Environmental Engineering Reference
In-Depth Information
TABLE 3.12
Free Energy Values for the Dissolution of Hydrocarbons in Water
Cavity Surface
G
c
G
t
Δ
G
calc
Δ
G
expt
Area, Å
2
Compound
(kJ/mol)
(kJ/mol)
(kJ/mol)
(kJ/mol)
−
16.1
Methane
122.7
22.8
6.7
8.1
−
24.3
Ethane
153.1
31.7
7.4
7.5
Propane
180.0
39.8
−
31.7
8.2
8.3
n
-Butane
207.0
48.4
−
39.0
9.4
9.0
n
-Pentane
234.0
57.0
−
46.2
10.8
9.8
2,2,3-Trimethylpentane
288.5
75.1
−
62.7
12.4
11.9
Cyclopentane
207.1
48.4
−
41.3
7.0
5.0
Cyclohexane
224.9
54.1
−
47.2
6.9
5.2
Source:
From Hermann, R.B. 1972.
Journal of Physical Chemistry
76, 2754-2759.
3.4.4 S
TRUCTURE
-A
CTIVITY
R
ELATIONSHIPS AND
A
CTIVITY
C
OEFFICIENTS IN
W
ATER
This section deals with different methods by which activity coefficients can be
estimated from solute structural parameters. In cases where reliable experimental
values are not available, there will arise the need to obtain estimates of activity
coefficients from correlations. Since activity coefficients are inversely related to
mole fraction solubility (or molar solubility), it is enough to know one param-
eter to obtain the other. From time to time in this section, we will use these
interchangeably.
The activity coefficients of solutes in water can be related to several solute parame-
ters such as molecular surface area, molar volume, octanol-water partition constants,
and normal boiling points. This technique of estimation is called the structure-activity
relationship (SAR). These correlations are given in Table 3.13.
E
XAMPLE
3.14 E
STIMATING
A
CTIVITY
C
OEFFICIENT FROM
M
OLECULAR
A
REA
Assess the applicability of the equation
γ
i
=
exp
(
Δ
G
m
/RT)
for the solubility of
benzene in water. Explain any discrepancy.
Let us determine the molecular surface area of benzene by assuming a spherical
shape for the molecule. This is clearly an approximation. The molecular radius can be
determined from the molar volume as
r
=
(
3
M/
4
πρ
N)
1
/
3
=
3.9Å. Hence, the surface
area of a molecule is given by 4
π
r
2
=
149Å
2
. Since
σ
i/w
for the benzene-water system
is 35 mN/m, we obtain
Δ
G
m
=
23 kJ/mol. Hence
γ
i
=
3.35
×
10
5
.
Now let us use the actual surface area of benzene obtained via a computer calculation.
The value is 109.5Å
2
. We then obtain
Δ
G
m
=
23 kJ/mol. Hence
γ
i
=
1.11
×
10
4
.
The actual experimental value at 298 K is 2.43
×
10
3
.
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