BINARY VAPOR-LIQUID
EQUILIBRIUM
 Nonideal Liquid Solutions

If a molecule contains a hydrogen atom attached
to a donor atom (O, N, F, and in certain cases C),
the active hydrogen atom can form a bond with
another molecule containing a donor atom.
two water molecules
coming close together

Table 2.7 shows qualitative estimates of deviations from Raoult’s law for binary
pairs when used in conjunction with Table 2.8.

Positive deviations correspond to values of iL > 1. Nonideality results in a
variety of variations of (iL) with composition, as shown in Figure 2.15
(Seader & Henely) for several binary systems, where the Roman numerals
refer to classification groups in Tables 2.7 and 2.8.
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BINARY VAPOR-LIQUID
EQUILIBRIUM
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BINARY VAPOR-LIQUID
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
Figure 2.15a: Normal heptane (V) breaks ethanol (II) hydrogen
bonds, causing strong positive deviations.
n-heptane(v)-Ethanol
(II) system
(Semi-log paper)
Note: Ethanol molecules form H-bonds between each other and n-heptane
breaks these bond causing strong (+) deviation.
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
iL>1
In Figure 2.15b,
Similar Figure
2.15a but less positive
deviations occur when acetone (III) is added
to formamide (I).

In Figure 2.15c,
Hydrogen bonds are broken and formed with
chloroform (IV) and methanol (II) resulting in
an unusual positive deviation curve for
chloroform that passes through a maximum.
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In Figure 2.15d,
Chloroform (IV) provides active hydrogen
atoms that can form hydrogen bonds with
oxygen atoms of acetone (III), thus causing
negative deviations

Non-ideal solution effects can be incorporate into K-value formation
into different ways.
1.
Non-ideal liquid solution at near ambient
pressure
2.
Non-ideal liquid solution at moderate
pressure and TC.
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1.
Repulsion
Molecules that are dissimilar enough from each
other will exert repulsive forces
e. g: polar H2O molecules – organic hydrocarbon
Component(1)
x1

+
molecules.
i > 1
Component(2)

x2
When dissimilar molecules are mixed together
due to the repulsion effects, a greater partial
pressure is exerted, resulting in positive
deviation from ideality.
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+
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BINARY VAPOR-LIQUID
EQUILIBRIUM

Fore the last two figures, as the mole fraction x1 increases its 1 →1, as
its mole fraction x1 decreases 1 increases till it reaches to 1 (activity
coefficient at infinite dilution)
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
Attraction
When dissimilar molecules are mixed together, due to the attraction
effects, a lower partial pressure is exerted, resulting in negative
deviation from ideality.
i < 1 are called negative deviation from ideality.
Component(1)
x1
Component(2)
x2
-
 1
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BINARY VAPOR-LIQUID
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
Example:
calculate ij of methanol – water system for the following data 760 mmHg
Vapor phase
Liquid phase
ym = 0.665
xm = 0.3
yw = 0.33
xw = 0.7
Vapor Pressure Data at 78 oC (172.1°F)
Methanol: Pmsat = 1.64 atm
Water: Pwsat = 0.43 atm
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Vapor phase
ym = 0.665
yw = 0.33
Liquid phase
xm = 0.3
xw = 0.7
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BINARY VAPOR-LIQUID
EQUILIBRIUM
solution
For methanol
Py m  Pmsat x m  mL
1  0.665  1.64  0.3  mL
γ mL  1.35 atm 1.0 ( Repulsion)
(increase in partial pressure P)
For water
Pyw  Pwsat xw wL
1 0.335  0.43  0.7  mL
γ wL  1.11 atm  1.0 ( Repulsion)
(increase in partial pressure P)
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
How to calculate iL of Binary Pairs
Many empirical and semi-theoritical equations exists for estimating
activity coefficients of binary mixtures containing polar and/ or nonpolar species.
These equations contain binary interaction parameters, which are
back calculated from experimental data.
Table (2.9) show the different equations used to calculate iL.
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BINARY VAPOR-LIQUID
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THERMODYNAMICS OF
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Table (2.10) shows the equations used to calculate excess volume,
excess enthalpy and excess energy.
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Example. (problem 2.23 (
Benzene can be used to break the ethanol/water azeotrope so as to
produce nearly pure ethanol. The Wilson constants for the
ethanol(1)/benzene(2) system at 45°C are A12 = 0.124 and A21 = 0.523.
Use these constants with the Wilson equation to predict the liquid-phase
activity coefficients for this system over the entire range of composition
and compare them, in a plot like Figure 2.16, with the following
experimental results [Austral. J. Chem., 7, 264 (1954)]:
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Let: 1 = ethanol and 2 = benzene
The Wilson constants are A12 = 0.124 and A21 = 0.523 From Eqs. (4),
Table 2.9,
Using a spreadsheet and noting that  = exp(ln ), the following values
are obtained,
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 Activity coefficient at infinite dilution
Modern experimental techniques are available for accurately and rapidly
determining activity coefficient at infinite dilution (iL )
Appling equaion(3) in table (2.9) (van Laar (two-constant)) to conditions:
Xi = 0
and then
lin  i 
xj = 0
Aij
[1  ( xi Aij ) /( x j A ji )]
lin   Aij or   e

i
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
i
2
, xi  0
Aij
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THERMODYNAMICS OF
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lin  j 
A ji
[1  ( x j A ji ) /( xi Aij )]
lin  j  A ji or  j  e
2
, xj  0
A ji
Component(1)
x1
Component(2)

x2

+
+
Repulsive  > 1.0
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