Dr Saad Al-Shahrani ChE 334: Separation Processes 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. 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. BINARY VAPOR-LIQUID EQUILIBRIUM two water molecules coming close together
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Dr Saad Al-ShahraniChE 334: Separation Processes
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.
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.
BINARY VAPOR-LIQUID EQUILIBRIUM
two water molecules coming close together
Dr Saad Al-ShahraniChE 334: Separation Processes
BINARY VAPOR-LIQUID EQUILIBRIUM
Dr Saad Al-ShahraniChE 334: Separation Processes
BINARY VAPOR-LIQUID EQUILIBRIUM
Dr Saad Al-ShahraniChE 334: Separation Processes
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.
BINARY VAPOR-LIQUID EQUILIBRIUM
Dr Saad Al-ShahraniChE 334: Separation Processes
In Figure 2.15b,
Similar Figure 2.15a but less positive
deviations occur when acetone (III) is added
to formamide (I).
BINARY VAPOR-LIQUID EQUILIBRIUM
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.
iL>1
Dr Saad Al-ShahraniChE 334: Separation Processes
BINARY VAPOR-LIQUID EQUILIBRIUM
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.
2.
Non-ideal liquid solution at near ambient pressure
Non-ideal liquid solution at moderate pressure and TC.
Dr Saad Al-ShahraniChE 334: Separation Processes
1. Repulsion
Molecules that are dissimilar enough from each other will exert repulsive forces
BINARY VAPOR-LIQUID EQUILIBRIUM
Component(1)
x1
Component(2)
x2
e. g: polar H2O molecules – organic hydrocarbon
molecules.
i > 1
When dissimilar molecules are mixed together due to the repulsion effects, a greater partial pressure is exerted, resulting in positive deviation from ideality.
+
+
Dr Saad Al-ShahraniChE 334: Separation Processes
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)
BINARY VAPOR-LIQUID EQUILIBRIUM
Dr Saad Al-ShahraniChE 334: Separation Processes
Attraction
When dissimilar molecules are mixed together, due to the attraction effects, a lower partial pressure is exerted, resulting in negative deviation from ideality.
BINARY VAPOR-LIQUID EQUILIBRIUM
i < 1 are called negative deviation from ideality.
Component(1)x1
Component(2)x2
1
2
--
Dr Saad Al-ShahraniChE 334: Separation Processes
Example:
calculate ij of methanol – water system for the following data 760 mmHg
Vapor phase
ym = 0.665
yw = 0.33
BINARY VAPOR-LIQUID EQUILIBRIUM
Liquid phase
xm = 0.3
xw = 0.7
Vapor Pressure Data at 78 oC (172.1°F)
Methanol: Pmsat = 1.64 atm
Water: Pwsat = 0.43 atm
Vapor phase
ym = 0.665
yw = 0.33
Liquid phase xm = 0.3xw = 0.7
Dr Saad Al-ShahraniChE 334: Separation Processes
BINARY VAPOR-LIQUID EQUILIBRIUM
solution
For methanol
mLmsatmm xPPy
wLwsatww xPPy
mL 3.064.1665.01
P) pressure partialin (increase
Repulsion) ( 1.0 atm 1.35 γmL
For water
mL 7.043.0335.01
P) pressure partialin (increase
Repulsion) ( 1.0 atm 1.11 γ wL
Dr Saad Al-ShahraniChE 334: Separation Processes
BINARY VAPOR-LIQUID EQUILIBRIUM
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 non-
polar 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.
Dr Saad Al-ShahraniChE 334: Separation Processes
BINARY VAPOR-LIQUID EQUILIBRIUM
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
Table (2.10) shows the equations used to calculate excess volume, excess enthalpy and excess energy.
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
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)]:
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
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,
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
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:
