2.4.1. Adsorption Kinetic

The mechanism through which adsorbate particles bind to the absorbent surface is adsorption. Through column or section configuration, the adsorption process is achieved. Kinetic studies are a curve (or line) which characterizes the speed of persistence or transfer of a solution at a given adsorbent dosage, temperature, and pH with an aqueous atmosphere to phase boundaries. Two major processes occur in adsorption: physical adsorption and chemical adsorption. Physical adsorption is due to poor attraction forces (van der Waals), whereas chemical adsorption requires the creation of a tight bond that facilitates the activation of atoms in between the solvent and the substrate [68,69].

Pseudo-first-order kinetic model is a simple kinetic model which describes the process of adsorption and is the pseudo-first-order equation suggested by Lagergren [70,71].

$$\mathbf{Q}\mathbf{t} = \mathbf{Q}\mathbf{e}[1 - \exp(-\mathbf{K}\_1\mathbf{t})] \tag{3}$$

where Qe (mg/g) is the amount of the contaminants adsorbed at equilibrium, Qt (mg/g) is the amount of Dic and Caf adsorbed at time t (min), k1 (L/min) is the rate constant of the pseudo-first-order adsorption.

Pseudo-second-order kinetic model is the kinetic equation that was developed for the adsorption process [72]. The equations are given below:

$$\text{Qt} = \text{Qe}(\frac{\text{Qe.K}\_2\text{.t}}{1 + \text{Qe.K}\_2\text{.t}}) \tag{4}$$

where Qe (mg/g) is the amount of the contaminants adsorbed at equilibrium, Qt (mg/g) is the amount of Dic and Caf adsorbed at time t (min), k2 (g/mg. min) is the rate constant of the second-order adsorption.

#### 2.4.2. Adsorption Isotherms

Any adsorption system's isotherm is an equation which relates to the amount of adsorbate on the adsorbent surface and the adsorbent's concentration or partial pressure at constant temperature [73]. The most used adsorption isotherms model contaminants for removal are the Langmuir isotherm, Freundlich isotherm, Temkin isotherm, and BET (Brunauer–Emmett–Teller) isotherm which are used to gain extensive knowledge on the relationships between the adsorbent surface and the adsorbate [74,75]. Two classic isotherm equations, namely Langmuir and Freundlich, were selected in this study to determine the isotherm parameters.

Langmuir adsorption is made up of four assumptions. The adsorbent's surface is homogenous, implying that practically all binding sites are equal. Adsorbed molecules do not encounter each other. The method of adsorption is similar in all situations, where a monolayer is always assumed to be formed. It has been developed to clarify gas–solid adsorption where monolayer adsorption is directly proportionate to the fraction of the adsorbent surface, which is opened, while desorption is proportional to the portion of the adsorbent surface covered. The Langmuir isotherm is given as [76,77].

$$\text{Qe} = \frac{\text{Qm.Kl.Ce}}{1 + \text{Kl.Ce}} \tag{5}$$

where Ce is adsorbate's concentration at equilibrium (mg/L), Qm is quantity of molecules adsorbed on the adsorbent's surface at any time (mg/g), and K*l* is the Langmuir constant (L/mg). When Ce/Qe is plotted against Ce, a straight line with a slope of 1/Qm and an intercept of 1/K*l* Qm is obtained.

Freundlich isotherm maintains multi-layer as well as heterogeneous molecular adsorption and gives an interpretation that describes the heterogeneity of the surface, and furthermore, the exponential function of the active site and their energy [78,79]. The mathematical expression of Freundlich isotherm is:

$$\text{Qe} = \text{Kf.Ce}^{1/\text{ n}} \tag{6}$$

where K*f* is Freundlich constant or adsorption capacity (L/mg), n represents the extent of heterogeneity in the surface and furthermore characterizes how the adsorbate is distributed on the adsorbent surface. In addition, the exponent (1/n) indicates the absorbent system's favorability and efficiency. As ln (Qe) is plotted against ln (Ce), a straight line with a slope of 1/n and an intercept of ln (K*f)* emerges.
