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1
SCHOOL OF CHEMICAL ENGINEERING
CEIC3001 Advanced Thermodynamics and Separation
NONIDEALITY IN THE LIQUID PHASE
CONTENTS
VLE by Modified Raoult's Law .
......................................................................................
2
Partial Molar Properties.
...................................................................................................
3
The Ideal Solution .
...........................................................................................................
5
The Activity Coefficient: Species
i
in a Solution of Liquids .
..........................................
6
Models for the Excess Gibbs Energy .
..............................................................................
7
Margules Equations.
.....................................................................................................
7
Nonideal gas and nonideal solution: the Gamma/Phi Formulation of VLE.
...............
10
HIGHLIGHTS
1.
The
Modified Raoult’s Law
describes an equilibrium system where the vapour
behaves as an ideal gas and the liquid mixture is a
nonideal solution
.
2.
The deviation of each species
i
from nonideal solution behaviour is described
by
an
activity coefficient
i
:
sat
i
i
i
i
P
x
P
y
3.
The deviation of a a liquid mixture from ideal solution behaviour is measured by the
excess Gibbs energy
G
E
4.
Several models can be used to correlate and predict activity coefficients, of which
the
Margules equation
is one of the simplest, with only two parameters for a binary
system.
5.
When the vapour is not an ideal gas and the liquid mixture is not an ideal solution,
the
GammaPhi
formulation may be used to describe VLE:
sat
i
i
i
i
i
P
x
P
y
6.
i
and
i
depend on
T, P
and composition in a complex manner and are usually
calculated using computer simulation software.
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VLE by Modified Raoult's Law
a modified form of Raoult's law is expressed as
sat
i
i
i
i
i
P
x
P
y
p
(1)
where
i
= activity coefficient of component
i
in the liquid phase
the activity coefficient is a function of
T
and liquidphase composition and accounts
for nonideal
solution behaviour
modified Raoult's law provides a satisfactory description of VLE data for a wide
range of nonelectrolyte mixtures
such mixtures typically include solutions of organic solvents, e.g. MEK/toluene, and
solutions of water and watermiscible organic solvents, e.g. H
2
O/MeOH
if values of the activity coefficient are known, Eq. 1 can be used to generate
Pxy
and
Txy
diagrams via bubblepoint and dewpoint calculations
it is still assumed that the vapour phase behaves as an ideal gas
N
i
i
i
i
P
x
P
1
sat
(2)
Eq. 2 can also be solved for
x
i
and summed over all species as follows
N
i
N
i
i
i
i
i
P
P
y
x
11
sat
1
(3)
rearrangement of Eq. 3 leads to an alternative expression for
P
N
i
i
i
i
P
y
P
1
sat
/
1
(4)
Eqs 1, 2 and 4 are used for bubblepoint and dewpoint calculations but the iteration
procedures are more complex than those for the standard form of Raoult's law (see
Example 10.3 in the 6th ed. text)
given a set of experimental
values of
Pxy
data (or
Txy
data), Eq. 1 also provides a
means of determining experimental
values of
i
sat
i
i
i
i
P
x
P
y
(5)
the more general problem though is that we need to develop equations which allow
us to calculate
i
the excess Gibbs energy can be used for this purpose
3
Partial Molar Properties
in the previous lecture the fugacity of a pure gas was introduced using the
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This note was uploaded on 03/26/2012 for the course CHEM ENG CEIC at University of New South Wales.
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