## 3 Results and Discussion
### Removal of Lead from Aqueous Solution
#### 3.4.3 Adsorption Isotherm  
The adsorption isotherms of Pb (II) onto different clays in the study are shown in Figure 10. In the case of C1, C2, C3 and C4 clays, the adsorption isotherms can be assigned to Langmuir L-type, which started with the steep initial portion followed by the plateau covering a wide range of equilibrium concentrations, especially in the case of C2 clay. The L-shaped (Langmuir) isotherm is characterized by a decreasing of slope as the concentration increases since vacant adsorption sites decrease as the adsorbent becomes covered. Such adsorption behavior could be explained by the high affinity of the adsorbent for the adsorbate at low concentrations, which then decreases as the concentration increases. In the present study, the observed L-type isotherm can be attributed to the existence of high amounts of  
Figure 9: Initial pH effects on the amount (mg/g) of Pb (II) removed by different clays in the study; agitation speed (130 rpm), contact time 6 h, temperature (25 \({}^{\circ}\)C) and initial adsorbate concentration (300 mg/L). playgorskite and montmorillonite in these clays, where previous studies declared that the adsorption of Pb (II) on neat palygorskite and neat montmorillonite obeyed L-type isotherms [38; 41; 43]. However, the adsorption isotherm from the C5 clay is near to S-type, where with an S-type isotherm the slope initially increases with adsorbate concentration, but eventually decreases and becomes zero as vacant adsorbent sites are filled [44]. This type of isotherm indicates that, at a low concentration, the surface has a low affinity for the adsorbate, which increases at higher concentrations. This trend can be attributed to the existence of different minerals in this clay and to the fact that calcite is the dominant mineral in the sample with 39%. The adsorption data of lead onto different clays in the study were correlated using different four models equations--namely, Langmuir [45; 46], Freundlich [47; 48], Temkin [49; 50; 51] and Dubinin-Radushkevich [52; 53; 54; 55; 56; 57]. The Langmuir model assumes the formation of a monolayer adsorbate on the outer surface of the adsorbent and uniform energies of adsorption onto the surface and no migration of adsorbate on the surface of adsorbent [45; 46]. The linear form of Langmuir equation (Equation (2)) is given as:  
\[\frac{\mathrm{C_{e}}}{\mathrm{q_{e}}}=\ \frac{1}{\mathrm{bq_{max}}}+\ \frac{ \mathrm{C_{e}}}{\mathrm{q_{max}}} \tag{2}\]  
where \(\mathrm{q_{e}}\) is the equilibrium capacity concentration of adsorbate (lead solution) on adsorbent (clay) (mg/g), \(\mathrm{C_{e}}\) is the equilibrium concentration of adsorbate in solution (mg/L), \(\mathrm{q_{max}}\) is the maximum monolayer adsorption capacity of adsorbent and b is the Langmuir adsorption constant (L/mg), which is related to free energy of adsorption. The Freundlich model assumes the adsorption characteristics for the heterogeneous surface [47; 48]. The linear form of model can be written as the following (Equation (3)):  
\[\log\mathrm{q_{e}}=\ \log\mathrm{K_{f}}+\ \frac{1}{\mathrm{n}}\log\mathrm{C_{e}} \tag{3}\]  
where \(\mathrm{K_{f}}\) (L/g) and n (dimensionless) are Freundlich isotherm constants, which incorporate the factors affecting adsorption capacity and intensity, respectively. Figure 10: Adsorption isotherms of lead onto clays in the study; agitation speed (130 rpm), contact time 6 h, pH 6 and temperature 25 \({}^{\circ}\)C.  
On the other hand, the Temkin model suggests that heat of adsorption of all molecules in the layer decreases linearly rather than logarithmically with coverage and a uniform distribution of bounding energies up to a certain maximum value [49; 50; 51].