Environmental Engineering Reference
In-Depth Information
in this particular case. It therefore does not sufficiently justify choosing the Langmuir
model.Very small errors in the data can throw the prediction of the adsorption maximum
off by as much as 50%, and hence the isotherm fit may be weakened considerably. If
severalmeasurementsareavailableateachconcentrationvalue,thenan
F
-statisticcanbe
done on each point and the lack-of-fit sum-of-squares determined to obtain quantitative
reinforcement of the observations. The necessity for multiple determinations of multi-
point adsorption data needs no emphasis.
The second example is that of a
liquid-gas
system. In partitioning experiments at
the air-water interface, it is important to obtain the ability of surface-active molecules
to enrich at the interface. I will choose, as an example, the adsorption of
n
-butanol
at the air-water interface. The measurement is carried out by determining the surface
pressure
Π = σ
aw
− σ
aw
and using the Gibbs equation to get
Γ
i
. The following data
were obtained at 298 K (Kipling, 1965).
Equilibrium Aqueous
Adsorbed Concentration
Γ
i
(mol/cm
2
)
Concentration
C
i
(mol/L)
1.26
×
10
−
10
0.0132
0.0264
2.19
0.0536
3.57
0.1050
4.73
0.2110
5.33
0.4330
5.85
0.8540
6.15
A plot of 1
/
Γ
i
versus 1
/C
i
was made. The slope of the plot was 8.5
×
10
7
and the
interceptwas1.41
×
10
9
withan
r
2
of0.9972.Hence,
Γ
m
i
=
7.1
×
10
−
10
mol/cm
2
,and
K
Lang
=
16.6 L/mol. Figure 3.15 represents the experimental data and the Langmuir
isotherm fit to the data. There is good agreement, although at large
C
i
values the
adsorption is somewhat over-predicted. The maximum adsorption capacity,
Γ
m
i
can
m
be used to obtain the area occupied by a molecule on the surface,
a
m
=
1
/(N
Γ
i
)
=
23
×
10
−
16
cm
2
. The total molecular surface area
A
m
is 114
×
10
−
16
cm
2
. The lat-
ter area is closer to the cross-sectional area occupied by the
−
(CH
2
)
n
−
group on the
surface when oriented perpendicular to the surface. Therefore,
n
-butanol is likely ori-
ented normal to the surface with its OH group in the water and the long chain alkyl
group away from the water surface. Most other surfactants also occupy such an orien-
tation at the air-water interface at low concentrations. One can explain this by invoking
the concepts of hydrophobicity and hydrophobic interactions described in the earlier
section.
The third example is the adsorption of two neutral organic compounds, namely, 1,2-
dichloroethane (DCE) and 1,1,1-trichloroethane (TCE) on soils. These compounds are
significant soil and groundwater pollutants resulting from leaking storage tanks and
improperly buried hazardous waste. The data are from Chiou, Peters, and Freed (1979)
and are for a typical silty loam soil.
continued
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