Environmental Engineering Reference
In-Depth Information
A plot of ln
(
1
/x
i
)
versus
(
1
/T)
is then obtained (Figure 3.18). The slope of the plot is
4845 K, the intercept is 2.328, and the correlation coefficient is 0.999. From the slope
we obtain the total enthalpy change,
Δ
H
i
, as 4845
×
8.314
×
10
−
3
=
40.3 kJ/mol.
The excess enthalpy of solution is then given by
h
i
=
40.3
−
16.1
=
24.2 kJ/mol. The
excess free energy at 298 K is given by
g
i
=
RT
ln
γ
i
=
42 kJ/mol. The contribution
from excess entropy is
TS
i
=−
17.8 kJ/mol. The entropy of solution is, therefore,
S
i
=−
59.8 J/K mol.
(b) The solubility data for benzene are given as follows (May et al., 1983).
x
i
T
(K)
4.062
×
10
−
4
290.05
4.073
×
10
−
4
291.75
4.129
×
10
−
4
298.15
4.193
×
10
−
4
298.95
Benzene has a melting point of 5.5
◦
C and a boiling point of 80.1
◦
C. Its molecular
weight is 78.1. Determine the excess functions of solution of benzene in water.
Since benzene is a liquid at the temperatures given, we can ignore the
enthalpy contribution from phase changes. Hence the equation for solubility of
liquids given earlier can be used. A plot of ln
(
1
/x
i
)
versus
(
1
/T)
can be made
(Figure 3.20). The slope is 261.8 K, the intercept is 6.907 and the correlation
coefficient obtained is 0.861. The excess enthalpy of solution is then given by
h
i
10
−
3
)
=
(
261.8
)(
8.314
×
=
2.2 kJ/mol. The free energy of solution at 298.15 K
is
g
i
18.9 kJ/mol. Hence the excess entropy of solution of benzene is
S
i
=
=
−
56 J/K mol.
It should be noted that in addition to the unfavorable entropy contribution, the
enthalpy contribution also contributes toward the unfavorable excess Gibbs free
energy of solution for large molecules in water.
3.4.3.3
Hydrophobic Interactions between Solutes
Having discussed the hydration phenomena of a nonpolar solute in water, it is natu-
ral to ask what are the consequences of bringing two such solutes near one another
in water. This process is called
hydrophobic interaction
. Since the introduction of
any nonpolar residue in water is an unfavorable process, it is likely that a hydropho-
bic compound in water will seek out another of its own kind to interact with. In
other words, the solute-solute interaction for hydrophobic compounds in water is an
attempt to partially offset the entropically unfavorable hydration process. Accord-
ingly, the free energy, enthalpy, and entropy of hydrophobic interactions should all
be of opposite sign to that of hydrophobic hydration. It is also true that hydrophobic
interactions for two solutes in water are even larger than in free space (vacuum).
For example, Israelchvili (1992) calculated that for two methane molecules in free
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