Biomedical Engineering Reference
In-Depth Information
Likewise, the kinetic data at different pH (2.00, 3.00, 3.41, 3.94 and 5.00) also fitted the
pseudo second order model and the adsorption rate was characterized by a sharp rise from
5.49 x 10
-4
- 2.48 x 10
-3
g/mg min for a pH change from 2-3, accounting for a rapid decrease
in competing hydrogen ions by 10 times [71]. However, a sudden drop in rate from 2.48 x 10
-3
-
1.40 x 10
-3
g/mg min occurred for a pH increase from 3-3.41. When the pH was raised from
2-3 and 3-3.94, the dye uptake increased proportionately by 97.72 and 101.14 mg/g for a 10-
fold decrease in the hydrogen ion concentration, respectively [71].
4.1.1. Boyd's Ion Exchange Model
The kinetic data was also analyzed using an ion exchange model proposed by Boyd et al.
[78], who postulated the adsorption kinetics for exchange of ions by organic zeolites to be a
chemical phenomenon. The exchange reaction between two monovalent ions can be
expressed according to the mass law as
A
+
+ BR
B
+
+ AR
If m
A+
and m
B+
denote the concentrations of the ions A
+
and B
+
in solutions, and n
AR
and
n
BR
the moles of A
+
and B
+
in the adsorbent, respectively, then the net reaction rate can be
written as follows:
dn
AR
= k (m
)(n
) - k (m
)(n
)
(6)
=-n
(k m
+k m
)+k m
E
1
+
BR
2
+
AR
dt
A
B
AR
1
+
2
+
1
+
A
B
A
where
k
1
and
k
2
are the forward and reverse specific rate constants, respectively, and E is a
constant defined by
E=n +n
. When both concentrations of A
+
and B
+
in solution are
kept constant, then, on integration, Eq.(6) becomes
AR
BR
km E
1
+
-St
n=
A
-e)=q
(7)
AR
t
km
+k m
1
+
2
+
A
B
S=k m
+k m
where
, and Eq.(7) can be rewritten as
1
+
2
+
A
B
S
⎛
⎞
log(1- F) = -
t
(8)
⎜
⎟
2.303
⎝
⎠
where F is the fractional attainment of equilibrium at time t, calculated by the ratio between
the amounts adsorbed (mg/g) at time t and at infinite time (F=q
t
/q∞), and S (L/min) is the ion
exchange rate constant. The kinetic data fitted with Eq.8 gave linear curves (plots not shown)
with high correlation (r
2
=0.954-0.998) and the rate constant (S) values are summarized in
Table 6 [27,70,71]. The difference in S values for different dye adsorption by γ-PGA may be
