1. CHEE 311J.S. Parent1 1. Science of Thermodynamics Concerned with knowing the physical state of a system at equilibrium. A concise (mathematical) description of the system’s state at different conditions allows us to calculate:  heat and work effects associated with a process  the maximum work obtained or minimum work required for such a transformation  whether a process can occur spontaneously In CHEM 244, thermodynamics was used to derive relationships amongst variables (P,T)that define a system at equilibrium.  Heat engines, refrigeration cycles, steam power plants  Dealt only with closed systems of constant composition (usually 1-component systems such as H 2 O)

2. CHEE 311J.S. Parent2 CHEE 311 - Thermodynamics of Mixtures Thermodynamics II is concerned with the properties of mixtures 1. Quantifying phase equilibrium behaviour  At a given pressure and temperature, how many phases exist in a system?  What is the composition of each phase?  What are the thermodynamic properties (U,S,Cp,V m,…) of each phase and the system as a whole? 2. Describing systems that undergo chemical reactions  Under specified conditions, to what extent does a reaction take place?  What is the equilibrium composition of the system?  How much heat is evolved/absorbed by the reaction and the mixing of reactants?

3. CHEE 311J.S. Parent3 Thermodynamic Systems The first step in all problems in thermodynamics is to define a system, either a body or a defined region of space. Types of Systems: Isolated:no transfer of energy or matter across the system boundaries Closed: possible energy exchange with the environment but no transfer of matter Open: exchange of energy and matter with the environment Phase: part of a system that is spatially uniform in its properties (density, composition,...)

4. CHEE 311J.S. Parent4 Thermodynamic Properties Concerned with macroscopic properties of a body, not atomic properties  Volume, surface tension, viscosity, etc  Divided into two classes Intensive Properties: (density, pressure,…)  specified at each point in the system  spatially uniform at equilibrium  Usually, specifying any 2 intensive variables defines the values of all other intensive variables I j = f(I 1, I 2 )(j=3,4,5,…,n)  This holds for mixtures as well, but composition must also be defined I j = f(I 1, I 2, x 1,x 2,…,x m-1 )(j=3,4,5,…,n) for an m-component mixture.

5. CHEE 311J.S. Parent5 Thermodynamic Properties Extensive Properties: (volume, internal energy,...)  Additive properties, in that the system property is the sum of the values of the constituent parts  Usually, specifying any 2 intensive and one extensive (conveniently the system mass) defines the values of all other extensive variables E j = m * f(I 1, I 2, x 1,x 2,…,x m-1 )(j=3,4,5,…,n) for an m-component mixture.  The quotient E i / m (molar volume, molar Gibbs energy) is an intensive variable, often called a specific property

6. CHEE 311J.S. Parent6 Phase Diagram for CO 2

7. CHEE 311J.S. Parent7 Ideal Mixture Behaviour Intermediate-boiling Systems, including Raoult’s Law Behaviour

8. CHEE 311J.S. Parent8 Non-Ideal Vapour-Liquid Equilibria (VLE) Systems having a minimum boiling azeotrope: We also observe systems with a maximum boiling azeotrope.

9. CHEE 311J.S. Parent9 Non-Ideal VLE, LLE and VLLE Systems having partially miscible liquid phases:

10. CHEE 311J.S. Parent10 Phase Behaviour of Diethylether

11. CHEE 311J.S. Parent11 1. Phase Rule for Intensive Variables SVNA-12.2 For a system of  phases and N species, the degree of freedom is: F = 2 -  + N  # variables that must be specified to fix the intensive state of the system at equilibrium Phase Rule Variables: The system is characterized by T, P and (N-1) mole fractions for each phase  Requires knowledge of 2 + (N-1)  variables Phase Rule Equations: At equilibrium  i  =  i  =  i  for all N species  These relations provide (  -1)N equations The difference is F = 2 + (N-1)  - (  -1)N = 2-  +N

12. CHEE 311J.S. Parent12 VLE in Single Component Systems For a two phase (  =2) system of a single component (N=1): F = 2-  + N F = 2- 2 + 1 = 1 Therefore, for the single component system, specifying either T or P fixes all intensive variables.

13. CHEE 311J.S. Parent13 Correlation of Vapour Pressure Data P i sat, or the vapour pressure of component i, is commonly represented by Antoine’s Equation: For acetonitrile (Component 1): For nitromethane (Component 2): These functions are the only component properties needed to characterize ideal VLE behaviour

14. CHEE 311J.S. Parent14 VLE in Binary Systems For a two phase (  =2), binary system (N=2): F = 2- 2 + 2 = 2 Therefore, for the binary case, two intensive variables must be specified to fix the state of the system.

15. CHEE 311J.S. Parent15 VLE in Binary Systems Alternately, we can specify a system pressure (often atmospheric) and examine VLE behaviour as a function of temperature and composition.

16. CHEE 311J.S. Parent16 Calculations using Raoult’s Law Raoult’s Law for ideal phase behaviour relates the composition of liquid and vapour phases at equilibrium through the component vapour pressure, P i sat. Deriving this expression, relating the composition of each phase at a given P,T at equilibrium, will be the objective of the next two weeks of the course.  Given the appropriate information, we can apply Raoult’s Law to the solution of 5 types of problems: »Dew Point: Pressure and Temperature »Bubble Point: Pressure and Temperature »P,T Flash

17. CHEE 311J.S. Parent17 Dew and Bubble Point Calculations Dew Point Pressure: Given a vapour composition at a specified temperature, find the composition of the liquid in equilibrium Given T, y 1, y 2,... y n find P, x 1, x 2,... x n Dew Point Temperature: Given a vapour composition at a specified pressure, find the composition of the liquid in equilibrium Given P, y 1, y 2,... y n find T, x 1, x 2,... x n Bubble Point Pressure: Given a liquid composition at a specified temperature, find the composition of the vapour in equilibrium Given T, x 1, x 2,... x n find P, y 1, y 2,... y n Bubble Point Temperature: Given a vapour composition at a specified pressure, find the composition of the liquid in equilibrium Given P, x 1, x 2,... x n find T, y 1, y 2,... y n

18. CHEE 311J.S. Parent18 1. Why all the theory? Parts of CHEE 311 are quite abstract (and, admittedly, a little dry). It is therefore important that the applications of thermodynamic theory be stressed. At the end of the course, you will understand the fundamental underpinning of thermodynamics and you will have used this knowledge to solve engineering problems. In this lecture, three areas that draw on an advanced knowledge of thermodynamics are described and demonstrated: A. Describing and Predicting Phase Stability B. Coping with Non-Ideal Behaviour C. Extending Experimental Data to Describe Complex Systems

19. CHEE 311J.S. Parent19 Phase Stability Thermodynamics is concerned with the state and properties of a system under specific conditions. The stability of a given phase is of practical concern as conditions are sought to affect a change in the system.  Under what conditions does a phase become unstable, resulting in a change of state?  What property of the system determines phase stability?

20. CHEE 311J.S. Parent20 Phase Stability As an example of phase stability, consider the solid-vapour equilibrium of a system in contact with a heat bath.  Increased volatilization raises U and S of the system.  Increased crystallization decreases U and S. We will see that the equilibrium state is determined by a balance of “order” and “disorder” (U and S), such that free energy (F or G) is minimized. The state of a system for which the free energy is minimized is that for which the total entropy (heat bath and system of interest) is maximized.

21. CHEE 311J.S. Parent21 Stability of Polymer Solutions An issue of practical importance in polymer production is the recovery of material from solution. Consider a solution of 5 wt% of an acrylonitrile-butadiene copolymer (34% AN, Mw = 250,000) in acetone.  We want to separate the polymer from the solvent using a clean process that yields a manageable material.  What means do we have for doing so?  How are we generating instability in the original solution? Acetone + NBR AcetoneNBR

22. CHEE 311J.S. Parent22 Vapour Pressure of Pure Acetone and Water If presented with the problem of separating water and acetone in the mixture by distillation, what would you do? From the vapour pressure curves (vap-liq line for a pure component), it is clear that acetone and water have different volatility.  Does this guarantee that distillation is possible?  What tools do you have/need for design purposes?

23. CHEE 311J.S. Parent23 Pxy diagram for Acetone-Water Mixtures: 25°C Obviously, for distillation to be effective there must exist conditions where a liquid and a vapour exist at equilibrium, and the compositions of these phases must differ. According to the phase rule, for two phases to exist in the acetone- water system, we have __ degrees of freedom.

24. CHEE 311J.S. Parent24 Txy diagram for Acetone-Water Mixtures: 1 bar If our system were fixed at atmospheric pressure, we would need to vary temperature - Txy diagram is more appropriate.

25. CHEE 311J.S. Parent25 Coping with Non-Ideal Behaviour The phase equilibrium tool you are most familiar with, Raoult’s Law, adequately describes systems that behave ideally. This refers to the strength and nature of interactions between components in a mixture.  Few systems of practical importance are sufficiently ideal to warrant the use of Raoult’s Law. Suppose we wanted to separate by room temperature distillation the acetone-water mixture that we created in the isolation of our polymer.  At 25°C, between what two pressures will two phases exist in the acetone-water system containing equimolar quantities of the two components? Raoult’s LawPhase Diagram P max P min

26. CHEE 311J.S. Parent26 Txy diagram for Acetone-Water Mixtures: 3.4 bar At higher pressure, the acetone-water system becomes increasingly non-ideal, as illustrated by the Txy diagram below.  How do we describe these systems?  Can we predict complications such as azeotropes? Note the lack of experimental data above 123°C - How can we extrapolate to higher temperatures in an accurate manner?

27. CHEE 311J.S. Parent27 Extending Experimental Data Design exercises become increasingly complex as additional components are added. Suppose our polymer solution was not NBR+acetone, but NBR+acetone+2-butanone. How does the acetone-MEK-water system behave?  There is limited data on ternary systems over awide range of conditions A principle objective of CHEE 311 is to give you the tools to handle non-ideal mixtures of any composition through the use of models that generalize phase behaviour and programs that carry out tedious calculations.