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The pseudo-first order kinetic model provided a poor description of the data for the biosorption of Pb (II) ions, as is evident from their correlation coefficient (R2) values in Table 3. In previous reports where the pseudo-first order kinetic model disagrees with experimental values, this discrepancy was attributed to a time lag, which probably caused the presence of the boundary layer or external resistance controlling the beginning of the sorption process. The pseudo-second order kinetic model is more likely to predict the kinetic behaviour of the biosorption with chemical sorption being the rate-controlling step (Unlu & Ersoz 2006; Abbas et al. 2012). The linear plot of t/qt versus t for the pseudo-second order model for the biosorption of Pb (II) ions onto WSH is presented in Figure 5. It is clear from Table 3 that the R2 value for the pseudo-second order model is high. This result suggests that the biosorption of Pb (II) ions onto WSH follows the pseudo-second order kinetic model well. Several authors that studied the adsorption of divalent metals on heterogeneous sorbents had reported that most metal sorption kinetics follow the pseudo-second order mechanism (Suguna & Kumar 2013; Amer et al. 2015).

Table 3

Comparison of pseudo-first and second-order biosorption of Pb (II) ions on WSH

Pseudo-first order
Pseudo-second order
k1R2qeS.DK2R2qeS.D
−0.013 0.782 0.230 0.1133 −0.680 0.999 0.795 0.4431 
Pseudo-first order
Pseudo-second order
k1R2qeS.DK2R2qeS.D
−0.013 0.782 0.230 0.1133 −0.680 0.999 0.795 0.4431 

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