Chemical Engineering Thermodynamics
Lecturer: Zhen-xi Jiang (Ph.D. U.K.)
School of Chemical Engineering
Chapter 10
Vapor/Liquid Equilibrium: Introduction
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
Departure 偏离，偏差
Mole-fraction-weighted sum
摩尔分数加权和
Dew point 露点
Bubble point 泡点
Azeotrope 共沸物
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
Subcooled liquid 过冷液体
Superheated vapor 过热蒸汽
Partial pressure 分压
Simple model 简单模型
Mathematical model 数学模型
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
Flash 闪蒸
Flash calculation 闪蒸计算
Flash distillation 闪蒸，闪发蒸馏
Flash evaporation 闪发蒸发，闪发蒸馏
Equilibrium ratio 平衡比（K）
Relative volatility 相对挥发度（α）
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
What is a model?
A model is a simplified mathematical
description of a system or process, used to
assist calculations and predictions.
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
What is modeling?
Generally, the process of representing a
real-world object or phenomenon as a set
of mathematical equations.
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
What is simulation?
The process of imitating a real phenomenon
with a set of mathematical formulas. Advanced
computer programs can simulate chemical
reactions, distillation and heat transfer
processes. If the simulation is done on
computer, it is known as computer simulation.
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
Example for Model, Modeling and Simulation
Raoult’s law is the mathematical model of
ideal mixtures. The process of finding Raoult’s
law for VLE behavior of ideal mixtures is
known as system modeling. Using the Raoult’s
law to do dew point and bubble point
calculation is simulation of the ideal system.
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
Saturated liquid and Subcooled liquid
If a substance exists as a liquid at the saturation
temperature, it is called a saturated liquid. If
the temperature of the liquid is lower than the
saturation temperature, it is called a subcooled
liquid.
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
Saturated vapor and Superheated vapor
If a substance exists entirely as vapor at the
saturation temperature, it is called a saturated
vapor. When the vapor is at a temperature
greater than the saturation temperature, it is
said to exist as superheated vapor.
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
Flash distillation is a single stage separation
technique. A liquid mixture feed is pumped through a
heater to raise the temperature and enthalpy of the
mixture. It then flows through a valve and the
pressure is reduced, causing the liquid to partially
vaporize. Once the mixture enters a big enough
volume， the liquid and vapor separate. Because the
vapor and liquid are in such close contact up until the
"flash" occurs, the product liquid and vapor phases
approach equilibrium.
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
Flash (or partial) evaporation is the partial
vaporization that occurs when a saturated liquid
stream undergoes a reduction in pressure by passing
through a throttling valve or other throttling device.
This process is one of the simplest unit operations. If
the throttling valve or device is located at the entry
into a pressure vessel so that the flash evaporation
occurs within the vessel, then the vessel is often
referred to as a flash drum.
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
10 Vapor/Liquid Equilibrium: Introduction
Special terms：
flash calculation 闪蒸计算
已知系统总组成，求一定温度、压力下，达到平衡
的气液两组组成与数量之比。是汽液平衡计算的基
本内容之一。
Questions：
What is saturated liquid?
什么是饱和液体?
What is subcooled liquid?
什么是过冷液体？
What is for Flash calculation？
闪蒸计算是要做什么？
You may answer the questions in English or Chinese.
Questions
Chapter 10
Vapor/Liquid Equilibrium: Introduction
10 Vapor/Liquid Equilibrium: Introduction
For what processes? For separation!
Processes such as distillation, adsorption, and
extraction bring phases of different
composition into contact, and when the phases
are not in equilibrium, mass transfer between
the phases alters their compositions. Both the
extent of change and the rate of transfer
depend on the departure of the system from
equilibrium.
Thus, for quantitative treatment of mass
transfer the equilibrium T, P, and phase
compositions must be known.
10 Vapor/Liquid Equilibrium: Introduction
VLE is one of phase equilibria in chemical industry. VLE is key important phase equilibrium.
The most commonly encountered coexisting
phases in industrial practice are vapor and
liquid, although liquid/liquid, vapor/liquid, and
liquid/solid systems are also found.
Contents of this chapter
In this chapter the nature of equilibrium is
discussed, and then two rules are considered.
These two rules give the number of
independent variables required to determine
equilibrium states.
10 Vapor/Liquid Equilibrium: Introduction
There follows in Sec. 10.3 a qualitative
discussion of vapor/liquid phase behavior.
In Sec. 10.4 the two simplest formulations are
introduced that allow calculation of
temperature, pressure, and phase compositions
for systems in vapor/liquid equilibrium.
10 Vapor/Liquid Equilibrium: Introduction
The two simplest formulations (models)
The first, known as Raoult’s law, is valid only
for systems at low to moderate pressures and
in general only for systems comprised of
chemically similar species.
The second, known as Henry’s law, is valid for
any species present at low concentration, but
as presented here is also limited to systems at
low to moderate pressures.
10 Vapor/Liquid Equilibrium: Introduction
A modification of Raoult’s law that removes
the restriction to chemically similar species is
treated in Sec. 10.5.
Finally in Sec. 10.6 calculations based on
equilibrium ratios or K-value are considered.
Sec. 10.7 is about relative volatility. This is an
addition to this textbook. The mentioned above
is the contents and structure of this chapter.
10 Vapor/Liquid Equilibrium: Introduction
Questions?
What are the contents in this chapter?
这一章都包含哪些内容？
Equilibrium： VLE, LLE, SLE
Nature of Equilibrium
Raoult’s law
Henry’s law
Modified Raoult’s law
Calculation based on K-values
Relative volatility
10.1 The Nature of Equilibrium
Equilibrium is a static condition in which no
changes occur in the macroscopic properties of
a system with time.
This implies a balance of all potentials in
different phases at same temperature and
pressure. Potentials are the driving force to
cause a change.
10.1 The Nature of Equilibrium
What is equilibrium? The conditions for equilibrium.
An isolated system consisting of liquid and
vapor phases in intimate contact eventually
reaches a final state wherein no tendency
exists for change to occur within the system.
The temperature, pressure, and phase
compositions reach final values which
thereafter remain fixed.
10.1 The Nature of Equilibrium
Measures of Composition
The three most common measures of
composition are:
mass fraction,
mole fraction, and
molar concentration
10.1 The Nature of Equilibrium
Question:
How many measures of composition will be
used in this chapter?
这一章要用到几种混合物浓度的表示方法？
Three. There are
mass fraction,
mole fraction, and
molar concentration
10.2 The Phase Rule & Duhem’s Theorem
The phase rule for non-reacting systems,
presented without proof in Sec. 2.7, results
from application of a rule of algebra.
The intensive state of a P V T system
containing N chemical species and πphases in
equilibrium is characterized by the intensive
variables, temperature T, pressure P, and N-1
mole fractions for each phase.
The masses of the phases are not phase-rule
variables.
10.2 The Phase Rule & Duhem’s Theorem
An independent phase-equilibrium equation
may be written connecting intensive variables
for each of the N species for each pair of
phases present. Thus, the number of
independent phase-equilibrium equations is
(π-1) • N . The difference between the number
of phase-rule variables and the number of
independent equations connecting them is the
number of variables that may be independently
fixed. ．
10.2 The Phase Rule & Duhem’s Theorem
Called the degrees of freedom of the system F,
the number is:
F = 2 + (N-1) •π – (π-1) • N
Upon reduction, this becomes the phase rule:
10.2 The Phase Rule & Duhem’s Theorem
Duhem’s theorem
It is another rule, similar to the phase rule, but less
celebrated. It applies to closed systems at
equilibrium for which the extensive state as well as
intensive state of the system is fixed. The state of
such a system is said to be completely determined,
and is characterized not only by the 2 + (N-1) •π
intensive phase-rule variables but also by theπ
extensive variables represented by the masses (or
mole numbers) of the phases.
10.2 The Phase Rule & Duhem’s Theorem
Thus the total number of variables is:
2 + (N-1) •π + π = 2 + N •π
For a closed system formed from specified
amount of the chemical species present, a
material-balance equation can be written for
each of the N chemical species.
10.2 The Phase Rule & Duhem’s Theorem
These in addition to the (N-1) •π phaseequilibrium equations represent a number of
independent equations equal to:
(π-1) • N + N = π • N
The difference between the number of
variables and the number of equations is
therefore:
2 + N •π - π • N = 2
10.2 The Phase Rule & Duhem’s Theorem
On the basis of this result, Duhem’s theorem is
stated as follows:
For any closed system formed initially from
given masses of prescribed chemical species,
the equilibrium state is completely determined
when any two independent variables are fixed.
10.2 The Phase Rule & Duhem’s Theorem
Question：
Restate Duhem’s theorem.
重述杜亥姆定理
For any closed system formed initially from given masses of
prescribed chemical species, the equilibrium state is completely
determined when any two independent variables are fixed.
10.3 VLE: Qualitative Behavior
10.3 VLE: Qualitative Behavior
Fig.10.2(a) present a T-x1-y1 diagram and Fig.
10.2(b) a P-x1-y1 diagram.
Other possible plots are vapor mole faction y1
vs. liquid mole fraction x1 for either the
constant-T conditions of Fig.10.2(a) or the
constant-P conditions of Fig.10.2(b).
10.4 Simple Models For VLE
The preceding section describes what is
observed through experiment. When
thermodynamics is applied to vapor/liquid
equilibrium, the goal is to find by calculation
the temperatures, pressures, and compositions
of phases in equilibrium.
10.4 Simple Models For VLE
Figure 10.8: P x y diagrams at constant T:
(a) tetrahydrofuran(1)/carbon tetrachloride(2) at 30 ℃
(b) chloroform(1)/tetrahydrofuran(2) at 30 ℃
10.4 Simple Models For VLE
Figure 10.8: P x y diagrams at constant T:
(c) furan(1)/carbon tetrachloride(2) at 30 ℃
(d) ethanol(1)/toluene(2) at 65 ℃
10.4 Simple Models For VLE
Figure 10.9: t x y diagrams at constant P (1 atm.):
(a) tetrahydrofuran(1)/carbon tetrachloride(2) at 30 ℃
(b) chloroform(1)/tetrahydrofuran(2) at 30 ℃
10.4 Simple Models For VLE
Figure 10.9: t x y diagrams at constant P (1 atm):
(c) furan(1)/carbon tetrachloride(2) at 30 ℃
(d) ethanol(1)/toluene(2) at 65 ℃
10.4 Simple Models For VLE
This Figure shows four types of systems:
Ideal, real, Maximum and Minimum azeotropes
10.4 Simple Models For VLE
Raoult’s Law - Assumptions
The two major assumptions required to reduce
VLE calculations to Raoult’s law are:
1. The vapor phase is an ideal gas.
2. The liquid phase is an ideal solution.
10.4 Simple Models For VLE
Raoult’s Law - restrictions
The first assumption means that Raoult’s law
can apply only for low to moderate pressures.
The second assumption implies that the law
can have approximate validity only when the
system species are chemically similar.
10.4 Simple Models For VLE
Raoult’s Law - mathematical expression
Mathematical expression for Raoult’s law is
Where xi is a liquid phase mole fraction, yi is a
vapor phase mole fraction, and Pisat is the
vapor pressure of pure species i at the
temperature of the system. The product yi P is
known as the partial pressure of species i.
10.4 Simple Models For VLE
Raoult’s Law – applications
The Raoult’s law, simple model for VLE,
provides a realistic description of actual
behavior for a relatively small class of systems.
Nevertheless, it is useful for displaying VLE
calculations in their simplest form, and it also
serves as a standard of comparison for more
complex systems.
10.4 Simple Models For VLE
Raoult’s Law – limitation
A limitation of Raoult’s law is that it can be
applied only to species of known vapor
pressure, and this requires the species to be
“subcritical,” i.e., to be at a temperature below
its critical temperature.
10.4 Simple Models For VLE
Raoult’s Law – feature for species with mole
fraction approaching unity
An important and useful feature of Raoult’s
law is that it is valid for any species present at
a mole fraction approaching unity, i.e. one
provided only that the vapor phase is an ideal
gas. Chemical similarity of the constituent
species is not here a requirement.
10.4 Simple Models For VLE
Dew point and Bubble point Calculations
For the calculations there are four classes:
BUBL P: for given xi and T calculate yi and P
DEW P: for given yi and T calculate xi and P
BUBL T: for given xi and P calculate yi and T
DEW T: for given yi and P calculate xi and T
10.4 Simple Models For VLE
Dew point and Bubble point Calculations
Equations used for the calculations:
10.4 Simple Models For VLE
Example 10.1
See online course for using MathCAD to
solve this example problem.
10.4 Simple Models For VLE
Bubblepoint
dewpoint
10.4 Simple Models For VLE
dewpoint
Bubblepoint
10.4 Simple Models For VLE
Henry’s Law
Application of Raoult’s law to species i
requires a value for Pisat at the temperature of
application, and thus is not appropriate for a
species whose critical temperature is less than
the temperature of application.
10.4 Simple Models For VLE
Henry’s Law
If a system of air in contact with liquid water
is presumed at equilibrium, then the air is
saturated with water. The mole fraction of
water vapor in the air is usually found from
Raoult’s law applied to the water with the
assumption that no air dissolves in the liquid
phase.
10.4 Simple Models For VLE
Henry’s Law
Thus, the liquid water is regarded as pure and
Raoult’s law for the water (species 2) becomes
y2 P = P2sat
10.4 Simple Models For VLE
Henry’s Law
If we wish to calculate the mole fraction of air
dissolved in the water, the Raoult’s law cannot
be applied, because the critical temperature of
air is much lower that surrounding temperature.
This problem can be solved by Henry’s law.
yi P = xiHi
where Hi is Henry’s constant.
10.4 Simple Models For VLE
Henry’s Law
Henry’s constants come from experiment, and
Table 10.1 lists values at 25℃ for a few gases
dissolved in water.
10.4 Simple Models For VLE
Questions：
There is no bubble point for pure species.
True or False?
There is no boiling point for liquid mixture.
True or False?
How many types of systems for liquid mixtures?
Four: Ideal, real, maximum and minimum boiling point azeotropes
10.4 Simple Models For VLE
Questions：
Raoult’s law is valid for liquid-liquid mixtures.
True or False?
Henry’s law is valid for gas-liquid mixtures.
True or False?
How many types of systems for liquid mixtures?
Four: Ideal, real, maximum and minimum boiling point azeotropes
Question time
Any Questions ?
This is End of the Lecture
Thanks !