q t ¼
1
β
ln αβ
ð Þ þ
1
β
ln t
ð9:7Þ
where α is the initial adsorption rate (mg/gÁmin) and β is the desorption constant
(g/mg). Table 9.6 lists some of the adsorption of heavy metals over agricultural
waste-derived adsorbents and the best fit model according to the study. Most of the
works listed used at least the pseudo-first-order and pseudo-second-order kinetic
equations and second-order equations fit to all systems in the table. The use of
pseudo-second-order equation has a distinct advantage, which is no prior data of the
equilibrium parameter, q e is needed to calculate the rate constant, thus reducing the
experimental errors in calculation [72].
5 Adsorption Isotherms
The adsorption isotherms are the relationship between the amount of adsorbate that
is adsorbed over a unit mass of adsorbent (q e ) and the amount of adsorbate that is left
in the solution (C e ) at equilibrium under constant temperature [78]. The simplest
relation is given by two parameter isotherm models, where the most widely applicable models are Langmuir and Freundlich isotherms. The Dubinin-Radushkevich
isotherm is commonly used to estimate the apparent free energy that can be used to
determine the nature of sorption, whether it is physisorption or chemisorption.
Table 9.6 Comparison of best fit kinetic models for adsorption of heavy metals on natural fibres
Source of fibre
Metal
Rate constant
Kinetic model
Reference
Almond shell
Co(II)
0.0204 g/mgÁmin
2nd order
[37]
Ni(II)
0.0136 g/mgÁmin
2nd order
[37]
Arachis hypogaea
Cd(II)
1.512 g/mgÁmin
2nd order
[38]
Ni(II)
1.524 g/mgÁmin
2nd order
[38]
Banana frond
B(II)
2.66 g/mgÁmin
2nd order
[73]
Fe
6.05 g/mgÁmin
2nd order
[73]
Banana pseudostem
Cd(II)
0.01 g/mgÁmin
2nd order
[62]
Brown seaweed
Pb(II)
0.25 Â 10
À3 g/mgÁmin
2nd order
[74]
Castor leaf
Cd(II)
111.7 g/mgÁmin
2nd order
[61]
Pb(II)
105.5 g/mgÁmin
2nd order
[61]
Fig sawdust
Pb(II)
0.009 g/mgÁmin
2nd order
[59]
Orange peel
Cr(VI)
0.3948 mmol/gÁh
2nd order
[75]
V(V)
1.571 mmol/gÁh
2nd order
[75]
Peanut shell
Pb(II)
0.2467 Â 10
3 g/mgÁmin
1st and 2nd order
[66]
Pineapple peel
Cr(VI)
0.0135 g/mgÁmin
2nd order
[50]
Rice husk ash
Se(IV)
0.0094 g/μgÁmin
2nd order
[76]
Tea leaves
Cs(I)
–
2nd order
[77]
9 Agricultural Waste-Derived Adsorbents for Decontamination of Heavy Metals
383
1
β
ln αβ
ð Þ þ
1
β
ln t
ð9:7Þ
where α is the initial adsorption rate (mg/gÁmin) and β is the desorption constant
(g/mg). Table 9.6 lists some of the adsorption of heavy metals over agricultural
waste-derived adsorbents and the best fit model according to the study. Most of the
works listed used at least the pseudo-first-order and pseudo-second-order kinetic
equations and second-order equations fit to all systems in the table. The use of
pseudo-second-order equation has a distinct advantage, which is no prior data of the
equilibrium parameter, q e is needed to calculate the rate constant, thus reducing the
experimental errors in calculation [72].
5 Adsorption Isotherms
The adsorption isotherms are the relationship between the amount of adsorbate that
is adsorbed over a unit mass of adsorbent (q e ) and the amount of adsorbate that is left
in the solution (C e ) at equilibrium under constant temperature [78]. The simplest
relation is given by two parameter isotherm models, where the most widely applicable models are Langmuir and Freundlich isotherms. The Dubinin-Radushkevich
isotherm is commonly used to estimate the apparent free energy that can be used to
determine the nature of sorption, whether it is physisorption or chemisorption.
Table 9.6 Comparison of best fit kinetic models for adsorption of heavy metals on natural fibres
Source of fibre
Metal
Rate constant
Kinetic model
Reference
Almond shell
Co(II)
0.0204 g/mgÁmin
2nd order
[37]
Ni(II)
0.0136 g/mgÁmin
2nd order
[37]
Arachis hypogaea
Cd(II)
1.512 g/mgÁmin
2nd order
[38]
Ni(II)
1.524 g/mgÁmin
2nd order
[38]
Banana frond
B(II)
2.66 g/mgÁmin
2nd order
[73]
Fe
6.05 g/mgÁmin
2nd order
[73]
Banana pseudostem
Cd(II)
0.01 g/mgÁmin
2nd order
[62]
Brown seaweed
Pb(II)
0.25 Â 10
À3 g/mgÁmin
2nd order
[74]
Castor leaf
Cd(II)
111.7 g/mgÁmin
2nd order
[61]
Pb(II)
105.5 g/mgÁmin
2nd order
[61]
Fig sawdust
Pb(II)
0.009 g/mgÁmin
2nd order
[59]
Orange peel
Cr(VI)
0.3948 mmol/gÁh
2nd order
[75]
V(V)
1.571 mmol/gÁh
2nd order
[75]
Peanut shell
Pb(II)
0.2467 Â 10
3 g/mgÁmin
1st and 2nd order
[66]
Pineapple peel
Cr(VI)
0.0135 g/mgÁmin
2nd order
[50]
Rice husk ash
Se(IV)
0.0094 g/μgÁmin
2nd order
[76]
Tea leaves
Cs(I)
–
2nd order
[77]
9 Agricultural Waste-Derived Adsorbents for Decontamination of Heavy Metals
383