A Conceptual Model for Depicting the Relationships between Toluene Degradation and Fe(III) Reduction with Different Fe(III) Phases as Terminal Electron Acceptors

Abstract

Iron reduction is one of the most crucial biogeochemical processes in groundwater for organic contaminants biodegradation, especially in the iron-rich aquifers. Previous research has posited that the reduction of iron and the biodegradation of organic substances occur synchronously, with their processes adhering to specific quantitative relationships. However, discrepancies between the observed values of iron reduction and organic compound degradation during the reaction and their theoretical counterparts have been noted. To find out the relationship between organic substance biodegradation and iron reduction, this study conducted batch experiments utilizing toluene as a typical organic compound and electron donor, with various iron minerals serving as electron acceptors. Results indicate that toluene degradation follows first-order kinetic equations with different degradation rate constants under different iron minerals, but the generation of the iron reduction product Fe(II) was not uniform. Based on these dynamic relationships, a conceptual model was developed, which categorizes the reactions into two phases: the transformation of toluene to an intermediate-state dominated phase and the mineralization of the intermediate-state dominated phase. This model revealed the relationships between toluene oxidation and Fe(II) formation in the toluene biodegradation through iron reduction. The coupling mechanism of toluene degradation and iron reduction was revealed, which is expected to improve our ability to accurately assess the attenuation of organic contaminants in groundwater.

1. Introduction

Organic contaminants, particularly benzene compounds, are widespread in the groundwater of sites contaminated with substances such as petroleum, posing significant adverse effects on both the environment and the economy [1,2,3,4,5,6]. Due to the prevalent anaerobic conditions in the groundwater of polluted sites [7,8], anaerobic biodegradation has become a crucial approach for addressing organic pollution in site remediation. Organic contaminants undergo biological degradation through processes such as nitrate reduction, iron reduction, manganese reduction, sulfate reduction, and methane production [9,10,11].

Iron, as one of the most abundant elements in the Earth’s crust, constitutes approximately 6% of its surface. It is one of the most abundant electron acceptors, and the dissimilatory iron reduction process stands out as a primary mechanism in anaerobic biodegradation [12]. Research on the iron reduction of organic compounds, especially aromatic hydrocarbons, is particularly crucial [13].

Over the past three decades, researchers have extensively studied dissimilatory iron-reducing bacteria and the reduction of iron-containing minerals. These minerals, including ferrihydrite, goethite, amorphous iron minerals, magnetite, iron-bearing clay minerals, jarosite, and schwertmannite, among others [14,15,16,17,18,19,20,21], serve as electron acceptors in dissimilatory iron reduction reactions, while certain compounds serve as electron donors in these reactions.

CH₃COOH + 8Fe³⁺ + 4H₂O→8Fe²⁺ + 2HCO₃− + 10H⁺ ΔH = 651.98 kJ/mol

(1)

C₆H₆ + 30Fe³⁺ + 18H₂O→30Fe²⁺ + 6HCO₃− + 36H⁺ ΔH = −475.92 kJ/mol

(2)

C₇H₈ + 36Fe³⁺ + 21H₂O→36Fe²⁺ + 7HCO₃⁻ + 43H⁺ ΔH = −550.39 kJ/mol

(3)

C₆H₅OH + 28Fe³⁺ + 17H₂O→28Fe²⁺ + 6HCO₃⁻ + 34H⁺ ΔH = −468.99 kJ/mol

(4)

C₈H₁₀ + 42Fe³⁺ + 24H₂O→42Fe²⁺ + 8HCO₃⁻ + 50H⁺ ΔH = −637.7 kJ/mol

(5)

In actual pure cultivation experiments, iron-reducing bacteria utilize trivalent iron compounds as electron acceptors for the biological degradation of compounds such as acetate, benzene, toluene, phenol, ethylbenzene, and xylene isomers [22,23]. In these reactions, the electron donor–substrate and the electron acceptor–trivalent iron react in a specific ratio. However, the actual ratio often deviates from the theoretical ratio.

Taking the extensively studied organic pollutant, toluene, as an example, the theoretical molar ratio of toluene oxidation to the generated reduced iron in the reaction is 1/36. However, previous studies [24,25,26,27] have found that the ratio of these two components often exceeds the theoretical value of 1/36. The following two perspectives explain this phenomenon: firstly, it is suggested that some organic carbon may be bound to bacterial cells, ultimately promoting biomass growth [28]. On the other hand, it is possible that toluene has undergone partial loss over time. Whether it is due to the loss of synthesized biomass or the adsorption and volatilization loss of toluene over time, these processes are functions of time. However, as of now, no coupled analysis has been conducted regarding the temporal evolution between toluene oxidation and iron reduction.

In order to delve into the stoichiometric relationship of the microbial degradation reaction of toluene with iron under pure cultivation conditions, we designed and conducted an experiment. Four prevalent and extensively studied iron oxides commonly found in geological formations—amorphous iron hydroxide, hematite, magnetite, and goethite—were selected as electron acceptors. Toluene served as the electron donor in this experiment. Based on the above study, a dynamic model for characterizing the relationships between toluene oxidation and Fe(II) formation in toluene biodegradation through iron reduction was developed.

Understanding the coupling mechanism between toluene degradation and ferrous reduction is crucial for accurately quantifying the degradation of pollutants such as toluene, offering new insights and directions. If the degradation amount is underestimated according to the production of iron, the pollution source leakage estimate will be insufficient, and the assessment will be misleading, resulting in insufficient risk understanding.

2. Materials and Methods

2.1. Preparation of Fe(III) Oxide

Amorphous iron hydroxide was synthesized through gradually neutralizing a solution containing 0.4 mol/L FeCl₃ with 10 mol/L NaOH until the pH reached 7.0. The metal oxide suspensions underwent three centrifugation and washing cycles before being resuspended in distilled water. Subsequently, the metal oxides were suspended in a basal medium [29]. This process resulted in the formation of brick-red mineral particles with no apparent crystal structure and an amorphous morphology, characterized by a high surface area.

Hematite and magnetite were procured from Guoming Mineral Resources. In order to closely mimic natural conditions, naturally occurring ores were carefully selected. To achieve the highest surface area, the minerals were ground to particles of 350 mesh size. The chosen hematite was a reddish-brown powder with a primary composition of Fe₂O₃, while magnetite was pure black with a primary composition of Fe₃O₄.

Goethite was prepared by dissolving unhydrolyzed Fe(NO₃)₃·9H₂O in distilled water to create a fresh 1 mol/L Fe(NO₃)₃ solution. Taking 100 mL of the 1 mol/L Fe(NO₃)₃ solution in a 2 L polyethylene bottle, 180 mL of the 5 mol/L KOH solution was rapidly added via stirring, resulting in the formation of brownish-red hydrated iron ore precipitation. The suspension was promptly diluted to 2 L with distilled water and incubated at 70 °C for 60 h in a sealed polyethylene bottle [30]. This process yielded fibrous and needle-like crystals of yellow mineral powder.

2.2. Inoculum Source

The site is located in a petroleum and chemical industrial area in Northwest China, near the gas condensate storage tanks at a purification plant. The water table depth ranges from 3.2 to 4.7 m below the ground surface. The vadose and saturated zones are primarily composed of fine sands. Groundwater flows generally from north to south. Due to gas condensate releases from the storage tanks and groundwater flow, contaminants spread nearly across the site. These contaminants are largely light-end petroleum hydrocarbons, such as benzenes and other small volatile hydrocarbons (C6–C9).

In areas where the benzene and iron content jointly exceed contamination standards, soil samples were taken for bacterial inoculation. Under anaerobic conditions, 100 g of soil was concentrated in a 600 mL glass bottle with a medium containing 250 mg NH₄Cl per liter, 600 mg NaH₂PO4, 100 mg KCl, 0.1 mmol toluene, 3.6 mmol amorphous ferric hydroxide, 10 mL mineral solution, and 10 mL vitamin solution [31]. The contents of trace elements and vitamin solutions are listed in

Table 1. The components of the vitamin solution.

Components	Concentration (mg/L)
Biotin	2.0
Folic acid	2.0
Pyridoxine HCL	10.0
Riboflavin	5.0
Thiamine	5.0
Nicotinic acid	5.0
Pantothenic acid	5.0
B-12	0.1
p-Aminobenzoic acid	5.0
Thioctic acid	5.0

and

Table 2. The components of the mineral solution.

Components	Concentration (g/L)
Trisodium nitrilotriacetic acid	1.5
MgSO4.	3
MnSO4·H2O	0.5
NaCl	1
FeSO4·7H2O	0.1
CaCl2·2H2O	0.1
CoCl2·6H2O	0.1
ZnCl2	0.13
CuSO4·5H2O	0.01
AIK(SO4)2·12H2O	0.01
H3BO3	0.01
Na2MoO4	0.025
NiCl2·6H2O	0.024
Na2WO4·2H2O	0.025

. After 20 days of dark incubation at 25 °C, 60 mL of the culture medium was transferred to a new sterile bottle with 500 mL of fresh medium. This process was repeated 10 times over 200 days, enriching the bacterial strains with iron-reducing capabilities.

2.3. Anaerobic Incubation with Different Iron Oxides

The experiments followed the same procedure as the enrichment process, using the same medium but replacing the amorphous ferric hydroxide with four different types of iron minerals, as shown in Figure 1. Negative control groups were constructed in the same manner, with the bacterial solution being replaced by purified water. Each type of iron mineral had three parallel experimental groups and three parallel control groups. On days 1, 3, 5, 7, 12, 18, 22, 28, 32, and 40, water samples were collected from each microcosm for analysis. The concentrations of toluene, total ferrous, and total iron in the solution were measured. The sampling process was conducted under strict anaerobic conditions.

2.4. Analytical Method

Toluene Analysis Method: Toluene samples were analyzed using headspace-based gas chromatography (Nexis GC-2030, Shimadzu, Kyoto, Japan) with an automated headspace sampler (HS-10, Shimadzu, Kyoto, Japan). The headspace operating conditions were as follows: low shaking of the tested sample solution at 35 °C for 2 min, a GC cycle time of 25 min, and a vial pressurization time of 0.1 min. The gas chromatograph was equipped with a capillary column (HP-5, Shimadzu, Kyoto, Japan) and a flame ionization detector (FID). The injector, detector, and column temperatures were held at 150, 200, and 100 °C, respectively. Air and hydrogen served as fuel gases for the FID. Nitrogen served as a carrier gas, and the flow rate was 40.1 mL/min.

Ferrous Iron Analysis Method: The ortho-phenanthroline colorimetric method is utilized [32]. Before conducting the ferrous iron test, a uniformly mixed culture suspension of 0.5 milliliters is injected into 4.3 milliliters of 0.5 mol/L hydrochloric acid and subjected to extraction at 30 °C for 24 h. Subsequently, 2.4 milliliters of the extraction solution are taken, and 0.32 milliliters of 6 mol/L hydrochloric acid, 0.32 milliliters of 2 mmol/L ammonium fluoride, 0.32 milliliters of 1% o-phenanthroline, 0.48 milliliters of ammonium acetate buffer, and 0.16 milliliters of distilled water are added. The absorbance of the solution is measured at 510 nm using a UV spectrophotometer (UV2550). Then, the total dissolved ferrous iron concentration is calculated according to the standard curve formula, $c\left({Fe}^{2+}\right)=c\times n$, where $c$ represents the ferrous iron concentration in the water sample as measured by the spectrophotometer in mg/L, and $n$ is the dilution factor. As the dissolution of iron minerals gradually decreases during the reaction, the experiment employs the method of multiplying the proportion of dissolved ferrous iron values to total iron by the amount of total iron minerals added in order to determine the total ferrous iron generated during the reaction.

2.5. Data Statistical Processing

The toluene and ferrous iron concentration data were presented as mean ± S.D. Duncan’s multiple range test, conducted using SPSS Statistics 22.0, was employed to assess the differences among the three systems, with a significance level set at p = 0.05.

To investigate the degradation kinetics of toluene in various systems with different iron oxides as electron acceptors, we assumed first-order kinetics for the reactions. To determine the degradation rate constants, we conducted a series of experiments where the concentration of toluene was monitored over time. The concentration data were then processed through calculating the natural logarithm of the ratio of the remaining concentration at time t (C_t) to the initial concentration (C₀). This relationship is represented as ln(C_t/C₀).

Subsequently, we plotted ln(C_t/C₀) against time (t) for each system. According to the first-order reaction kinetics equation, ln(C_t/C₀) = −kt., where k is the degradation rate constant. The slope of each line corresponds to the negative of the first-order degradation rate constant (k). Through determining these slopes, we were able to calculate the degradation rate constants for toluene in each system with different iron oxides.

The mean absolute percentage error (MAPE) is a metric used for assessing the accuracy of a predictive model. The calculation process is as follows:

For each observed value $y_i$ and its corresponding predicted value $\widehat{y_i}$, calculate the absolute percentage error (APE):

$${\mathrm{A}\mathrm{P}\mathrm{E}}_I=\left|\frac{y_i-\widehat{y_i}}{y_i}\right|\times 100$$

(6)

Compute the average of all APEs, resulting in the mean absolute percentage error (MAPE):

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\frac{1}{n}{\sum }_{i=1}^n{\mathrm{A}\mathrm{P}\mathrm{E}}_I$$

(7)

Here, $n=3,$ represents the number of observed values.

3. Results

3.1. The Relationship of Toluene over Time under Different Iron Mineral Conditions

Toluene degradation follows first-order kinetics, and the corresponding first-order reaction kinetics equations for toluene under four different electron acceptors are shown in

Table 3. Four Fe(III) oxides and their kinetic equations and parameters for toluene degradation.

Group	First-Order Kinetic Equation	R2	Reaction Rate Constant
Amorphous iron hydroxide group	CAT = C0e−0.128t	0.98	0.128
Hematite group	CHT = C0e−0.027t	0.97	0.027
Magnetite group	CMT = C0e−0.025t	0.99	0.025
Goethite group	CGT = C0e−0.073t	0.99	0.073

. The reaction rate constant graphs for the microbial treatment and sterile control groups in various electron acceptor systems are shown in Figure 2.

3.2. The Relationship of Ferrous Products over Time under Different Iron Mineral Conditions

In the case of the four electron acceptors, assuming that all electrons from toluene mineralization are used to reduce Fe(III), iron is finally recovered in the form of Fe(II). The theoretical formula for the real-time concentration of Fe(II) is obtained through converting the fitted toluene degradation kinetics formula. According to reaction Equation (3), The theoretical formula for the Fe(II) concentration is obtained using C_Fe(II) = 36C₀(1 − e^−kt), where k is the degradation rate constant of toluene. The theoretical and actual Fe(II) concentration graphs in the four different electron acceptors are shown in Figure 3.

To elucidate the relationship between theoretical predictions and experimental observations of ferrous iron (Fe(II)) generation from toluene oxidation, and to verify the accuracy and reliability of theoretical models in predicting Fe(II) generation under different conditions, we performed MAPE (mean absolute percentage error) analysis for different groups. The MAPE for four different iron oxides (amorphous iron hydroxide, hematite group, magnetite group, goethite group) are 2864%, 457%, 510%, and 381%, respectively.

3.3. The Relationship between Toluene and Ferrous Products under Different Iron Mineral Conditions

In order to investigate the proportional relationship between the consumption of toluene and the generation of ferrous iron during the reaction process, we measured the toluene consumption (vertical axis) and ferrous iron generation (horizontal axis) at specific time points (3rd, 5th, 7th, 12th, 18th, 22nd, 28th, and 40th days) in the biodegradation of toluene. These findings are visually depicted in the two-dimensional graph shown in Figure 4.

According to the graph, the vertical axis, from bottom to top, represents the increasing amount of toluene consumption, while the horizontal axis, from left to right, represents the gradually increasing ferrous iron production, reflecting the progression of the reaction over time.

Hematite group: At the beginning of the reaction, the toluene consumption increases slowly from 0 mmol/L, and the ferrous iron production also starts at 0 mmol/L and increases gradually. If the initial toluene consumption and ferrous iron production follow the theoretical ratio of 1/36, the curve would tend toward the direction of the theoretical curve. However, as observed in the graph, from the first point to the second point, the curve deviates from the theoretical curve toward the Y-axis, indicating higher toluene consumption and relatively insufficient ferrous iron production. From the first point to the sixth point, the slope of the curve decreases, gradually approaching the slope of the theoretical curve, indicating a gradual reduction in toluene consumption and a relative increase in ferrous iron production from 0 to 22 days, reaching a stage where toluene and iron approach the theoretical 1/36 ratio. From the sixth point to the seventh point, a temporary equilibrium is reached, indicating that at some point between 22 and 28 days, toluene consumption and iron production are in a theoretical 1/36 ratio. From the seventh point to the eighth point, the slope of the curve is less than the slope of the theoretical curve, indicating that from 28 to 40 days, the ratio of toluene to iron is less than the theoretical 1/36 ratio. Similar analyses were conducted for the fitting relationship between toluene consumption and ferrous iron production in the hematite, magnetite, and goethite groups, as shown in

Table 4. Phases of the coupled relationship between toluene consumption and ferrous iron reduction for four Fe(III) oxides.

Group	Time Periods with Slopes Greater than 1/36	Time Periods with Slopes Approximately Equal to 1/36	Time Periods with Slopes Less than 1/36
Amorphous iron hydroxide Group	0–22	22–28	28–40
Hematite Group	0–12	12–28	28–40
Magnetite Group	0–22	22–28	28–40
Goethite Needle Group	0–18	18–22	22–40

.

4. Discussion

4.1. Toluene Degradation under Different Iron Mineral Conditions

Under anaerobic conditions mediated by dissimilatory iron-reducing microorganisms, the degradation reaction between toluene and various iron minerals undergoes a series of slow and sequential steps. Initially, toluene enters the microbial cells from the aqueous solution, followed by a series of intracellular reactions leading to gradual degradation within the microbial cells. Ultimately, electrons are transferred from the microbial cells to the iron minerals attached to the dissimilatory iron-reducing microorganisms. Throughout this process, Fe(III) in the iron minerals undergoes reduction [33].

The degradation of toluene follows first-order kinetics, consistent with previous studies by researchers [34,35]. During the preliminary degradation of toluene under four types of iron minerals, the first-order kinetic reaction rate constants are, respectively, as follows: amorphous iron hydroxide group, 0.128 d⁻¹; hematite group, 0.027 d⁻¹; magnetite group, 0.025 d⁻¹; and goethite group, 0.073 d⁻¹. The reaction rate constant depends on the temperature, activation energy, and concentration, and the activation energy depends on the structure (mineral type) and its interaction with the toluene, in this case. In the experiment, amorphous iron hydroxide appears as aggregates of amorphous irregularly shaped particles, while hematite exhibits long needle-like crystals. Hematite primarily exists as granular crystals, and magnetite exists in the form of inverse spinel. Amorphous iron hydroxide with a lower crystallinity and a slightly higher crystallinity of hematite demonstrate higher reaction rate constants. In contrast, hematite with a higher crystallinity exhibits lower reaction rate constants. We observed that the crystallinity of iron minerals affects their interaction with reactants such as toluene. This confirms the existence of a certain relationship between the crystallinity and reaction rate constants, although this relationship may be influenced by various factors [36].

Crystals with a higher crystallinity often have a more complete and compact crystal structure, resulting in a smaller surface area and lower exposure of active sites. In contrast, crystals with a lower crystallinity may have more grain boundaries and defects, leading to an increased surface area and more exposed active sites, thereby promoting the adsorption and conversion of reactants and increasing the reaction rate constants.

Internally, crystals with a higher crystallinity typically have a more complete and ordered structure, limiting the diffusion of reactants within the crystal and affecting the rate of reaction. In contrast, crystals with a lower crystallinity may have more grain boundaries and defects, allowing reactants to diffuse more easily within the crystal, thereby increasing the reaction rate constants. Crystals with a higher crystallinity often have higher bond energy and higher activation energy, increasing the energy required for the reaction to occur and consequently reducing the reaction rate constants. In contrast, crystals with a lower crystallinity may have lower bond energy and lower activation energy, making the reaction easier to occur and thus increasing the reaction rate constants.

It should be noted that the relationship between the crystallinity and reaction rate constants is influenced by specific reaction systems, reaction conditions, and crystal structures, and is not an absolute rule. The order of rate constants is amorphous iron hydroxide > goethite > hematite > magnetite. In this study, we focused on exploring the effect of the reactant structure on reaction rate constants, particularly for iron minerals with different crystallinities, providing valuable insights into the reaction kinetics between iron minerals and organic pollutants.

During the degradation process of toluene, the theoretical amount of iron reduction is much higher than the actual reduction amount. This suggests that the complete oxidation of toluene and the reduction of iron do not occur synchronously. This discrepancy may be due to the degradation process of toluene not being a one-step mineralization, but rather involving intermediate states, leading to the incomplete reduction of ferrous iron and poor model fitting [28,37].

4.2. The Conceptual Model of the Interrelationship between Toluene Degradation and Iron Reduction Processes

Observation reveals a deviation between the experimental curve and the theoretical straight line. Initially, the slope of the experimental curve exceeds that of the theoretical curve. As the reaction progresses, the slope gradually decreases, eventually becoming less than that of the theoretical curve. This suggests the occurrence of electron-delayed ferrous iron reduction during the reaction. After analysis, three potential reasons have been identified. Firstly, during the extracellular anaerobic respiration of microorganisms with solid electron acceptors, electrons are typically transported by electron shuttles, leading to the storage of some electrons on these shuttles. This storage mechanism may cause a deviation in the stoichiometric ratio between toluene and iron during the reaction process [38]. Secondly, the synthetic metabolism and assimilation by microorganisms may result in the partial assimilation of toluene as a carbon source, promoting microbial biomass growth. With an increase in the microbial population, the amount of assimilated toluene also increases, leading to the accumulation of un-reduced toluene inside microbial cells. This accumulation prevents the detection of toluene, resulting in delayed electron transfer, which can be released upon microbial decay, achieving delayed electron release [39]. Thirdly, toluene may be completely degraded into multiple intermediate products within a short period of time. These intermediate products may accumulate during the degradation pathway, causing delayed electron transfer. For example, under the catalysis of benzoyl-CoA synthase, fumarate is added to the methyl group of toluene to form benzoyl succinate. Subsequently, a series of modified β-oxidation reactions occur after the addition reaction, converting phenylsuccinic acid into benzoyl-CoA, which is an intermediate product of the anaerobic degradation of aromatic compounds. Then, benzoyl-CoA is reduced by benzoyl-CoA reductase to form non-aromatic products, with the final products being CO₂ and H₂O [40]. Only one suspected intermediate product was found in the gas chromatography analysis. It is speculated that many intermediates have their specificity, and a specific treatment is required for each intermediate product to achieve the identification of the product. The existence cycle of each intermediate is short, and the identification and characterization of intermediate products can be specialized in the later stage.

Under the influence of microorganisms, all intermediate states can undergo mineralization. For instance, electron shuttles can transfer all their electrons to an electron acceptor, transitioning from a reduced state to an oxidized state, thereby achieving the reconversion of the electron shuttle storage state [41]. Similarly, biomass storage states can be consumed through microbial growth and decay, resulting in the depletion of the electron storage state [39]. Intermediate products, such as benzyl-succinate, benzyl-succinyl-CoA, E-phenylitaconyl-CoA, (hydroxymethylphenyl)-succinyl-CoA, benzoylsuccinyl-CoA, benzoyl-CoA, and succinyl-CoA, are present throughout the reaction process. The electron storage states of these intermediates can be gradually consumed over time [42,43,44]. Consequently, the degradation capability of intermediate states, whether in the form of an electron shuttle storage state, biomass storage state, or intermediate product storage state, can release electrons for utilization via the iron electron acceptor, leading to the reduction of trivalent iron to divalent iron.

In summary, there exists an intermediate state of electron storage. Here, it is referred to as the intermediary state (electron shuttle storage state, biomass storage state, intermediate product storage state), as shown in Figure 5. The first-order degradation of toluene mentioned earlier might be toluene converting into an intermediate state. Due to the presence of this intermediate state, this reaction is more complex than a single-step reaction. Here, we discuss a relatively simpler continuous reaction process divided into two stages. Let us assume that toluene undergoes a series of processes, first generating the intermediate state B, which then further transforms into the final product C. The entire series of reactions can be represented as follows:

$$\mathrm{t}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{e}\stackrel{v_1}{\to }B\stackrel{v_2}{\to }C$$

(8)

In the first stage, the conversion of toluene into an intermediate state dominates the reaction process. In the initial phase, the rate of toluene conversion is high, indicating a significant rate of intermediate state generation, while the rate of intermediate state consumption is low $(v_1>v_2)$. Primarily, two types of reactions occur as follows: the conversion of toluene into the intermediate state and the subsequent conversion of the intermediate state into the final product. However, the conversion of toluene into the intermediate state is the predominant reaction, leading to the accumulation of the intermediate state. This indicates that this stage of the reaction is primarily driven by the conversion of toluene into the intermediate state. The initial first-order kinetics equation for toluene consumption represents the initial conversion of toluene, but the conversion of toluene is not completely mineralized, resulting in the generation of ferrous iron not following first-order kinetics. This suggests that there is still an intermediate state carrying some electrons. The ratio of toluene consumption to iron reduction is greater than 1/36.

As the reaction progresses, the rate of toluene conversion gradually decreases along with the decreasing concentration of toluene. The rate of intermediate state generation diminishes, resulting in an accumulation of the intermediate state. Meanwhile, the rate of transformation of the intermediate state also increases. When the generation rate of the intermediate state equals its consumption rate $(v_1=v_2)$, the accumulation of the intermediate state ceases, reaching its maximum value. At this point, a balance is achieved between the conversion of toluene into the intermediate state and the transformation of the intermediate state into the final product, with the ratio of toluene conversion to iron reduction equaling 1/36.

The rate of toluene conversion continues to decrease, and the generation rate of the intermediate state slows down. The consumption rate of the intermediate state exceeds its generation rate $\left(v_1<v_2\right)$, indicating that, in this stage, two reactions primarily occur: toluene conversion to an intermediate state and the subsequent transformation of the intermediate state into the final product. There is minimal generation of the intermediate state but there is significant consumption. The intermediates accumulated in the early stage of this phase begin to gradually deplete. Overall, this stage signifies a predominance of the transformation of the intermediate state. Consequently, in the overall reaction, the electrons obtained from ferrous iron reduction exceed those released from toluene consumption during this period. In other words, the lagged electrons at this point contribute to the reduction of ferrous iron. The ratio of toluene conversion to iron reduction is less than 1/36.

It can be inferred that under microbial mediation, the degradation reaction of toluene using trivalent iron minerals as electron acceptors is likely to proceed in stages rather than in a single step; initially, toluene is transformed into certain intermediate states, and eventually transformed into final products. Therefore, through analysis, we have developed this conceptual model, as shown in Figure 6.

By integrating experimental data into the model, we can ascertain the predominant stages of various iron minerals. The slope of the regression line, depicted in Figure 4, with the ferrous iron concentration on the x-axis and toluene consumption on the y-axis (representing the ratio of toluene consumption to iron reduction, hereinafter referred to as “the slope”), effectively delineates the phases of different iron minerals within the model. Those with slopes greater than 1/36 denote the dominant phase of toluene transitioning to an intermediate state, while those with slopes less than 1/36 signify the dominant phase of intermediate state mineralization. The phases of the coupled relationship between toluene consumption and ferrous iron reduction for four Fe(III) Oxides represents the division of stages, as illustrated in Table 4.

In the process of toluene transformation to an intermediate-state-dominated phase, the slopes are largest for magnetite and amorphous iron hydroxide, followed by goethite, and then red hematite. A larger slope indicates a faster oxidation rate of toluene relative to the iron reduction rate, with a rapid accumulation of the intermediate state. Active oxidized iron acts as a catalyst, promoting the rapid degradation of toluene. The catalytic effects are in the following order: magnetite > amorphous iron hydroxide > goethite > red hematite.

Through analyzing the duration of toluene transformation to the intermediate-state-dominated phase, the process is longest in amorphous iron hydroxide and magnetite, followed by goethite, and then by red hematite. This suggests that different activities of oxidized iron lead to different accumulation times of the intermediate state. The order of accumulation times is as follows: amorphous iron hydroxide and magnetite > goethite > red hematite.

Arranging based on the slope of the line connecting the endpoint and starting point, the order is amorphous iron hydroxide > magnetite > goethite > red hematite. The slope of the line represents the final ratio of toluene consumption to ferrous iron reduction. This also suggests that higher activity of oxidized iron leads to a lower ratio of toluene consumption to ferrous iron reduction, which might be due to the high activity of oxidized iron affecting the iron reduction in the intermediate state of electron storage, resulting in the accumulation of electrons.

In addition, the microorganisms in the culture system of different minerals may be different, the degradation products may be different, and the ability to degrade intermediate products may be different, resulting in these differences in slope and time [45,46,47,48].

4.3. Implication

In the process of practical field application, special attention must be paid to the oxidation of toluene-like compounds and the reduction of iron. When considering the co-existence of toluene-like compounds and iron pollution in a site, it is not sufficient to rely solely on the iron content to assess the original quantity of contaminants. Evaluating the age of contaminants requires a comprehensive consideration of the iron content and cannot simply rely on specific coupling ratios. Additionally, factors such as the type of iron oxides, specific coupling conditions, and the delay in electron transfer must be taken into account. Therefore, in practical applications, it is essential to consider multiple factors comprehensively for a more accurate assessment and treatment of organic and iron pollution on the site.

The integration of our proposed model applies not only to organic contaminants, but also extends to biomass and organic acids. The coupling interaction with iron minerals, leading to the formation of complexes with iron, significantly influences the solubility and mobility of iron. We can further explore the significance of the interaction between carbon and iron in soil ecosystems. Microbes, through metabolic activities such as the decomposition of organic matter and redox reactions, play a regulatory role in the cycling of carbon and iron in the soil. The specific organic substances released by microbes, such as biochar and lignin, may mediate the reduction process of iron, thereby affecting the form and bioavailability of iron in the soil [49]. Our model provides a mechanism to elucidate this influence, particularly in the context of microbial involvement in oxidation–reduction processes.

Based on a comprehensive understanding of toluene degradation and iron reduction processes, the model can reasonably interpret experimental results and possesses a certain degree of universality. However, the model is only in its preliminary qualitative stage and is also subject to limitations imposed by experimental conditions and environmental factors, necessitating further investigation. The model provides important insights into the mechanisms and kinetics of organic degradation and iron reduction processes. Further research could reveal the time lag between toluene degradation and iron generation, providing deeper insights into the mechanism of toluene degradation.

The effect of temperature on the reaction rate is a classic phenomenon in chemical kinetics. Changes in temperature usually do not alter the fundamental mechanistic processes of a reaction [50]. Temperatures may vary the rate constant (k) and may affect the final results of the conceptual model curves, but they do not alter the reaction equations. Therefore, the presentation may vary at different temperatures, but the established model remains applicable because individual reaction mechanisms remain unchanged.

5. Conclusions

In the presence of iron minerals with varying crystallinity, the degradation of toluene does not coincide with the reduction of iron; the electrons released during toluene degradation fail to fully reduce the iron. Aside from the losses incurred during the toluene experimental process, the assimilation by microbial growth, and the pre-measurement losses of iron, the results indicate the presence of incompletely degraded intermediate states. Consequently, a conceptual model delineating the mutual relationship between toluene degradation and iron reduction processes is established as follows: the heterotrophic iron-reducing microorganisms participate in two reaction stages of toluene and iron mineral heterotrophic iron reduction. The first stage corresponds to the dominant phase of toluene conversion to an inter-mediate state, while the second stage pertains to the dominant phase of intermediate state mineralization.

This study delves into the relationship between toluene degradation and iron reduction, proposing a comprehensive conceptual model. It is helpful to deduce the coupling mechanism of toluene degradation and the ferrous reduction amount. It deepens our understanding of microbial involvement in degradation processes within complex environments, providing a significant theoretical framework and practical guidance for comprehending the degradation of toluene-like contaminants in subsurface environments.

In practical field applications, it is imperative to consider the specific types of iron minerals in the subsurface of the site when evaluating the natural attenuation degree of pollution and the age of the contaminants. Moreover, the delayed electron transfer phenomenon between contaminants and iron also impacts the site assessments. Therefore, this factor should be taken into account during the assessment process.