A Simple Green Method for the Determination of Hydrogen Peroxide and Fe(III)/Fe(II) Species Based on Monitoring the Decolorization Process of Polymethine Dye Using an Optical Immersion Probe

Abstract

We have found that the dye 1,3,3-trimethyl-2-((1′E,3′E,5′E)-5’-(1″,3″,3″-trimethylindol-(2′E)-ylidene)-penta-1″,3″-dien-1″-yl)-3H-indol-1-ium (DTMI-5) can be successfully used for the simple green determination of H₂O₂ and Fe(III)/Fe(II) species. The dye is characterized by a successful combination of spectral, protolytic, and redox properties, and the process of its decolorization in the Fenton reaction is monitored using an optical immersion probe. Theoretical calculations of the reactive sites in the DTMI-5 molecule under free radical attack reveal that the methine groups of the penta-1′,3′-dien-1′-yl linker serve as the primary reactive centers in Fe³⁺ or Fenton-type oxidation conditions. Density functional theory (DFT) calculations indicate that the redox potentials of the examined structures range from 0.34 to 1.65 eV. The experimentally observed broad peak at 340–360 nm, which appears after the interaction of DTMI-5 with the Fenton reagent, is attributed to the formation of aldehyde-type oxidation products, whose theoretical CIS(D) absorption maxima were 358.1 and 337.4 nm. The influence of various factors on the course of the reaction was experimentally investigated. The most important analytical characteristics of the methods, such as linearity intervals of calibration graphs, precision, LOD and LOQ values, selectivity coefficients, etc., were determined. The developed methods were applied to model and real samples (water, oxidation emulsion, and fertilizer).

1. Introduction

The Fenton reaction was first described in 1894. However, it only gained widespread popularity when it began being used for the decomposition and degradation of organic pollutants in the treatment of various water samples. Today, the Fenton reaction is widely used in water treatment technologies, and it can be applied to many types of wastewater, including those from pesticide and chemical production, the textile and petroleum industries, and pharmaceutical and food production. One of the disadvantages of this treatment technology is the need for acidifying or alkalizing agents. Additionally, water disinfection capabilities are somewhat limited [1].

The analytical aspects of this reaction have been studied little, although it is known to be useful for determining hydrogen hydroxide, iron species, and some organic dyes. One potential challenge is the complex kinetic–catalytic nature of this process, which is difficult to control by classical spectrophotometric approaches. A convenient solution may be to use an optical immersion probe, a tool that allows for real-time monitoring of changes in the systems without requiring a sample to be transferred into a cuvette. This approach enables monitoring of process kinetics with high frequency (e.g., every second after the addition of reagents). The optical probe allows for simultaneous stirring of the solution during measurement. In addition, the use of an optical probe creates opportunities to automate analysis procedures, reduce the number of routine manipulations required, and, as a result, improve the analytical performance of the method. It is also much cheaper than classical spectrophotometric equipment. The effectiveness of this approach was previously demonstrated in our work on the kinetic determination of chromium species (VI, III) [2].

Hydrogen peroxide is used as a disinfection agent, oxidant, and bleach in the food, chemistry, and cosmetics industries. On the other hand, it is an unstable compound that is toxic and potentially carcinogenic to living organisms [3]. The application of hydrogen peroxide in various fields leads to excessive environmental pollution. Traditionally, H₂O₂ is detected by titration or chromatography methods. However, chromatography is costly, and titration is not sensitive enough [4]. Chemiluminescent, fluorometric and electrochemical methods are also quite popular; however, they require quite expensive equipment and may be time-consuming. Therefore, the development of a simple method for monitoring its levels in industrial and pharmacological products, as well as environmental samples, is important.

Iron is an essential bioactive metal element for the environment and living organisms. Both excess and deficiency can lead to serious health problems. The maximum permissible concentration of iron in drinking water is 0.3 ppm, while in groundwater it should range from 0.1 to 10 ppm [5,6]. Environmental pollution with iron can be caused by corrosion, industrial pollution, and other sources. Iron can be determined with atomic absorption spectrometry, optical emission spectrometry, mass spectrometry, voltammetry, chromatography, and fluorescence methods. However, these methods are complex to operate, expensive, require major sample preparation, and are time-consuming. Spectrophotometric methods are cheaper, easier to operate, and provide sufficient sensitivity. Many spectrophotometric methods for the determination of Fe(III) or Fe(II) were represented in the literature. However, only a few methods enable the simultaneous determination of both species. Therefore, the development of a new method for monitoring of Fe(III)/Fe(II) species in environmental and technical samples is relevant and necessary.

Novel procedures for the spectrophotometric determination of hydrogen peroxide and Fe(III)/Fe(II) species with the help of an optical immersion probe are represented in this work. Analytes were determined based on monitoring the decolorization process of polymethine dye 1,3,3-trimethyl-2-((1′E,3′E,5′E)-5’-(1″,3″,3″-trimethylindol-(2″E)-ylidene)-penta-1′,3′-dien-1′-yl)-3H-indol-1-ium (DTMI-5) with H₂O₂ and iron using an optical immersion probe. This dye was chosen for its unique spectrophotometric and proteolytic properties, primarily the very high color intensity of its cationic form, which is dominant over a wide range of acidities. Moreover, the presence of a conjugated system of double bonds makes this molecule sensitive enough to oxidants to be used as a sensor. Although the Fenton reaction is well known, according to our knowledge, it was not described in the literature for the DTMI-5. Therefore, the reaction mechanism was investigated in detail by interpreting the results obtained experimentally by the spectrophotometric method and with theoretical calculations.

2. Experimental

2.1. Computational Details

The geometrical parameters of all the considered structures were optimized using the M06-2X DFT functional [7] with the def2-SVP basis set [8,9]. Gibbs free energy corrections, radical Fukui function (RFF) [10], and average local ionization energy (ALIE) [11] isosurfaces were also computed at this level of theory. All optimized geometries were confirmed as true minima, with no imaginary frequencies detected in the corresponding Hessians. Total electronic energies were calculated using the larger def2-TZVPP basis set [8,9]. Absorption spectra were computed at the CIS(D)/def2-SVP level of theory [12]. Water solvation effects were incorporated into all calculations using the conductor-like polarizable continuum model (CPCM) [13]. To increase computational efficiency without sacrificing accuracy, the resolution-of-identity (RI) and chain-of-spheres (COSX) approximations were employed throughout the calculations [14]. All DFT calculations were performed with the ORCA 5.0.4 software package [15], while RFF and ALIE were computed using Multiwfn 3.8 [16]. Visualization was carried out using VMD 1.9.4 [17].

2.2. Reagents and Equipment

All reagents used were of analytical grade purity. A 0.2 mM stock solution of DTMI-5 (Sigma Aldrich, Bratislava, Slovakia) was prepared by dissolving 27 mg of dye in 10 mL of ethanol and filling up to the mark with distilled water in a 250 mL flask. Furthermore, 30% hydrogen peroxide was bought from mikroCHEM (mikroCHEM, Bratislava, Slovakia). In addition, 0.01 M Fe(II) stock solution was prepared by dissolving 98 mg of Mohr’s salt (Centralchem, Bratislava, Slovakia) in distilled water and filling up to the mark with distilled water in a 25 mL flask. Then, 0.01 M Fe(III) stock solution was prepared by dissolving 101 mg of Fe(NO₃)₃·9H₂O (Centralchem, Bratislava, Slovakia) in distilled water and filling up to the mark with distilled water in a 25 mL flask. Both solutions were stored in the fridge maximally for a week. Furthermore, 1 M HCl solution was prepared by dilution of the proper volume of concentrated hydrochloric acid (ITES, Vranov nad Topľou, Slovakia). Possible 0.1 M interferent solutions were prepared by dissolving appropriate amounts of substances (Centralchem, Bratislava, Slovakia) in distilled water in 25 mL volumetric flasks. The Kallos 6% flavored oxidizing emulsion and crystalline hydrangea fertilizer were purchased locally (Slovakia).

A 1 cm double-pass optical immersion probe (Expedeon, Cambridge, UK) connected to a USB 4000 fiber optic spectrometer (Ocean Optics, Orlando, FL, USA) and an LS-1 tungsten halogen light source (Ocean Optics) was applied for conducting kinetic spectrophotometric measurements. OceanView 1.6.7 (Lite) spectroscopy software (Ocean Optics) was used to record data. After measurements, the optical immersion probe was washed with ethanol and water. The RH digital heating model magnetic stirrer (IKA-Werke GmbH&Co. KG, Staufen im Breisgau, Germany) was applied to stir the reaction mixture.

2.3. Procedure for H₂O₂ Determination

A sample solution containing H₂O₂, 0.7 mL of 1 mM Fe(II), and 0.35 mL of 0.2 mM DTMI-5 was placed in a 25 mL beaker. An optical immersion probe was placed into the solution. The magnetic stirrer was set to 200 rpm. Measurements were started, and immediately after, 0.35 mL of 1 M HCl was added to initiate the reaction, which was continued for a maximum of 200 s. The total volume of the resulting solution was 10 mL. The analytical wavelength was set to 637 nm, and the analytical signal was calculated as the difference between the initial absorbance of the solution and the absorbance at a fixed time. All measurements were performed at room temperature (20–22 °C).

2.4. Procedure for Fe(III)/Fe(II) Determination in the Presence of Hydrogen Peroxide

A sample solution containing Fe(II) or Fe(III) species, 0.1 mL of 0.01 M H₂O₂, and 0.35 mL of 0.2 mM DTMI-5 was placed in a 25 mL beaker. The optical immersion probe was inserted into the solution, and the magnetic stirrer was set to 200 rpm. Measurements were initiated, and immediately after this, 0.35 mL of 1 M HCl was added to start the reaction, which continued for a maximum of 350 s. The total volume of the resulting solution was 10 mL. The analytical wavelength was set to 637 nm, and the analytical signal was determined as the difference between the initial absorbance of the solution and the absorbance at a fixed time.

2.5. Procedure for Fe(III) Determination

A sample solution containing Fe(III) species and 0.35 mL of 0.2 mM DTMI-5 was placed in a 25 mL beaker. The optical immersion probe was inserted into the solution, and the magnetic stirrer was set to 200 rpm. Measurements were started, and immediately after, 0.35 mL of 1 M HCl was added to initiate the reaction, which continued for a maximum of 350 s. The total volume of the resulting solution was 10 mL. The analytical wavelength was set to 637 nm, and the analytical signal was determined as a difference between the initial absorbance of the solution and the absorbance at a fixed time.

2.6. Joint Determination of Fe(II) and Fe(III) Species

Fe(III) in the presence of Fe(II) was determined using the procedure described in Section 2.5. Then, the signal of both species was measured as described in Section 2.3. The analytical signal corresponding to Fe(III) was calculated from measurements without hydrogen peroxide and subtracted from the total analytical signal of Fe(III) and Fe(II) to determine the concentration of Fe(II). Alternatively, Fe(III) species can be masked using 1 mM NaF. In this case, a calibration curve for Fe(II) determination should be prepared in the presence of 1 mM NaF.

2.7. Real Sample Analysis

Tap water was diluted twofold prior to analysis.

A 100 mg sample of 6% oxidation emulsion, obtained from a local market, was accurately weighed and dissolved in distilled water. The resulting solution was accurately transferred to a 100 mL volumetric flask and diluted to the mark with distilled water. An aliquot of this solution was analyzed following the procedure described above.

A 100 mg sample of fertilizer, obtained from a local market, was boiled for 2–3 min with a small amount of 20% HCl. During this step, Fe species were elaborated from the Fe-EDTA complex. The solution was cooled and transferred to a 100 mL volumetric flask, then diluted to the mark with distilled water. An aliquot of this solution was analyzed using the same procedure.

3. Results and Discussion

3.1. Computational Interpretation of the Sensing Mechanism

According to available crystallographic data on salts based on the DTMI-5 cation, all double bonds are in the “E-” (trans) configuration [18,19,20]. However, to the best of the authors’ knowledge, no structural studies on the DTMI-5 cation in aqueous solution have been conducted. Therefore, DFT calculations were performed to determine the most stable form of DTMI-5 in water. Figure 1 shows the structures of DTMI-5, DTMI-5-Z (1,3,3-trimethyl-2-((1′E,3′E,5′E)-5′-(1″,3″,3″-trimethylindol-(2″Z)-ylidene)-penta-1,3-dien-1′-yl)-3H-indol-1-ium), and DTMI-5-ZZ (1,3,3-trimethyl-2-((1′Z,3′E,5′E)-5′-(1″,3″,3″-trimethylindol-(2″Z)-ylidene)-penta-1,3-dien-1′-yl)-3H-indol-1-ium), optimized at the CPCM-M06-2X/def2-SVP level of theory, with total Gibbs free energy differences (∆G) calculated at the CPCM-M06-2X/def2-TZVPP level. The ∆G values indicate that the DTMI-5 structure is 1.58 and 2.64 kcal/mol more stable than the alternative DTMI-5-Z and DTMI-5-ZZ forms, respectively. Therefore, subsequent calculations focused on the “all-E-configuration” structure of DTMI-5. A general view of DTMI-5 structure and atoms’ numbering is presented in Figure S1.

The next step in analyzing the mechanism of DTMI-5’s interaction with oxidants was to identify the sites in the DTMI-5 molecule most susceptible to HO• and HOO• radicals, which are commonly considered the active species produced by the Fenton reagent. ALIE and RFF isosurfaces were used as 3D descriptors of reactivity, providing insight into the molecular sites most sensitive to radical attack (see Figure 2). Low ALIE values correspond to positions where electrons are less tightly bound, making them more vulnerable to free radical attack. Regions with low ALIE values are highlighted in blue, and the three methine groups (1′, 3′, 5′) of the penta-1′,3′-dien-1′-yl moiety were identified as the most sensitive to free radical attacks.

Similarly, the RFF isosurface highlights the penta-1′,3′-dien-1′-yl moiety, as well as the carbon and nitrogen atoms connected to the indolyl systems. However, while the RFF indicates the chain most affected by free radical attack, it does not specify which particular atom is more likely to interact with a radical. Therefore, RFF atom indices were calculated using Equation (1), where RFF_i represents the index of the i-th atom. In this equation, q is the atomic partial charge of the i-th atom in molecular states with an increased (N + 1) or decreased (N − 1) number of electrons.

$${RFF}_i={\displaystyle \frac{q_i^{N-1}-q_i^{N+1}}{2}}$$

(1)

Considering that various electron density partitioning schemes can lead to different partial charges and RFF indices [21,22,23,24], partial charges were calculated using the Löwdin [25], Hirshfeld [26,27], Mulliken [27], and CHELPG [28] approaches, with the corresponding RFF indices summarized in Table S1. Figure 2 shows the highest RFF indices calculated using Hirshfeld partial charges. These calculated indices support the findings of the ALIE analysis. Specifically, the methine groups at positions 1′, 3′, and 5′ of the penta-1′,3′-dien-1′-yl linker have the highest RFF indices, suggesting that these groups are the most likely centers for the initial attack by free radicals.

Based on the above calculations of DTMI-5 reactivity and previously published data on the oxidation of similar compounds [29,30,31], several mechanisms for DTMI-5 oxidation were considered. Figure 3 illustrates the oxidation of DTMI-5 to the dication-radical state (DCR) (Figure 3b) and further oxidation leading to the introduction of hydroxyl groups into the molecule, followed by subsequent transformations. The possible formation of peroxide-containing structures was not considered, as these forms are expected to be less stable in the presence of Fe²⁺/³⁺ ions [32]. However, oxidative hydroxylation of the double bonds in the penta-1′,3′-dien-1′-yl linker results in cationic structures A34-1 (Figure 3c) and A56-1 (Figure 3d). Subsequent tautomerization of the conjugated double-bond system, along with deprotonation, leads to the corresponding ketones A34-2 (Figure 3e) and A56-2 (Figure 3f). Due to the disruption of double-bond conjugation, the hydroxyl group can rotate, forming structures A34-3 (Figure 3g) and A56-3 (Figure 3h), which contain O–H•••O = C intermolecular hydrogen bonds between the alcohol and ketone groups. Finally, through keto-enol tautomerization, structures A34-4 (Figure 3i) and A56-3 (Figure 3j) can be formed. Their stability can be explained by the increase in the number of double bonds involved in conjugation.

Alternatively, the oxidation of cyanine dyes can lead to aldehyde formation via the breaking of one of the linker’s double bonds and the oxidation of methine groups into aldehydes [30]. The oxidation of the first, second, or third double bond in the penta-1′,3′-dien-1′-yl moiety results in the formation of aldehyde pairs AN4 + AC1, AN2 + AC3, and AN0 + AC5, respectively (see Figure 4). It is important to note that further oxidation of the aldehydes into corresponding acids may occur. However, this study only considers the formation of the zwitterionic structure ICZ (see Figure 4a). While the proposed oxidation products do not fully represent the complete oxidation pathway of DTMI-5, they can be used to estimate the oxidation potential of the selected processes and to explain the experimentally observed absorption peaks in the 340–360 nm region.

The next step in our study was to calculate the oxidation potentials (U⁰) for the reactions that lead to the proposed oxidation products and their UV-Vis absorption maxima. U⁰ was calculated using Equation (2) and corresponds to general proton-coupled reduction reactions of the form Ox + n_ee− + n_pH+ → Red + n_wH₂O, where n_e, n_p, and n_w represent the number of electrons, protons, and water molecules involved in the reaction, respectively. ∆G⁰_sol was calculated according to the reactions summarized in Table S2. The absolute potential of the standard hydrogen electrode (U_SHE) was set at +4.43 V [33,34], and ∆G⁰_sol(H⁺), the solvation Gibbs free energy of protons, was taken as –11.38 eV [34,35]. The resulting U⁰ values are summarized in

Table 1. Redox potentials (U⁰, in V) of the reactions that lead to the considered oxidation products and UV-VIS absorption maxima (λ_max, in nm) of these products. Entries with the best match between the calculated absorption maxima and the experimental band at approximately 340–360 nm are highlighted in bold.

Structure	U0, V	λmax, nm
A56-1	+1.098	304.0
A34-1	+1.186	302.1
A56-2	+1.236	270.1
A34-2	+1.327	286.4
A56-3	+1.157	270.6
A34-3	+1.313	282.0
A56-4	+1.359	281.0
A34-3	+1.651	318.3
DCR	+0.827	424.9
ICZ	+0.335	237.0
AN4	+0.722	358.1
AC1	+0.722	302.9
AN2	+0.641	295.8
AC3	+0.641	316.4
AN0	+0.444	242.9
AC5	+0.444	337.4

. Notably, the formation of hydroxylated forms A34-x and A56-x is associated with U⁰ values higher than +1.0 V, whereas the formation of DCR, aldehyde-type structures, and the ICZ zwitterion shows U⁰ values below +0.9 V.

$$U^0=-{\displaystyle \frac{{∆G}_{sol}^0}{n_e}}-U_{SHE}$$

(2)

The obtained U⁰ values do not allow us to definitively determine which forms are more likely, as all the forms, at least theoretically, can be produced due to the very strong oxidation potential of the Fenton reagent (~2.0–2.8 V) or Fe³⁺ ions (+0.771 V). For this reason, the absorption spectra of the proposed structures were also considered. Absorption spectra were calculated at the CPCM-CIS(D)/def2-SVP level of theory. Our previous studies on the similar carbocyanine dye Astra Phloxine demonstrated the excellent accuracy of the CIS(D) method [36], which is why the calculated spectra can be considered reliable. The theoretical absorption maxima are summarized in Table 1.

It is worth emphasizing that structure AN4, with calculated λ_max and U⁰ values of 358.1 nm and +0.722 V, respectively, has an absorption maximum closely matching the experimental broad peak observed at 340–360 nm. This is slightly different from the literature value of 410 nm, but the deviation can be attributed to solvent effects, as the experimental spectrum was recorded in DMSO [36]. Similarly, the absorption maximum of AC5 (λ_max = 337.4 nm, U⁰ = +0.444 V) aligns well with the experimental broad peak in the 340–360 nm range.

The accuracy of the UV-Vis calculations is noteworthy. For instance, the predicted absorption maximum of AN2 (λ_max = 295.8 nm) falls between the experimental data recorded in DMSO (λ_max = 338 nm) [37], methanol (λ_max ~260 nm) [38], and water (λ_max ~ 270 nm) [38]. Additionally, the calculated absorption maximum of AN0 (λ_max = 242.9 nm) is close to experimental values measured in ethanol (λ_max = 251 nm) [39] and water (λ_max = 250 nm) [40]. These results indicate that the oxidation of DTMI-5 likely proceeds through reaction pathways leading to the formation of carbonyl compound pairs AN4 + AC1, AN2 + AC3, and AN0 + AC5. The possibility of the formation of the AN2 + AC3 pair is supported by its midpoint U⁰ value of +0.641 V. Additionally, none of the proposed oxidation products interfere with the primary signal of DTMI-5, as the absorption maxima of all structures are significantly blue-shifted. These findings are in line with the previously published work by Zhang et al. [30], where the authors proposed the structures for the photodegradation products of a similar cyanine dye based on the electrospray ionization mass spectrometry.

The UV-Vis absorption maxima of DTMI-5, AN4, and AC5 are attributed to π-π electron transitions within their conjugated π-bond systems. The first excited states of these structures are predominantly composed of HOMO → LUMO transitions. The isosurfaces of the HOMO and LUMO for these structures are presented in Figure S2.

3.2. Optimization of Reaction Conditions

The effect of DTMI-5 concentration was studied in the range from 1 to 7 µM. With the increase of DTMI-5 concentration, the analytical signal also raises, and at the same time, the reaction speed also slightly decreases. At concentrations higher than 7 µM, absorbance could not be measured correctly due to the very high value. Furthermore, 7 µM DTMI-5 concentration was chosen as an optimal one.

DTMI-5 reacts with hydrogen peroxide in the presence of Fe(II) or Fe(III) in an acidic medium. However, the dye itself can undergo transformations when the acidity of the medium changes, which is associated with its protolytic properties. For DTMI-5, the pK value is 0.762. This means that the intensely colored cationic form of the dye (ε₆₃₇ = 202,700) dominates at pH above 1.50. In a more acidic environment (pH less than 0.5), the already protonated colorless form of the dye prevails, which is characterized by significantly lower light absorption coefficient values (ε₄₈₅ = 22,200) [41]. Therefore, spectrophotometric determination using DTMI-5 is only possible in a slightly acidic environment, at pH 1.5 or higher. The effect of an acidic medium was studied in the range of HCl concentration from 0.005 to 0.05 M. After 0.03 M HCl concentration, the analytical signal stopped growing, and the time of the reaction end did not change. The same results were obtained for Fe(III) determination without hydrogen peroxide. Furthermore, 0.035 M HCl was used for further experiments.

The influence of stirring speed on absorbance was studied in the range from 0 to 400 rpm. It was found that after 150 rpm, the analytical signal stops to grow, and the time of the reaction end does not change. Therefore, 200 rpm stirring speed was chosen for further experiments to ensure passing the minimum threshold.

Optimization of Fe(II) concentration for hydrogen peroxide determination. The effect of Fe(II) concentration was studied from 10 to 100 µM. At concentrations higher than 70 µM Fe(II), the analytical signal stopped increasing, and the time of the reaction end did not change. Therefore, 70 µM Fe(II) concentration was applied for further experiments.

Optimization of H₂O₂ concentration for Fe(III)/Fe(II) determination. The effect of hydrogen peroxide concentration was studied in the range from 10 to 150 µM. At concentrations higher than 100 µM H₂O₂, the analytical signal stopped increasing, and the time of the reaction end did not change. Furthermore, 100 µM H₂O₂ concentration was applied for further experiments.

3.3. Interference Study

Some metal cations that could affect the speed of the DTMI-5 reaction with H₂O₂ and oxidants could serve as the main interferents. The interfering effect was considered absent if the change in the analytical signal did not exceed 5% compared to the difference between the solution’s absorbance in the presence of and without the analyte.

Ba²⁺, Mg²⁺, Zn²⁺, Pb²⁺, Co²⁺, Cu²⁺, Cd²⁺, Ca²⁺, Mn²⁺, Na⁺, K⁺, NO₃⁻, SO₄²⁻, Cl⁻, fructose, and saccharose do not interfere at concentrations not exceeding 10 mM in the case of determination of all three species. Al³⁺ does not interfere at concentrations not exceeding 3 mM. Tolerant concentration for Sr²⁺ and Ni²⁺ is 1 mM. Ag⁺ and Cr³⁺ do not interfere at 50 µM. Cr₂O₇²⁻-tolerant concentration is 10 µM.

Fe(III) does not interfere with Fe(II) determination at a concentration of 0.5 µM. Applying 10⁻³ M NaF as a masking agent increases tolerant concentrations up to 10 µM. However, it should be mentioned that in the case of using the masking agent, the calibration curve for Fe(II) detection should be built considering the influence of NaF. Fe(II) also partially reacts with NaF, which leads to a change in the calibration curve. In the case of Fe(III) determination (as described in Section 2.5), Fe(II) does not interfere up to 50 µM.

3.4. Analytical Parameters

The time of the complete finishing of the Fenton reaction depends on the concentrations of added hydrogen peroxide and Fe(II) or Fe(III). Kinetic curves of the Fenton reaction under different concentrations of hydrogen peroxide and Fe(II) or Fe(III) are shown in Figure 5. Both absorbance at a fixed time and time of the reaction end could be used as analytical signals. The LOD and LOQ values were calculated as the concentration equivalent to three times and ten times the ratio of the standard error of the regression to the slope of the calibration curve, respectively.

The concentration range for hydrogen peroxide determination was from 40 to 980 µM. The dependence of H₂O₂ concentration on the time of the reaction end had equation t(s) = 0.1145·C(M)^−0.686 with r² = 0.9972. After linearization, this dependence had a regression equation t(s) = 0.004·C(M)⁻¹ + 16.134 with r² = 0.9826. At 980 µM H₂O₂ concentration and higher, the Fenton reaction finishes 13 s after the measurements start. This time was chosen as a fixed time for absorbance measurements as an analytical signal. The dependence of absorbance at 13 s from hydrogen peroxide concentration also was not linear. After linearization, the regression equation is A = 0.4024·lnC(M) + 4.1986, with r² = 0.9631. The linear part of the initial dependence was up to 250 µM and characterized with a regression equation A = 3113.6·C(M) + 0.0338 with r² = 0.9980. It was used for LOD and LOQ calculations. LOD and LOQ were 12.3 and 40.9 µM, respectively. RSD values calculated for different concentrations ranged from 2.11 to 4.58%.

The concentration range for Fe(II) determination was from 3 to 70 µM. The dependence of Fe(II) concentration on the time of the reaction end had the equation t(s) = 0.0013·C(M)^−0.961 with r² = 0.9965. After linearization, this dependence had a regression equation t(s) = 0.0008·C(M)⁻¹ + 5.462 with r² = 0.9953. At 70 µM Fe(II) concentration and higher, the Fenton reaction finishes 13 s after the start of measurements. This time was chosen as a fixed time for absorbance measurements as an analytical signal. The dependence of absorbance at 13 s from Fe(II) concentration also was not linear. After linearization, it had regression equation A = 0.4171·lnC(M) + 5.3357 with r² = 0.946. The linear part of the initial dependence was up to 10 µM. A = 46667·C(M) with r² = 0.9988. It was used for LOD and LOQ calculations. LOD and LOQ were 0.88 and 2.95 µM, respectively. RSD values calculated for different concentrations were from 6.48 to 7.4%.

The concentration range for Fe(III) determination was from 1.32 to 45 µM. The relationship between Fe(III) concentration and the time of the reaction end was described by the equation t(s) = 0.0116·C(M)^−0.789 with r² = 0.9989. After linearization, the equation became t(s) = 0.0008·C(M)⁻¹ + 15.094 with r² = 0.9948. At Fe(III) concentrations of 45 µM and higher, the Fenton reaction was completed 25 s after the start of the measurements. This time, along with 13 s, was chosen as fixed times for absorbance measurements, which served as the analytical signal. For both time points, the dependence of absorbance upon Fe(III) concentration was not linear. After linearization, the regression equation for 25 s was A = 0.3767·lnC(M)+5.1863 with r² = 0.9897. The linear part of the absorbance vs. Fe(III) concentration dependence for 25 s was valid up to 6 µM, with the regression equation A = 111714·C(M) and r² = 0.9971. For the 13 s fixed time, the equation was A = 63365·C(M). The LOD and LOQ for 25 s were 0.39 and 1.32 µM, respectively. The RSD values calculated for different concentrations ranged from 1.76 to 5.12%.

In contrast to the Fenton reaction, the reaction of DTMI-5 with Fe(III) in the absence of H₂O₂ does not lead to complete oxidation of DTMI-5 at any concentrations of Fe(III). Although the reaction time varies with different concentrations of Fe(III), the difference in absorbance between the start and the completion of the reaction was chosen as the analytical signal (Figure 6). The linear concentration range for Fe(III) determination was from 0.5 to 6 µM, with a calibration curve given by A = 135930·C(M) and r² = 0.9996. The LOD and LOQ were 0.16 and 5.27 µM, respectively. The RSD values calculated for different concentrations ranged from 1.36 to 6.37%.

The environmental friendliness of the proposed method for Fe(III)/Fe(II) and H₂O₂ determination was evaluated with the Analytical GREEnness (AGREE) metric (Figure S3) [42]. The obtained score (0.68) demonstrates the high level of greenness of the proposed procedure. It has a low level of energy consumption, does not require any extraction or the use of toxic compounds, involves minimal sample preparation and a reduced number of operations, and is also semi-automatic. However, the method requires a relatively large volume of samples.

3.5. Analysis of Real Samples

The procedure for hydrogen peroxide determination was tested on Kallos 6% perfumed oxidation emulsion, and the results are presented in

Table 2. Determination of hydrogen peroxide in Kallos 6% perfumed oxidation emulsion. P = 0.95, n = 5.

Added H2O2, %	Found H2O2, %	Recovery, %
–	5.92 ± 1.15	–
9.07	15.9 ± 0.9	110.0
17.3	24.3 ± 2.5	106.4

. The manufacturer claims that the emulsion contains 6% H₂O₂. However, the proposed procedure found 5.92% H₂O_2. The addition of standards to the sample also showed good recoveries (106.4% and 110.0%).

Model solutions and real samples (tap water and fertilizer) were chosen to test procedures for the joint determination of Fe(II) and Fe(III) species (

Table 3. Determination of Fe(III)/Fe(II) in real and model samples. p = 0.95, n = 5.

Sample	Added Fe(II), µM	Added Fe(III), µM	Found Fe(II), µM	Recovery, %	Found Fe(III), µM	Recovery, %
Model solution 1	–	–	5.11 ± 1.18	102.2	2.43 ± 0.32	101.2
Model solution 2	–	–	16.8 ± 2.9	112.0	14.8 ± 0.7	98.7
Model solution 3	–	–	14.4 ± 2.7	96.0	5.89 ± 0.55	103.3
Tap water	–	–	˂LOD	–	0.592 ± 0.144	–
	–	3.22	˂LOD	–	3.93 ± 0.38	103.5
	8.91	–	9.46 ± 0.58	106.2	0.576 ± 0.097	–
Fertilizer 4	–	–	0.024 ± 0.003%	–	0.017 ± 0.001%	–
	–	0.028%	–	–	0.049 ± 0.002%	112.8
	0.032%	–	0.055 ± 0.007	96.9	0.018 ± 0.001%	–

¹ Model solution: 2.4 µM Fe(III), 5.0 µM Fe(II). Fe(II) was determined by masking Fe(III) with 1 mM NaF. ² Model solution: 15 µM Fe(III), 15 µM Fe(II). Fe(II) was determined by masking Fe(III) with 1 mM NaF. ³ Model solution: 5.7 µM Fe(III), 15 µM Fe(II). ⁴ The crystalline fertilizer contains 0.029% Fe in the form of EDTA chelate.

). Fe species in fertilizer were in the form of chelate, which required additional sample pretreatment to liberate the iron. Satisfactory recoveries, ranging from 96.0% to 112.8%, were obtained for all samples.

3.6. Comparison with Methods Proposed in the Literature

In recent years, many simple spectrophotometric methods have been proposed for the determination of H₂O₂, Fe(II), or Fe(III). Some of them are listed in

Table 4. Comparison of proposed methods with the spectrophotometry and colorimetry methods proposed in the literature.

Reagent	Sample	LOD, µM	Determination Range, µM	Ref.
H2O2
carbon silver nano-assembly	-	0.009	0.1–100	[43]
N,N-diethyl-p-phenylenediamine, Fe(II)	water	0.05	0–12	[44]
2,2′-azino-bis(3-ethylbenzothiazoline-6 sulfonate, Fe(II)	water	0.1	0–40	[45]
PtS2 nanosheets, 3,3′,5,5′-tetramethylbenzidine	-	0.33	1–100	[46]
peroxo-Fe(III)-EDTA complex	water	2.5	8.3–4080	[47]
DTMI-5, Fe(II)	oxidation emulsion	12.3	40–980	This work
Fe(II)
plasmonic Ag nanocomposite based on locust bean gum and Phyllanthus reticulatus anthocyanin	juice, ferrous fumarate, water	0.38	0.1–100	[5]
sulfur quantum dots	milk, honey, water	0.54	1.25–500	[48]
pomegranate peel extract	water	140 µg/L	1000–10,000 µg/L	[49]
DTMI-5, H2O2	water, fertilizer	0.88	3–70	This work
Fe(III)
nitroso R salt, NaI, cetyl trimethyl ammonium chloride	water, CRM, electrolyte, purification liquid	0.045 (total iron)	0.15–64	[50]
1-nitroso-2-naphthol-3,6-disulphonic acid disodium salt, hexadecyl trimethyl ammonium bromide	water	0.067	0.2–95	[51]
N-carbon dots	water	0.28	1–21	[52]
KSCN	bioethanol fuel	6.18 mg/L	0.5–10 mg/L	[53]
pomegranate peel extract	water	530 µg/L	1000–12,000 µg/L	[49]
tea extract	iron supplement samples	2000 µg/L	˂40,000 µg/L	[54]
DTMI-5	water, fertilizer	0.16	0.5–6	This work
DTMI-5, H2O2	water, fertilizer	0.39	1.32–45	This work

. The number of methods devoted to Fe(III) determination is significantly greater than those for Fe(II) determination. However, there have been only a few methods dedicated to the joint determination of both Fe(III) and Fe(II) species. It should also be noted that many fluorometric methods for the determination of H₂O₂, Fe(II), or Fe(III) have been proposed in recent years, including the use of quantum dots. These methods are usually very sensitive but are much more complex than the proposed method, requiring sophisticated and rarely used equipment in routine laboratory practice.

This article proposes a procedure for the joint determination of Fe(III)/Fe(II) species and H₂O₂. The application of an optical probe for measuring kinetic curves enables fast, reproducible measurements. The interval between recorded spectra was less than one second and could be further reduced for faster reactions. It also allows measurements to be taken from the very beginning of the reaction. The sensitivity of the proposed methods is sufficiently high to enable the analysis of many samples.

4. Conclusions

The Fenton reaction of DTMI-5 with hydrogen peroxide in the presence of iron is first proposed for the determination of H₂O₂ and Fe(III)/Fe(II) species.

The theoretical calculations of the reactive sites in the DTMI-5 molecule under free radical attack indicate that the methine groups of the penta-1′,3′-dien-1′-yl linker are the predominant reactive centers under oxidation conditions. The DFT-calculated redox potentials of the considered structures range from 0.34 to 1.65 eV, suggesting that all of them can form under the action of the Fenton reagent, a powerful oxidant. Among the proposed aldehyde-type products, the AN4 and AC5 structures are characterized by CIS(D)-calculated absorption maxima of 358.1 and 337.4 nm, respectively, which perfectly match the experimentally observed broad peak at 340–360 nm. The observed UV-Vis absorption maxima of the primary sensor (DTMI-5) and its oxidized forms (AN4 and AC5) result from π-π electron transitions in their conjugated π-bond systems.

The use of the optical immersion probe for spectrophotometric measurements allows for precise kinetic curve generation, eliminating the need to transfer the sample to a cuvette. It also enables proper stirring of the solution while measuring. Optical probes have great potential for application to other reaction systems, both with and without extraction applications. The proposed method is fast, easy to apply, does not require expensive equipment, and is environmentally friendly. LODs for H₂O₂, Fe(II), and Fe(III) determination were 12.3, 0.88, and 0.16 µM, respectively. The developed procedures were applied to the determination of hydrogen peroxide in oxidation emulsion and Fe(III)/Fe(II) species in model and real samples (tap water and fertilizer). The reaction system could also be further considered as a way of cleaning water from hydrogen peroxide.