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Unformatted text preview: om Antoine equations and
liquidphase activity coefficients over the entire composition range from fitting the infinitedilution coefficients to the van Laar equation, Eq. (3) in Table 2.9, using Eqs. (275). Thus,
KA = yA γ A PAs
=
xA
P γ A = exp (1) and AAW
xA
1+ A WA
xW AAW 2 KW = s
yW γ W PW
=
xW
P (3) and γ W = exp (2)
AWA xA
1 + W AW
xA AWA 2 (4) ∞
AAW = ln γ A = ln(8.12) = 2.094 AWA = ln γ ∞ = ln(4.13) = 1418
.
W
Substituting these van Laar coefficients into Eqs. (3) and (4),
2.094
1418
.
γ A = exp
(5) and γ W = exp
2
1 − xA
xA
1 + 0.6772
1+1.477
xA
1 − xA 2 (6) From the 7th edition of Perry's Chemical Engineers' Handbook, page 1321,
1210.595
1730.630
s
log PAs = 7.11714 −
(7) and log PW = 8.07131 −
(8)
T + 229.664
T + 233.426
where
Pi s = vapor pressure of component i in torr and T = o C Minimum stages by the Fenske equation:
First determine the relative volatilities at the top and bottom and take the geometric
average for use in the Fenske equation. Exercise 9.6 (continued)
Analysis: Fenske equation (continued)
Bubble point for the distillate composition.
γ Ps
From Eqs. (412), (1), and (2):
x Di Ki = x Di i i =1
(9)
P
i
i
In the distillate, xA = 0.95 and xW = 0.05. From Eqs. (3) and (4),
2.094
1418
.
γ A = exp
= 1.003 and γ W = exp
2
0.95 2.094
0.05 1418
.
1+
1+
0.05 1418
.
0.95 2.094 2 = 3.75 1003 PAs
.
3.75 PAs
+ 0.05
= 1 where vapor pressure is in torr.
975
975
Using Eqs. (7) and (8) with a spreadsheet, a trial and error calculation gives a distillate
temperature of 64oC. Then from Eqs. (1) and (2), αA,W = KA/KW = 1.48
Bubble point for the bottoms composition.
In the bottoms, xA = 0.02 and xW = 0.98. From Eqs. (3) and (4),
2.094
1418
.
γ A = exp
= 7.19 and γ W = exp
= 1.001
2
2
0.02 2.094
0.98 1418
.
1+
1+
0.98 1.418
0.02 2.094
Eq. (9) becomes: 0.95 7.19 PAs
1001PAs
.
+ 0.98
= 1 where vapor pressure is in torr.
975
975
Using Eqs. (7) and (8) with a spreadsheet, a trial and error calculation gives a distillate
temperature of 95oC. Then from Eqs. (1) and (2), αA,W = KA/KW = 27.7
The geometric mean relative volatility = [(1.48)(27.7)]1/2 = 6.40
Eq. (9) becomes: 0.02 log
From the Fenske equation (911), N min = xDA xBW xBA xDW log α A,W log
= 0.95 0.98
0.02 0.05
log 6.40 = 3.7 Minimum stages by the McCabeThiele method:
To obtain a yx equilibrium curve at 975 torr in terms of acetone mole fractions, we
can run bubblepoint temperature calculations, as above, for a set of points in the range of liquid
compositions between the distillate and bottoms compositions. For each point, the Kvalue and
vapor mole fraction for acetone are computed from Eq. (1). The results from a spreadsheet are as
follows: Exercise 9.6 (continued) Analysis: McCabeThiele method (continued)
T, oC
yA
xA
63.6
1.000
1.000
64.0
0.965
0.950
64.5
0.936
0.900
65.0
0.911
0.850
65.5
0.889
0.800
66.0
0.870
0.750
66.5
0.855
0.700
67.0
0.842
0.650
67.5
0.833
0.600
67.9
0.824
0.550
68.3
0.817
0.500
68.6
0.811
0.450
68.9
0.806
0.40...
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This document was uploaded on 02/24/2014 for the course CBE 2124 at NYU Poly.
 Spring '11
 Levicky
 The Land

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