2.7 Adsorption Kinetics
41
MPSD values (9.87–17.21) recorded for the pseudo-first-order model reveal unsatisfactory agreement between experimental and predicted (q e ) data. The obtained R
2
values for the pseudo-second-order model are higher and closer to one from (0.984–
0.999) as compared to the smaller values obtained for pseudo-first-order model which
is from (0.765–0.877). These results therefore suggested that the sorption kinetics
can be approximated by pseudo-second-order kinetic model for the adsorption of
selected metal ions onto grafted cross-linked chitosan.
2.8 Adsorption Equilibrium Isotherm
Adsorption isotherms indicate different models used to establish the amounts of
adsorbate molecules absorbed onto the adsorbent at constant temperature [1].
Isotherms such as Langmuir and Freundlich model were used herein to predict the
adsorption capacity of the adsorbent. The Langmuir model which is defined by 2.10
assumes that sorption of a molecule takes place at a specific binding site within the
adsorbent and that maximum adsorption occurs when molecules adsorbed on the
adsorbent surface form a saturation layer [32].
C e
q e
=
1
Q m
C e +
1
Q m K L
(2.10)
R L =
1
1 + K L C O
(2.11)
log q e = log K F +
1
n
log C e
(2.12)
where C e is the adsorbate concentration at equilibrium (mg/g), q e is the observed
adsorption capacity at equilibrium, Q m is the maximum adsorption capacity, K L is
the adsorption equilibrium constant, K F and n are constant representing the adsorption capacity and adsorption intensity, respectively. The slope and intercept of the
plot C e /q e versus C e in 2.10 define the parameters of Langmuir isotherm for the
adsorption of metal ions onto modified G/CR-CS. Expressing Langmuir model as a
dimensionless constant called the separation factor (2.11), and an adsorption system
can be suggested to be favourable or not. Hence, when R L > 1, R L = 1, R L = 0
and R L value is between 0 and 1, then adsorption indicates unfavourable, linear,
irreversible and favourable [34]. For a single adsorption system, C 0 is usually the
highest concentration of the liquid phase encountered [35].
On another hand, Freundlich adsorption model which is stipulated by 2.12 is
most often valid for heterogeneous surfaces and assumes that sorption active sites
are distributed exponentially with respect to their heat of adsorption and multilayer
adsorption [32]. With the plot of log q e against log C e , the parameters of Freundlich
model were determined.
41
MPSD values (9.87–17.21) recorded for the pseudo-first-order model reveal unsatisfactory agreement between experimental and predicted (q e ) data. The obtained R
2
values for the pseudo-second-order model are higher and closer to one from (0.984–
0.999) as compared to the smaller values obtained for pseudo-first-order model which
is from (0.765–0.877). These results therefore suggested that the sorption kinetics
can be approximated by pseudo-second-order kinetic model for the adsorption of
selected metal ions onto grafted cross-linked chitosan.
2.8 Adsorption Equilibrium Isotherm
Adsorption isotherms indicate different models used to establish the amounts of
adsorbate molecules absorbed onto the adsorbent at constant temperature [1].
Isotherms such as Langmuir and Freundlich model were used herein to predict the
adsorption capacity of the adsorbent. The Langmuir model which is defined by 2.10
assumes that sorption of a molecule takes place at a specific binding site within the
adsorbent and that maximum adsorption occurs when molecules adsorbed on the
adsorbent surface form a saturation layer [32].
C e
q e
=
1
Q m
C e +
1
Q m K L
(2.10)
R L =
1
1 + K L C O
(2.11)
log q e = log K F +
1
n
log C e
(2.12)
where C e is the adsorbate concentration at equilibrium (mg/g), q e is the observed
adsorption capacity at equilibrium, Q m is the maximum adsorption capacity, K L is
the adsorption equilibrium constant, K F and n are constant representing the adsorption capacity and adsorption intensity, respectively. The slope and intercept of the
plot C e /q e versus C e in 2.10 define the parameters of Langmuir isotherm for the
adsorption of metal ions onto modified G/CR-CS. Expressing Langmuir model as a
dimensionless constant called the separation factor (2.11), and an adsorption system
can be suggested to be favourable or not. Hence, when R L > 1, R L = 1, R L = 0
and R L value is between 0 and 1, then adsorption indicates unfavourable, linear,
irreversible and favourable [34]. For a single adsorption system, C 0 is usually the
highest concentration of the liquid phase encountered [35].
On another hand, Freundlich adsorption model which is stipulated by 2.12 is
most often valid for heterogeneous surfaces and assumes that sorption active sites
are distributed exponentially with respect to their heat of adsorption and multilayer
adsorption [32]. With the plot of log q e against log C e , the parameters of Freundlich
model were determined.