*2.2. Adsorption Equipment and Procedures*

Atenolol (C14H22N2O3) (molecular weight: 266,336 g/mol, melting point: 147 ◦C, solubility of 13.3 mg/mL (at 25 ◦C), pKa1 = 9.6; pKa2 = 13.88, polar surface area 84.6 Å2 [49], solutions were prepared with distilled water at different initial concentrations. The equilibrium test was carried out inside glass flasks using 50 mg of dried activated carbon in contact with 100 mL of the atenolol solution at different initial concentrations in an orbital incubator (Gallenkamp, model INR-250) with an equivalent stirring rate of 200 rpm at 25 ◦C. The kinetic tests of atenolol adsorption were performed using a 100 mL atenolol solution with an initial concentration of 50 mg/L and 50 mg of activated carbon samples under continuous stirring for different time intervals. The concentration of atenolol was analyzed using double beam UV–visible spectrophotometer from Shimadzo (Series UV-1900) at a maximum absorption wavelength of 274 nm.

Adsorption capacity, for each equilibrium concentration, was calculated as is expressed in Equation (1):

$$q\_{\varepsilon} = \frac{\mathcal{C}\_0 - \mathcal{C}\_{\varepsilon}}{w} \cdot V \tag{1}$$

where *q<sup>e</sup>* is the equilibrium adsorption capacity (mg/g), *C*<sup>0</sup> and *C<sup>e</sup>* are the initial and equilibrium concentrations, respectively, in mg/L; *V* is the solution volume (L) and *W* is the weight of the activated carbon (g).

The equilibrium adsorption data were fitted to the Langmuir, Freundlich, and Temkin adsorption isotherm models (Equations (2), (3) and (4), respectively).

$$q\_{\varepsilon} = \frac{q\_L \cdot K\_L \cdot \mathbb{C}\_{\varepsilon}}{1 + K\_L \cdot \mathbb{C}\_{\varepsilon}} \tag{2}$$

$$q\_{\ell} = \mathcal{K}\_f \cdot (\mathbb{C}\_{\mathfrak{e}})^{1/n} \tag{3}$$

$$q\_{\varepsilon} = \frac{\mathbb{R}\,T}{\mathbb{K}\_1} \cdot \ln(\mathrm{K}\_2\mathbb{C}\_{\mathrm{e}}) \tag{4}$$

where *K<sup>L</sup>* is the equilibrium constant of Langmuir equation (L/mg), *q<sup>L</sup>* is the maximum adsorption capacity (mg/g), *K<sup>f</sup>* is the Freundlich constant associated to the adsorption capacity ((mg/g)(L/mg)1/n) and *n* is the empirical parameter related to the energetic heterogeneity of the adsorption sites, where *K*<sup>1</sup> (J/mol) and *k*<sup>2</sup> (L/mg) is Temkin constant related to the heat of adsorption and isotherm constant, respectively [5].

The adsorption data were fitted to the first-order (Equation (5)), and second-order (Equation (6)) kinetic models for adsorption [48]:

$$\operatorname{Ln}\left(q\_{\ell}-q\_{t}\right) = \operatorname{Ln}\left(q\_{\ell}\right) - k\mathbf{1}t \tag{5}$$

$$\frac{t}{q\_t} = \frac{1}{k\_2 \cdot q\_\varepsilon 2} + \frac{1}{q\_\varepsilon} t \tag{6}$$

where *k*<sup>1</sup> (L/min) and *k*<sup>2</sup> (g/mg·min) are the kinetic constants for the pseudo-first-order and second-order equation, respectively, and *q<sup>e</sup>* is related to the adsorption capacity at equilibrium (mg/g).
