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Unformatted text preview: using Eqs.
(3), Table 2.9 for the van Laar equations and Eqs. (4), Table 2.9 for the Wilson equations.
Results from a spreadsheet are as follows: x1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0 γ1
21.17
10.13
5.56
3.44
2.35
1.75
1.40
1.198
1.079
1.018
1.000 van Laar γ2
1.000
1.039
1.154
1.354
1.661
2.11
2.77
3.71
5.06
7.02
9.84 γ1
21.17
6.63
3.76
2.61
2.00
1.631
1.387
1.219
1.103
1.029
1.000 Wilson______
γ2
1.000
1.054
1.162
1.310
1.510
1.784
2.174
2.77
3.74
5.58
9.84 Exercise 2.24 (continued)
Analysis: (c) (continued) Note that the Wilson activity coefficients vary more steeply at the infinitedilution ends.
(d) At the azeotropic point, x1 = 0.5941 and x2 = 0.4059. Using the van Laar
constants from part (a) with Eqs. (3), Table 2.9,
van Laar gives γ1 = 1.419, compared to 1.44 experimental
van Laar gives γ2 = 2.72, compared to 2.18 experimental
Using the Wilson constants from part (b) with Eqs. (4), Table 2.9,
Wilson gives γ1 = 1.400, compared to 1.44 experimental
Wilson gives γ2 = 2.147, compared to 2.18 experimental
The Wilson equation is acceptable for both components. The van Laar equation
gives poor agreement for isooctane.
(e) At 50oC, the vapor pressures are 221 torr for ethanol and 146 torr for
isooctane. Thus, system pressure will be low over the entire range of composition.
Therefore, the modified Raoult's law Kvalue expression, given by Eq. (4), Table 2.3
applies. When combined with Eq. (219), we obtain the following expression for
predicting the y  x curve:
x1γ 1 P1s
y1 =
(3)
P Exercise 2.24 (continued)
Analysis: (e) (continued)
By Raoult's law, partial pressure is given by pi = xiPis
Therefore, the modified Raoult's law gives pi = xi γi Pis
By Dalton's law, the sum of the partial pressures equals total pressure. Thus,
P= pi =
i xi γ i Pi s (4) i Using a spreadsheet with Eqs. (3) and (4) and the van Laar activity coefficients
from the table above in part (c), values of y1 are computed for values of x1:
x1
P, torr
y1
0.0
146
0.000
0.1
361
0.620
0.2
381
0.645
0.3
367
0.622
0.4
356
0.587
0.5
348
0.556
0.6
349
0.553
0.7
348
0.532
0.8
339
0.563
0.9
305
0.663
1.0
221
1.000
The yx plot exhibits the same characteristics as the system in Fig. 2.20. Therefore, the
van Laar equation erroneously predicts phase splitting. Exercise 3.1
Subject: Evaporation of a mixture of ethanol (AL) and ethyl acetate (AC) from a beaker into
still air within the beaker.
Given: Initial equimolar mixture of AL and AC, evaporating into still air at 0oC and 1 atm.
Vapor pressures and diffusivities in air of AL and AC at 0oC.
Assumptions: Wellmixed liquid and Raoult's law. Negligible bulk flow effect. Air sweeps
across the top of the beaker at a rate such the mole fractions of AL and AC in the air at the top of
the beaker are zero.
Find: Composition of the remaining liquid when 50% of the initial AL has evaporated.
Analysis: All of the masstransfer resistance is in the still air layer in the beaker, which
increases in height, z, as evaporation takes place. Apply Fick's law to both AL and AC with
negligible bulk flow...
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 Spring '11
 Levicky
 The Land

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