138
7 Use of Diethylenetriamine Grafted onto Glyoxal Cross-Linked …
Substitution in 7.6 for [R–NH 3
+ ]
[−NH 2 ] =
[−NH 2 ] T − n
M
∗
(1 − α)
(7.7)
where [M*] is the sum of adsorbent adsorbed at equilibrium by the adsorbent
generally known as q e ,
If the total amine sites are available for binding, then the total amine concentration
is associated with the maximum potential (q max ) and n, as shown in 7.8.
q max =
[−NH 2 ] T
n
(7.8)
This will result in
[−NH 2 ] = n((q max − q e )(1 − α))
(7.9)
Introducing 7.9 with 7.2
K ads =
q e
H
+
m
[n((q max − q e )(1 − α))]
n C e
(7.10)
Equation 7.10 is stated in computable quantities which can be applied in deriving
the constant of equilibrium. Taking the log of 7.10 from both sides,
log
q e
[n((q max − q e )(1 − α))]
n C e
= log K ads − m log
H
+
= log K ads + mpH
(7.11)
q e , C e and α obtained from practical test, q max , can be fitted in the graph of the
left-hand side of 7.11 against pH obtained at equilibrium. The value of n is selected
for some distinct number of cases, usually between 1 and 2. The value of K ads is
evaluated from the intercept of the linear plot on the y-axis, and the slope of the plot
is used to obtain m.
7.2.2 Kinetic Model
Kinetics was represented with a shrinking core model, based on the kinetic equations
that Swan et al. (1975) postulate. In this model, the adsorbate is expected to be binding
in the active core, which enters strongly into the inner part of the adsorbent as the
binding cycle proceeds. Intraparticle diffusion through the shell filled with adsorbate
is also the key mass transfer resistance for the binding phase, and the distribution
equation shown in 7.12 follows:
7 Use of Diethylenetriamine Grafted onto Glyoxal Cross-Linked …
Substitution in 7.6 for [R–NH 3
+ ]
[−NH 2 ] =
[−NH 2 ] T − n
M
∗
(1 − α)
(7.7)
where [M*] is the sum of adsorbent adsorbed at equilibrium by the adsorbent
generally known as q e ,
If the total amine sites are available for binding, then the total amine concentration
is associated with the maximum potential (q max ) and n, as shown in 7.8.
q max =
[−NH 2 ] T
n
(7.8)
This will result in
[−NH 2 ] = n((q max − q e )(1 − α))
(7.9)
Introducing 7.9 with 7.2
K ads =
q e
H
+
m
[n((q max − q e )(1 − α))]
n C e
(7.10)
Equation 7.10 is stated in computable quantities which can be applied in deriving
the constant of equilibrium. Taking the log of 7.10 from both sides,
log
q e
[n((q max − q e )(1 − α))]
n C e
= log K ads − m log
H
+
= log K ads + mpH
(7.11)
q e , C e and α obtained from practical test, q max , can be fitted in the graph of the
left-hand side of 7.11 against pH obtained at equilibrium. The value of n is selected
for some distinct number of cases, usually between 1 and 2. The value of K ads is
evaluated from the intercept of the linear plot on the y-axis, and the slope of the plot
is used to obtain m.
7.2.2 Kinetic Model
Kinetics was represented with a shrinking core model, based on the kinetic equations
that Swan et al. (1975) postulate. In this model, the adsorbate is expected to be binding
in the active core, which enters strongly into the inner part of the adsorbent as the
binding cycle proceeds. Intraparticle diffusion through the shell filled with adsorbate
is also the key mass transfer resistance for the binding phase, and the distribution
equation shown in 7.12 follows: