Environmental Engineering Reference
In-Depth Information
Ψ
changes with
κ
, which in turn is affected by the ionic strength
I
. Since
I
is
proportional to
, this suggests that at high ionic strength the compressed double
layer near the surface reduces the distance over which long-range interactions due
to the surface potential is felt in solution. This is the basis for flocculation as a
wastewater treatment process to remove particles and colloids. It is also the basis
for designing some air sampling devices that work on the principle of electro-
static precipitation. A number of other applications exist, which we shall explore
in Chapter 4.
The Guoy-Chapman theory is elegant and easy to understand, but it has a major
drawback. Since it considers particles as point charges, it fails when
x
→
r
, the radius
of a charged particle. Stern modified the inherent assumption of zero volume of
particles assuming that near the surface there is a region excluded for other particles.
In other words, there are a number of ions “stuck” on the surface that have to be
brought into solution before other ones from solution replace them. Thus, the drop-
off in potential near the surface is very gradual and almost flat till
x
reaches
r
, beyond
which the Guoy-Chapman theory applies.The region is called the
Sternlayer
. Further
modifications to this approach have been made, but are beyond the scope of this topic.
Interested students are encouraged to consult Bockris and Reddy (1970) for further
details.
κ
E
XAMPLE
3.20 C
ALCULATION OF
D
OUBLE-LAYER
T
HICKNESS
Calculate the double-layer thickness around a colloidal silica particle in a 0.001 M
NaCl aqueous solution at 298 K.
κ
=
(
4
π
e
2
/
ε
kT)
Σ
n
i
z
i
. We know that
Σ
n
i
z
i
=
2
n
,
e
=
4.802
×
10
−
10
C,
ε =
78.5,
k
=
1.38
×
10
−
16
erg/molecule K, and
T
=
298 K. Noting the relationship
between
C
i
and
n
i
given earlier, we can write
κ
2
2
=
1.08
×
10
15
C
i
, hence
κ =
3.28
×
10
7
,
C
1
/
2
=
1.038
×
10
6
cm
−
1
. Hence double-layer thickness 1
/
κ =
9.63
×
10
−
7
cm
(
=
96.3Å).
PROBLEMS
3.1
1
Calculate the mole fraction, molarity, and molality of each compound in
an aqueous mixture containing 4 g of ethanol, 0.6 g of chloroform, 0.1 g
of benzene, and 5
×
10
−
7
g of hexachlorobenzene in 200 mL of water.
3.2
1
A solution of benzene in water contains 0.002 mole fraction of benzene.
The total volume of the solution is 100 mL and has a density of 0.95 g/cm
3
.
What is the molality of benzene in solution?
3.3
2
Given the partial pressure of a solution of KCl (4.8 molal) is 20.22Torr at
298 K and that of pure water at 298 K is 23.76Torr, calculate the activity
and activity coefficient of water in solution.
3.4
2
Give that
μ
0
=−
386 kJ/mol for carbon dioxide on the molality scale,
calculate the standard chemical potential for carbon dioxide on the mole
fraction and the molarity scale.
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