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Chapter 11
LiquidLiquid Equilibrium
When two liquids are mixed, depending on the temperature and/or composition, either they
are completely miscible in each other and form a single phase or, they are partially miscible
(or, totally immiscible) in each other and form two separate phases. In the case of completely
miscible, i.e., single phase systems, the equations developed in Chapter 6 are applicable. What
we are interested in this chapter is the case when a liquid is partially miscible (or totally
immiscible) in another liquid. First, the reason for making liquids partially miscible in each
other will be investigated. Then, the procedure to determine the compositions in two separate
liquid phases that are in equilibrium with each other will be described. Such equilibrium
data are needed in various chemical and physical processes such as liquidliquid extraction and
tertiary oil recovery.
11.1 STABILITY OF MULTICOMPONENT LIQUID MIXTURES
For thermodynamically allowable changes at constant temperature and pressure, the criterion
(
dG
)
T,P
≤
0
(11.11)
indicates that all irreversible changes taking place at constant temperature and pressure must
decrease the total Gibbs energy of the system. When the system reaches equilibrium, no further
changes can occur and Gibbs energy reaches its minimum value.
Let us consider mixing of two liquids, 1 and 2, at constant temperature and pressure. The
Gibbs energy of this binary mixture is
G
mix
=
n
1
e
G
1
+
n
2
e
G
2
+
∆
G
mix
(11.12)
If the Gibbs energy of the mixture is lower than the summation of the Gibbs energies of pure
components, then components 1 and 2 will be miscible (totally or partially) in each other. This
statement is mathematically expressed as
G
mix
<n
1
e
G
1
+
n
2
e
G
2
(11.13)
or, in other words,
∆
G
mix
<
0
(11.14)
which is the criterion for miscibility (partial or complete).
The Gibbs energy of mixing is given by
∆
e
G
mix
=
∆
e
H
mix

{z
}
A
−
T
∆
e
S
mix

{z
}
B
(11.15)
Since mixing increases the degree of disorder within the system, the entropy change on mixing,
∆
e
S
mix
, is always positive. Thus, the term
B
in Eq. (11.15) is always positive. The heat of
mixing,
∆
e
H
mix
, is related to the energetic e
f
ects. In order to make a mixture of 1 and 2 from
343
pure components, it is necessary to break 11
(
E
1
)
and 22
(
E
2
)
bonds and form 12
(
E
12
)
bonds.
Depending on the magnitude of the interactions between like and unlike molecules,
∆
e
H
mix
may
take positive or negative values. Therefore, it is necessary to consider the following two cases.
Case (i): Exothermic mixing (
∆
e
H
mix
<
0
)
When
∆
e
H
mix
<
0
, interactions between unlike molecules are greater than those of like molecules,
i.e.,
E
12
>
E
1
+
E
2
2
(11.16)
In this case,
∆
e
G
mix
is negative for all compositions of components 1 and 2. Therefore, liquids
are completely miscible in each other and form a single phase. This situation is illustrated in
Figure 11.1.
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