Environmental Engineering Reference
In-Depth Information
Let us estimate the infinite dilution activity coefficients of some compounds using the
above information. In each case we start with the parent group, in this case the aromatic
ring for which the contribution is the value of
a
from the linear correlation. To this we
then add the contributions of the functional groups.
(a) Ethylbenzene: For this case we use the linear correlation directly with
n
=
8 giving
log
γ
i
=
3.39
+
2
×
0.58
=
4.55.
(b) C
6
H
5
-CH
2
-CH
2
-OH: Since this is a derivative of ethylbenzene, we add to it the
contribution from an OH group giving log
γ
i
=
4.55-1.90
=
2.65.
(c) Hexachlorobenzene: In this case we start with the basic group, that is, the aromatic
ring for which the contribution is 3.39, and then add to it the contributions from the
six Cl atoms. Hence, log
γ
i
7.59.
(d) Naphthalene: The basic building block in this case is again the benzene ring, but
we use the correlation for polyaromatics with
n
=
4. Hence, log
γ
i
=
3.39
+
6
×
0.70
=
=
3.39
+
4
×
0.36
=
4.83.
The above calculation is an illustration of what is available in the existing chemical
engineering literature for estimating activity coefficients through group contributions.
ThemethodofTsonopoulosandPrausnitz(1971)waschosenforillustrativepurposes.
It should be borne in mind that the same general method of obtaining group contri-
bution methods has also been reported by other investigators. Pierotti, Deal, and Derr
(1959)correlatedtheactivitycoefficientgroupcontributionsbasedonexistingliquid-
liquid and vapor-liquid equilibrium data. Wakita et al. (1986) reported a set of group
contribution parameters for a variety of aliphatic and aromatic fragments.
The group contribution approach has inherent drawbacks that are worth noting. It
is limited by the lack of availability of the requisite fragment values. In practice, there
are several groups for which group contributions are as yet unavailable. The method
also has limitations when it comes to distinguishing between geometric isomers of
a particular compound. Any group contribution approach is essentially approximate
since the contribution of any group in a given molecule is not always exactly the same
in another molecule. Moreover, the contribution made by one group in a molecule is
constant and nonvarying only if the rest of the groups in the molecule do not exert any
influence on it. In fact, this is a major drawback of any group contribution scheme.
3.4.5.2
Excess Gibbs Free Energy Models
There are several equations to estimate activity coefficients of liquid mixtures based
on excess Gibbs free energy of solution. These are summarized in Table 3.14. For
details of their derivation, see Sandler (1999).
3.4.5.3
Second Generation Group Contribution
Methods: The UNIFAC Method
The most useful and reliable method of activity coefficient estimation resulted from
the need for chemical engineers to obtain activity coefficients of liquid mixtures. In
the chemical process industry (CPI), the separation of components from complex
mixtures is a major undertaking. It was recognized early on that a large database for
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