**5.3 Sorption isotherms of Fe3+ ions processes using olive cake**

To conduct the isotherm were studied at the initial pH of solution which was adjusted at the optimum value (pH = 4.5) and the mass of olive cake which was taken as 0.3, 0.5, 0.75 and 1.0 g at different temperatures of 28, 35 and 45 ºC. Three adsorption isotherms models were used: Langmiur, Frendulich and Dubinin–Kaganer–Radushkevich (DKR) [21]. Figure 12 shows the experimental data that were fitted by the linear form of Langmiur model, *(Ce / qe)* versus *Ce*, at temperatures of 28, 35 and 45 <sup>0</sup> C. The values of max *<sup>q</sup>* and *b* were evaluated

Figure 11 represents the fitting data into the Freundlich model. We observe that the empirical formula of this model is found as ln 0.1058ln 1.2098 *e e q c* with <sup>2</sup> *R* value equals to 0.954. It can be seen that the Langmuir model has a better fitting model than Freundlich

The value of standard Gibbs free energy change calculated at 30 C is found to be -16.98 kJ/mol. The negative sign for <sup>0</sup> *<sup>G</sup>* indicates to the spontaneous nature of Fe3+ ions

> 200 300 400 500 600 700 800 900 **Ce**

5.5 5.7 5.9 6.1 6.3 6.5 6.7 6.9 **lnCe**

Fig. 11. Freundlich isotherm plot of *ln qe vs. ln* Ce, where *C*e is the equilibrium concentration

To conduct the isotherm were studied at the initial pH of solution which was adjusted at the optimum value (pH = 4.5) and the mass of olive cake which was taken as 0.3, 0.5, 0.75 and 1.0 g at different temperatures of 28, 35 and 45 ºC. Three adsorption isotherms models were used: Langmiur, Frendulich and Dubinin–Kaganer–Radushkevich (DKR) [21]. Figure 12 shows the experimental data that were fitted by the linear form of Langmiur model, *(Ce / qe)* versus *Ce*, at temperatures of 28, 35 and 45 <sup>0</sup> C. The values of max *<sup>q</sup>* and *b* were evaluated

**5.3 Sorption isotherms of Fe3+ ions processes using olive cake** 

Fig. 10. Langmuir isotherm model plot of *qe*/*Ce* of Fe3+ ions on JNZ *vs. Ce* (ppm) of Fe3+ ions.

as the former have higher correlation regression coefficient than the latter.

adsorption on the JNZ.

> 1.78 1.8 1.82 1.84 1.86 1.88 1.9 1.92 1.94

of Fe3+ ions concentration.

**lnqe**

**Ce/qe**

from the slope and intercept respectively for the three isothermal lines. These values of max *q* and *b* are listed in Table 1 with their uncertainty and their regression coefficients, *R* 2 . Table 3 shows that the values of *q* max and *b* are decreased when the solution temperature increased from 28 to 45 <sup>0</sup> C. The decreasing in the values of *q* max and *b* with increasing temperature indicates that the Fe3+ ions are favorably adsorbed by olive cake at lower temperatures, which shows that the adsorption process is exothermic. In order to justify the validity of olive cake as an adsorbent for Fe3+ ions adsorption, its adsorption potential must be compared with other adsorbents like eggshells [59] and chitin [24] used for this purpose. It may be observed that the maximum sorption of Fe3+ ions on olive cake is approximately greater 10 times than those on the chitin and eggshells.

Fig. 12. Langmuir isotherm model plot of *qe*/*Ce* of Fe3+ ions on olive cake *vs. Ce* (ppm) of Fe3+ ions.

Fig. 13. The linearized Freundlich adsorption isotherms for Fe3+ ions adsorption by olive cake at different temperatures. (Initial concentration of Fe3+ ions: 100 ppm, Agitation speed: 100 rpm, pH: 4.5, Contact time: 24 hr).

Thermodynamics Approach in the Adsorption of Heavy Metals 755

adsorption models were applied to describe the isotherms and isotherm constants.

The calculated results of the Langmuir and Freundlich isotherm constants are given in Table 5. It is found that the adsorptions of Fe2+ and Fe3+ ions on the chitosan and cross-linked chitosan beads correlated well (*R*>0.99) with the Langmuir equation as compared to the

Fig. 14. Adsorption isotherms of Fe3+ ions on chitosan and cross-linked chitosan beads.

Table 5. Langmuir and Freundlich isotherm constants and correlation coefficients

Table 6 lists the calculated results. Based on the effect of separation factor on isotherm shape, the *R*L values are in the range of 0<*R*L<1, which indicates that the adsorptions of Fe2+ and Fe3+ ions on chitosan and cross-linked chitosan beads are favourable. Thus, chitosan and cross-linked chitosan beads are favourable adsorbers. As mentioned earlier, chitosan and cross-linked chitosan beads are microporous biopolymers, therefore pores are large enough to let Fe2+ and Fe3+ ions through. The mechanism of ion adsorption on porous adsorbents may involve three steps [60 - 61]: (i) diffusion of the ions to the external surface of adsorbent; (ii) diffusion of ions into the pores of adsorbent; (iii) adsorption of the ions on the internal

Equilibrium data agreed very well with the Langmuir model.

Freundlich equation under the concentration range studied.

chitosan, chitosan-GLA and chitosan-ECH bead

The Freundlich constants *Kf* and *n*, which respectively indicating the adsorption capacity and the adsorption intensity, are calculated from the intercept and slope of plot ln *<sup>e</sup> q* versus ln*Ce* respectively, as shown in Figure 13. These values of *Kf* and *n* are also listed in Table 3 with their regression coefficients. It can be observed that the values of *Kf* are decreased with increasing the temperature of solution from 28 to 45 <sup>0</sup> C. The decreasing in these values with temperature confirms also that the adsorption process is exothermic. It can be also seen that the values of *1/n* decreases as the temperature increases. Our experimental data of values *Kf* and *1/n* are considered qualitatively consistence with those that found in adsorption of Fe3+ ions on eggshells [59] and chitin [24].

The negative value of <sup>0</sup> ΔG (Table 4)confirms the feasibility of the process and the spontaneous nature of sorption. The values of <sup>0</sup> ΔH and <sup>0</sup> ΔS are found to be -10.83 kJ/mol and 19.9 J/mol-K, respectively (see Table 4). The negative values of <sup>0</sup> ΔH indicate and exothermic sorption reaction process. The positive value of <sup>0</sup> ΔS shows the increasing randomness at the solid/liquid interface during the sorption of Fe3+ ions onto olive cake.


Table 3. Langmuir, Freundlich and DKR constants for adsorption of Fe3+ ions on olive cake


Table 4. Thermodynamics parameters for the adsorption of Fe3+ ions on olive cake.

## **5.4 Sorption isotherms of Fe3+ ions processes using chitosan and cross-linked chitosan beads**

A batch adsorption system was applied to study the adsorption of Fe2+ and Fe3+ ions from aqueous solution by chitosan and cross-linked chitosan beads [60 - 61]. The adsorption capacities and rates of Fe2+ and Fe3+ ions onto chitosan and cross-linked chitosan beads were evaluatedas shown in Figure 14. Experiments were carried out as function of pH, agitation period, agitation rate and concentration of Fe2+ and Fe3+ ions. Langmuir and Freundlich

The Freundlich constants *Kf* and *n*, which respectively indicating the adsorption capacity and the adsorption intensity, are calculated from the intercept and slope of plot ln *<sup>e</sup> q* versus ln*Ce* respectively, as shown in Figure 13. These values of *Kf* and *n* are also listed in Table 3 with their regression coefficients. It can be observed that the values of *Kf* are decreased with increasing the temperature of solution from 28 to 45 <sup>0</sup> C. The decreasing in these values with temperature confirms also that the adsorption process is exothermic. It can be also seen that the values of *1/n* decreases as the temperature increases. Our experimental data of values *Kf* and *1/n* are considered qualitatively consistence with those that found in

The negative value of <sup>0</sup> ΔG (Table 4)confirms the feasibility of the process and the spontaneous nature of sorption. The values of <sup>0</sup> ΔH and <sup>0</sup> ΔS are found to be -10.83 kJ/mol and 19.9 J/mol-K, respectively (see Table 4). The negative values of <sup>0</sup> ΔH indicate and exothermic sorption reaction process. The positive value of <sup>0</sup> ΔS shows the increasing randomness at the solid/liquid interface during the sorption of Fe3+ ions onto olive cake.

Table 3. Langmuir, Freundlich and DKR constants for adsorption of Fe3+ ions on olive cake

Table 4. Thermodynamics parameters for the adsorption of Fe3+ ions on olive cake.

**5.4 Sorption isotherms of Fe3+ ions processes using chitosan and cross-linked** 

A batch adsorption system was applied to study the adsorption of Fe2+ and Fe3+ ions from aqueous solution by chitosan and cross-linked chitosan beads [60 - 61]. The adsorption capacities and rates of Fe2+ and Fe3+ ions onto chitosan and cross-linked chitosan beads were evaluatedas shown in Figure 14. Experiments were carried out as function of pH, agitation period, agitation rate and concentration of Fe2+ and Fe3+ ions. Langmuir and Freundlich

**chitosan beads** 

adsorption of Fe3+ ions on eggshells [59] and chitin [24].

adsorption models were applied to describe the isotherms and isotherm constants. Equilibrium data agreed very well with the Langmuir model.

The calculated results of the Langmuir and Freundlich isotherm constants are given in Table 5. It is found that the adsorptions of Fe2+ and Fe3+ ions on the chitosan and cross-linked chitosan beads correlated well (*R*>0.99) with the Langmuir equation as compared to the Freundlich equation under the concentration range studied.

Fig. 14. Adsorption isotherms of Fe3+ ions on chitosan and cross-linked chitosan beads. chitosan, chitosan-GLA and chitosan-ECH bead


Table 5. Langmuir and Freundlich isotherm constants and correlation coefficients

Table 6 lists the calculated results. Based on the effect of separation factor on isotherm shape, the *R*L values are in the range of 0<*R*L<1, which indicates that the adsorptions of Fe2+ and Fe3+ ions on chitosan and cross-linked chitosan beads are favourable. Thus, chitosan and cross-linked chitosan beads are favourable adsorbers. As mentioned earlier, chitosan and cross-linked chitosan beads are microporous biopolymers, therefore pores are large enough to let Fe2+ and Fe3+ ions through. The mechanism of ion adsorption on porous adsorbents may involve three steps [60 - 61]: (i) diffusion of the ions to the external surface of adsorbent; (ii) diffusion of ions into the pores of adsorbent; (iii) adsorption of the ions on the internal

Thermodynamics Approach in the Adsorption of Heavy Metals 757

Fig. 16. Langmuir plot for the adsorption of Fe3+ ions on activated carbon obtained from

Fig. 17. Langmuir plot for the adsorption of Fe3+ ions on activated carbon obtained from

pericarp of rubber fruit.

coconut shell.


surface of adsorbent. The first step of adsorption may be affected by metal ion concentration and agitation period. The last step is relatively a rapid process.

Table 6. RL values based on the Langmuir equation

## **5.5 Adsorption of Fe3+ ions on activated carbons obtained from bagasse, pericarp of rubber fruit and coconut shell**

The adsorptions of Fe3+ ions from aqueous solution at room temperature on activated carbons obtaining from bagasse, pericarp of rubber fruit and coconut shell have been studied [62]. The adsorption behavior of Fe3+ ions on these activated carbons could be interpreted by Langmuir adsorption isotherm as monolayer coverage. The maximum amounts of Fe3+ ions adsorbed per gram of these activated carbons were 0.66 mmol/g, 0.41 mmol/g and 0.18 mmol/g, respectively. The mechanism by which the adsorption of Fe3+ ions onto the activated carbon can be performed after being reduced to Fe3+ ions [63].

Figures 15 to 17 show the Langmuir plots that have the greatest values of iron adsorption on three types of activated carbons. The maximum adsorption at monolayer coverage on bagasse, pericarp of rubber fruit and coconut shellare in the range 0.25 - 0.66 mmol/g, 0.11 - 0.41 mmol/g and 0.12 - 0.19 mmol/g, respectively. The experimental result shows that the amount of iron ion adsorbed on activated carbons decreased with increasing adsorption temperature. This suggested that the adsorption mechanism was physical adsorption, in contrast to chemical adsorption in which the amount of adsorbate adsorbed on an adsorbent increases with increasing adsorption temperature [63].

Fig. 15. Langmuir plot for the adsorption of Fe3+ ions on activated carbon obtained from bagasse.

surface of adsorbent. The first step of adsorption may be affected by metal ion concentration

**5.5 Adsorption of Fe3+ ions on activated carbons obtained from bagasse, pericarp of** 

The adsorptions of Fe3+ ions from aqueous solution at room temperature on activated carbons obtaining from bagasse, pericarp of rubber fruit and coconut shell have been studied [62]. The adsorption behavior of Fe3+ ions on these activated carbons could be interpreted by Langmuir adsorption isotherm as monolayer coverage. The maximum amounts of Fe3+ ions adsorbed per gram of these activated carbons were 0.66 mmol/g, 0.41 mmol/g and 0.18 mmol/g, respectively. The mechanism by which the adsorption of Fe3+ ions onto the activated carbon can be performed after being reduced to Fe3+ ions [63].

Figures 15 to 17 show the Langmuir plots that have the greatest values of iron adsorption on three types of activated carbons. The maximum adsorption at monolayer coverage on bagasse, pericarp of rubber fruit and coconut shellare in the range 0.25 - 0.66 mmol/g, 0.11 - 0.41 mmol/g and 0.12 - 0.19 mmol/g, respectively. The experimental result shows that the amount of iron ion adsorbed on activated carbons decreased with increasing adsorption temperature. This suggested that the adsorption mechanism was physical adsorption, in contrast to chemical adsorption in which the amount of adsorbate adsorbed on an adsorbent

Fig. 15. Langmuir plot for the adsorption of Fe3+ ions on activated carbon obtained from

and agitation period. The last step is relatively a rapid process.

Table 6. RL values based on the Langmuir equation

increases with increasing adsorption temperature [63].

**rubber fruit and coconut shell** 

bagasse.

Fig. 16. Langmuir plot for the adsorption of Fe3+ ions on activated carbon obtained from pericarp of rubber fruit.

Fig. 17. Langmuir plot for the adsorption of Fe3+ ions on activated carbon obtained from coconut shell.

Thermodynamics Approach in the Adsorption of Heavy Metals 759

**Isotherm Constants Fe(III)**  Langmuir - 16.3500 qmax - 0.0800 b 0.9321 R2 33.1000

n 0.6900 Kf 3.9800 R2 0.9222 q(%) 8.8100

 4.0\*10-6 qD 104.4800 E 353.5500 R2 0.9461 q (%) 24.5200

Table 8. Isotherm constant for adsorption of Fe3+ ions onto Raphia palm fruit endocarp (nut)

The activation energy of any reaction process depicts the energy barrier which the reactants must overcome before any reaction could take place. High activation energy to react hence

High and low concentration level of Fe3+ ions can be adsorbed on different types of natural adsorbents. This process can be used to remove Fe3+ ions from aqueous solutions. The thermodynamic isotherms indicate the behavior picture of Fe3+ ions onto the surface of natural adsorbent as homogenous or heterogeneous monolayer coverage. It depends on the chemical nature of adsorbent surfaces. Mostly, the thermodynamic parameters show the spontaneous and exothermic adsorption processes of Fe3+ ions onto the surfaces of natural

**Constants (KJ/mol/K) Fe(III)**  H - 2560.4600 S 19.1900 EA 2094.8000 Sn 0.0900 R2 (Vant Hoff) 0.4633 R2 (Sticking Probability) 0.4747

q(%)

decrease in reaction rate.

**6. Conclusion** 

Table 9. The activation energy of Fe(III)

adsorbents, indicating of easier handling.

from aqueous solution

Freundlich

Dubinin-Radushkevich

Study of the temperature dependence on these adsorptions has revealed them to be exothermic processes with the heats of adsorption of about -8.9 kJ/mol, -9.7 kJ/mol and -5.7 kJ/mol for bagasse, pericarp of rubber fruit and coconut shell, respectively. The value of Langmuir isotherm constant for the maximum adsorption at monolayer coverage (X*max*) and the heats of adsorption (H*ads*) of Fe3+ ions on three types of activated carbons was summarized in Table 7.


Table 7. The maximum adsorption of iron ion at monolayer coverage (X*max*) and the heats of adsorption (H*ads*) for iron ion on three types of activated carbons and activation temperature at 600 ºC

## **5.6 Adsorption of Fe3+ ions on unmodified raphia palm (Raphia Hookeri) fruit endocarp**

The adsorption of aqueous Fe3+ ions onto the surface of Raphia palm fruit endocarp (nut) was studied in a batch system [64 – 67]. The influence of initial Fe3+ ions concentration, temperature and particle size was investigated and the results showed that particle size and temperature affected the sorption rate and that the adsorption was fast with a maximum percentage adsorption of 98.7% in 20 min as initial metal ion concentration was increased. There is a general decrease in sorption efficiency as the particle size is increased. The increased sorption with smaller particle size means that there is higher external surface area available for adsorption with smaller particle at a constant total mass.

Four isotherms; Langmuir, Freundlich, Dubinin-Radushkevich (D-R) and Temkin were used to model the equilibrium sorption experimental data. The sorption process was found to follow chemisorption mechanism. From Dubinin-Radushkevich (D-R) isotherm, the apparent energy of adsorption was 353.55 Kj/mol. The apparent energy shows if the sorption process follows physisorption, chemisorption or ion exchange. It has been reported:


From the result obtained, the sorption of Fe3+ ions onto Raphia palm fruit endocarp (nut) was chemisorption process.

In order to describe the thermodynamic behaviuor of the sorption of Fe3+ ion onto Raphia palm fruit endocarp (nut) from aqueous solution, thermodynamic parameters including Gº, Hº, Sº, were evaluated. The value of Hº is negative indicating exothermic process. The standard Gibbs free energy indicates that the the sorption process is spontaneous in nature and also feasible. The decreasing in Gº values with increasing temperature shows a decrease in feasibility of sorption at higher temperature.

Study of the temperature dependence on these adsorptions has revealed them to be exothermic processes with the heats of adsorption of about -8.9 kJ/mol, -9.7 kJ/mol and -5.7 kJ/mol for bagasse, pericarp of rubber fruit and coconut shell, respectively. The value of Langmuir isotherm constant for the maximum adsorption at monolayer coverage (X*max*) and the heats of adsorption (H*ads*) of Fe3+ ions on three types of activated carbons was

Raw Materials **X**max Hads (KJ/mol)

Table 7. The maximum adsorption of iron ion at monolayer coverage (X*max*) and the heats of

The adsorption of aqueous Fe3+ ions onto the surface of Raphia palm fruit endocarp (nut) was studied in a batch system [64 – 67]. The influence of initial Fe3+ ions concentration, temperature and particle size was investigated and the results showed that particle size and temperature affected the sorption rate and that the adsorption was fast with a maximum percentage adsorption of 98.7% in 20 min as initial metal ion concentration was increased. There is a general decrease in sorption efficiency as the particle size is increased. The increased sorption with smaller particle size means that there is higher external surface area

Four isotherms; Langmuir, Freundlich, Dubinin-Radushkevich (D-R) and Temkin were used to model the equilibrium sorption experimental data. The sorption process was found to follow chemisorption mechanism. From Dubinin-Radushkevich (D-R) isotherm, the apparent energy of adsorption was 353.55 Kj/mol. The apparent energy shows if the sorption process follows physisorption, chemisorption or ion exchange. It has been

From the result obtained, the sorption of Fe3+ ions onto Raphia palm fruit endocarp (nut)

In order to describe the thermodynamic behaviuor of the sorption of Fe3+ ion onto Raphia palm fruit endocarp (nut) from aqueous solution, thermodynamic parameters including Gº, Hº, Sº, were evaluated. The value of Hº is negative indicating exothermic process. The standard Gibbs free energy indicates that the the sorption process is spontaneous in nature and also feasible. The decreasing in Gº values with increasing

Bagasse 0.66 - 8.9 Pericarp of Rubber Fruit 0.41 - 9.7 Coconut Shell 0.19 - 5.7

adsorption (H*ads*) for iron ion on three types of activated carbons and activation

**5.6 Adsorption of Fe3+ ions on unmodified raphia palm (Raphia Hookeri) fruit** 

available for adsorption with smaller particle at a constant total mass.

1. Physiasorption processes have adsorption energies <40 Kj/mol 2. Chemisorption processes have adsorption energies > 40 Kj/mol

3. Chemical ion exchange have adsorption energies between 8.0 and 16 Kj/mol 4. Adsorption is physical in nature have adsorption energies <8.0 Kj/mol

temperature shows a decrease in feasibility of sorption at higher temperature.

summarized in Table 7.

temperature at 600 ºC

**endocarp** 

reported:

was chemisorption process.


Table 8. Isotherm constant for adsorption of Fe3+ ions onto Raphia palm fruit endocarp (nut) from aqueous solution


Table 9. The activation energy of Fe(III)

The activation energy of any reaction process depicts the energy barrier which the reactants must overcome before any reaction could take place. High activation energy to react hence decrease in reaction rate.
