Chemistry Reference
In-Depth Information
Equation 7.20 with respect to V
max
is involved, and will be not discussed here. It is,
however, readily appreciated that, when the electrolyte concentration is increased,
the magnitude of
k
in the exponent of V
el
also increases (compression of diffuse
layers), so that the maximum caused by it becomes lower. At a certain value of
C, the curve V(h) will become similar to curve b in Figure 7.8 with V
max
= 0. In
accordance with all that has been said before, coagulation will become fast starting
from this concentration. This is therefore the
critical concentration
, C
cc
. In other
words, the critical concentration (C
cc
) can be estimated from simultaneous solution
of following:
dV(h)/dh = 0 and V(h) = 0
(7.21)
One can write the following:
dV(h)/dh = [−(64 C
cc
RT ψ
2
)/
k
exp
(
−
k
cr
h
cr
)
+
K/
(h
cr
3
) = 0
(7.22)
and
V(h) = [(64 C
cc
RT ψ2)/
k
cr
exp(
−
k
cr
h
cr
)
−
K/
(2 h
cr
2) = 0
(7.23)
After expanding these expressions, as related to h and C, this becomes (Schulze-
Hardy Rule for suspensions in water)
C
cc
= 8.7 10
−39
/Z
6
A
2
C
cc
Z
6
= constant
(7.24)
where the constant includes (Hamaker constant is approximately 4.2 10
−19
J).
Concentrations of ion to the sixth power of various valencies are inversely propor-
tion to valency.
Z = 1:(2
6
)0.016:(3
6
)0.0014:(4
6
)0.000244
(7.25)
The flocculation concentrations of mono-, di-, and trivalent gegen ions should, from
this theory, be expected as
1: (1/2)
6
: (1/3)
6
(7.26)
It thus becomes obvious that the colloidal stability of charged particles is dependent on
i. Concentration of electrolyte
ii. Charge on the ions
iii. Size and shape of colloids
iv. Viscosity
The critical concentration (critical coagulation concentration) is thus found to depend
on the type of electrolyte used, as well as on the valency of the counterion. It is seen
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