Nonideal Behavior Dicky Dermawan @gmail.com ITK-234 Termodinamika Teknik Kimia II.
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Transcript of Nonideal Behavior Dicky Dermawan @gmail.com ITK-234 Termodinamika Teknik Kimia II.
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Nonideal Behavior
Dicky Dermawanwww.dickydermawan.net78.net
ITK-234 Termodinamika Teknik Kimia II
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Nonideal Behavior, Outline
Introduction: Effect of Nonideality Partial Molar Properties Residual Properties
Fugacity & Fugacity Coefficient
Excess Properties Activity & Activity Coefficient
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Intorduction: Effect of Nonideality:
Tetrahydrofuran(1)/Carbon-tetrachloride(2)
t-x-y diagramP-x-y diagram
30oC 1 atm
P-xy Diagram Acetonitril(1)/Nitrometana(2) @
75oC
40
45
50
55
60
65
70
75
80
85
0 0.2 0.4 0.6 0.8 1
x1, y1
P
txy diagram Acetonitril(1)/Nitromethane(2)
65
70
75
80
85
90
0 0.2 0.4 0.6 0.8 1x1, y1
t, oC
@ P = 70 kPa
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Effect of Nonideality: Chloroform(1)/Tetrahydrofuran(2)
t-x-y diagramP-x-y diagram
30oC 1 atm
P-xy Diagram Acetonitril(1)/Nitrometana(2) @
75oC
40
45
50
55
60
65
70
75
80
85
0 0.2 0.4 0.6 0.8 1
x1, y1
P
txy diagram Acetonitril(1)/Nitromethane(2)
65
70
75
80
85
90
0 0.2 0.4 0.6 0.8 1x1, y1
t, oC
@ P = 70 kPa
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Effect of Nonideality: Furan(1)/Carbontetrachloride(2)
t-x-y diagramP-x-y diagram
30oC 1 atm
P-xy Diagram Acetonitril(1)/Nitrometana(2) @
75oC
40
45
50
55
60
65
70
75
80
85
0 0.2 0.4 0.6 0.8 1
x1, y1
P
txy diagram Acetonitril(1)/Nitromethane(2)
65
70
75
80
85
90
0 0.2 0.4 0.6 0.8 1x1, y1
t, oC
@ P = 70 kPa
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Effect of Nonideality: Ethanol(1)/Toluene(2)
t-x-y diagramP-x-y diagram
65oC1 atm
P-xy Diagram Acetonitril(1)/Nitrometana(2) @
75oC
40
45
50
55
60
65
70
75
80
85
0 0.2 0.4 0.6 0.8 1
x1, y1
P
txy diagram Acetonitril(1)/Nitromethane(2)
65
70
75
80
85
90
0 0.2 0.4 0.6 0.8 1x1, y1
t, oC
@ P = 70 kPa
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Effect of Nonideality: x – y Diagram at Constant P = 1
atm
a. Tetrahydrofuran(1)/Carbon-tetrachloride(2)
b Chloroform(1)/Tetrahydrofuran(2)
c. Furan(1)/Carbontetrachloride(2)
d. Ethanol(1)/Toluene(2)
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Partial Molar Properties
.etc,Gor ,V ,S ,H ,UM iiiiii
ii Mx MSolution Properties:
….are properties of component i in the state of mixtures, which, in general
different from that in the state of pure species
Partial Properties:
Pure-species Properties: .etc,Gor ,V ,S ,H ,UM iiiiii
NOT: ii Mx M
What physical interpretation can be given for, viz. partial molar
volume ?
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Methanol – Water Mixture, An Example
For pure species at 25oC:Methanol (1) : V1 = 40.727
cm3/molWater (2) : V2 = 18.068 cm3/molWhat is the volume of 10 moles of methanol/water solution containing 30% mol of methanol?
Most people would think, logically:
Mol of methanol : 0.3 x 10 moles = 3 moles
Mol of water : (1-0.3) x 10 moles = 7 moles
Volume of methanol : 3 moles x 40.727 = 122.181 cm3
Volume of water : 7 moles x 18.068 = 126.476 cm3
Thus, the total volume : 122.181 + 126.476= 248.657 cm3
Wrong answer! The correct answer is 240.251 cm3
Thus there is 240.251 – 248.657 = -8.406 cm3 deviation from expected value
ii Mx M
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More on Partial Molar Properties
jn,P,Ti
i n
nMM
.dn
n
nMdP
P
nMdT
T
nMnMd i
n,P,Tin,Tn,Pj
.),.........n,n,n,P,T(MnM 321
.....dn
n
nMdn
n
nM
dPP
nM dT
T
nMnMd
2,...n,n,P,T2
1,...n,n,P,T1
n,Tn,P
3132
ii Mx MNOT: ii Mx M
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Chemical Potential as Partial Molar Property
Criteria for Vapor - Liquid Equilibria
i
PP
TT
ig
i
g
g
jn,P,Tii n
)nG(
The chemical potential of i-th component is
defined as:
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Chemical Potential as Partial Molar Property
jn,P,Ti
in
nGG
ii G
.dn
n
nGdP
P
nGdT
T
nGnGd i
n,P,Tin,Tn,Pj
If we set M = G:
Thus:
jn,P,Tii n
)nG(
The definition of chemical potential:
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Evaluation of Partial Molar Properties Methanol – Water Mixture Example
Methanol mol fraction
Molar volume, mL/mol
0 18.10.114 20.30.197 21.90.249 23.00.495 28.30.692 32.90.785 35.20.892 37.9
1 40.7
16
20
24
28
32
36
40
0 0.2 0.4 0.6 0.8 1
x1
Mix
ture
Pro
per
ty M
M
2M
1M1
21 x
MxMM
112 x
MxMM
ii Mx M
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ExerciseA group of students came across an unsuspected supply
of laboratory alcohol, containing 96 mass-percent ethanol and 4 mass-percent water.
As an experiment they decided to convert 2 L of this material into vodka, having a composition of 56 mass-percent ethanol and 44 mass-percent water. Wishing to perform the experiment carefully, they search the literature and found the following partial-specific volume data for ethanol – water mixtures at 25oC and 101.3 kPa.
The specific volume of water at 25oC is 1.003 L/kg. How many L of water should be added to the 2
L of laboratory alcohol, and how many L of vodka result?
1.243 1.273 L/kg ,V
0.953 0.816 L/kg ,V
In vodka ethanol 96% In
OHEt
OH2
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Fugacity, f
PlndTRdG ig
flndTRdG
lndTRdGR
Ideal gas :
Real gas :
P
f
igR GGG Residual Gibbs energy :
Fugacity coefficient :
lnTR
GR
At constant T
Residual Property
igR VVV
P
RT)1Z(VR
dPVdTSdG
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Evaluation of Pure Component Fugacity, fi
dPVdG Ri
Ri
P
0
Ri
Ri dP
RT
V
RT
dG
Pf ii
Real gas :
Pure Component Fugacity Coefficient:
The fugacity :
i
Ri lnTR
G
At constant T:
P
0
i
Ri
P
dP)1Z(
RT
G
P
0
ii P
dP)1Z( ln
P
RT)1Z(V i
Ri
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Evaluation of Pure Component Fugacity, fi
From the following compressibility data for hydrogen at 0oC, determine the fugacity of
hydrogen at 950 atm
P, atm Z P, atm Z
100 1.069 600 1.431200 1.138 700 1.504300 1.209 800 1.577400 1.283 900 1.649500 1.356 1000 1.720
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Evaluation of Pure Component Fugacity, fi
From the following compressibility data for isobutane,
determine the fugacity of butane at various temperature and pressure
P/bar 340 K 350 K 360 K 370 K 380 K
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Evaluation of Pure Component Fugacity, fi from
Equation of State
RT
PB1Z
RT
PV ii
i RT
PB ln i
i
10
c
c BBTR
PB
Virial :
6.1r
0
T
422.0083.0B
2.4r
1
T
172.0139.0B
cr T
TT
10
r
ri BB
T
P ln
cr P
PP
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Critical Constants & Accentric Factors:Paraffins
Tc/K Pc/bar Vc/10-6m3.mol-1 Zc
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Critical Constants & Accentric Factors:
Olefin & Miscellaneous Organics
Tc/K Pc/bar Vc/10-6m3.mol-1 Zc
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Critical Constants & Accentric Factors:
Miscellaneous Organic CompoundsTc/K Pc/bar Vc/10-6m3.mol-1 Zc
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Critical Constants & Accentric Factors:
Elementary Gases
Tc/K Pc/bar Vc/10-6m3.mol-1 Zc
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Critical Constants & Accentric Factors:
Miscellaneous Inorganic CompoundsTc/K Pc/bar Vc/10-6m3.mol-1 Zc
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Evaluation of Pure Component Fugacity, fi from Virial Equation of State, Example
Using virial equation of state,
calculate the fugacity and fugacity coefficient of:
1. Pure methyl-ethyl-ketone
2. Pure toluene
at 50oC and 25 kPa.
The required data:
ij Tcij/K Pcij/bar Vcij/cm3.mol-1 Zcij wij
11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257
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Evaluation of Pure Component Fugacity, fi from
Equation of State
TRZ
Pbh i
ci
5.2ci
2
i P
TR42748.0a
h1
h
TRb
a
h1
1Z
5.1i
i
Redlich-Kwong:
5.1TRb
aZ)h1(ln1Z ln
ci
cii P
TR08664.0b
}to be solved simultaneously
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Evaluation of Pure Component Fugacity, fi from Redlich-Kwong Equation of StateUsing Redlich - Kwong equation of state,
calculate the fugacity and fugacity coefficient of:
1. Pure methyl-ethyl-ketone
2. Pure toluene
at 50oC and 25 kPa.
The required data:
ij Tcij/K Pcij/bar Vcij/cm3.mol-1 Zcij wij
11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257
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Evaluation of Pure Component Fugacity, fi :
Pitzer’s Generalized Correlation
T,Pf rr0
i
1
i0
ii
T,Pf rr1
i
cr P
PP
cr T
TT
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Evaluation of Pure Component Fugacity, fi :
Pitzer’s Generalized Correlation
cr P
PP
cr T
TT
0i
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Evaluation of Pure Component Fugacity, fi :
Pitzer’s Generalized Correlation
cr T
TT
0i
cr P
PP
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Evaluation of Pure Component Fugacity, fi :
Pitzer’s Generalized Correlation
cr P
PP
cr T
TT
1i
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Evaluation of Pure Component Fugacity, fi :
Pitzer’s Generalized Correlation
cr P
PP
cr T
TT
1i
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Evaluation of Pure Component Fugacity, fi : Pitzer Correlation
Using Pitzer Correlation,
calculate the fugacity and fugacity coefficient of:
1. Pure methyl-ethyl-ketone
2. Pure toluene
at 50oC and 25 kPa.
The required data:
ij Tcij/K Pcij/bar Vcij/cm3.mol-1 Zcij wij
11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257
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Evaluation of LiquidPure Component Fugacity, fi
dPVTR
1
f
fln
P
P
isati
i
sati
Poynting factor
Fugasity of saturated vapor,
calculated exactly as calculating gas phase fugacity
TR
PPVexpP f
satiisat
isat
ii
Since Vl is a weak function of P at temperatures well below Tc:
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Estimation of Liquid Density
Rackett Equation:
cr P
PP
cr T
TT
V
Vcr
2857.0r )T1(
ccsat ZVV
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Examples ofEvaluation of Liquid Pure Component Fugacity, fi
11.5
Estimate the fugacity of liquid acetone at 110oC and 275 bar.
At 110oC the vapor pressure of acetone is 4.36 bar and the molar volume of
saturated-liquid acetone is 73 cm3.mol-1
11.6
Estimate the fugacity of liquid n-butane at 120oC and 34 bar.
At 120oC the vapor pressure of n-butane is 22.38 bar and the molar volume of
saturated-liquid n-butane is 137 cm3.mol-1
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Examples ofEvaluation of Liquid Pure Component Fugacity, fi11.10
The normal boiling point of n-butane is 0.5oC.
Estimate the fugacity of liquid n-butane at this temperature
and 200 bar.
11.11
The normal boiling point of 1-pentene is 30.0oC.
Estimate the fugacity of liquid 1-pentene at this temperature
and 350 bar.
11.12
The normal boiling point of isobutane is -11.8oC.
Estimate the fugacity of liquid isobutane at this temperature and
150 bar.
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Examples ofEvaluation of Gas & Liquid Pure Component Fugacity, fi
253 P1041.11P1086.91Z
11.13
Prepare plots of f vs P and f vs P for isopropanol at 200oC for the pressure range
from 0 to 50 bar. For the vapor phase, values of Z are given by:
Where P is in bars. The vapor pressures of isopropanol at 200oC is 31.92 bar, and
the liquid-phase isothermal compressibility k at 200oC is 0.3.10-3 bar-1,
independent of P.
TP
V
V
1
Hint: Critical constants:
Vc = 219 cm3/mol Tc 508,8 K
Pc = 53,7 bar Zc = 0,278
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Examples ofEvaluation of Gas & Liquid Pure Component Fugacity, fi
11.14
Prepare plots of f vs P and f vs P for 1,3-butadiene at 40oC for the pressure range
from 0 to 10 bar. At 40oC The vapor pressures of 1,3-butadiene is 4.287 bar.
Assume virial model to be valid for the vapor phase.
The molar volume of saturated liquid 1,3-butadiene at 40oC is 90.45 cm3.mol-1
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Fugacity of Steam and Water,Using Steam Table
)SS(T
HH
R
1
*P
fln *
ii
*iii
P* : lowest value of P in steam table
At P >= Pisat, i.e. liquid phase water:
TR
PPVexpP f
satiisat
isat
ii
Up to Pisat, i.e. gas phase water (steam):
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Example of Steam and Water Fugacity Calculation Using Steam Table
11.7
From data in the steam tables, determine a good estimate for f/fsat of liquid water at
100oC and 100 bar, where fsat is the fugacity of saturated liquid at 100oC.
11.8
Steam at 13000 kPa and 380oC undergoes an isothermal change of state to a pressure of
275 kPa. Determine the ratio of the fugacity in the final state to that in the initial
state
11.9
Steam at 1850 psia and 700oF undergoes an isothermal change of state to a pressure of
40 psia. Determine the ratio of the fugacity in the final state to that in the initial
state
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Fugacity of Mixtures
By Byy2ByB 222
21221112
1
1ij
0
cij
cijjiij BB
P
TRBB
i
ijj
ji ByyB
Are formulated exactly as calculation for pure component, but we use Mixing
Rules to obtain the parameters
Virial
:
For binary mixtures, i = 1,2 and j = 1,2
icomponent pure of BBB iii
2ji
ij
)k1(TTT ijcjcicij2
1
cij
cijcijcij V
TRZP
2
ZZZ
cjcicij
3
cjcicij 2
VVV
31
31
RT
PB ln i
i
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Example of Calculation forFugacity of Mixtures Using Virial EquationEstimate the fugacity and fugacity coefficient of an equimolar mixture of methyl-ethyl-ketone
(1) and toluene (2) at 50oC and 25 kPa
The required data are as follows:
ij Tcij/K Pcij/bar Vcij/cm3.mol-1 Zcij wij
11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257
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Fugacity of Components in Mixture
Py
f̂ˆ i
ii
n
lnn ˆln
jnP,T,ii
i
Ri ˆ lnTR
G
Thus:
i
Ri lnTR
G
is partial molar property of)ˆln( i )ln( i
Virial, binary mixtures:
)yB(RT
Pˆ ln
)yB(RT
Pˆ ln
122
1222
122
2111
12111212 BBB2
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Fugacity of Components in Binary Mixtures, Example using Virial Eqn.Estimate the fugacity and fugacity coefficient of methyl-ethyl-ketone (1) and toluene (2) for an
equimolar mixture at 50oC and 25 kPa.
Set all kij = 0
The required data are as follows:
ij Tcij/K Pcij/bar Vcij/cm3.mol-1 Zcij wij
11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257
11.18
Estimate the fugacity and fugacity coefficient of ethylene (1) and propylene (2) for a binary
mixture of 25% ethylene as a gas at 200oC and 20 bar.
Set all kij = 0
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More on Virial Eqn:Fugacity of Ternary and Multicomponent Mixtures
iiikikkk )2(yy
2
1B
TR
Pˆ ln
1ij
0
cij
cijjiij BB
P
TRBB
i
ijj
ji ByyB
Mixing Rules :
For ternary mixtures, i = 1,2,3 and j = 1,2,3
icomponent pure of BBB iii
BBB2
BBB2
iiii
kkiiikik
ikki
kk
ii
0
0
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More on Virial: Fugacity ofTernary & Multicomponent Mixtures Example
11.19
Estimate the fugacity and fugacity coefficient of each component in a ternary mixture of
methane (1) / ethane (2) / propane (3) at 40oC and 20 bar with the composition of 17%
methane and 35% ethane
Set all kij = 0
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Evaluation of Mixture Fugacity, f, from Equation of
State
TRZ
Pbh
i j
ijji ayya
h1
h
TRb
a
h1
1Z
5.1
Redlich-Kwong:
5.1TRb
aZ)h1(ln1Z ln
i
ii byb
}to be solved simultaneously
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Evaluation of Mixture Fugacity, f , using Redlich-Kwong Equation of StateUsing Redlich - Kwong equation of state,
calculate the fugacity and fugacity coefficient of an equimolar mixture of methyl-ethyl-
ketone (1) and toluene (2) at 50oC and 25 kPa
The required data:
ij Tcij/K Pcij/bar Vcij/cm3.mol-1 Zcij wij
11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257
![Page 50: Nonideal Behavior Dicky Dermawan @gmail.com ITK-234 Termodinamika Teknik Kimia II.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649de85503460f94ae23ea/html5/thumbnails/50.jpg)
Evaluation of Component Fugacity in Mixture Fugacity, f, from
Equation of State
)h1ln(a
ax2
b
b
RTb
a)h1(Zln)1Z(
b
bˆ ln kk1k
15.1
11
Redlich-Kwong:
5.1TRb
aZ)h1(ln1Z ln
)h1ln(a
ax2
b
b
RTb
a)h1(Zln)1Z(
b
bˆ ln kk2k
25.1
22
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Evaluation of Mixture Fugacity, f , using Redlich-Kwong Equation of StateUsing Redlich - Kwong equation of state,
calculate the fugacity and fugacity coefficient of MEK and toluene in equimolar
mixture of methyl-ethyl-ketone (1) and toluene (2) at 50oC and 25 kPa
The required data:
ij Tcij/K Pcij/bar Vcij/cm3.mol-1 Zcij wij
11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257
![Page 52: Nonideal Behavior Dicky Dermawan @gmail.com ITK-234 Termodinamika Teknik Kimia II.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649de85503460f94ae23ea/html5/thumbnails/52.jpg)
UTS 1
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Excess Gibbs Energy
igR GGG
jn,P,Ti
i n
GnM
ii Mx MSolution Properties:
Partial Properties:
Pure-species Properties: .etc,Gor ,V ,S ,H ,UM iiiiii
Residual Property
Excess Property idE GGG Partial Property of the Excess Property id
iiE
i GGG
Partial Property of the Excess Property igii
Ri GGG
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Excess Gibbs Energy
igR GGG
.etc,Gor ,V ,S ,H ,UM iiiiii
ii Mx MSolution Properties:
Partial Properties:
Pure-species Properties: .etc,Gor ,V ,S ,H ,UM iiiiii
Residual Property
Excess Property idE GGG Partial Property of the Excess Property id
iiE
i GGG
Partial Property of the Excess Property igii
Ri GGG
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Activity Coefficient
i
iii f
f̂lnTRGG
flndTRdG
)xln(TRGG iiid
i
Definition of fugacity:
Integration
ii
iidii fx
f̂lnTRGG
ii
iE
i
fx
f̂ln
TR
G
The definition of activity coefficient gi
(Ideal solution)
in,P,Ti
Eln
n
RT/Gn
j
ii
Elnx
TR
G
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Models for Binary Mixtures Activity Coefficient:Margules(1856 – 1920)
21212121
ExAxA
RTxx
G
jn,P,Ti
E
i n
RT/Gnln
22112212
12
11221122
21
x)AA(2Axln
x)AA(2Axln
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Models for Binary Mixtures Activity Coefficient:van Laar
2'
211'
12
'21
'12
21
E
xAxA
AA
RTxx
G
jn,P,Ti
E
i n
RT/Gnln
2
1'12
2'21'
212
2
2'21
1'12'
121
xA
xA1Aln
xA
xA1Aln
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Models for Binary Mixtures Activity Coefficient:Wilson
RT
aexp
V
V 21
2
121
RT
aexp
V
V 12
1
212
i2112
21
x& T of tindependen ,tstanconsa,a
2 & 1 liquid pure of memolar volu V ,V
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Models for Binary Mixtures Activity Coefficient:Renon: NonRandom Two-Liquid (NRTL)
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Models for Multicomponent MixturesActivity Coefficient:Wilson
i j
ijji
Exlnx
RT
G
j k
jkjj
kikijji
x
xxln1 ln
j)(i 1
j)(i RT
aexp
V
V
ij
ij
i
jij
ncompositio & T of tindependen ,tstanconsa
i liquid pure of memolar volu V
ij
i
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Models for Multicomponent Mixtures Activity Coefficient:
UNIversal QUAsi Chemical (UNIQUAC)(Abrams & Prausnitz)
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UNIquac Functional-groupActivity Coefficient (UNIFAC)(Aa Fredenslund,Rl Jones & JM Prausnitz)
Models for Multicomponent Mixtures Activity Coefficient:
Ri
Cii ln ln ln
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UNIFAC: Rk & Qk
Models for Multicomponent Mixtures Activity Coefficient:
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UNIFAC: Rk & Qk
Example
Models for Multicomponent Mixtures Activity Coefficient:
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UNIFAC: amk
Models for Multicomponent Mixtures Activity Coefficient: