*2.2. Kinetics Matching*

In the case of the classical Fenton process, it involves catalytic radical oxidation and final coagulation combined with coprecipitation. The applied modification of the process causes the concentration of iron (II) ions to change due to the dissolution of metallic iron— Fe (II)—amount constantly increasing. In addition, as a result of UV irradiation, there is an increased reduction in iron (III) during the Fenton reaction to iron (II), which results in at least a theoretical decrease in homogeneous catalyst demand. The use of magnetite and hematite as cocatalysts, and metallic iron, leads to the appearance of the surface of solid catalyst heterogeneous processes, including sorption or ion exchange. All these processes are at least partially independent and sometimes even antagonistic. Therefore, describing the kinetics of the treatment process is not easy. Four equations were used to describe the kinetics:

• First-order reaction with respect to the TOC value:

$$\text{TOC} = \text{TOC}\_0 \times \text{e}^{-\text{kt}} \tag{1}$$

• Second-order reaction with respect to the TOC value:

$$\text{TOC} = \left(\text{kt} + 1/\text{TOC}\_0\right)^{-1} \tag{2}$$

• Modified first-order reaction with respect to the TOC value:

$$\text{TOC} = (\text{TOC}\_0 - \text{b}) \times \text{e}^{-\text{kt}} + \text{b} \tag{3}$$

• Modified second-order reaction with respect to the TOC value:

$$\text{TOC} = (\text{kt} + (\text{TOC}\_0 - \text{b})^{-1})^{-1} + \text{b} \tag{4}$$

Equations (1) and (2) are the descriptions of the usual first- and second-order kinetics. Typically, however, the kinetics of a specific chemical reaction is described with clearly defined substrates and products. In the case of the description of wastewater, it is a complex mixture of many chemical compounds present in various concentrations. From a practical point of view, it is not possible to determine the concentrations of all chemical compounds and, most importantly, to predict all chemical reactions taking place. Therefore, collective parameters such as BOD5, COD, and TOC are described. In the case of treatment processes where hydrogen peroxide is used, it may remain after the process. While we ran the process to ensure that it was decomposed (and iodometrically checked), the decomposition of hydrogen peroxide takes time. Hydrogen peroxide is a well-known disruptor in COD measurement. During radical oxidation, wastewater is at least partially sterilized, which also affects BOD determination. Although both disturbing factors (in the determination of BOD and COD) can be eliminated, from a practical point of view, it is easier to use TOC notation, which is considered more reliable and unambiguous in its interpretation. Therefore, it was decided to describe all kinetics in relation to one collective TOC parameter. The idea behind first- and second-order kinetics is that the reaction can be

completed, i.e., until the substrate is completely used. Under the conditions of our experiment, this means zeroing the TOC value and complete decomposition of the pollutants. However, it is not possible to obtain complete TOC elimination. There is always a certain amount left, hence the idea to modify the description of kinetics. As such, there was a certain number of compounds that could be removed in our process, but some would be persistent to decomposition. The amounts of these substances can be described as possible and impossible to remove TOC. Value "b" Equations (3) and (4), represents the content of this persistent, so-called "hard" TOC. The remaining amount of nonpersistent TOC can still be decomposed, and the description is related to first- or second-order kinetics. An example of the application of four kinetic models is presented in Figure 1. The best match was obtained for the modified second-order kinetics model. be completed, i.e., until the substrate is completely used. Under the conditions of our experiment, this means zeroing the TOC value and complete decomposition of the pollutants. However, it is not possible to obtain complete TOC elimination. There is always a certain amount left, hence the idea to modify the description of kinetics. As such, there was a certain number of compounds that could be removed in our process, but some would be persistent to decomposition. The amounts of these substances can be described as possible and impossible to remove TOC. Value "b" Equations (3) and (4), represents the content of this persistent, so-called "hard" TOC. The remaining amount of nonpersistent TOC can still be decomposed, and the description is related to first- or second-order kinetics. An example of the application of four kinetic models is presented in Figure 1. The best match was obtained for the modified second-order kinetics model.

**Figure 1.** Example kinetic model results: 1500/1500/1000 Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 1:1, UV irradiation, pH = 3.0. **Figure 1.** Example kinetic model results: 1500/1500/1000 Fe3O4/Fe2O3/Fe<sup>0</sup> doses (mg/L) H2O2/COD mass ratio 1:1, UV irradiation, pH = 3.0.

### *2.3. Treatment Processes 2.3. Treatment Processes*

Detailed doses and proportions of the reagents used during the research on CW catalytic treatment are presented in Table S1, while treatment results are shown in Figures Detailed doses and proportions of the reagents used during the research on CW catalytic treatment are presented in Table S1, while treatment results are shown in Figures 2–5.

2–5. Treatment is more effective as the process takes longer to run. The use of UV light increases the effectiveness of the treatment compared to a non-light-assisted process with the same doses of reagents.

In each of the non-light-assisted experiments, the most intensive TOC removal, around 50 mg/L, was obtained in the first 15 min. Such a situation could be observed, for, e.g., 2:1 H2O2/COD ratio and 250/250/1500 mg/L Fe3O4/Fe2O3/Fe<sup>0</sup> catalyst doses (Figure 3). In the mentioned sample, after 30 min of the process, TOC was 221.7 mg/L; for 15 min from the first measurement, it was decreased by 27 mg/L. During subsequent measurements made at 15-, 30-, and 60-min time differences, TOC decreased more slowly. A better treatment effect was obtained by using a lower ratio of 1:1 H2O2/COD. The lowest TOC, 182.0 mg/L, was obtained for 1:1 H2O2/COD ratio and 500/500/3000 mg/L Fe3O4/Fe2O3/Fe<sup>0</sup> catalyst doses after a 120 min process time (Figure 2). The second-lowest TOC, 198.4 mg/L, was for 1:1 H2O2/COD ratio and 500/500/1000 mg/L Fe3O4/Fe2O3/Fe<sup>0</sup> catalyst doses. The highest TOC 218.0 mg/L, only 28.8% TOC removal after a 120-min process time, was obtained for 375/375/250 mg/L Fe3O4/Fe2O3/Fe<sup>0</sup> catalyst doses and 2:1 H2O2/COD ratio. On the basis of the presented data, for non-light-assisted processes, with regard to catalyst doses at constant values of hydrogen peroxide, lower TOC values were achieved for higher doses of the catalysts: 4000 mg/L, slightly lower for 2000 mg/L,

and the lowest for 1000 mg/L. In most cases, lower values of TOC were recorded for the lower 1:1 H2O2/COD ratio. The TOC values determined after the treatment process with the 2:1 H2O2/COD ratio were higher than the value for 1:1 H2O2/COD ratio. The exception was the process involving 1000 mg/L of hematite, 1000 mg/L of magnetite, and 2000 mg/L of metallic iron, in which the difference was 40 mg/L. *Catalysts* **2021**, *11*, x FOR PEER REVIEW 5 of 14 *Catalysts* **2021**, *11*, x FOR PEER REVIEW 5 of 14

**Figure 2.** Cosmetic wastewater (CW) treatment results with different Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 1:1, without UV irradiation, pH = 3.0. **Figure 2.** Cosmetic wastewater (CW) treatment results with different Fe3O4/Fe2O3/Fe<sup>0</sup> doses (mg/L) H2O2/COD mass ratio 1:1, without UV irradiation, pH = 3.0. **Figure 2.** Cosmetic wastewater (CW) treatment results with different Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 1:1, without UV irradiation, pH = 3.0.

2:1, without UV irradiation, pH = 3.0. **Figure 3.** CW treatment results with different Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 2:1, without UV irradiation, pH = 3.0. **Figure 3.** CW treatment results with different Fe3O4/Fe2O3/Fe<sup>0</sup> doses (mg/L) H2O2/COD mass ratio 2:1, without UV irradiation, pH = 3.0.

*Catalysts* **2021**, *11*, x FOR PEER REVIEW 6 of 14

**Figure 4.** CW treatment results with different Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 1:1, UV irradiation, pH = 3.0. **Figure 4.** CW treatment results with different Fe3O4/Fe2O3/Fe<sup>0</sup> doses (mg/L) H2O2/COD mass ratio 1:1, UV irradiation, pH = 3.0. **Figure 4.** CW treatment results with different Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 1:1, UV irradiation, pH = 3.0.

**Figure 5.** CW treatment results with different Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 2:1, UV irradiation, pH = 3.0. **Figure 5.** CW treatment results with different Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 2:1, UV irradiation, pH = 3.0. **Figure 5.** CW treatment results with different Fe3O4/Fe2O3/Fe<sup>0</sup> doses (mg/L) H2O2/COD mass ratio 2:1, UV irradiation, pH = 3.0.

Treatment is more effective as the process takes longer to run. The use of UV light increases the effectiveness of the treatment compared to a non-light-assisted process with the same doses of reagents. In each of the non-light-assisted experiments, the most intensive TOC removal, around 50 mg/L, was obtained in the first 15 min. Such a situation could be observed, for, e.g., 2:1 H2O2/COD ratio and 250/250/1500 mg/L Fe3O4/Fe2O3/Fe0 catalyst doses (Figure 3). In the mentioned sample, after 30 min of the process, TOC was 221.7 mg/L; for 15 min from the first measurement, it was decreased by 27 mg/L. During subsequent measurements made at 15-, 30-, and 60-min time differences, TOC decreased more slowly. A better treatment effect was obtained by using a lower ratio of 1:1 H2O2/COD. The lowest TOC, 182.0 mg/L, was obtained for 1:1 H2O2/COD ratio and 500/500/3000 mg/L Fe3O4/Fe2O3/Fe0 Treatment is more effective as the process takes longer to run. The use of UV light increases the effectiveness of the treatment compared to a non-light-assisted process with the same doses of reagents. In each of the non-light-assisted experiments, the most intensive TOC removal, around 50 mg/L, was obtained in the first 15 min. Such a situation could be observed, for, e.g., 2:1 H2O2/COD ratio and 250/250/1500 mg/L Fe3O4/Fe2O3/Fe0 catalyst doses (Figure 3). In the mentioned sample, after 30 min of the process, TOC was 221.7 mg/L; for 15 min from the first measurement, it was decreased by 27 mg/L. During subsequent measurements made at 15-, 30-, and 60-min time differences, TOC decreased more slowly. A better treatment effect was obtained by using a lower ratio of 1:1 H2O2/COD. The lowest TOC, 182.0 mg/L, was obtained for 1:1 H2O2/COD ratio and 500/500/3000 mg/L Fe3O4/Fe2O3/Fe0 In the light-assisted process, the lowest TOC, 134.1 mg/L (56.2% TOC removal), was obtained after 120 min for 1:1 H2O2/COD ratio and 500/500/1000 mg/L Fe3O4/Fe2O3/ Fe<sup>0</sup> catalyst doses (Figure 5). In the initial phase of the process, a slower decrease in TOC value was visible for the 2:1 H2O2/COD ratio, to 260–270 mg/L. However, a faster decrease was observed in the mixture of iron compounds mass equal to 4000 mg/L. This may indicate that the weight of the catalysts was optimal for the higher dose of hydrogen peroxide and accelerated the process. For smaller total catalyst concentrations, 2:1 H2O2/COD ratio led to the inhibition of the reaction. The decrease in TOC value for 4000 mg/L of catalyst 2:1 H2O2/COD ratio was comparable with that in samples with a lower oxidant concentration for up to 30 min. After this time, for the 1:1 H2O2/COD ratio, reactions slowed down significantly. An exception may be the sample of 500/500/1000 mg/L Fe3O4/Fe2O3/Fe<sup>0</sup>

catalyst doses, where TOC decreased throughout the experiment. In this case, the heterocatalytic reaction could have contributed to the steady decline. The optimal selection of reagent doses ensured the decomposition of the organic pollutants on the surface of the catalysts. For a higher concentration of the oxidant, the given doses of the catalysts did not give an outstanding result, and at a lower concentration of H2O2, it had a greater effect on TOC decomposition. In the experiments where the concentration of iron compounds was 4000 mg/L, there was no visible difference in the rate of the processes, resulting from the concentration of hydrogen peroxide. For the experiments carried out at the concentration of iron compounds of 2000 and 1000 mg/L, however, there was a difference according to the dose of hydrogen peroxide. Lower concentrations of the oxidant resulted in faster TOC removal in the first few minutes of the experiment. At higher concentrations, removal was slower, and more time was required for the reaction to come to a halt. Even though the reaction took longer, in most cases, efficiency for TOC removal at a higher concentration of H2O<sup>2</sup> did not exceed the effectiveness for the 1:1 H2O2/COD ratio. The exceptions were the concentrations of 1000/1000/3000 mg/L Fe3O4/Fe2O3/Fe<sup>0</sup> , in which efficiency was higher at a higher oxidant concentration.

Additionally, an experiment was performed that demonstrated the influence of pH on the efficiency of the pollutant oxidation process (Figure 6). The process was the most effective at pH 2 and 3. The processes carried out at a pH greater than 3 were ineffective, and the decrease in TOC value from 15 min until the end of the experiment was not significant. At pH 2 and 3, TOC decrease was visible throughout the process. At pH 2, sediment in the sample was swollen and occupied the largest volume compared to in the other samples. Sediment after the process carried out at pH 4 was a reddish color and had a volume comparable to that in the processes at pH 3. Obtained sediment during the experiment at pH 5 was brown, and its amount was the smallest in comparison to that formed during the process at other pH values. In the experiment carried out at pH 6, the sediment after the process was reddish, and its structure was comparable to that of the sediment at pH 3 and 4. The red may have indicated the presence of iron (III) hydroxide, which is formed at a high solution pH. *Catalysts* **2021**, *11*, x FOR PEER REVIEW 8 of 14

**Figure 6.** CW treatment results at different pH, 500/500/1000 Fe3O4/Fe2O3/Fe0 doses (mg/L) H2O2/COD mass ratio 1:1, UV irradiation. **Figure 6.** CW treatment results at different pH, 500/500/1000 Fe3O4/Fe2O3/Fe<sup>0</sup> doses (mg/L) H2O2/COD mass ratio 1:1, UV irradiation.

H2O2 is a weak acid. Its stability increases with a decrease in pH value, which may impede its catalytic decomposition into a hydroxyl ion and radical. However, these effects were not strongly observed during the experiment. Hydrogen peroxide under alkaline H2O<sup>2</sup> is a weak acid. Its stability increases with a decrease in pH value, which may impede its catalytic decomposition into a hydroxyl ion and radical. However, these effects

conditions decomposes rapidly with the evolution of oxygen. For this reason, no attempt

served in all experiments at the termination stage of the Fenton reaction. In the case of iron (II) and (III), its source in the process was twofold: the surface of stable iron oxides magnetite and hematite, and the dissolution of metallic iron. The solubility (corrosion) of metallic iron occurs quickly under strongly acidic conditions; under neutral conditions, the process is very slow. Therefore, in neutral conditions, contact between the reactants is difficult to achieve during the entire duration of the process. In an acidic environment, due to the constant increase in the content of dissolved iron, its availability, and thus the intensity of the Fenton reaction, increases steadily with time. Additionally, the form of iron is strongly pH-dependent. At pH 5, iron hydroxides with small solubility begin to form, and the coagulation process begins. For iron hydroxide, due to minimal solubility, the optimal value for carrying out the coagulation process was around 6.0 and above 8.5. This was another reason for abandoning the experiment in alkaline conditions, as radicals were terminated on the sludge flocs, which resulted in rapidly decreasing process effi-

The statistical analysis was described on the basis of Miller [32]. ANOVA was used to determine the magnitude of variability in the average concentrations of TOC and to check whether differences in the average test results for TOC for individual process conditions (for different doses of catalysts) may have been caused by random errors (Tables

Variance is estimated using two methods: the method determining the variability within a given sample, and variability between samples. The difference in the performed tests was the different durations and reagent doses of the process. The above statement is

If the hypothesis were true, then there would be no large difference between calculated values. If the hypothesis were not true, then the between-group estimate would be greater than the intergroup estimate. This is due to the high variability between samples.

ciency.

S2 and S3, Figures S4 and S5).

a null hypothesis.

were not strongly observed during the experiment. Hydrogen peroxide under alkaline conditions decomposes rapidly with the evolution of oxygen. For this reason, no attempt was made to operate the process under alkaline conditions. However, the presence of the formation of oxygen bubbles hindering the sedimentation of the formed sludge was observed in all experiments at the termination stage of the Fenton reaction. In the case of iron (II) and (III), its source in the process was twofold: the surface of stable iron oxides magnetite and hematite, and the dissolution of metallic iron. The solubility (corrosion) of metallic iron occurs quickly under strongly acidic conditions; under neutral conditions, the process is very slow. Therefore, in neutral conditions, contact between the reactants is difficult to achieve during the entire duration of the process. In an acidic environment, due to the constant increase in the content of dissolved iron, its availability, and thus the intensity of the Fenton reaction, increases steadily with time. Additionally, the form of iron is strongly pH-dependent. At pH 5, iron hydroxides with small solubility begin to form, and the coagulation process begins. For iron hydroxide, due to minimal solubility, the optimal value for carrying out the coagulation process was around 6.0 and above 8.5. This was another reason for abandoning the experiment in alkaline conditions, as radicals were terminated on the sludge flocs, which resulted in rapidly decreasing process efficiency.

The statistical analysis was described on the basis of Miller [32]. ANOVA was used to determine the magnitude of variability in the average concentrations of TOC and to check whether differences in the average test results for TOC for individual process conditions (for different doses of catalysts) may have been caused by random errors (Tables S2 and S3, Figures S4 and S5).

Variance is estimated using two methods: the method determining the variability within a given sample, and variability between samples. The difference in the performed tests was the different durations and reagent doses of the process. The above statement is a null hypothesis.

If the hypothesis were true, then there would be no large difference between calculated values. If the hypothesis were not true, then the between-group estimate would be greater than the intergroup estimate. This is due to the high variability between samples. To check if the difference was significant, Snedecor's one-sided F test with α = 0.05 was performed.

The following null hypothesis was made for ANOVA: the tests were performed accurately, and reproducibility was achieved in TOC results. The value of the F parameter was lower than that of the critical F, which means that the hypothesis is true. The mean values in the samples were similar, and similar conclusions were found during TOC analysis. Even the optimal value did not significantly differ from the other values. From the perspective of the performed tests, this is a favorable phenomenon, as it proved the accuracy and repeatability of the performed tests. However, the process itself was not effective, and from the perspective of the conducted process, its effectiveness was not favorable.
