Solution Thermodynamic: Vapor/Liquid Equilibrium (VLE) PTT 201/4 THERMODYNAMICS SEM 1 (2013/2014)
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Transcript of Solution Thermodynamic: Vapor/Liquid Equilibrium (VLE) PTT 201/4 THERMODYNAMICS SEM 1 (2013/2014)
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Solution Thermodynamic:
Vapor/Liquid Equilibrium (VLE)
PTT 201/4 THERMODYNAMICSSEM 1 (2013/2014)
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Nature of Equilibrium– Definition– Measures of composition
VLE : Qualitative behaviorSimple Models for VLE - Raoult’s Law - Dewpoint & Bubblepoint Calculations with Raoult’s Law - Henry’s LawVLE by modified Raoult’s lawVLE from K-value correlations
Chapter Outline (Smith)
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THE NATURE OF EQUILIBRIUM
Equilibrium : A static condition in which no changes occur in the macroscopic properties of a system with time.
The T, P, composition reaches final value which will remain fixed: equilibrium
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m
m
m
mx iii
V
xC ii
iiiMxM
Measures of composition
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VLE: State of coexistence of L & V phases A condition where a liquid phase and vapor phase
are in equilibrium with each other At this condition: rate of evaporation (liquid → vapor) = rate of condensation (vapor → liquid)
VLE: QUALITATIVE BEHAVIOR
Binary mixture: Mixture that contains two constituents e.g: mixture of liquid and vapor at an equilibrium level takes place when liquid and vapor are allowed to contact to each other in a closed location
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• Under surface- sat. V states (P-T-y1)
• Upper surface- sat. L states (P-T-x1)
• Liquid at F, reduces pressure at constant T & composition along FG, the first bubble appear at L – bubble point: a point when a liquid forms the first bubble of vapor and begins to evaporate
• As pressure reduces, more & more L vaporizes until completed at W; point where last drop of L (dew) disappear – dew point: a point when a vapor forms the first droplet of liquid and begins to condense
Fig. 10.1 – Shows the P-T-composition surfaces of equilibrium states of
saturated V & saturated L of a binary system
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SIMPLE MODELS FOR VLE
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Raoult’s Law
• V phase is an ideal gas– Applicable for low to moderate
pressure• L phase is an ideal solution
– Valid only if the species are chemically similar (size, same chemical nature e.g. isomers such as ortho-, meta- & para-xylene)
Assumptions;
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NiPxPy satiii ,...,2,1
Where;
pressure Total :
species pure of pressureVapor :
fraction mole phase:
fraction mole phase:
P
iP
Vy
Lx
sati
i
i
1
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BUBL P: Calculate {yi} and P, given {xi} and T
DEW P: Calculate {xi} and P, given {yi} and T
BUBL T: Calculate {yi} and T, given {xi} and P
DEW T: Calculate {xi} and T, given {yi} and P
Dewpoint & Bubblepoint Calculations with Raoult’s Law
FIND GIVEN
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For binary systems to solve for bubblepoint calculation (T is given);
1i iy
i
satiiPxP 1212 xPPPP satsatsat
PPx
ysat
11
1
2
3
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i
satii Py
P1
Raoult’s law equation can be solved for xi to solve for dewpoint calculation (T is given) 1i i
x
satsat PyPyP
2211//
1
satPPy
x1
1
1
4
5
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Example 1
Binary system acetonitrile(1)/nitromethane(2) conforms closely to Raoult’s law. Vapor pressure for the pure species are given by the following Antoine equations:
00.209
64.972,22043.14ln
00.224
47.945,22724.14ln
02
01
CtkPaP
CtkPaP
sat
sat
a)Prepare a graph showing P vs. x1 and P vs. y1 at temperature 750C
b)Prepare a graph showing t vs. x1 and t vs. y1 for a pressure of 70 kPa
i
ii
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a) BUBL P calculations are required. Since this is a binary system, Eq. 2 may be used.
)(1212 AxPPPP satsatsat
At 750C, the saturated pressure is given by Antoine equation;
98.4121.83 21 satsat PP
Substitute both values in (A) to find P;
kPaP
P
72.66
6.098.4121.8398.41
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The corresponding value of y1 is found from Eq. 1, sat
iii PxPy
x1 y1 P/kPa
0.0 0.0000 41.98
0.2 0.3313 50.23
0.4 0.5692 58.47
x1 y1 P/kPa
0.6 0.7483 66.72
0.8 0.8880 74.96
1.0 1.0000 83.21
7483.0
72.66
21.836.0111
P
Pxy
sat
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At point c, the vapor composition is y1=0.6, but the composition of liquid at c’ and the pressure must read from graph or calculated. Thus DEW P calculations are required. By using Eq. 3;
satsat PyPyP
2211
1
For y1=0.6 and t=750C
kPaP 74.5998.414.021.836.0
1
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And by Eq. 1,
4308.0
21.83
74.596.0
1
11
satP
Pyx
This is the liquid-phase composition at point c’
b) When P is fixed, the T varies along T1sat and
T2sat, with x1 & y1. T1sat & T2sat are calculated
from Antoine equation;
ii
isati C
PA
Bt
ln
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For P=70kPa, T1sat=69.840C, T2sat=89.580C. Select T between these two temperatures and calculate P1sat &
P2sat for the two temperatures.
Evaluate x1 by Eq. (A). For example;
satsat
sat
PP
PPx
21
21
5156.0
84.4676.91
84.46701
x
Get y1 from Eq. 1
6759.0
70
76.915156.0111
P
Pxy
sat
e.g; select T= 78˚C
Substituting T= 78˚C into (i) and (ii)
P1sat = 91.76 kPa
P2sat = 46.84 kPa
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Summary;
x1 y1 T/˚C
0.0000 0.0000 89.58 (t2sat)
0.1424 0.2401 86
0.3184 0.4742 82
0.5156 0.6759 78
0.7378 0.8484 74
1.0000 1.0000 69.84 (t1sat)
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1. For pressure low It is so low that it can be assume as ideal gas
2. For species present as a very dilute solution in liquid phase
Assumptions;
Henry’s Law
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NiHxPy iii ,...,2,1
Where;
pressure Total :
constant sHenry' :
fraction mole phase:
fraction mole phase:
P
H
Vy
Lx
i
i
i
Henry’s Law
6
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Example 2
Assuming that carbonated water contains only CO2(1) and H2O(2), determine the compositions of the V & L phases in a sealed can of ‘soda’ & the P exerted on the can at 100C. Henry’s constant for CO2 in water at 100C is about 990 bar and x1=0.01.
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Henry’s law for species 1 & Raoult’s law for species 2 are written;
111 HxPy satPxPy 222
With H1=990 bar & P2sat = 0.01227 bar (from steam tables at 100C)
barP
P
912.9
01227.099.099001.0
satPxHxP 2211
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Then by Raoult’s law, Eq. 1 written for species 2;
0012.0
912.9
01227.099.0222
P
Pxy
sat
Whence y1=1-y2=0.9988, and the vapor phase is nearly pure CO2, as expected.
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The 2nd assumption of Raoult’s Law is abandoned, taking into account the deviation from solution
ideality in L phase.
Thus, activity coefficient is introduced in Raoult’s Law
NiPxPy satiiii ,...,2,1
VLE BY MODIFIED RAOULT’S LAW
7
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Activity coefficients are function of T & liquid phase composition, x
1i iy
i
satiii PxP
i
satiii Py
P
1
For bubble point
For dew point
Since;
1i ix
8
9
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AZEOTROPE
A mixture that has a constant composition of liquid and vapor phase
When x1=y1, the dew point and bubble point curves are tangent to the same horizontal line
A boiling L of this composition produce a vapor exactly the same composition; L does not change in composition as it evaporates
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VLE FROM K-VALUE CORRELATTIONS
The partition between liquid and vapor phases of a chemical species is equilibrium ratio, Ki.
i
ii x
yK
This quantity is called K-value.
10
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satiii PxPy K-value for Raoult’s Law
P
PK
sati
i
K-value for modified Raoult’s Lawsatiiii PxPy
P
PK
satii
i
11
12
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Hence,
For binary systems to solve for bubble point calculation;
1i iy
1 ii ixK
For binary systems to solve for dew point calculation;
1i ix
Hence, 1ii
i
K
y
13
14
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K-value from DePriester chart-Low T range
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K-value from DePriester chart-High T range
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When given a mixture of composition at certain T or P;
Bubble point
- System is almost vaporized
- The given mole fraction is yi
- Need to satisfy equation 13
- Composition of dew is xi=yi/Ki
Dew point
- System is almost condensed
- The given mole fraction is xi
- Need to satisfy equation 14
- Composition of bubble is yi=Kixi
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The End