*2.4. Isotherm Equations*

Langmuir and Freundlich adsorption isotherms were produced based on the equilibrium adsorption data. However, the Langmuir model assumes that biosorption takes place at specific homogeneous sites on the adsorbent by monolayer coverage, while the Freundlich model is empirical and assumes sorption on a heterogeneous surface.

The linear form of the Langmuir model is [31]

$$\frac{C\_{\mathcal{E}}}{q\_{\mathcal{E}}} = \frac{1}{q\_{m}} C\_{\mathcal{E}} + \frac{1}{b\_{L}q\_{m}} \tag{1}$$

where *Ce* is the equilibrium concentration of ion in the solution (mg/L), *qe* is the amount of ion adsorbed per gram of adsorbent at equilibrium (mg/g), *qm* is the monolayer biosorption capacity (mg/g) and *bL* is the affinity constant related to the binding strength of adsorption (L/mg). The values of *qm* and *bL* can be determined from the linear plot of *Ce*/*qe* versus *Ce*.

The linear form of the Freundlich model is [32]

$$
\ln q\_{\varepsilon} = \ln K\_F + \frac{1}{n} \ln \mathcal{C}\_{\varepsilon} \tag{2}
$$

where *Ce* is the equilibrium concentration of ion in the solution (mg/L), *qe* is the amount of ion adsorbed per gram of adsorbent at equilibrium (mg/g), *KF* is a constant relating to the biosorption capacity (mg/g) (L/mg)1/<sup>n</sup> and 1/*n* is an empirical parameter relating to the biosorption intensity. The values of *KF* and 1/*n* can be determined by plotting ln *qe* versus ln *Ce*.
