Environmental Engineering Reference
In-Depth Information
solutionfollowidealbehavior.Asmentionedintheprevioussections,theactivitycoef-
ficient
γ
i
representsnonidealbehaviorinaqueoussystems.Theactivitycoefficientcan
beobtainedexperimentally,andwhereitcannotbedetermineddirectly,chemicalengi-
neers have devised theoretical models to compute the activity coefficients from cor-
relations with other solute parameters (e.g., surface area, volume, and octanol-water
partition constants) or group-interaction parameters (e.g., UNIFAC and NRTL).
3.4.1.1
Excess Functions and Activity Coefficients
Apart from the activity coefficient that is a measure of nonideality, another quantity
that is also indicative of the same is the
excess partial molar Gibbs energy
denoted
by
g
E
and defined as
G
actual
−
G
ideal
. This is an experimentally accessible quantity.
Other thermodynamic functions such as excess molar enthalpy and entropy can also
be defined in a similar fashion. By definition all excess functions are zero for
x
i
=
0
and
x
i
=
1. Some authors use excess Gibbs function as a more appropriate measure
of deviation from ideality than activity coefficient. The relationship between excess
function and activity coefficient is easily derived. For component
i
in solution, the
excess molar Gibbs free energy is defined as
RT
ln
f
i
(
actual
)
f
i
(
ideal
)
g
i
=
=
RT
ln
γ
i
,
(3.54)
x
i
f
l
i
.
The excess molar Gibbs function for solution is then given by
x
i
γ
i
f
l
0
where
f
i
(
actual
)
=
and
f
i
(
ideal
)
=
i
=
RT
i
g
E
x
i
g
i
=
x
i
ln
γ
i
.
(3.55)
i
E
XAMPLE
3.11 E
XCESS
G
IBBS
E
NERGY OF
S
OLUTION
A solution of benzene has a benzene mole fraction of 1
×
10
−
5
and a benzene activity
coefficient of 2400. What is the excess Gibbs free energy of benzene in solution?
g
i
=
RT
ln
γ
i
=
8.314
×
10
−
3
×
(
kJ/K mol
)
×
298
(
K
)
7.78
=
19.3 kJ/mol.
3.4.2 A
CTIVITY
C
OEFFICIENT AND
S
OLUBILITY
Solubility in liquids (especially water) is of special relevance in environmental engi-
neering since water is the most ubiquitous of all solvents on earth. Hence considerable
effort has gone into elucidating the solubility relationships of most gases, liquids, and
solids in water. Water is called a
universal solvent
and it richly deserves that name.
Some compounds are easily soluble in water to very high concentrations; some are
completely miscible with water at all proportions, and some have very limited solu-
bility in water. These extremes of solubility are of special interest to an environmental
chemist or engineer. As we will see in the next section, the structure of water still
evokes considerable debate.
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