Environmental Engineering Reference
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series of n -alkanes, n -alkenes, and n -dienes. For n -alkanes, each CH 2 group added
to the molecule increases the logarithm of the aqueous activity coefficient of the
solute by a constant factor of 0.44 units. The increase in activity coefficients for aro-
matic hydrocarbons, aliphatic acids, alcohols, and substituted phenols also showed
a similar trend. Thus came the recognition that the solubility (activity coefficient)
of different substituent groups on a parent compound can be separately ascertained.
This would then enable one to predict the solubility of other members of the homol-
ogous series. This rationalization led Prausnitz and coworkers (1999) to develop a
set of group contribution parameters for obtaining the infinite dilution activity coef-
ficients of aromatic and aliphatic substituent groups on benzene. They noted that
the log
γ i of a series of alkylbenzenes can be expressed in the form of a linear
equation, that is,
γ i
log
=
a
+
b
·
(n
6 ) ,
(3.69)
6) is therefore the
number of carbon atoms in addition to the benzene ring. The constant (designated
a) represents the contribution from the parent group (in this case the aromatic ring).
Additional atoms or groups attached to the aromatic ring or the aliphatic side chains
then make specific contributions to the activity coefficient. The same general form of
the equation (with different values of a and b) also represents the activity coefficients
of polyaromatic hydrocarbons in water.
where n is the total number of carbon atoms in the molecule, ( n
E XAMPLE 3.17 S OLUBILITY FROM G ROUP C ONTRIBUTIONS
The following group contribution values were reported by Tsonopoulos and Prausnitz
(1971) for aromatic and aliphatic substitutions on the benzene ring.
Substituent Position
Aliphatic
Group or Atom
on Ring
Side Chain
Cl
0.70
Br
0.92
OH
1.70
1.90
C = C
0.30
The constants a and b for benzene derivatives and polyaromatic hydrocarbons are given
below:
Compound Class
a
b
Alkylbenzenes
3.39
0.58
Polyaromatics
3.39
0.36
continued
 
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