3.2.4. Effect of Temperature

In catalytic illumination oxidative systems, temperature is considered a vital parameter that affects reaction rates. To explore the influence of temperature on the reaction kinetics, Levafix Dark Blue dye oxidation experiments over a temperature range from 25 ◦C to 60 ◦C were undertaken. The results in Figure 10 display superior oxidation leading to an increase in the Levafix Dye removal efficacy, achieving complete removal with a shorter reaction time when the temperature is elevated.

**Figure 10.** Temperature effect on Levafix removal via Fullers' earth-based Fenton process.

An examination of Figure 10 found that elevating the temperature from 25 ◦C to 60 ◦C for the aqueous Levafix solution attained a shorter reaction time of only 10 min and an enhancement from 97% to 100%. According to the previously cited literature [24], reaction rates are normally more efficient at higher temperatures. The various data cited in the literature [29,30] show that temperature elevation has a positive effect on Fenton systems for some wastewater-treated effluents.

#### 3.2.5. Kinetics and Thermodynamics

In this section, the reaction kinetics and thermodynamics of Levafix dye oxidation via the photo-Fenton-modified system are investigated. In the current study, the photo-Fenton oxidation kinetics of Levafix dye using a modified reaction, the Fuller's earth-based photo-Fenton process, was evaluated for various contact times varying from 0 to 20 min under isothermal conditions at the following operating temperatures: 25, 40, 50, and 60 ◦C. Moreover, the zero-, first-, and second-order reaction kinetics were assessed for the modified Fenton oxidation reaction according to the following equations: Equation (11) for the zero-, Equation (12) for the first-, and Equation (13) for the second-order reaction kinetics [31]:

$$\mathbf{C}\_t = \mathbf{C}\_o - \mathbf{k}\_o \mathbf{t} \tag{11}$$

$$\mathbf{C}\_{\mathbf{t}} = \mathbf{C}\_{\mathbf{0}} - \mathbf{e}^{\mathbf{k}\_{\mathbf{t}}\mathbf{t}} \tag{12}$$

$$\left(\frac{1}{\mathbf{C}\_t}\right) = \left(\frac{1}{\mathbf{C}\_0}\right) - \mathbf{k}\_2 \mathbf{t} \tag{13}$$

where C is the concentration of the Levafix dye; Ct is the concentration of the Levafix dye at time t; Co is the Levafix dye's initial concentration; t is the reaction time; and k0, k1, and k2 represent the kinetic rate constants for the zero-, first-, and second-order reaction kinetics, respectively.

The reaction kinetics most appropriate for Levafix removal were assessed by plotting Equations (11)–(13) for the experimental results data. The kinetic parameters, as well as the regression coefficients (*R*2), for each reaction order were investigated, and the data are tabulated in Table 3. Examining the data in Table 3 revealed that the reaction is well-fitted to a second-order reaction. Further, the kinetics constant of the second-order reaction constant, k2, was notably affected by the reaction temperature, increasing with the temperature elevation. This investigation is associated with the generation of the ˙OH species since it is a product of the reaction of Fuller's earth with hydrogen peroxide. Moreover, another kinetics value of importance is t1/2 (the half-life of a reaction), which signifies the essential time needed for the reactant's initial concentration to decrease by half. An examination of Table 3 revealed that the calculated t1/2 is a function of the reaction temperature; t1/2 declines with increasing temperature. Various researchers in other studies have confirmed that the Fenton reaction follows second-order reaction kinetics.

To fully understand the modified Fenton reaction based on the use of Fullers' earth oxidation to oxidize Levafix dye molecules, thermodynamic parametric data were quantified. Arrhenius formula was used to investigate the activation energy, *<sup>k</sup>*<sup>2</sup> <sup>=</sup> *Ae* <sup>−</sup>*Ea RT* , with the activation energy (Ea) of the Levafix dye oxidation being based on the second-order kinetic constant, where R is the gas constant (8.314 J mol−1K−1), T is the temperature in kelvin, and A is the pre-exponential factor that is considered to be constant with respect to temperature [32]. Taking the natural log of the Arrhenius formula yields the following:

$$
\ln \mathbf{k}\_2 = \ln \mathbf{A} - \frac{\mathbf{E\_a}}{\mathbf{RT}} \tag{14}
$$


**Table 3.** Fitted rate constants for the oxidation reaction of dye-containing wastewater \*.

\* k0, k1, k2: kinetic rate constants of zero-, first-, and second-reaction kinetic models; Co and Ct: dye concentrations at initial time and time *t*; *t*: time; R2: correlation coefficient; t1/2 half-life time.

A plot of ln k2 versus 1/T could be used to investigate the value of Ea (Figure 11). Figure 11 displays the relationship of the Levafix Dark Blue dye oxidation through the modified Fuller's earth-based photo Fenton system reaction. The value of Ea of the process was recorded to be 50.8 K J mol<sup>−</sup>1.

**Figure 11.** Plot of ln k2 versus 1000/T for the modified Fuller's earth Fenton system.

Other various thermodynamic variables, such as the enthalpy (ΔH ), entropy (ΔS ), and free energy (ΔG ) of activation, were assessed utilizing Eyring's equation with the utilization of Ea and k2 values according to the following relation [24]:

$$\mathbf{k}\_2 = \frac{\mathbf{k}\_\mathrm{B} \mathbf{T}}{\mathrm{h}} \mathbf{e}^{(-\frac{\mathrm{AC}}{\mathrm{RT}})} \tag{15}$$

where kB is the Boltzmann constant, and h is Planck's constant. The thermodynamic parameters for Levafix dye oxidation were estimated accordingly, and they are displayed in Table 4.

**Table 4.** Thermodynamic properties of organics removal using modified Fuller's earth Fenton oxidation.


An investigation of the data in Table 4 found that the positive values of ΔH across the studied temperature range indicate that the reaction is endothermic. Moreover, ΔG exhibited positive values, which means that the process is non-spontaneous. This result might be because of the formation of a well-solvated structure between the dye molecules and the OH radical species. Moreover, the negative entropy values also support this.
