View
224
Download
4
Category
Tags:
Preview:
Citation preview
CHEE 311 J.S. Parent 1
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 processthe 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 plantsDealt only with closed systems of constant composition (usually 1-component systems such as H2O)
CHEE 311 J.S. Parent 2
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,Vm,…) 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?
CHEE 311 J.S. Parent 3
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,...)
CHEE 311 J.S. Parent 4
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
Ij = f(I1, I2) (j=3,4,5,…,n) This holds for mixtures as well, but composition must also be
defined
Ij = f(I1, I2, x1,x2,…,xm-1) (j=3,4,5,…,n)for an m-component mixture.
CHEE 311 J.S. Parent 5
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
Ej = m * f(I1, I2, x1,x2,…,xm-1) (j=3,4,5,…,n)
for an m-component mixture.
The quotient Ei / m (molar volume, molar Gibbs energy) is an intensive variable, often called a specific property
CHEE 311 J.S. Parent 6
Phase Diagram for CO2
CHEE 311 J.S. Parent 7
Ideal Mixture Behaviour
Intermediate-boiling Systems, including Raoult’s Law Behaviour
CHEE 311 J.S. Parent 8
Non-Ideal Vapour-Liquid Equilibria (VLE)
Systems having a minimum boiling azeotrope:
We also observe systems with a maximum boiling azeotrope.
CHEE 311 J.S. Parent 9
Non-Ideal VLE, LLE and VLLE
Systems having partially miscible liquid phases:
CHEE 311 J.S. Parent 10
Phase Behaviour of Diethylether
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
-25 0 25 50Temperature (oC)
To
tal P
ress
ure
(at
m)
CHEE 311 J.S. Parent 11
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
CHEE 311 J.S. Parent 12
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.
VLE for Pure Components
0
200
400
600
800
270 320 370 420Temperature: K
Pre
ssu
re: k
Pa
Acetonitrile Nitromethane
CHEE 311 J.S. Parent 13
Correlation of Vapour Pressure Data
Pisat, 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
CTB
APln sati
224C/T
47.29452724.14kPa/Pln sat
1
209C/T
64.29722043.14kPa/Pln sat
2
CHEE 311 J.S. Parent 14
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.
Acetonitrile(1) - Nitromethane(2) @ 75C
40
50
60
70
80
90
0.0 0.2 0.4 0.6 0.8 1.0x1,y1
Pre
ssu
re,
kPa
y1 x1
CHEE 311 J.S. Parent 15
VLE in Binary Systems
Alternately, we can specify a system pressure (often atmospheric) and examine VLE behaviour as a function of temperature and composition.
Acetonitrile(1) Nitromethane(2) @ 70kPa
65.0
70.0
75.0
80.0
85.0
90.0
0.00 0.20 0.40 0.60 0.80 1.00x1,y1
Tem
p,
deg
C
y1 x1
CHEE 311 J.S. Parent 16
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, Pi
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
PP
xy sat
i
i
i
CHEE 311 J.S. Parent 17
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, y1, y2,... yn find P, x1, x2, ... xn
Dew Point Temperature:Given a vapour composition at a specified pressure, find the composition of the liquid in equilibrium
Given P, y1, y2,... yn find T, x1, x2, ... xn
Bubble Point Pressure:Given a liquid composition at a specified temperature, find the composition of the vapour in equilibrium
Given T, x1, x2, ... xn find P, y1, y2,... yn
Bubble Point Temperature:Given a vapour composition at a specified pressure, find the composition of the liquid in equilibrium
Given P, x1, x2, ... xn find T, y1, y2,... yn
CHEE 311 J.S. Parent 18
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
CHEE 311 J.S. Parent 19
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?
CHEE 311 J.S. Parent 20
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.
CHEE 311 J.S. Parent 21
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 Acetone NBR
CHEE 311 J.S. Parent 22
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 ispossible?
What tools do youhave/need for design
purposes?
Vapour Pressure - Acetone, Water
0
200
400
600
800
0 20 40 60 80 100
Temperature (deg C)
Pre
ssu
re (
mm
Hg
)
Acetone
Water
CHEE 311 J.S. Parent 23
Pxy diagram for Acetone-Water Mixtures: 25°CObviously, 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.
Acetone-Water at 25C
0
50
100
150
200
250
0.0 0.2 0.4 0.6 0.8 1.0xAc, yAc
Pre
ss
ure
(m
mH
g)
xAc
yAc
CHEE 311 J.S. Parent 24
Txy diagram for Acetone-Water Mixtures: 1 barIf our system were fixed at atmospheric pressure, we would need to vary temperature - Txy diagram is more appropriate.
Acetone-Water at 726 mmHg
40
50
60
70
80
90
100
110
0.0 0.2 0.4 0.6 0.8 1.0xAc, yAc
Te
mp
era
ture
(d
eg
C)
xAc
yAc
CHEE 311 J.S. Parent 25
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 Law Phase Diagram
Pmax
Pmin
CHEE 311 J.S. Parent 26
Txy diagram for Acetone-Water Mixtures: 3.4 barAt 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?
Acetone-Water at 2585 mmHg
60
70
80
90
100
110
120
130
140
150
0.0 0.2 0.4 0.6 0.8 1.0xAc, yAc
Te
mp
era
ture
(d
eg
C)
xAc
yAc
Note the lack of experimental data above 123°C - How can we extrapolate to higher temperatures in an accurate manner?
CHEE 311 J.S. Parent 27
Extending Experimental Data
Design exercises become increasinglycomplex as additional components are added.Suppose our polymer solution was notNBR+acetone, but NBR+acetone+2-butanone.
How does the acetone-MEK-watersystem behave?
There is limited data on ternary systems over a wide range of conditions
A principle objective of CHEE 311 is to giveyou the tools to handlenon-ideal mixtures of any composition through the use of models that generalize phase behaviour and programs that carry out tedious calculations.
Recommended