Solution Thermodynamics: Applications Chapter 12-Part III.
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Transcript of Solution Thermodynamics: Applications Chapter 12-Part III.
Solution Thermodynamics: Applications
Chapter 12-Part III
Other models for GE/RT
0...
0..
....)()( 22121
21
CB
CBA
xxCxxBARTxx
G E
Obtain activity coefficients from the one-parameter Margules equation
12212
212
,,1
21
2121
ln)1(
)1(
)(
2
AxxAx
n
n
n
An
nRT
nG
nn
nA
RT
Gn
n
n
n
nAxAx
RT
G
nPT
E
E
E
problem
• For methanol(1)/methyl acetate(2), the 1-parameter Margules equation gives a reasonable prediction of the activity coefficients, with A = 2.771 -0.00523 T.
• Vapor pressures as functions of T are known. T are in Kelvin.
• a) Calculate P and {yi} for T = 318.15K and x1 =0.25
VLE, BUBL P calculation
satiiii PxPy For i =1, 2
Calculate 1 and 2 at T and x1 =0.25 using Margules 1-parameter
A(T) = 1.107
1 = 1.8642 = 1.072
and calculate P = 73.5 kPa and y1 = 0.282
Calculate P and {yi} given T = 318.15K and x1 =0.25
Calculate P and {xi} given T = 318.15K and y1 =0.60
VLE, DEW P calculationP1
sat, P2sat, and A are the same as in the first part
But, we don’t know xi, and 1, 2 are functions of x1, x2
For good initial guesses, solve the problem with Raoult’s law
sat
satsat
P
Pyx
Py
Py
P
11
11
22
2
11
1
1
Evaluate 1, 2, and return to 1)until P converges
1)Solution:
P = 62.89 kPax1 = 0.8171 = 1.0382 = 2.094
Calculate T and {yi} given P = 101.33 kPa and x1 =0.85
ii
isati C
PA
BT
ln
VLE, BUBL T calculationTo obtain an initial T, get the saturation temperatures of both components (from Antoine)
Use a mole-fraction weighted average of these values to get T
T1sat = 337.71; T2
sat = 330.08 K
For that T calculate A, 1, 2 and =P1sat/P2
sat
/22111 xx
PP sat
Then calculate
Get T from Antoine and return to (1)
(1)
111
1
lnC
PA
BT
sat
Once T converges,calculate y1
Calculate T and {xi} given P = 101.33 kPa and y1 =0.40
VLE, DEW T calculationSame P as in BUBLT calculation, saturation temperatures are the same, get weighted mole fraction average for initial T = 333.13 K
Since we don’t know {xi} use Raoult’s law to initialize {i}
(1) At the initial T, evaluate A, P1sat, P2
sat,
Calculate x1 = y1P/1 P1sat Calculate 1, 2
2
2
1
11
yyPP sat
New value of T from Antoine and return to (1)
111
1
lnC
PA
BT
sat
Once T converges,calculate x1
Find the azeotropic pressure and the azeotropic composition for T = 318.15 K
Define the relative volatility
2
2
1
1
12
xyx
y
How much is 12 at the azeotrope?
Get 12 from the VLE equations
From the one-parameter Margules equation
212
221 ln;ln AxAx
)exp(
;)exp(
2
1112
2
1012 11 AP
P
P
APsat
sat
xsat
sat
x
Calculate these values from the data at T = 318.15K
224.0;052.2 112012 11 xx
This means that 12 is =1 at some point between x1 = 0 and x1 = 1
Double azeotrope
At the azeotrope, 12 = 1
kPaPP
yx
xA
xA
P
P
P
P
satazaz
azaz
az
az
az
sat
sat
az
az
sat
sat
76.73
;325.0
388.0)21(ln
)21(ln
47.1
;
11
11
1
2
1
12
1
1
2
2
1
22
1112
The Van-Laar equation
2
1'12
2'21'
212
2
2'21
1'12'
121
2'211
'12
'21
'12
21
1ln
1ln
xA
xAA
xA
xAA
xAxA
AA
RTxx
GE