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In-Depth Information
With suitable data it is possible to estimate the infinite dilution activity coefficients
by assuming that when the composition of a component is near a mole fraction of
1.0, its activity coefficient is 1.0. For example, in the system A - B the composition of
component A in phase I,
x
1
, is 0.002 and the composition of component B in phase
II,
x
I
2
, is 0.01. Applying equation (6.30) for each component yields, approximately at
infinity,
I
1
II
2
998.
If the
b
i
·
j
parameters are required because the application involves a variable tem-
perature, several points must be regressed, although an initial value can be obtained
from one data point using one of the methods above.
When regressing ternary systems, two possibilities exist: (1) fit the two solvents
with mutual solubility data and fit the four remaining parameters with ternary data
while holding the two previously determined parameters constant; or (2) fit all six
parameters with ternary data. Using the ternary data of Sugi and Katayama (1978)
shown in Table 6.4, we look next at examples of both methods.
γ
=
495 and
γ
=
TABLE 6.4 LLE Data for the System
n
-Hexane (2)-Ethanol (2)-Acetonitrile (3)
Mole Fraction Phase I
Mole Fraction Phase II
Temperature
◦
K
N
-Hexane
Ethanol
N
-Hexane
Ethanol
313.15
0.8831
0.0166
0.0968
0.0879
313.15
0.8674
0.0251
0.1003
0.1299
313.15
0.8546
0.0332
0.1054
0.1622
313.15
0.8372
0.0433
0.125
0.1942
313.15
0.8101
0.0567
0.1367
0.2169
313.15
0.7821
0.0772
0.1522
0.2331
313.15
0.7272
0.1086
0.2053
0.2695
313.15
0.6912
0.1269
0.2249
0.2748
First Method
An estimate of the mutual solubility data is made by extrapolating a
plot of the data from Figure 6.6, resulting in
x
1
=
0
.
9and
x
I
1
=
0
.
09. The estimates
calculated for the parameters are
b
13
=−
553
.
43076
b
31
=−
18
.
956075
Holding
b
13
and
b
31
constant and fitting the remaining four parameters to the experi-
mental data yields the following results:
b
12
10
.
801713
b
21
=−
169
.
74093
b
23
=
215
.
31305
b
32
=−
178
.
56357
=
Second Method
Parameters obtained by calculating the values of six parameters
using one data point are
b
12
=−
494
.
10342
