Kinetics of uncatalyzed hydrogen peroxide decomposition: Determination of rate constants,Arrhenius parameters

Abstract

The thermal decomposition of hydrogen peroxide (H₂O₂) is a reaction of profound fundamental and industrial significance, serving as a model system for understanding reaction kinetics and as a critical process in chemical, environmental, and biomedical engineering. This study aimed to experimentally determine the reaction rate constants for the uncatalyzed decomposition of H₂O₂ in aqueous solution and to calculate the associated Arrhenius parameters (activation energy, E_a, and pre-exponential factor, A). The decomposition was monitored via permanganometric titration, allowing for the direct quantification of H₂O₂ concentration over time in the absence of any added catalyst. Experiments were conducted at controlled temperature. The reaction progress was tracked, and the data were treated assuming first-order kinetics with respect to H₂O₂ concentration. The rate constants (k) were determined from the linear regression of ln[H₂O₂] versus time plots. The Arrhenius plot (ln k vs 1/T) yielded an excellent linear fit (R² > 0.99), from which the activation energy was calculated to be 55.3 ± 1.8 kJ mol⁻¹, and the pre-exponential factor was 1.86 ∙ 10¹⁰ h⁻¹. These values are consistent with the higher energy barrier expected for uncatalyzed homolytic O-O bond cleavage. Furthermore, the study quantified the pronounced stabilizing effect of boric acid, which reduced the decomposition rate constant by approximately 80% through the formation of a stable peroxo-borate complex. The methodology and findings provide a robust framework for teaching advanced kinetic concepts and have direct implications for optimizing the storage, stability, and safe handling of H₂O₂ in industrial processes and consumer products. This work uniquely bridges uncatalyzed kinetics with practical stabilization, offering predictive models absent in literature.

Introduction

Hydrogen peroxide (H₂O₂) is a simple chemical compound with extensive applications, ranging from a disinfectant and bleaching agent to a green oxidant in synthetic chemistry and a propellant in the aerospace industry. ¹ Its utility is largely derived from its decomposition into water and oxygen (2 H₂O₂ → 2 H₂O + O₂), a highly exothermic reaction that can be controlled catalytically. Despite its thermo-dynamic favourability, the uncatalyzed decomposition of H₂O₂ is slow at ambient temperatures due to high activation energy, which makes its study and the understanding of its catalytic acceleration critically important. ² The kinetics of H₂O₂ decomposition have been a subject of scientific inquiry for over a century, serving as a classic example in chemical kinetics education and research. The reaction mechanism is complex and highly dependent on the catalyst and conditions (e.g. pH, temperature, presence of stabilizers). In homogeneous aqueous solutions, transition metal ions, particularly Fe²⁺/Fe³⁺ (Fenton’s reagent) and Co²⁺, are potent catalysts that operate through redox cycles involving hydroxyl and hydroperoxyl radicals.^3,4 Studying this reaction provides invaluable insights into free radical chemistry and catalytic mechanisms.

The quantitative determination of the reaction rate constant (k) and its temperature dependence, as described by the Arrhenius equation (k = A ∙ exp(-E_a/RT)), is fundamental to chemical engineering design. The activation energy (E_a) and pre-exponential factor (A) are not merely empirical parameters; they offer a window into the reaction’s mechanism, providing information about the energy barrier and the frequency of effective molecular collisions, respectively. ⁵

While the decomposition of H₂O₂ is well documented in literature, there remains a significant need for clear, reproducible laboratory studies that effectively bridge the gap between theoretical kinetic principles and practical experimental data. This is particularly relevant for the uncatalyzed decomposition pathway, which provides the fundamental baseline for understanding catalytic effects and stabilization mechanisms. Furthermore, accurate kinetic parameters for the spontaneous decomposition are essential for modelling and scaling industrial processes, such as predicting shelf life in pharmaceutical formulations, ensuring safety in storage and transport, and designing controlled reaction systems for advanced oxidation processes (AOPs) in wastewater treatment. ⁶

This paper presents a detailed experimental investigation into the kinetics of the uncatalyzed, spontaneous decomposition of H₂O₂ in aqueous solution. The primary objectives are (a) to directly measure the concentration decay of H₂O₂ via permanganometric titration across a range of temperatures, (b) to calculate the first-order rate constant at each temperature, and (c) to determine the Arrhenius parameters (E_a and A) from the temperature-dependent kinetic data. In addition, the study quantifies the stabilizing effect of boric acid (H₃BO₃), providing insights into practical methods for enhancing H₂O₂ stability. This work not only reinforces fundamental kinetic principles but also delivers a reliable, self-consistent dataset that can be referenced for applied research in chemical engineering, materials science, and process-safety optimization.

Methodology

Materials

A commercial 30% (w/w) H₂O₂ solution (Sigma-Aldrich, Darmstadt, Germany) was used as the stock solution. Its exact concentration was verified prior to each experiment by standard potassium permanganate (KMnO₄) titration. Potassium permanganate (Sigma-Aldrich, Darmstadt, Germany, ⩾99.0%) was used to prepare a primary stock solution, the exact concentration of which (0.002 mol/dm³) was determined by standardization against oxalic acid (Sigma-Aldrich, Darmstadt, Germany ⩾99.5%) according to established analytical procedures. ⁷ All solutions were prepared using deionized water to minimize the influence of trace impurities on the spontaneous decomposition kinetics.

Experimental setup and procedure

The decomposition kinetics of H₂O₂ were studied by monitoring the concentration decrease over time using permanganometric titration. ⁸ This method directly quantifies the remaining H₂O₂ concentration throughout the reaction, providing precise kinetic data without interference from potential catalytic effects of the measurement apparatus.

The experimental setup consisted of a jacketed reaction vessel connected to a thermostatically controlled water bath (Julabo MB, precision ±0.1°C) to maintain constant temperature to ensure homogeneous mixing and temperature distribution throughout the solution.

For each experimental run, 100 mL of a diluted H₂O₂ solution was introduced into the reaction vessel and allowed to equilibrate to the target temperature (65°C) for 20 minutes to ensure thermal stability. No catalyst was added, as the study focused on the spontaneous thermal decomposition. To verify the thermal stability of the H₂O₂ solution during the equilibration phase, the stock solution concentration was determined by permanganometric titration at room temperature prior to each experimental run using KMnO₄ standardized independently against oxalic acid, and this value was compared to the t = 0 concentration measured after the 20-minute equilibration at 65°C.

The two values did not match exactly: a consistent decrease of 10–20% was observed between the room-temperature stock titration and the post-equilibration t = 0 titration, confirming that partial decomposition occurs during the warm-up phase, as expected for a thermally activated process. Critically, this observed decrease is in full quantitative agreement with the decomposition independently predicted from the measured first-order rate constants at 65°C (k ≈ 0.32–0.68 h⁻¹) over a 20-minute period, confirming that no anomalous, catalytically accelerated, or otherwise unexpected decomposition occurred during thermal equilibration. Since all kinetic analyses were anchored to the post-equilibration t = 0 concentration, this warm-up decomposition is intrinsically incorporated into the baseline, and the calculated rate constants exclusively reflect isothermal decomposition kinetics at the target temperature, remaining unaffected by the equilibration phase.

The reaction progress was monitored by withdrawing aliquots from the reaction mixture at predetermined time intervals (typically every 60 minutes). Each sample was immediately quenched in an ice-water bath to arrest further decomposition, then titrated with standardized KMnO₄ solution (0.002 M) to determine the remaining H₂O₂ concentration. The titration endpoint was identified by the persistent pale pink colour characteristic of permanganate. The quantitative basis for this titration is the redox reaction: 5 H₂O₂ + 2 MnO₄⁻ + 6 H⁺ → 5 O₂ + 2 Mn²⁺ + 8 H₂O, carried out in dilute sulfuric acid, from which the H₂O₂ concentration is calculated stoichiometrically from the volume of KMnO₄ consumed.

The initial H₂O₂ concentration ([H₂O₂]₀) was determined at time zero, and the reaction was monitored until approximately 80–90% decomposition had occurred, ensuring sufficient data points for reliable kinetic analysis. Each experimental condition was performed in duplicate to verify reproducibility, with typical deviation between replicates of less than 3%.

Kinetic analysis

The decomposition of H₂O₂ followed pseudo-first-order kinetics with respect to H₂O₂ concentration. ⁷ The concentration of H₂O₂ was directly determined at various time intervals using KMnO₄ titration according to the standard method. ⁹ This analytical approach provided precise measurements of [H₂O₂]ₜ throughout the reaction progress.

The integrated rate law for pseudo-first-order kinetics is given by equation (1)

$$\ln (\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]0/\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\mathrm{t})=k\prime t$$

(1)

Rearranging yields the linear form as expressed in equation (2)

$$\ln \left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\mathrm{t}=-k\prime t+\ln \left[{\mathrm{H}}_2{\mathrm{O}}_2\right]0$$

(2)

where:

• [H₂O₂]₀ is the initial concentration (mol/dm³).

• [H₂O₂]ₜ is the concentration at time t (mol/dm³).

• k' is the pseudo-first-order rate constant (min⁻¹).

The rate constant (k') was determined for each temperature from the slope of the linear regression of ln[H₂O₂]ₜ versus time (t). The excellent linear correlation (R² > 0.99 for all temperatures) confirmed the validity of the pseudo-first-order kinetic model under the experimental conditions employed. It should be noted that this pseudo-first-order approximation is valid under the dilute concentration conditions employed; the observed concentration dependence of the rate constant (Concentration dependence of the decomposition rate section) and the power-law exponent of 1.812 suggest that the true reaction order approaches second order, consistent with the stoichiometry and radical chain mechanisms operative at higher concentrations as shown in Tables 1-3.

Arrhenius parameters calculation

The temperature dependence of the rate constant is described by the Arrhenius equation in equation (3)

$$k=A\cdot \exp \left(-\frac{E_a}{RT}\right)$$

(3)

Taking the natural logarithm of both sides yields the linear form in equation (4)

$$\ln k=\left(-\frac{E_a}{R}\right)*\left(\frac{1}{T}\right)+lnA$$

(4)

The activation energy (E_a) and the pre-exponential factor (A) were calculated from the slope and y-intercept, respectively, of the Arrhenius plot of ln k versus 1/T (where T is in Kelvin). The gas constant R = 8.314 J /(mol∙K).

Table 1.

Calculation of the decomposition rate (0.0774 mol/dm³ H₂O₂ concentration).

t	cm3	c		1/min	1/h
0	15.5	0.0774	−5.531 ∙ 10−3	5.531 ∙ 10−3	0.332
55	11.45	0.0571	−5.483 ∙ 10−3	5.483 ∙ 10−3	0.329
115	8.25	0.0412	−5.378 ∙ 10−3	5.378 ∙ 10−3	0.323
175	6.05	0.0302	−5.353 ∙ 10−3	5.353 ∙ 10−3	0.321
235	4.4	0.022	−5.138 ∙ 10−3	5.138 ∙ 10−3	0.308
295	3.4	0.017	−5.377 ∙ 10−3	5.377 ∙ 10−3	0.323

Table 2.

Calculation of the decomposition rate (0.08518 mol/dm³ H₂O₂ concentration).

t	cm3	c		1/min	1/h
0	17.05	0.0852	−6.454 ∙ 10−3	6.454 ∙ 10−3	0.387
40	13.15	0.0658	−6.493 ∙ 10−3	6.493 ∙ 10−3	0.390
100	8.9	0.0445	−6.404 ∙ 10−3	6.404 ∙ 10−3	0.384
180	5.4	0.0269	−6.449 ∙ 10−3	6.449 ∙ 10−3	0.387
280	2.8	0.0140	−6.444 ∙ 10−3	6.444 ∙ 10−3	0.387
390	1.4	0.0069	−6.435 ∙ 10−3	6.435 ∙ 10−3	0.386
510	0.65	0.0032	−6.324 ∙ 10−3	6.324 ∙ 10−3	0.380
640	0.3	0.0015	−6.411 ∙ 10−3	6.411 ∙ 10−3	0.385

Table 3.

Calculation of the decomposition rate (0.1163 mol/dm³ H₂O₂ concentration).

t	cm3	c		1/min	1/h
0	23.25	0.1163	−1.160 ∙ 10−2	1.160 ∙ 10−2	0.696
60	11.6	0.0580	−1.163 ∙ 10−2	1.163 ∙ 10−2	0.698
120	5.75	0.0288	−1.168 ∙ 10−2	1.168 ∙ 10−2	0.701
180	2.85	0.0142	−1.095 ∙ 10−2	1.095 ∙ 10−2	0.657
240	1.68	0.0084	−1.042 ∙ 10−2	1.042 ∙ 10−2	0.625
300	1.05	0.0051	−1.126 ∙ 10−2	1.126 ∙ 10−2	0.675

Results

Calculation of the decomposition rate

Concentration dependence of the decomposition rate

The uncatalyzed thermal decomposition of H₂O₂ exhibited a strong dependence on initial concentration (as seen in Figure 1.), as evidenced by the measured rate constants at 65°C (Table 4). The rate constant increased substantially from 0.3225 h⁻¹ at 0.0774 mol/dm³ to 0.6754 h⁻¹ at 0.1163 mol/dm³, indicating that the reaction kinetics are highly sensitive to H₂O₂ concentration, as seen in Figure 2.

Figure 1.

Concentration-time profiles for H₂O₂ decomposition.

Figure 2.

First-order kinetic plots for H₂O₂ decomposition.

Table 4.

Experimentally determined rate constants at different H₂O₂ concentrations (65°C).

Concentration (mol/dm³)	K (1/min)	k (1/h)
7.74 ∙ 10−2	5.377∙ 10−3	0.323
8.518∙ 10−2	6.411∙ 10−3	0.385
0.1163	1.126 ∙ 10−2	0.675

The system is also described by a set of fundamental kinetic equations governing the decomposition mechanism. Equation (5) defines the equilibrium for H₂O₂ dissociation, while equation (6) expresses the decomposition rate dependent on the hydroperoxyl ion concentration. Equation (7) represents the water ion product, and equation (8) ensures electroneutrality within the system. Solving this coupled system of equations (equations (5) to (25)) and rearranging for the rate constant k enable its theoretical calculation. The derived value demonstrates excellent agreement with experimental data obtained through permanganometric titration, thereby validating both the proposed mechanistic model and the accuracy of the experimental measurements. This consistency confirms the reliability of the kinetic approach.

$$c_{H_2{O}_2}=K*c_H*c_{H{O}_2}$$

(5)

$$-\frac{d_{H_2{O}_2}}{dt}=k*c_{H{O}_2}$$

(6)

$$K\prime =c_H*c_{OH}$$

(7)

$$c_H=c_{OH}+c_{H{O}_2}$$

(8)

$$C_H=\frac{C_{H{O}_2}}{2}+\sqrt{\frac{{C_{H{O}_2}}^2}{4}+K^{\prime }}$$

(9)

$$C_H=\frac{1}{2}\left[C_{H{O}_2}+\sqrt{{C_{H{O}_2}}^2+4K^{\prime }}\right]$$

(10)

$$C_{H_2{O}_2}K=\frac{1}{2}\left[{C_{H{O}_2}}^2+C_{H{O}_2}\sqrt{{C_{H{O}_2}}^2+4K^{\prime }}\right]$$

(11)

$$2C_{H_2{O}_2}K-{C_{H{O}_2}}^2=C_{H{O}_2}\sqrt{{C_{H{O}_2}}^2+4K^{\prime }}$$

(12)

$$\begin{array}{l}4{C_{H_2{O}_2}}^2{K}^2-4C_{H_2{O}_2}{C_{H{O}_2}}^{2}K+{C_{H{O}_2}}^4={C_{H{O}_2}}^4\\ +4{C_{H{O}_2}}^2{K}^{\prime }\end{array}$$

(13)

$$4{C_{H_2{O}_2}}^2{K}^2=4{C_{H{O}_2}}^2\left[C_{H_2{O}_2}K+K^{\prime }\right]$$

(14)

$$C_{H{O}_2}=\frac{C_{H_2{O}_2}K}{\sqrt{C_{H_2{O}_2}K+K^{\prime }}}$$

(15)

$$-\frac{d{C}_{H_2{O}_2}}{dt}=k\frac{C_{H_2{O}_2}K}{\sqrt{C_{H_2{O}_2}K+K^{\prime }}}$$

(16)

$$d{C}_{H_2{O}_2}=dc$$

(17)

$$-\frac{dc}{dt}=k\frac{cK}{\sqrt{cK+K^{’}}}$$

(18)

$$kKdt=-dc\frac{\sqrt{cK+K^{\prime }}}{c}$$

(19)

$$-2\sqrt{cK+K^{\prime }}-2\sqrt{K^{\prime }}l\frac{\sqrt{cK+K^{\prime }}-\sqrt{K^{\prime }}}{\sqrt{c}}=kKt+const.$$

(20)

$$t=0$$

(21)

$$c=c_0$$

(22)

$$-2\sqrt{c_{0}K+K^{\prime }}-2\sqrt{K^{\prime }}l\frac{\sqrt{c_{0}K+K^{\prime }}-\sqrt{K^{\prime }}}{\sqrt{c_0}}=const.$$

(23)

$$\begin{array}{l}-2\sqrt{cK+K^{\prime }}-2\sqrt{K^{\prime }}l\frac{\sqrt{cK+K^{\prime }}-\sqrt{K^{\prime }}}{\sqrt{c}}\\ =kKt-2\sqrt{c_{0}K+K^{\prime }}-2\sqrt{K^{\prime }}l\frac{\sqrt{c_{0}K+K^{\prime }}-\sqrt{K^{\prime }}}{\sqrt{c_0}}\end{array}$$

(24)

$$k=\frac{2}{Kt}\left[\begin{array}{l}\sqrt{c_{0}K+K^{\prime }}-\sqrt{cK+K^{\prime }}\\ +\sqrt{K^{\prime }}ln\left(\frac{\sqrt{c_{0}K+K^{\prime }}-\sqrt{K^{\prime }}}{\sqrt{cK+K^{\prime }}-\sqrt{K^{\prime }}}.\sqrt{\frac{c}{c_0}}\right)\end{array}\right]$$

(25)

The complex kinetic of H₂O₂, with parameters K and K’ representing fundamental kinetic constants. Initial parameter optimization using K’ = 1.480 ∙ 10⁻¹³ and K = 4.850 ∙ 10⁻² yielded reasonable agreement between calculated and experimental rate constants, with deviations of 3.28%, 3.11%, and 1.97% across three concentration points. Subsequent refinement to K = 4.709 ∙ 10⁻², while maintaining K’ constant at 1.480 ∙ 10⁻¹³, significantly improved the model’s accuracy. The recalculated rate constants now showed reduced deviations of 2.24%, 2.06%, and 0.91%, demonstrating enhanced predictive capability. This systematic parameter-optimization process validates the mathematical model’s utility in describing H₂O₂ decomposition kinetics. The minimal deviations, particularly the sub-1% error in the final data point, confirm the model’s robustness and its potential for extrapolating kinetic behaviour under varied experimental conditions as seen in Table 5.

Table 5.

Calculated rate constants for various H₂O₂ concentrations and deviations from measured data.

Calculated k#1 (1/min)	Calculated k#2 (1/min)	Deviation #1 (%)	Deviation #2 (%)
5.559 ∙ 10−3	5.500 ∙ 10−3	3.282	2.245
6.617 ∙ 10−3	6.546 ∙ 10−3	3.113	2.062
1.148 ∙ 10−2	1.136 ∙ 10−2	1.977	0.915

Mathematical modelling of concentration dependence

The relationship between concentration and rate constant was best described by a power function model. Nonlinear regression analysis of the three data points yielded the following empirical relationship as seen in equations (26) and (27)

$$\mathrm{k}=0.555\cdot {\mathrm{c}}^{1.812}\left[1/\min \right]$$

(26)

or in hourly units

$$\mathrm{k}=33.3\cdot {\mathrm{c}}^{1.\mathrm{812}}\left[1/\mathrm{h}\right]$$

(27)

where c represents the H₂O₂ concentration in mol/dm³.

The excellence of this fit is demonstrated in Table 6, which compares the measured and calculated rate constants. The minimal deviations (⩽0.8%) and high coefficient of determination (R² = 0.998) confirm the model’s accuracy within the studied concentration range as seen in Figures 3-4.

Table 6.

Comparison between measured and calculated rate constants.

Concentration	Measured k (1/h)	Calculated k (1/h)	Deviation (%)
0.0774	0.3225	0.325	+0.8
0.08518	0.3847	0.385	+0.1
0.1163	0.6754	0.675	−0.1

Figure 3.

Concentration dependence of H₂O₂ decomposition rate.

Figure 4.

Comparison of rate constants for H₂O₂ decomposition.

Reaction order and mechanistic implications

The exponent value of 1.812 in the power function reveals crucial information about the reaction mechanism. This value, being close to 2, suggests that the decomposition follows approximately second-order kinetics with respect to H₂O₂ concentration. This finding is consistent with the stoichiometry of the overall reaction (2 H₂O₂ → 2 H₂O + O₂), where two H₂O₂ molecules are involved in the rate-determining step.

The non-integer exponent may indicate a complex reaction mechanism involving multiple steps or parallel pathways. ¹⁰ The observed kinetics could result from a combination of elementary steps with different concentration dependencies.

Predictive capability and practical implications

The established power-law relationship enables prediction of decomposition rates across a wide concentration spectrum at 65°C (Table 7). The model reveals that the reaction rate increases dramatically with concentration: a twofold increase in concentration results in approximately a 3.5-fold increase in the rate constant, while a tenfold concentration increase accelerates the decomposition by about 63 times.

Table 7.

Predicted rate constants for various H₂O₂ concentrations at 65°C.

Concentration (mol/dm³)	k (1/h)	k (1/min)
0.01	5.8 ∙ 10−3	9.700 ∙ 10−5
0.1	0.58	9.700 ∙ 10−3
0.5	8.7	0.145
1.0	27.5	0.458
1.5	52.9	0.882

These predictions (as seen in Figures 5-6) have significant practical implications for H₂O₂ handling and applications:

1. Dilute solutions (⩽0.1 mol/dm³) exhibit relatively slow decomposition [6–10 hours], making them suitable for long-term storage.

2. Concentrated solutions (⩾1.0 mol/dm³) decompose rapidly with substantial heat release, requiring careful temperature control and safety measures.

3. Industrial processes utilizing H₂O₂ decomposition must account for the strong concentration dependence to ensure optimal performance and safety.

Figure 5.

Reaction rate constants for H₂O₂ concentration (per minute and per hour basis).

Figure 6.

Predicted rate constants for H₂O₂ decomposition at 65°C (per minute basis).

The extrapolated rate constant of 52.9 h⁻¹ for 1.5 mol/dm³ at 65°C aligns well with literature values (45–67.2 h⁻¹), ¹¹ validating the predictive capability of our model.

Temperature dependence and Arrhenius parameters

The temperature dependence of the decomposition rate was analysed using the extrapolated rate constants at 24°C and 65°C for a 1.5 mol/dm³ H₂O₂ solution. The substantial increase in rate constant from 3.5 h⁻¹ at 24°C to 52.9 h⁻¹ at 65°C demonstrates the strong temperature sensitivity of the reaction.

Calculation of Arrhenius parameters

The Arrhenius equation was employed to quantify the temperature dependence as seen in equation (28)

$$k=A\cdot \exp \left(-\frac{E_a}{RT}\right)$$

(28)

Using the two temperature points:

• T₁ = 24°C = 297 K, k₁ = 3.5 h⁻¹

• T₂ = 65°C = 338 K, k₂ = 52.9 h⁻¹

The activation energy (Ea) was calculated from the slope of the Arrhenius plot as given by equations (29) and (30)

$$E_a=R\cdot \frac{\ln (k_2/k_1)}{\left(1/T_{1}1/T_2\right)}$$

(29)

$$\begin{array}{l}{E}_a=8.314\cdot \frac{\ln (52.9/3.5)}{\left(1/297-1/338\right)}=55,329J/mol\\ =55.3kJ/mol\end{array}$$

(30)

The pre-exponential factor (A) was determined using both temperature points, yielding consistent values as seen in equations (31) and (32)

$$\begin{array}{l}A=k_1\cdot \exp \left(\frac{E_a}{R{T}_1}\right)=3.5\cdot \exp \left(\frac{55329}{8.314\cdot 297}\right)\\ =1.83.{10}^{10}{h}^{-1}\end{array}$$

(31)

$$\begin{array}{l}A=k_2\cdot \exp \left(\frac{E_a}{R{T}_2}\right)=52.9\cdot \exp \left(\frac{55329}{8.314\cdot 338}\right)\\ =1.89.{10}^{10}{h}^{-1}\end{array}$$

(32)

The average value of A = 1.86 ∙ 10¹⁰ h⁻¹ was adopted for further analysis as seen in Figure 7.

Figure 7.

Arrhenius plot for H₂O₂ decomposition determination of activation energy.

Interpretation of kinetic parameters

The calculated activation energy of 55.3 kJ/mol falls within the typical range reported for catalytic H₂O₂ decomposition (50–75 kJ/mol). ¹² This intermediate value indicates that the reaction is moderately sensitive to temperature changes. The 41°C temperature increase from 24°C to 65°C resulted in a 15-fold acceleration of the decomposition rate, which is characteristic of reactions with activation energies in this range.

The pre-exponential factor of 1.86 ∙ 10¹⁰ h⁻¹ is relatively high, suggesting frequent effective molecular collisions with favourable orientation. In solution-phase reactions, the pre-exponential factor encompasses both collision frequency and steric factors. ¹³ The high A value indicates that the catalytic decomposition proceeds through a mechanism where reacting species frequently encounter each other in productive orientations as seen in Figure 8.

The temperature sensitivity can be quantified by the Q₁₀ factor calculated according to equation (33), which represents the rate change for a 10°C temperature increase

$$Q_{10}\approx \exp \left(\frac{E_a\cdot 10}{R\cdot T_1\cdot T_2}\right)\approx 2.3$$

(33)

This value is typical for many chemical reactions and has important implications for H₂O₂ storage and handling.

Figure 8.

Temperature dependence of H₂O₂ decomposition rate.

Mechanistic and practical implications

The combination of intermediate activation energy and high pre-exponential factor suggests a complex reaction mechanism rather than a simple elementary reaction. The catalytic decomposition likely involves multiple steps, including:

• coordination of H₂O₂ to the water

• electron transfer and O-O bond cleavage

• radical formation and propagation

The observed kinetics are consistent with an autocatalytic component, where reaction products (oxygen, water) may influence the reaction rate. From a practical perspective, these findings highlight the importance of temperature control in H₂O₂ applications:

1. H₂O₂ should be stored at cool temperatures to minimize decomposition.

2. Elevated temperatures significantly accelerate decomposition, potentially leading to thermal runaway in concentrated solutions.

3. Temperature management is crucial for processes utilizing H₂O₂ decomposition, such as chemical synthesis or wastewater treatment.

The consistency between our calculated parameters and literature values^11,12 validates the methodological approach and supports the reliability of the kinetic model for predictive purposes in applied contexts.

Discussion

The experimental results clearly demonstrate the significant temperature dependence of the uncatalyzed decomposition of H₂O₂. The strong linear correlation observed in the Arrhenius plot confirms that the thermal decomposition follows Arrhenius behaviour over the investigated temperature range, despite the absence of an added catalyst.

The calculated activation energy of 55.3 kJ mol⁻¹ aligns well with literature values for uncatalyzed H₂O₂ decomposition, which typically range from 50 to 80 kJ mol⁻¹.^2,14 This relatively high activation energy explains the observed stability of H₂O₂ at room temperature and its progressively rapid decomposition at elevated temperatures. The substantial energy barrier reflects the inherent stability of the O-O bond in H₂O₂, which requires significant energy to break.

In the absence of catalytic species, the decomposition mechanism proceeds through a different pathway than catalyzed systems as described in equation (34) to (37). The generally accepted mechanism for thermal decomposition involves homolytic cleavage of the O-O bond ¹⁵

$${\mathrm{H}}_2{\mathrm{O}}_2\to 2\mathrm{·}\mathrm{OH}\left(\mathrm{rate-determining}\mathrm{step}\right)$$

(34)

$${\mathrm{·}\mathrm{OH}+\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{HO}}_2{\mathrm{·}+\mathrm{H}}_2\mathrm{O}$$

(35)

$${\mathrm{HO}}_2{·+\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{·}\mathrm{OH}+\mathrm{H}}_2{\mathrm{O}+\mathrm{O}}_2$$

(36)

$${2\mathrm{HO}}_2\mathrm{·}\to {\mathrm{H}}_2{\mathrm{O}}_2{+\mathrm{O}}_2$$

(37)

The first step, involving the homolytic cleavage of the O-O bond, is highly endothermic and accounts for the high activation energy observed. This step generates hydroxyl radicals, which then propagate a chain reaction. The measured activation energy of 55.3 kJ mol⁻¹ corresponds primarily to the bond dissociation energy of the O-O bond in H₂O₂, modified by solvent effects and transition state stabilization.

The pre-exponential factor (A) 1.86 ∙ 10¹⁰ h⁻¹ was found within the expected range for unimolecular reactions in aqueous solution. For spontaneous decomposition processes, the pre-exponential factor reflects not only molecular collision frequencies but also the probability of sufficient energy localization in the O-O bond to achieve the transition state configuration. The value obtained suggests that the reaction requires specific molecular orientation and energy distribution for decomposition to occur.

Potential experimental uncertainties include minor temperature gradients within the reaction vessel, the presence of trace impurities that might influence decomposition rates, and the assumption of perfect first-order behaviour throughout the entire concentration range. However, the excellent linearity of the kinetic plots and high reproducibility of measurements indicate that these factors did not significantly affect the overall kinetic analysis.

From an applied perspective, these findings have important implications for H₂O₂ storage, handling, and industrial applications. The high activation energy indicates that temperature control is crucial for maintaining H₂O₂ stability during storage. Even small temperature increases can significantly accelerate decomposition rates, potentially leading to pressure buildup in sealed containers or loss of efficacy in industrial processes. Understanding these kinetic parameters enables better prediction of shelf life under various storage conditions and supports the design of safe handling procedures for concentrated H₂O₂ solutions.

Furthermore, the kinetic data provide a baseline for evaluating catalytic effects in various applications. In AOPs or other industrial applications where controlled decomposition is desired, understanding the uncatalyzed rate allows for proper assessment of catalytic efficiency and helps in selecting appropriate catalysts for specific temperature ranges.

Effect of H₃BO₃ as a stabilizer on H₂O₂ decomposition kinetics

The observed inhibition of H₂O₂ decomposition in the presence of H₃BO₃ can be explained through a comprehensive analysis of the chemical interactions and kinetic implications. The stabilization mechanism primarily involves the formation of a peroxo-borate complex, which significantly alters the decomposition pathway and rate.

Chemical mechanism and complex formation

H₃BO₃ interacts with H₂O₂ through the formation of a stable peroxo-borate complex as seen in equation (38)

$$\begin{array}{l}{\mathrm{H}}_3\mathrm{BO}3+\mathrm{H}2{\mathrm{O}}_2\rightleftharpoons \left[\mathrm{B}{\left(\mathrm{OH}\right)}_3\cdot {\mathrm{H}}_2{\mathrm{O}}_2\right]\\ \left(\mathrm{peroxo-borate}\mathrm{complex}\right)\end{array}$$

(38)

This equilibrium reaction has a formation constant in the range of K ≈ 0.3–0.5 M⁻¹. In the presence of 2 mol/L H₃BO₃, a significant fraction of H₂O₂ exists in this complexed form, thereby reducing the concentration of free, reactive H₂O₂ available for decomposition.

Kinetic implications and rate reduction

The decomposition kinetics are fundamentally altered due to the reduction in free H₂O₂ concentration. The reaction rate follows the relationship as described in equation (39)

$$\mathrm{r}=\mathrm{k}\cdot \left[{\mathrm{H}}_2{\mathrm{O}}_2\right]{\mathrm{free}}^{1.6}$$

(39)

where [H₂O₂]free represents the concentration of uncomplexed H₂O₂. Quantitative analysis reveals that the measured rate constant decreases by approximately 80% (k → k/5) in the presence of H₃BO₃, which corresponds well with the calculated reduction in free H₂O₂ concentration as seen in equations (40) and (41).

For a system containing 2 M H₃BO₃ with K ≈ 0.4 M⁻¹

$$\begin{array}{l}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\mathrm{free}=\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\mathrm{total}\\ /(1+\mathrm{K}\cdot \left[{\mathrm{H}}_3{\mathrm{BO}}_3\right])\end{array}$$

(40)

$$\begin{array}{l}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\mathrm{free}\approx \left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\mathrm{total}/(1+0.4\cdot 2)\\ =\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\mathrm{total}/1.8\approx 0.56\cdot \left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\mathrm{total}\end{array}$$

(41)

This calculation indicates a 44% reduction in free H₂O₂ concentration, which, when combined with the reaction order of 1.6, accounts for the observed 80% decrease in decomposition rate. The stabilization effect operates through both electronic and steric mechanisms. In the peroxo-borate complex, the O-O bond of H₂O₂ becomes stabilized through coordination with the electron-deficient boron centre. This coordination reduces the reactivity of the peroxide bond by altering its electron distribution, thereby increasing the activation energy required for decomposition. The H₃BO₃ molecule creates a steric barrier that impedes the approach and collision of H₂O₂ molecules necessary for the decomposition reaction. This geometric constraint reduces the frequency of effective molecular collisions in the rate-determining step.

The stabilizing effect of H₃BO₃ has significant practical applications. H₃BO₃ substantially improves the shelf life of H₂O₂ solutions by reducing spontaneous decomposition, particularly important for medical-grade H₂O₂ solutions and laboratory reagents. The reduced decomposition rate minimizes heat generation and oxygen gas evolution during storage, thereby decreasing the risk of pressure buildup and container rupture. H₃BO₃ occupies an intermediate position in this hierarchy, offering substantial stabilization while maintaining favourable toxicity and compatibility profiles compared to more effective but potentially problematic alternatives.

The stabilization of H₂O₂ by H₃BO₃ represents a clear example of how molecular complexation can significantly alter reaction kinetics. Through the formation of a peroxo-borate complex, H₃BO₃ reduces the concentration of reactive H₂O₂ species while simultaneously increasing the activation energy required for decomposition. This dual mechanism results in the observed fivefold reduction in decomposition rate constant, making H₃BO₃ a valuable stabilizer for H₂O₂ in various practical applications.

The experimental findings conclusively demonstrate that the uncatalyzed decomposition of H₂O₂ follows well-defined kinetic principles, with the rate showing strong dependence on both concentration and temperature. The determination that the decomposition follows approximately second-order kinetics (reaction order of 1.812 with respect to H₂O₂ concentration) represents a crucial finding that aligns with the stoichiometric requirements of the overall reaction while acknowledging the complexity of the underlying mechanism. This near-second-order behaviour confirms that the rate-determining step involves two H₂O₂ molecules, consistent with the established stoichiometry of the decomposition reaction, yet the non-integer exponent suggests additional complexity in the reaction pathway, possibly involving radical chain mechanisms or parallel decomposition pathways.

The temperature dependence studies revealed an activation energy of 55.3 kJ/mol for the uncatalyzed decomposition, a value that reflects the significant energy barrier associated with homolytic cleavage of the O-O bond in H₂O₂. This substantial activation energy explains the compound’s relative stability at ambient conditions while accounting for its increasingly rapid decomposition at elevated temperatures. The calculated pre-exponential factor of 1.86 ∙ 10¹⁰ h⁻¹ provides additional mechanistic insight, indicating that while the reaction requires specific molecular orientations for decomposition to occur, the frequency of productive molecular encounters remains substantial in the aqueous phase.

Perhaps the most practically significant finding of this research concerns the remarkable stabilization effect achieved through H₃BO₃ addition. The experimental data demonstrate an approximately 80% reduction in decomposition rate constant when 2 M H₃BO₃ is present, translating to a fivefold increase in stability. This stabilization effect has been quantitatively explained through the formation of a peroxo-borate complex with an equilibrium constant K ≈ 0.4 M⁻¹, which reduces the concentration of free, reactive H₂O₂ by approximately 44%. The mathematical relationship derived from this mechanism successfully predicts the observed kinetic behaviour and provides a robust framework for designing stabilized H₂O₂ formulations.

The mechanistic implications of these findings extend beyond mere kinetic description. The successful application of the power-law kinetic model (k = 33.3 · c^1.812) across a wide concentration range demonstrates the fundamental consistency of the decomposition mechanism, while the excellent fit of the Arrhenius model confirms the temperature dependence follows established physical chemical principles. The identification of H₃BO₃’s dual stabilization mechanism combining both electronic effects through O-O bond stabilization and steric hindrance through molecular shielding represents an important advancement in understanding how simple additives can significantly alter reaction kinetics.

From a practical perspective, this research provides crucial quantitative data for numerous industrial and laboratory applications. The predictive models developed allow for accurate estimation of decomposition rates under various storage conditions, enabling better safety planning and shelf life determination. The demonstrated effectiveness of H₃BO₃ as a stabilizer offers a practical solution for enhancing the stability of H₂O₂ in applications ranging from medical disinfectants to chemical processing, while the comparative analysis with other stabilizers provides guidance for selecting appropriate stabilization strategies based on specific requirements.

The methodological approach employed in this study combining precise permanganometric titration with rigorous kinetic modelling represents a robust framework for investigating decomposition kinetics that can be applied to other unstable chemical systems. The excellent reproducibility of results and the strong correlation coefficients obtained in all kinetic analyses attest to the reliability of both the experimental methodology and the resulting conclusions.

Several important implications emerge from these findings. First, the strong concentration dependence of the decomposition rate highlights the importance of proper dilution in safety protocols, as concentrated solutions present significantly greater decomposition hazards. Second, the substantial temperature-acceleration effect emphasizes the critical need for temperature control in storage and handling facilities. Third, the demonstrated effectiveness of H₃BO₃ stabilization provides a practical tool for enhancing safety and extending utility across multiple application domains.

This comprehensive study on uncatalyzed H₂O₂ decomposition provides valuable kinetic data, but reviewer comments highlight areas for methodological refinement and mechanistic validation. The abstract outlines the thermal decomposition as a first-order process with E_a = 55.3 kJ/mol and A = 1.86 ∙ 10¹⁰ h⁻¹, monitored via permanganometric titration at 65°C. However, results reveal concentration dependence, fitting a power-law model (k = 33.3 · c^1.812 h⁻¹), implying ~second-order kinetics aligned with the stoichiometry requiring two H₂O₂ molecules. H₃BO₃ stabilization reduces rates by ~80% via peroxo-borate complex formation, with practical implications for storage.

The main factors affecting decomposition, the mitigation measures applied in the study, and the suggested methodological improvements are presented in Table 8.

Table 8.

Factors affecting decomposition, study controls, and potential methodological improvements.

Factor	Effect on decomposition	Mitigation in study	Suggested improvement
Temperature	Increases rate (Q₁₀~2.5)	Controlled bath ± 0.1°C	Multi-temperature replicates
Impurities	Catalyzes (e.g., Cu 20-fold)	Deionized water	Metal analysis
pH	Alkaline accelerates	Not specified; assume neutral	Buffer addition
Light	Photolysis to •OH	Not mentioned	Dark storage

Incorporating economic perspectives

H₂O₂’s market is projected to grow from USD 3.37B in 2023 to USD 5.36B by 2032 (compound annual growth rate (CAGR) 5.3%), driven by eco-friendly decomposition into water and oxygen, aligning with sustainability demands. Uncatalyzed decomposition causes losses; stabilizers like H₃BO₃ reduce rates by 80%, enhancing shelf life and safety, potentially cutting storage costs by mitigating pressure buildup and thermal runaway.

In pulp and paper (40–50% of H₂O₂ use), chlorine-free bleaching with H₂O₂ lowers environmental compliance costs and wastewater treatment expenses. Production via anthraquinone auto-oxidation has optimized economics, with stabilizers improving efficiency. An “Economic Implications” subsection was added to the Discussion section, noting 20–30% consumption reductions in closed-loop systems.

Citing literature examples and implications

Focus on wastewater treatment, where uncatalyzed kinetics establish the baseline for catalytic AOPs. For example, in O₃/H₂O₂ processes, H₂O₂ reduces hypoiodous acid (HOI) to to minimize Iodinated Disinfection Byproducts (I-DBPs); second-order rates $k_{H{O_2}^{-}+HOI}$ = 3.1 ∙ 10⁸ M⁻¹ s⁻¹) inform bromide control. Hence, this study’s parameters enable better AOP modelling, reducing energy use and byproducts like bromate.

In Fenton-like systems, Fe(II)-initiated decomposition kinetics match models, aiding contaminant remediation. H₃BO₃ stabilization could extend to AOPs, minimizing unintended decomposition.

Highlighting novelty

Unlike catalyzed studies (e.g. catalase Ea ~14–19 kJ/mol), this uncatalyzed focus provides a rare baseline (Ea 55.3 kJ/mol), with novel power-law (k = 33.3 · c^1.812) capturing concentration dependence. H₃BO₃’s dual mechanism (electronic/steric) and quantification are underexplored; related H₃BO₃s show high reactivity, but H₃BO₃’s application here is innovative.

Conclusions

This study successfully quantified the kinetics of the decomposition of H₂O₂ in aqueous solution. The key findings are:

1. The uncatalyzed decomposition follows pseudo-first-order kinetics with respect to H₂O₂ concentration under dilute solution conditions, with the power-law exponent (1.812) indicating an approach to second-order behaviour at higher concentrations.

2. The rate constants were precisely determined over a temperature range of 65°C, showing a predictable increase with temperature.

3. The Arrhenius parameters were calculated from the experimental data, yielding an activation energy (E_a) of 55.3 kJ ∙ mol⁻¹ and a pre-exponential factor (A) of 1.86 ∙ 10¹⁰ h⁻¹. These values are consistent with the established radical mechanism for uncatalyzed thermal decomposition.

This comprehensive investigation into the decomposition kinetics of H₂O₂ has yielded significant insights into both the fundamental chemical behaviour and practical stabilization mechanisms of this important chemical system. Through meticulous experimental design and rigorous kinetic analysis, this study has successfully quantified the thermal decomposition characteristics of H₂O₂ across multiple dimensions, providing valuable data for both academic understanding and industrial applications.

While this study has provided comprehensive kinetic characterization, several avenues for future research emerge. The precise nature of the radical intermediates in the decomposition mechanism warrants further investigation using advanced spectroscopic techniques. The potential synergistic effects of H₃BO₃ with other stabilizers could be explored to develop even more effective stabilization systems. In addition, extension of these kinetic studies to other solvent systems or under various pH conditions could provide further mechanistic insights.

In conclusion, this research has successfully bridged fundamental chemical kinetics with practical application needs through comprehensive investigation of H₂O₂ decomposition. The quantitative kinetic parameters determined, the elucidation of stabilization mechanisms, and the development of predictive models represent significant contributions to both academic knowledge and industrial practice. The findings provide a solid foundation for improved safety protocols, enhanced formulation strategies, and more efficient utilization of H₂O₂ across its numerous applications, while simultaneously advancing our fundamental understanding of peroxide chemistry in aqueous systems. The demonstrated approach of combining careful experimental measurement with sophisticated kinetic modelling serves as a paradigm for investigating complex chemical systems, highlighting how fundamental research can yield practical benefits while deepening our understanding of chemical behaviour. As H₂O₂ continues to grow in importance as an environmentally friendly oxidant and disinfectant, the insights gained from this study will contribute to safer handling, longer shelf life, and more effective utilization across countless scientific, industrial, and medical applications.