00am & Monday 8:00am - 9:00am MEP 261 Class ZA Dr. Walid A. Aissa Associate Professor, Mech. Engg. Dept. Faculty of Engineering

### Vapor Pressure Lowering

Colligative Properties A colligative property is a property of a solution that depends on the concentration of solute particles, but not on their chemical identity. We will study 4 colligative properties

### Boltzmann Distribution Law

Boltzmann Distribution Law The motion of molecules is extremely chaotic Any individual molecule is colliding with others at an enormous rate Typically at a rate of a billion times per second We introduce

### 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

### Chapter 6 Thermodynamics: The First Law

Key Concepts 6.1 Systems Chapter 6 Thermodynamics: The First Law Systems, States, and Energy (Sections 6.1 6.8) thermodynamics, statistical thermodynamics, system, surroundings, open system, closed system,

### Experiment 12E LIQUID-VAPOR EQUILIBRIUM OF WATER 1

Experiment 12E LIQUID-VAPOR EQUILIBRIUM OF WATER 1 FV 6/26/13 MATERIALS: PURPOSE: 1000 ml tall-form beaker, 10 ml graduated cylinder, -10 to 110 o C thermometer, thermometer clamp, plastic pipet, long

### 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

### Chemistry 13: States of Matter

Chemistry 13: States of Matter Name: Period: Date: Chemistry Content Standard: Gases and Their Properties The kinetic molecular theory describes the motion of atoms and molecules and explains the properties

### UNIT-III PROPERTIES OF PURE SUBSTANCE AND STEAM POWER CYCLE

UNIT-III PROPERTIES OF PURE SUBSTANCE AND STEAM POWER CYCLE Pure Substance A Pure substance is defined as a homogeneous material, which retains its chemical composition even though there may be a change

### 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

### Lesson 5 Review of fundamental principles Thermodynamics : Part II

Lesson 5 Review of fundamental principles Thermodynamics : Part II Version ME, IIT Kharagpur .The specific objectives are to:. State principles of evaluating thermodynamic properties of pure substances

### 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

### 10.7 Kinetic Molecular Theory. 10.7 Kinetic Molecular Theory. Kinetic Molecular Theory. Kinetic Molecular Theory. Kinetic Molecular Theory

Week lectures--tentative 0.7 Kinetic-Molecular Theory 40 Application to the Gas Laws 0.8 Molecular Effusion and Diffusion 43 Graham's Law of Effusion Diffusion and Mean Free Path 0.9 Real Gases: Deviations

### Extensive variables: volume, mass, energy Intensive variables: pressure, temperature, density

Properties of Gases If a gas is sufficiently dilute it obeys the ideal gas law The ideal gas law can also be written PV = nrt A molar quantity is indicated by the bar across the top. The ideal gas law

### Type: Single Date: Homework: READ 12.8, Do CONCEPT Q. # (14) Do PROBLEMS (40, 52, 81) Ch. 12

Type: Single Date: Objective: Latent Heat Homework: READ 12.8, Do CONCEPT Q. # (14) Do PROBLEMS (40, 52, 81) Ch. 12 AP Physics B Date: Mr. Mirro Heat and Phase Change When bodies are heated or cooled their

### The Gas, Liquid, and Solid Phase

The Gas, Liquid, and Solid Phase When are interparticle forces important? Ron Robertson Kinetic Theory A. Principles Matter is composed of particles in constant, random, motion Particles collide elastically

### a. Isoteniscope Vapor Pressure and Molecular Weight of a Pure Liquid

Vapor Pressure and Molecular Weight of a Pure Liquid Purpose The purpose of this lab is to measure the enthalpy and entropy of vaporization of n-pentane. You will also determine the molecular weight of

### Gas Laws. The kinetic theory of matter states that particles which make up all types of matter are in constant motion.

Name Period Gas Laws Kinetic energy is the energy of motion of molecules. Gas state of matter made up of tiny particles (atoms or molecules). Each atom or molecule is very far from other atoms or molecules.

### 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

### COLLIGATIVE PROPERTIES:

COLLIGATIVE PROPERTIES: A colligative property is a property that depends only on the number of solute particles present, not their identity. The properties we will look at are: lowering of vapor pressure;

### Sample Exercise 15.1 Writing Equilibrium-Constant Expressions

Sample Exercise 15.1 Writing Equilibrium-Constant Expressions Write the equilibrium expression for K c for the following reactions: Solution Analyze: We are given three equations and are asked to write

### Chapter 5 Energy Relationships in Chemistry: Thermochemistry

Chapter 5 Energy Relationships in Chemistry: Thermochemistry In order to study thermochemical changes, we first have to define (a) system that specify part of the universe of interest to us. (b) surrounding

### Chapter 5 Thermochemistry

Chapter 5 Thermochemistry I. Nature of Energy Energy units SI unit is joule, J From E = 1/2 mv 2, 1J = 1kg. m 2 /s 2 Traditionally, we use the calorie as a unit of energy. 1 cal = 4.184J (exactly) The

### Answer, Key Homework 6 David McIntyre 1

Answer, Key Homework 6 David McIntyre 1 This print-out should have 0 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

### 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

### 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

### 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

### Chem. 1A Final Exam Review Problems From ch. 11, 12 & 13

Chem. A Final Exam Review Problems From ch., 2 & 3 f Multiple Choice Identify the choice that best completes the statement or answers the question.. Place the following cations in order from lowest to

### PV (0.775 atm)(0.0854 L) n = = = 0.00264 mol RT -1-1

catalyst 2 5 g ¾¾¾¾ 2 4 g 2 g DH298 = rxn DS298 C H OH( ) C H ( ) + H O( ) 45.5 kj/mol ; = 126 J/(K mol ) ethanol ethene water rxn 1 atm 760 torr PV (0.775 atm)(0.0854 L) n = = = 0.00264 mol RT -1-1 (0.08206

### a) Use the following equation from the lecture notes: = ( 8.314 J K 1 mol 1) ( ) 10 L

hermodynamics: Examples for chapter 4. 1. One mole of nitrogen gas is allowed to expand from 0.5 to 10 L reversible and isothermal process at 300 K. Calculate the change in molar entropy using a the ideal

### Chem 338 Homework Set #2 solutions September 12, 2001 From Atkins: 2.8, 2.15, 2.16, 2.17, 2.18, 2.21, 2.23, 2.26

Chem 8 Homework Set # solutions September 1, 001 From Atkins:.8,.15,.16,.17,.18,.1,.,.6.8) A sample of methane of mass 4.50 g occupies 1.7 L at 10 K. (a) Calculate the work done when the gas expands isothermally

### Chapter 8 and 9 Energy Balances

Chapter 8 and 9 Energy Balances Reference States. Recall that enthalpy and internal energy are always defined relative to a reference state (Chapter 7). When solving energy balance problems, it is therefore

### PHASE DIAGRAM WORKSHEET #2 Period Date

PHASE DIAGRAM WORKSHEET #2 Name Period Date At standard temperature and pressure, bromine (Br 2 ) is a red liquid. Bromine sublimes when the temperature is 25 0 C and the pressure is 101.3 kpa. The phase

### 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

### 1. Thermite reaction 2. Enthalpy of reaction, H 3. Heating/cooling curves and changes in state 4. More thermite thermodynamics

Chem 105 Fri 10-23-09 1. Thermite reaction 2. Enthalpy of reaction, H 3. Heating/cooling curves and changes in state 4. More thermite thermodynamics 10/23/2009 1 Please PICK UP your graded EXAM in front.

### 2.5(a) Enthalpy. Chapter 2. The First Law. P.27

2.5(a) Enthalpy Chapter 2. The First Law. P.27 Justification 2.1 The relation H = q p For a general infinitesimal change in the state of the system, U changes to U + du, p changes to p + dp, and V changes

### Entropy Changes & Processes

Entropy Changes & Processes Chapter 4 of Atkins: he Second Law: he Concepts Section 4.3, 7th edition; 3.3, 8th edition Entropy of Phase ransition at the ransition emperature Expansion of the Perfect Gas

### The Relationships Between. Internal Energy, Heat, Enthalpy, and Calorimetry

The Relationships Between Internal Energy, Heat, Enthalpy, and Calorimetry Recap of Last Class Last class, we began our discussion about energy changes that accompany chemical reactions Chapter 5 discusses:

### Calorimetry: Heat of Vaporization

Calorimetry: Heat of Vaporization OBJECTIVES INTRODUCTION - Learn what is meant by the heat of vaporization of a liquid or solid. - Discuss the connection between heat of vaporization and intermolecular

### Absorption of Heat. Internal energy is the appropriate energy variable to use at constant volume

6 Absorption of Heat According to the First Law, E = q + w = q - P V, assuming P-V work is the only kind that can occur. Therefore, E = q V. The subscript means that the process occurs at constant volume.

### k is change in kinetic energy and E

Energy Balances on Closed Systems A system is closed if mass does not cross the system boundary during the period of time covered by energy balance. Energy balance for a closed system written between two

### Chapter 5 Thermochemistry

Chapter 5 Thermochemistry 1. The ΔE of a system that releases 14.4 J of heat and does 4.8 J of work on the surroundings is J. (a). 19.2 J (b). 14.4 J (c). 4.8 J (d). - 19.2 J Explanation: The ΔE can be

### Name Chemistry / / Melting/Freezing/Boiling & Condensing

Name Chemistry / / Melting/Freezing/Boiling & Condensing As a substance melts, freezes, boils or condenses, heat is either absorbed or released. But, as this change in state occurs, there is no change