Kinetics of Performic Acid Synthesis and Decomposition - Industrial

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Kinetics of Performic Acid Synthesis and Decomposition Elio Santacesaria,*,† Vincenzo Russo,‡ Riccardo Tesser,‡ Rosa Turco,‡ and Martino Di Serio‡ †

Eurochem Engineering srl., Via Codogno 5, IT-20139, Milan, Italy Department of Chemical Sciences, University of Naples “Federico II”, Via Cinthia, IT-80126, Naples, Italy

‡

S Supporting Information *

ABSTRACT: The kinetics of performic acid decomposition was studied with a gasvolumetric technique in which we measured the volume of gas developed over time as a consequence of the reaction. Several kinetic runs were performed in the presence of catalytic amounts of H2SO4 and H3PO4 and in autocatalytic conditions by mixing solutions of HCOOH and H2O2. The trends of the curves of the gas volume (CO2) released, as a function of time, were all characterized by a more or less long induction time, followed by a straight line. Induction time appeared to be related to the kinetics of performic acid formation, rapidly reaching the equilibrium, while the successive linear trends corresponded to performic acid decomposition. A kinetic model was developed to interpret all the kinetic runs performed. The kinetic parameters with the best fits were determined, and the model was used to also simulate kinetic runs performed by other authors.

1.0. INTRODUCTION Among peroxycarboxylic acids, peracetic and performic acids are very powerful oxidants, which are environmentally friendly and commonly used in industry for many purposes, such as chemical processing, bleaching, and disinfection.1 In chemical processing, peroxycarboxylic acids are used, more specifically, to convert alkenes in epoxides, ketones to esters, and amines to nitro compounds. Peroxycarboxylic acids are simply prepared by putting the corresponding carboxylic acid in contact with a solution of hydrogen peroxide. An equilibrium is reached in a relatively short interval, but peroxycarboxylic acids are unstable and decompose more or less slowly with time. Performic and peracetic acids are the most employed peroxycarboxylic acids in industrial processes. Performic acid has shown to be more active than peracetic acid, making it a more popular oxidizing agent. In the presence of a catalytic amount of a mineral acid (H2SO4 or H3PO4), performic acid is used, in particular, in the epoxidation of soybean (ESBO) or other vegetable oils,2−5 which occurs according to the following reaction:

in order to start a new oxidizing cycle. It is clear that in order to optimize the epoxidation process the kinetics of performic acid formation and decomposition must be known. Despite the importance of the industrial production of ESBO, very few papers are available in the literature concerning the reaction between formic acid and hydrogen peroxide.6−11 Moreover, the works have been mainly focused on studying the behavior of acetic acid with hydrogen peroxide, using sulfuric acid instead of phosphoric acid as catalyst. Notwithstanding, it is known that the epoxidation of vegetable oils with performic acid is faster than the one with peracetic acid12,13 and that sulfuric acid promotes the epoxide ring opening reaction, lowering the yields in ESBO. It is further known that peracids and peroxide are not stable and decompose when the temperature increases over a certain threshold that is specific to each compound. Previous works have shown that, in an acid environment, hydrogen peroxide is stable below 100 °C,8 while performic acid is susceptible to decomposition even at room temperature.5−10 Performic acid can decompose according to two different mechanisms, an ionic mechanism occurring according to the following stoichiometry:9 HCOOOH → HCOOH +

1 O2 2

(3)

and a radicalic mechanism occurring through the overall reaction below:8,9 This reaction is extremely exothermic (ΔH = −55 kcal/mol) and occurs in biphasic conditions. Formic and performic acids are partitioned between the oil see and the aqueous phase, while water and hydrogen peroxide are not soluble in oil. Epoxidation occurs in the oil phase between the performic acid and the double bonds, restoring formic acid as a consequence of the reaction. Formic acid comes back by diffusion to the aqueous phase where it is oxidized once again to performic acid © XXXX American Chemical Society

HCOOOH → CO2 + H 2O

(4)

Special Issue: Tapio Salmi Festschrift Received: February 10, 2017 Revised: April 14, 2017 Accepted: April 15, 2017

A

DOI: 10.1021/acs.iecr.7b00593 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research The first reaction indirectly consumes only H2O2, while the second reaction consumes both HCOOH and H2O2. For epoxidation it is, therefore, crucial to know the kinetics of both performic acid synthesis and decomposition as well as all the factors affecting these two reaction rates. As already mentioned, very few papers5−10 have been published dealing with this subject and reports concerning the kinetic results are in strong disagreement, as can be seen in the next section where a brief survey of the available literature is reported. There is disagreement on the value of the equilibrium constant of reaction 1 and in particular on the performic acid decomposition for what concerns both the stoichiometry of the reaction and the effect of acidity on the decomposition rate. For this reason, we studied the decomposition reaction by adopting a gas-volumetric technique based on the measurement of the volume of gas produced with time as a consequence of the reaction itself. This technique yields more accurate results compared to the chemical methods evaluating the performic acid and the hydrogen peroxide concentration for the large volume of gas produced. We observed that all the gasvolumetric kinetic runs showed a more or less long induction time that was strictly related to the rate of performic acid synthesis. Therefore, with the mentioned technique, it was also possible to collect information also on the kinetics of performic formation. In contrast to previous works on the subject, we showed that the performic acid decomposition rate was independent of acidity. A kinetic model, with related parameters for synthesis and decomposition of performic acid, was developed for the interpretation of all the kinetic runs performed. This model was able to simulate not only our gasvolumetric kinetic runs but also kinetic runs performed by other authors. 1.1. A Survey of the Available Literature on the Formation and Decomposition of Performic Acid. In a pioneering work, Monger and Redlich6 studied the equilibrium and formation rate of performic acid in both the presence and absence of H2SO4 as catalyst, at different temperatures, opportunely changing the initial composition. The authors determined performic acid concentration and residual hydrogen peroxide, separately. According to the authors, the equilibrium constant changed moderately with both reagents concentration and temperature falling in the range 0.5−2. The same authors identified a second order kinetics for the synthesis reaction and estimated an activation energy of 58.61 kJ/mol. Although this work is not rigorous enough in not considering the contribution of performic acid decomposition, it is nonetheless useful for the estimation of the equilibrium constant of performic synthesis. The first work studying the kinetics of peroxyformic acid formation was published by Mosovsky et al.7 The kinetics was studied only at 45 °C in a continuous well-stirred reactor using HCOOH (99% b.w.; 26.24 mol/L), H2O2 (30−70% b.w. from 10.5 to 29.8 mol/L) and 0−0.1 mol/L H2SO4. The volume of the reactor was 40 cm3. Formic acid was mixed with sulfuric acid and was fed at the inlet of the reactor independently of hydrogen peroxide. The ratio H2O2/HCOOH was kept 1:2.67. Steady state conditions were reached after 3−4 h. The authors considered the following reaction scheme: H 2O2 + HCOOH ↔ HCOOOH + H 2O

(5)


(6)

2H 2O2 → 2H 2O + O2

(7)

with the following rate equations: Related to the equilibrium reaction 5: r1 = {k1[H 2O2 ][HCOOH] − k −1[H 2O][HCOOOH]} *[H+]

(8)

Related to the performic acid decomposition: r2 = k 2[HCOOOH][H+]

(9)

Related to the hydrogen peroxide decomposition: r3 = k 3[H+][H 2O2 ]2

(10)

The best fitting (Model I) was obtained by the authors with the kinetic constants: k1 = 1 ± 0.49 L6 mol−2 h−1; k−1 = 2.68 ± 1.57 L6 mol−2 h−1; k2 = 0; k3= 0.29 ± 0.04 dm6 mol−2 h−1. Another model (Model II) considered the main reaction always at equilibrium assuming: Ke = k1/k−1 = 0.32 ± 0.03. The two models suggested by the authors, however, present some drawbacks. First of all, in the described experimental conditions, hydrogen peroxide was stable and only performic acid decomposed, as results also from previous studies.8,9 Moreover, the acidity of the reaction mixture, in the absence of sulfuric acid, was overestimated since performic acid was considered by the authors to have the same dissociation constant of formic acid, while the acidity of performic acid is actually much lower. All the considerations, previously mentioned, were evaluated in depth by De Filippis et al.8 These authors studied the kinetics of both the formation and decomposition of performic acid in the absence of a mineral acid catalyst. The reactions were just promoted by the acidity of formic acid. The kinetic runs were made in a range of temperature between 30 and 60 °C. The authors excluded the direct hydrogen peroxide decomposition that would occur at a temperature greater than 100 °C. Furthermore, the gaschromatographic analysis determined that only CO2 was obtained in their experimental conditions. Therefore, the reaction scheme considered by these authors was the following: H 2O2 + HCOOH ↔ HCOOOH + H 2O

(11)


(12)

These authors at different temperatures and at a constant ratio H2O2/HCOOH performed a series of kinetic runs. In each run, they used 16 cm3 of H2O2 (50% b.w.) + 8 cm3 of HCOOH (98% b.w.). The authors withdrew small samples at different times and analyzed residual hydrogen peroxide and performic acid, separately. The performed runs were simulated by assuming the following kinetic model: d[H 2O] d[HCOOOH] = r1 − r2 = r1 + r2 dt dt d[H 2O2 ] d[HCOOH] = − r1 = −r1 dt dt

(13)

with: r1 = {k1[H 2O2 ][HCOOH] − k −1[H 2O][HCOOOH]}*[H+] (14) +

r2 = k 2[HCOOOH][H ]

(15)

The model shows that the decomposition was strongly affected by temperature. Experimental data were collected and simulated considering the evolution with time of both B


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this approach is not correct. However, their model was based on two reactions that were the reversible synthesis:

performic acid formation and hydrogen peroxide depletion. De Filippis et al.8 assumed a value for the equilibrium constant Ke1 = k1/k−1 = 0.8, at 25 °C, on the basis of the previously described work by Monger et al.6 and by that of Ramos et al.14 The change of the equilibrium value with temperature was estimated by De Filippis et al.8 by applying the Van’t Hoff equation after the determination of the enthalpy change of the reaction. The heat formation of formic acid, hydrogen peroxide, and water have already been reported in the literature, while there is still a lack of information concerning the heat formation of performic acid. Following Benassi and Taddei,15 De Filippis and co-workers8 assumed a value of −272.1 kJ/mol for performic acid formation. The hydrogen ion concentration was determined by considering only the dissociation constant of formic acid (pKa = 3.75 at 25 °C), the dissociation constant of performic acid being much lower (pKa = 7.3 at 25 °C). The dependence on temperature of the dissociation constant of formic acid was determined by the relation: pK a = −57.528 +

2773.9 + 9.1232 T

H 2O2 + HCOOH ↔ HCOOOH + H 2O

and the already mentioned decomposition, respectively. This last aspect is the main difference with respect to the approach followed by De Filippis et al.8 The hydrogen ion concentration was determined as [H +] = (K faCa)1/2

ln K fa = −

(16)

(17)

According to the authors, both pre-exponential factors were expressed as (L6 mol−2 s−1), while the activation energies were measured in (J/mol). As remarked by the same authors, the results of the kinetics of performic acid formation obtained by De Filippis and co-workers8 were in strong disagreement with the data previously obtained by other authors, such as Shapilov et al.16 and Ramos et al.14 The authors justified the disagreement with the fact that other authors neglected the decomposition of performic acid in their kinetic data elaboration. However, it must be stressed that also the work of De Filippis et al.8 is somewhat lacking; first, because the effect of changing the ratio H 2 O 2 /HCOOH was not considered, and second, because the effect of hydrogen ion concentration on performic acid decomposition was not experimentally verified also considering that the pH, in the presence of formic acid, did not change very much. These issues were dealt with in the recently published work by Sun et al.9 These authors repeated the kinetic work conducted by De Filippis et al.,8 reproducing the reaction in the absence of a mineral acid, but also considered the effect of sulfuric acid on the reacting system. Unfortunately, this work is confusing in terms of data interpretation. The authors mentioned the possibility of both decomposition reactions of performic acid occurring, namely: HCOOOH → CO2 + H 2O

(18)

2HCOOOH → 2HCOOH + O2

(19)

with

ΔG° = 21 kJ/mol

(23)

r1 = {k1[H 2O2 ][HCOOH] − k −1[H 2O][HCOOOH]} *[H+]

(24)

that is, equal to the expression (14) used by De Filippis et al. and r2 = k 2[HCOOOH]

(25)

9

+

Initially, Sun et al. assumed r2 = f([H ],T) but then they did not observe this dependence for r2, in particular by working in the presence of sulfuric acid. The best fitting of the experimental data with the model proposed by Sun et al.9 provided the following kinetic parameters: ⎛ 75200 ⎞ ⎟ k1 = 3.99 × 1010 exp⎜ − ⎝ RT ⎠ ⎛ 40400 ⎞ ⎟ k −1 = 1.10 × 105 exp⎜ − ⎝ RT ⎠ ⎛ 95400 ⎞ ⎟ k 2 = 2.68 × 1013 exp⎜ − ⎝ RT ⎠

(26)

(27)

where k1 and k−1, according to the authors, were expressed in (L2 mol−2min−1), while k2 in (L mol−1min−1). Sun et al.9 found kinetic constants, which were lower than the ones given by De Filippis et al.8 and attributed this disagreement (i) to the difference of the kinetic equation adopted, (ii) to the difference in the dissociation constant of formic acid determined with different equations, and (iii) to the difference in the calculation of the equilibrium constant of the synthesis reaction. However,

and arbitrarily assumed, in the absence of any experimental support, a stoichiometry of the type: 3HCOOOH → 2HCOOH + CO2 + O2 + H 2O

ΔGo RT

Although the approach developed by the authors concerning the performic acid decomposition reaction is questionable, the work is interesting for the reported experimental data that could be reinterpreted with a more suitable model. The runs in this case were made by mixing 5.5 cm3 of HCOOH (88% b.w.) with 34.5 cm3 of H2O2 (30% b.w.) in a 100 cm3 flask. A great difference with the data collected by De Filippis et al.8 was directly observable at 30 °C in which the formation of performic acid never reached a maximum value but the system simply slowly arrived at an equilibrium. This means that according to the data collected by Sun et al.,9 at 30 °C, the performic acid decomposition rate was negligible, which was not so in the runs as shown by De Filippis et al.8 However, it must also be pointed out that the solutions used by De Filippis et al.8 were more concentrated for both H2O2 (13 mol/L instead of 8.42 mol/L) and HCOOH (8 mol/L instead of 3.16 mol/L). The reaction rates considered in this case were

k1 = 13065.1 exp( −43524.2/RT ) k 2 = 6.51 × 109 exp( −72627.9/RT )

(22)

The value of Kfa at different temperatures was calculated according to the following relation:

The mathematical regression analysis made on all the experimental runs brought to the following kinetic constants:

and

(21)

(20)

This is simply the sum of the two decomposition reactions, which means they assumed that the two independent reactions 18 and 19 always occurred at the same reaction rate. Clearly, C


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Industrial & Engineering Chemistry Research ⎡ 97300 ⎛ 1 1 ⎞⎤ ⎜ ⎟⎥ k −1 = 3.77 × 10−6⎢ − − ⎣ R ⎝T 298 ⎠⎦

by reinterpreting the mass balance of an equilibrium run of performic acid formation reported by these authors, we found that the decomposition occurred with the stoichiometry, as suggested by De Filippis et al.8 according to reaction 12, since both hydrogen peroxide and formic acid were consumed as a consequence of the decomposition. Moreover, an equilibrium constant of 1.13 at 45 °C was recalculated from their experimental data, which was in reasonable agreement with the findings of De Filippis et al.8 Sun et al.9 also made some runs in the presence of sulfuric acid with the aim of evaluating the effect of hydrogen ion concentration in particular on the decomposition reaction. According to their results it seems that sulfuric acid has a stabilizing effect on the decomposition, besides, the system is not sensitive to the increase in concentration of sulfuric acid, that is, the rates are similar at different sulfuric acid concentrations. This behavior suggests that the kinetics of performic acid decomposition does not depend on proton concentration. Leveneur et al.11 in a recent work studied the reaction in the presence of acid exchange resin as acid catalyst, but in the same work examined also the homogeneous contribution and compared the parameters found for this reaction with the ones of both De Filippis et al.8 and Sun et al.9 Their comparison of the parameters is reported in Table 1:

Dimension was reported in both cases as (L2 mol−2 s−1). From the kinetic data the equilibrium constants of performic acid formation were also determined as Keq =

Sun et al.9 De Filippis et al.8 Leveneur et al.11

k1

ΔE1

k2

ΔE2

J/mol

s−1

J/mol

2.95 × 10−4 9.26 × 10−4

75200 43522

0.87 × 10−4

20000

9.53 × 10−5 7.66 × 10−3 (L mol−1s−1) 0.13 × 10−3

(30)

2.0. EXPERIMENTAL SECTION 2.1. Apparatus, Methods, and Reagents. Different kinetic runs were performed to evaluate the kinetics of performic acid formation and decomposition in the presence of H3PO4 and H2SO4, respectively, in a catalytic amount and in the absence of such mineral acids, with the scope of evaluating the influence of the hydrogen ion concentration on the rates of the involved reactions. All runs were made by measuring, with a gas-volumetric technique, the amount of gas developed over time with a simple apparatus, consisting in a 150 cm3 jacketed reactor, connected to an ultrathermostat to obtain a good regulation of the temperature. A thermocouple immerged in the liquid solution monitored temperature. The gas developed by performic acid decomposition was conveyed to a gasvolumetric system, which first passed through a condenser to avoid any water loss by evaporation. The reading error of the gas-volumetric system was less than 5%. These measurements are considered to be more precise than the chemical analysis of both the performic acid formed and the residual hydrogen peroxide, considering that a volume of about 12 L of gas is developed, at room temperature, for one mole of decomposed performic acid. In the runs performed by us, the maximum amount of developed gas measured was 450 cm3 for the limited volume of the apparatus collecting the gas. The reactor was a glass flask and the reaction solution was wellstirred by a magnetic rod. The temperature and pH of the solution were continuously monitored. An electric resistance heated the reactor at the desired temperature. All the reagents employed were purchased by Fluka at the maximum degree of purity available, with the exception of hydrogen peroxide (55− 60% b.w.), which was kindly supplied by Solvay SpA.

95400 72624 95100

As can be seen, there is an order of magnitude between the kinetic constant of peroxyformic acid formation by De Filippis et al.8 and Leveneur et al.11 and the activation energies are quite different. This disagreement should promote further research on the subject. Some interesting works were published by Ebrahimi and coworkers,10,13 who studied the synthesis of performic and peracetic acid in continuous microreactors, using sulfuric acid as catalyst. They used HCOOH (90% b.w.) and H2O2 (50% b.w.) as reagents and H2SO4 (96% b.w.) as catalyst. First of all, they confirmed that HCOOH was much more reactive than CH3COOH, considering the former reached equilibrium in 4 min at 313 K, while the latter required more than 10 min at 343 K. Furthermore, it is interesting to note that, according to these authors, sulfuric acid concentration strongly influenced the rate of performic formation. On the contrary, the decomposition rate was negligible, in this case, as a consequence of a very low residence time in the microreactor. As expected, also temperature had a great influence on the synthesis reaction rate. No kinetic approach was reported by the authors to interpret the kinetic runs of the work.10 A kinetic analysis was, instead, reported in a successive work by the same authors.13 The kinetic parameters found as best fitting for the performic acid formation were ⎡ 75700 ⎛ 1 1 ⎞⎤ ⎜ ⎟⎥ k1 = 5.43 × 10−6⎢ − − ⎝ ⎣ R T 298 ⎠⎦

⎡ 21600 ⎛ 1 k1 1 ⎞⎤ ⎜ ⎟⎥ = 1.44 exp⎢ − ⎣ R ⎝T k −1 298 ⎠⎦

The equilibrium values found at 278, 283, 288, 293, and 303 K, respectively, were 2.70, 2.28, 1.95, 1.67, and 1.25, respectively. In conclusion, some kinetic and equilibrium constants have been proposed by different authors to describe the reaction of synthesis and decomposition of performic acid but the values found, as well as results highlighted, are in strong disagreement with each other. Further work should be promoted to identify the correct kinetic model and most reliable kinetic parameters to describe performic acid synthesis and decomposition, which is the main aim of the present work.

Table 1. Kinetic Parameters Determined by Leveneur et al.11 in Comparison with De Filippis et al.8 and Sun et al.9 L2 mol−2 s−1

(29)

3.0. RESULTS A list of the experimental tests related to both the hydrogen peroxide and performic acid decomposition activity, in the presence of H3PO4, is reported in Table S1 of the Supporting Information. Runs 1−5 were performed just to test the possible independent hydrogen peroxide decomposition. No decomposition occurred, in more than 1 h of reaction time, confirming the findings of De Filippis et al.8 concerning the hydrogen peroxide stability. Runs 6−14 were performed to test performic acid decomposition, investigating, in particular, the

(28) D


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Figure 1. Runs performed by using H3PO4 as catalyst: (A) runs performed at different temperatures (run 6 = 50 °C, run 7 = 60 °C, run 8 = 70 °C) in the presence of a constant amount of H3PO4 (0.64g), formic acid (6.3 g), and H2O2 (about 24g); (B) runs performed at different H3PO4 content (run 6 = 1.28%, run 9 = 0.69%, run 10 = 0.37%), at 50 °C and in the presence of a constant amount of formic acid (6.3 g) and H2O2 (about 24g).

Figure 2. Runs performed by using H3PO4 as catalyst: (A) runs performed at different H2O2 content (run 6 = 48.22%, run 11 = 35.99%, run 12 = 19.71%), at 50 °C and in the presence of a constant amount of formic acid (6.3 g) and H3PO4 (0.64g); (B) runs performed at different FA content (run 6 = 12.61%, run 13 = 6.29%, run 14 = 3.13%), at 50 °C and in the presence of a constant amount of H3PO4 (0.64 g) and H2O2 (about 24 g).

performic acid decomposition may not be promoted by acidity. To verify this aspect, we found it most appropriate to conduct decomposition runs in the presence of a stronger acid, such as sulfuric acid, which is completely dissociated. For this reason additional runs were performed in the presence of sulfuric acid with the mean scope to evaluate the role of acidity in promoting the decomposition of performic acid. The experimental tests of performic acid decomposition, performed in the presence of H2SO4, are summarized in the Supporting Information (Table S2). The experimental results obtained are reported in Figures 3 and 4. Linear trends were again obtained for all the runs made after a very short induction time. A considerable effect of both temperature and formic acid concentration on the decomposition rate were confirmed also in the presence of sulfuric

dependence of the reaction rate on both the temperature and the reagents/catalyst ratio. The experimental results obtained are reported in Figures 1 and 2. By observing all the runs made it can be noted that, apart from a more or less short induction time, all the runs showed a linear trend of the gas volume released with time. Furthermore, by observing Figures 1 and 2 we can come to the conclusion that temperature and formic acid concentration both had a strong effect on the production of gas derived from performic acid decomposition. In contrast, the influence of the H3PO4 concentration was very small. We can give two different interpretations to this behavior. The first is based on the fact that, considering the low dissociation level of this acid (pKa = 2.14), the pH does not change very much by changing the acid concentration. Another more reliable interpretation is that E


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Figure 3. Runs performed by using H2SO4 as catalyst. (A) Runs performed at different temperatures (run 15 = 50 °C, run 16 = 60 °C, run 17 = 70 °C) in the presence of a constant amount of H2SO4 (0.72g), formic acid (6.3 g), and H2O2 (about 24g); (B) runs performed at different H2SO4 content (run 15 = 1.43%, run 18 = 0.78%, run 19 = 0.39%), at 50 °C and in the presence of a constant amount of formic acid (6.3 g) and H2O2 (about 24 g).

Figure 4. Runs performed by using H2SO4 as catalyst: (A) runs performed at different H2O2 content (run 15 = 48.21%, run 20 = 35.42%, run 21 = 19.71%), at 50 °C and in the presence of a constant amount of formic acid (6.3 g) and H2SO4 (0.72g); (B) runs performed at different FA content (run 15 = 12.63%, run 22 = 6.31%, run 23 = 3.14%), at 50 °C and in the presence of a constant amount of H2SO4 (0.72 g) and H2O2 (about 24 g).

case, the acidity of the reaction environment was only attributed to the presence of formic acid having a pKa= 3.75. In Table S3 are reported the experimental tests related to the performic acid decomposition performed in the absence of mineral acid. The experimental results obtained are reported in Figure 5. The first observation that should be underlined concerning the runs of Figure 5 is that the induction time was much more prolonged in agreement with the dependence of performic acid formation rate on proton concentration. The length of the induction time was strictly correlated with the kinetics of performic acid formation, which is known to depend on acidity. The great effect of temperature was also confirmed, as well as the effect of the formic acid concentration. The behavior of H2O2 was also similar to the results previously observed.

acid. On the contrary, the effect of sulfuric acid concentration was small considering that the slopes of gas volume released were the same independently of the concentration of sulfuric acid. As sulfuric acid is completely dissociated, we can conclude that hydrogen ion concentration had no influence on the performic acid decomposition rate and the small observed differences could be attributed to the different rates of performic acid formation giving place to different induction times. The behaviors observed for the runs performed at different H2O2 concentrations were similar to the ones previously observed in the presence of H3PO4 despite the hydrogen ion concentrations being very different in the two mentioned cases. These behaviors, therefore, appear to be uncorrelated with the acidity of the solution. Finally, we studied the kinetics in the absence of mineral acid as catalyst. In this F


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Figure 5. Runs performed in the absence of mineral acids: (A) Runs performed at different temperatures (run 24 = 50 °C, run 25 = 60 °C, run 26 = 70 °C) in the presence of a constant amount of formic acid (6.3 g) and H2O2 (about 24g). (B) runs performed at different H2O2 content (run 24 = 48.96%, run 27 = 20.01%), at 50 °C and in the presence of a constant amount of formic acid (6.3 g). (C) runs performed at different FA content (run 24 = 12.81%, run 28 = 6.40%, run 29 = 3.10%), at 50 °C and in the presence of a constant amount of H2O2 (about 24 g).

4.0. DISCUSSION 4.1. Description of the Adopted Kinetic Model. Keeping in mind the occurring equilibrium reaction of PFA formation H 2O2 + HCOOH ↔ HCOOOH + H 2O

(31)

(38)

d[CO2 ] = r2 dt

(39)

Equation 39, in particular, gives the moles of CO2 produced per liter of reacting solution. This means that to obtain the effective volume of gas evolved in cm3 we must perform the following calculation:

and the main consecutive decomposition reaction HCOOOH → CO2 + H 2O

d[H 2O] = r1 + r2 dt

(32)

we tested a kinetic model of the type: ⎛ 1 [PFA][H 2O] ⎞ r1 = k1[H+][FA][H 2O2 ]⎜1 − ⎟ Ke [FA][H 2O2 ] ⎠ ⎝

volume of gas =

(34) 8,9

That is, as opposed to previous authors, we considered the rate of this reaction independently of the environment’s acidity, as shown by our experimental results. According to this model, in order to evaluate the evolution with time of all the chemical components involved, we must write and solve the mass balance equations for a batch reactor as

d[FA] = −r1 dt

(35)

d[H 2O2 ] = −r1 dt

(36)

d[PFA] = r1 − r2 dt

(37)

(40)

where VM corresponds to the gas molar volume and VL is the liquid volume in the reactor in cm3. The solution of these ordinary differential equation systems requires the knowledge of (i) the kinetic parameters k1 and k2 and their dependence on temperature, which implies also the knowledge of the two activation energies ΔE1 and ΔE2; (ii) the value of the equilibrium constant Ke and its dependence on temperature, that is the knowledge of the enthalpy of the reaction, and (iii) the [H+] concentration by considering all the parameters that contribute to this concentration, such as the formic acid dissociation, the phosphoric or sulfuric acid dissociations, the change with temperature of the corresponding dissociation constants and that of the ionic product of water Kw. 4.2. Estimation of the Equilibrium Constant for Performic Formation. According to Leveneur et al.,11 on the basis of calorimetric measurements, the reaction enthalpy change of performic synthesis would be −4840 (J/mol) with a value of 0.96 at 30 °C. This means that, according to these authors, the reaction should be moderately exothermic with the equilibrium constant in the order of 0.7−0.8 in the temperature range of 60−75 °C. Recently, Ebrahimi et al.13 confirmed the moderate exothermicity of this reaction and evaluated the Ke values from kinetic data, at different temperatures (see relation 30). The values determined by Ebrahimi et al.13 were somewhat greater than the ones found by Leveneur et al.11 However, both

(33)

where r1 was the rate of performic acid formation. As the formula suggests, both the forward and reverse reactions were catalyzed by the acid environment, in agreement with other authors, while the decomposition reaction was interpreted simply with a first order kinetic law of the type:

r2 = k 2[PFA]

[CO2 ] × VM × VL 1000

G


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Industrial & Engineering Chemistry Research were comparable to the values obtained by Monger et al.,6 who reported values of Ke not exceeding 2 at the same temperature range, while Sun et al.9 determined a value of 1.13 at 45 °C, by analyzing the equilibrium composition, in agreement with De Filippis et al.8 at the same temperature conditions. Considering the enthalpy change proposed by Leveneur et al.11 and by Ebrahimi et al.,13 together with the other available values, for our simulation we assumed a reasonable value of −10000 J/mol of enthalpy change, starting from a value of 1.6 for the equilibrium constant at 298 K, that was the following: ⎡⎛ −10000 ⎞ ⎛ 1 1 ⎞⎤ ⎟ × ⎜ KeT = Ke298 exp⎢⎜ − ⎟⎥ ⎣⎝ R ⎠ ⎝ 298 T ⎠⎦

the dissociation constant of HCOOH as a function of temperature can be calculated with the following relationship: logK aFA = − (173.624/T ) + 17.88348 log T − 0.0280397T − 39.06123

More recently, Kim et al.18 have proposed the following relationship that fits well with the experimental results: pK

(41)

(3) [HCOOH] + [HCOO−] − [HCOOH]◦ = 0 (4) [HCOO−] + [OH−] − [H+] = 0

× 10−3 × 10−8 × 10−13 × 106 × 10−2 [H+] [OH−] = 10−14

H3PO4 ⇄ H+ + H 2PO4 −

k1 = 7.11 × 10−3

(48)

H 2PO4 − ⇄ H+ + HPO4 =

k 2 = 6.31 × 10−8

(49)

HPO4 = ⇄ H+ + PO4 3 −

4.4. Hydrogen Ion Concentration in the Formic− Performic Acid System. In the absence of mineral acids the acidity is only due to the dissociation of formic acid:

[H+][HCOO−] [HCOOH]

(42)

(43)

−log K1 =

To evaluate the proton concentration correctly, at different temperatures, it is necessary to know the dependence of both KaFA and Kw on this parameter. Kw has been shown to be highly dependent on temperature and the following relation interpolates Kw values well at different temperatures: K w = 8.754 × 10−10 exp( −1.01 × 106 /T 2)

k 3 = 4.8 × 10−13

(50)

As suggested, K1 is comparable with the dissociation constant of formic acid kaFA = 1.8 × 10−4; therefore, [H+] concentration must be rigorously calculated by considering all the equilibrium constants but, more specifically, K1, KaFA and their dependence on temperature. The dependence of k1 on temperature was determined by Bates19 whose data were interpolated with the following relationship:

The dissociation constant of performic acid is too low and therefore can be neglected. Hence, we can write K aFA =

(47)

in which Kw and KaFA are calculated at different temperatures with the previously reported equations. 4.5. Hydrogen Ion Concentration in the H3PO4− Formic Acid System. In this case the acidity of the system is the result of the contribution of both H3PO4 and HCOOH. H3PO4 gives place to three different dissociation equilibria:

1.77 × 10−4 7.90 × 10−8

HCOOH ⇄ H+ + HCOO−

(46)

(2) [H+]*[OH−] − K w = 0

dissociation constant at 25 °C and ionic product

7.11 6.31 4.80 2.40 1.20 Kw=

= −57.528 + 2773.9/T + 9.1232 ln T

(1) [H+]*[HCOO−] − K aFA[HCOOH] = 0

Table 2. Ionic Dissociation Constants at 25 °C

HCOOH → H+ + HCOO− HCOOOH ⇄ H+ + HCOOO− H3PO4 ⇄ H+ + H2PO4− H2PO4− ⇄ H+ + HPO4= HPO4= ⇄ H+ + PO43− H2SO4 ⇄ H+ + HSO4− HSO4−⇄ H+ + SO4= H2O ⇄ H+ + OH−

aFA

To evaluate the [H+] concentration for different HCOOH concentrations and different temperatures the following algebraic four equations system must be solved after any integration step of eqs 35−39:

4.3. Determination of Hydrogen Ions Concentration at Different Temperatures. As suggested, [H+] concentration appears to affect the rate of performic acid formation. It is, therefore, important to evaluate the concentration, at the reaction temperature, in particular when H3PO4 is used as catalyst and/or in the absence of mineral acid. Three different calculation programs were developed to determine [H+] concentration, at the reaction temperature and in the presence of (i) a mixture of H2SO4 and HCOOH, (ii) a mixture of H3PO4 and HCOOH, and (iii) HCOOH alone, respectively. In Table 2 are reported the dissociation constants for all the mentioned acids at 25 °C.

type of dissociation

(45)

799.31 − 4.5535 + 0.013486T T

(51)

The equilibrium constants K2 and K3 are too small and their dependence on temperature can be neglected. Thus, we considered only the dependence of K1 and KaFA by adopting the relations 51 and 45, respectively. To obtain the [H+] concentration in a solution containing both H3PO4 and HCOOH requires again to solve the following algebraic eight equations system after any integration step of eqs 35−39:

(44)

Different works have been published concerning the dissociation constant of HCOOH, in particular to mention are those by Harned et al.17 and Kim et al.18 Their results are in good agreement with each other. According to Harned et al.,17 H


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Industrial & Engineering Chemistry Research (1) [H+][H 2PO4 −] − K1[H3PO4 ] = 0

already described, and by carefully examining, more specifically, the effect of pH, temperature, as well as of the concentration of both formic acid and hydrogen peroxide. The effect of pH was well tested by comparing the behavior of the runs performed (i) in the presence of sulfuric acid (low pH), (ii) phosphoric acid (intermediate pH), and (iii) formic acid alone (higher pH). To this end, we examined the influence of the other factors mentioned above for the three levels of pH described, that is, we divided the runs according to the catalyst used: sulfuric acid, phosphoric acid, formic acid. Moreover, as the HCOOOH decomposition lowers the HCOOH concentration, the [H+] concentration was adjusted after each integration step by solving the algebraic systems, previously described. In all cases, the best fitting kinetic parameters were determined for each single run by applying the least-square method to all the experimental points. The obtained results are reported run by run in the corresponding tables reported in the Supporting Information of this work. Then, an average value of the kinetic constants, collected at the same temperature, was determined together with the standard deviations. The kinetic constants, determined at different temperatures, were arranged in an Arrhenius plot and submitted to linear regression analysis to determine the average activation energy and related standard deviation. 4.8. Simulation of the Runs Performed in the Presence of Sulfuric Acid. Nine kinetic runs were performed in the presence of H2SO4 as catalyst (see Table S2). Runs 15, 16, and 17 were carried out in very similar conditions where only temperature (50, 60, and 70 °C, respectively) was changed. Runs 15, 18, and 19 were made at different concentrations of H2SO4, runs 15, 20, and 21 were made at different initial concentrations of H2O2, while runs 15, 22, and 23 were performed at different initial concentrations of HCOOH. The best fitting kinetic parameters, as already mentioned, were determined for each single run and reported in Table S2. All the kinetic runs, performed in the presence of H2SO4 as catalyst, were simulated with satisfactory results by using the kinetic model already described and with the following optimized parameters:

(2) [H+][HPO4 =] − K 2[H 2PO4 −] = 0 (3) [H+][PO4 3 −] − K3[HPO4 =] = 0 (4) [H+][OH−] − K w = 0 (5) [H3PO4 ] + [H 2PO4 −] + [HPO4 =] + [PO4 3 −] − [H3PO4 ]° = 0 (6) [H 2PO4 −] + 2[HPO4 =] + 3[PO4 3 −] + [OH−] + [HCOO−] − [H+] = 0 (7) [H+][HCOO−] − K aFA[HCOOH] = 0 (8) [HCOO−] + [HCOOH] − [HCOOH]° = 0 (52)

4.6. Hydrogen Ion Concentration in the H2SO4− Formic Acid System. Sulfuric acid is completely dissociated as H 2SO4 → H+ + HSO4 −

(53)

The second dissociation constant is equal to K2sulf = 1.2 × 10−2 at 25 °C, which is a dissociation constant greater than that of formic acid:

HSO4 − ⇄ H+ + SO4 =

(54)

The dependence of this second dissociation constant on temperature has already been reported and the results are described in three works published by Dickson et al.,20 Wu et al.,21 and Marshall et al.22 Marshall et al.,22 in particular, determined K2sulf in a very large range of temperature, that is, 0−350 °C, and compared their data with that obtained from others. The points of the plots obtained were interpolated with the following relation: log K 2sulf = 56.889 − 19.8858 log T − 2.307.9/T (55)

− 0.006473T

or alternatively with the more approximated relation: log K 2sulf = 91.471 − 33.0024 log T − 3520.3/T

⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k1T = k1 ‐ 323 exp⎢⎜ − ⎝ ⎠ ⎝ ⎣ R T 323 ⎠⎦ ⎡⎛ −47518 ± 3061 ⎞ ⎟ = (1.03 ± 0.05) × 10−3 exp⎢⎜ ⎠ ⎣⎝ 8.314

(56)

Also in this case to evaluate the [H+] concentration the following system of algebraic equations must be solved: (1) [H+][HSO4 −] − K1sulf [H 2SO4 ] = 0 +

=

⎛1 1 ⎞⎤ ⎜ ⎟⎥ − ⎝T 323 ⎠⎦

−

(2) [H ][SO4 ] − K 2sulf [HSO4 ] = 0 (3) [H+][OH−] − K w = 0

(58)

⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k 2T = k 2 ‐ 323 exp⎢⎜ − ⎝ ⎠ ⎝ ⎣ R T 323 ⎠⎦ ⎡⎛ −87497 ± 2374 ⎞ ⎟ = (9.61 ± 1.56) × 10−5 exp⎢⎜ ⎠ ⎣⎝ 8.314

(4) [H 2SO4 ] + [HSO4 −] + [SO4 =] − [H 2SO4 ]° = 0 (5) [HSO4 −] + 2[SO4 =] + [OH−] + [HCOO−] − [H+] = 0

⎛1 1 ⎞⎤ ⎟⎥ − ⎝T 323 ⎠⎦

(6) [H+][HCOO−] − K aFA[HCOOH] = 0

⎜

(7) [HCOO−] + [HCOOH] − [HCOOH]° = 0 (57)

(59)

in which relation 41 was used to evaluate Ke. An example of simulation related to run 17 is reported in Figure 6 and Figure S2. Obviously, the model was able to simulate also the evolution with time of both the performic acid concentration and the residual amount of hydrogen peroxide.

4.7. Simulations of HCOOOH Decomposition Runs Based on the Measurement of the Volume of CO2 Evolved with Time. All the runs performed were interpreted by solving the system of differential eqs (relations 35−39), I


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⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k 2T = k 2 ‐ 323 exp⎢⎜ − ⎣⎝ R ⎠⎝ T 323 ⎠⎦ ⎡⎛ −98989 ± 3014 ⎞ ⎟ = (1.36 ± 0.32) × 10−4 exp⎢⎜ ⎠ ⎣⎝ 8.314 ⎛1 1 ⎞⎤ ⎜ ⎟⎥ − ⎝T 323 ⎠⎦

where relation 41 was used to evaluate Ke. An example of simulation related to run 6 is reported in Figure 6 and Figure S1. 4.10. Simulation of the Runs Performed in the Absence of Mineral Acids. Six kinetic runs were performed in the absence of mineral acids (see Table S3). Runs 25, 26, and 27 were performed in similar conditions by changing only the temperature (50, 60, and 70 °C, respectively). Runs 25 and 29 were made at different H2O2 concentrations, while runs 25, 30, and 31 were made at different HCOOH concentrations. As results from the best fitting parameters obtained for each run, which are reported in Table S3, k2 presented a satisfactory constant value changing in a narrow range between 1.33 × 10−4 and 1.66 × 10−4, with the only exception of run 29 that required a higher value of 2.05 × 10−4. Also k1 values at 50 °C remained almost constant, falling in the narrow range of 0.0010−0.0012, which were values comparable to those found for the runs performed in the presence of either H2SO4 or H3PO4. All the kinetic runs, performed in the absence of mineral acids, were simulated with satisfactory results by using the kinetic model already described with the following optimized parameters:

Figure 6. Runs performed at 50 °C with a fixed amount of formic acid (6.3 g) and hydrogen peroxide (about 24 g) but using different catalysts: run 6 = H3PO4 (0.64 g), run 17 = H2SO4 (0.72 g) and run 24 in the absence of mineral catalyst. The lines correspond to simulation profiles and the symbols to experimental data.

4.9. Simulation of the Runs Performed in the Presence of Phosphoric Acid. Nine kinetic runs were performed in the presence of H3PO4 as catalyst (see Table S1). Runs 6, 7, and 8 were carried out in similar conditions by changing only the temperature (50, 60, and 70 °C, respectively). Runs 6, 9, and 10 were done at different concentrations of H3PO4, runs 6, 11, and 12 were made at different concentrations of H2O2, while runs 6, 13, and 14 were made at different concentrations of HCOOH. The best fitting kinetic parameters were determined for each single run and reported in Table S1. As the data reported in Table S1 suggests, k2 presented an almost constant value for all runs performed at 50 °C, changing in a narrow range between 1.15 × 10−4 and 1.55 × 10−4. These results once again confirm the reliability of the adopted kinetic model. Moreover, as the k2 values obtained were greater than those obtained in the presence of sulfuric acid, we can come to the conclusion that a high acidity has a stabilizing effect on performic acid as it occurs for H2O2, which is stabilized by the presence of small amounts of a strong acid. Also k1 values, at 50 °C, remained relatively constant, falling in the narrow range 0.0010−0.0013, which were values comparable to the results of the runs performed in the presence of H2SO4. All the kinetic runs, performed in the presence of H3PO4 as catalyst, were simulated with satisfactory results by using the kinetic model already described with the following optimized parameters:

⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k1T = k1 ‐ 323 exp⎢⎜ − ⎣⎝ R ⎠⎝ T 323 ⎠⎦ ⎡⎛ −55304 ± 1288 ⎞ ⎟ = (1.20 ± 0.16) × 10−3 exp⎢⎜ ⎠ ⎣⎝ 8.314 ⎛1 1 ⎞⎤ ⎜ ⎟⎥ − ⎝T 323 ⎠⎦

(62)

⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k 2T = k 2 ‐ 323 exp⎢⎜ − ⎣⎝ R ⎠⎝ T 323 ⎠⎦ ⎡⎛ −105073 ± 8419 ⎞ ⎟ = (1.60 ± 0.32) × 10−4 exp⎢⎜ ⎠ ⎣⎝ 8.314 ⎛1 1 ⎞⎤ ⎟⎥ − ⎝T 323 ⎠⎦

⎜

(63)

where relation 41 was used to evaluate Ke. In conclusion, only two runs (run 21 and 27) out of 24 total runs showed scattered values of the kinetic parameters and both aforementioned runs were characterized by a low H2O2 concentration. An example of simulation related to run 24 is reported in Figure 6 and Figure S3. 4.11. Simulations of the Kinetic Runs of HCOOOH Formation and Decomposition Performed by Sun et al.9 with Our Kinetic Model. Sun et al.9 published different experimental results concerning the formation and decomposition of performic acid both in the presence of sulfuric acid, at 45 °C, and in the absence of mineral acids, at different reaction temperatures (30, 40, 50, and 60 °C, respectively). We reinterpreted their runs with our kinetic model by using the parameters we found in our experimental conditions, as a first

⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k1T = k1 ‐ 323 exp⎢⎜ − ⎣⎝ R ⎠⎝ T 323 ⎠⎦ ⎡⎛ −83816 ± 2905 ⎞ ⎟ = (1.16 ± 0.13) × 10−3 exp⎢⎜ ⎠ ⎣⎝ 8.314 ⎛1 1 ⎞⎤ ⎜ ⎟⎥ − ⎝T 323 ⎠⎦

(61)

(60) J


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Industrial & Engineering Chemistry Research approximation. These runs, as those of De Filippis et al.,8 are interesting in that they give experimental results concerning the evolution with time of both the performic acid and hydrogen peroxide concentrations. Moreover, Sun et al.9 also made three different runs in the presence of H2SO4, all performed at 45 °C, by changing only the concentration of H2SO4. These last runs were reinterpreted with our model and the best fitting parameters are reported in Table S4. It is interesting to note that, to correctly simulate run 32 with the same parameters of runs 30 and 31, we had to increase the value of Ke to 1.5 instead of 1.24. This gave a certain degree of uncertainty to the equilibrium constant value. Also interesting was the fact that the values of the parameters obtained were comparable to those obtained at 50 °C in our runs performed in the presence of H2SO4. Lastly, these runs confirmed the reliability of our kinetic model in which performic acid decomposition was not promoted by the [H+] concentration. Sun et al.9 also made five different runs in the presence of HCOOH alone, that is, in the absence of mineral acids. All these runs were carried out in the same experimental conditions by changing only the temperature. These runs were simulated and determined by fitting not only the values of k1 and k2 but also the Ke values. The values obtained in this way are reported in Table S5. As the results suggest, k1 and k2 both reasonably increased with temperature. Performic acid concentration, moreover, increased, not showing any decrease, in the runs performed at 20 and 30 °C, respectively, since the decomposition rate was apparently negligible at the lower temperatures described. Therefore, we assumed the decomposition rates at 20 and 30 °C as null, and determined their values by fitting the best k1 and Ke values for these two runs. The parameters of Table S5 were arranged in an Arrhenius plot, which is reported in Figure 7, and compared with the kinetic constant determined by us with the gas volumetric procedure. As can be observed, k1 values determined from our runs were somewhat higher but presented a similar activation energy that those obtained by Sun et al.,9 while, k2 values showed a greater activation energy.

On the basis of the plots of Figure 7 we were able to formulate a relation for both k1 and k2 as a function of temperature and to evaluate the corresponding activation energies for the kinetic runs made by Sun et al.:9 ⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k1T = k 2 ‐ 303 exp⎢⎜ − ⎣⎝ R ⎠⎝ T 303 ⎠⎦ ⎡⎛ −70000 ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ = 1.0 × 10−4 exp⎢⎜ − ⎣⎝ 8.314 ⎠⎝ T 303 ⎠⎦

(64)

⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k 2T = k 2 ‐ 303 exp⎢⎜ − ⎣⎝ R ⎠⎝ T 303 ⎠⎦ ⎡⎛ −52000 ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ = 6.0 × 10−5 exp⎢⎜ − ⎣⎝ 8.314 ⎠⎝ T 303 ⎠⎦

(65)

An example of simulation of a kinetic run by Sun et al.9 is reported in Figure 8. The model also simulated the amount of CO2 released that was not measured by the authors. 4.12. Simulations of the Kinetic Runs of HCOOOH Formation and Decomposition Performed by De Filippis et al.8 with Our Kinetic Model. As did Sun et al.,9 De Filippis et al.8 also performed four kinetic runs of HCOOOH formation and decomposition in the same experimental conditions, again changing only the temperature of reaction. The temperatures adopted were 30, 40, 50, and 60 °C, respectively. Also these runs were simulated with our model. It must be noted, however, that De Filippis and coworkers8 assumed an initial molar concentration of hydrogen peroxide of 13 mol/L. On the basis of the H2O2 concentration declared by the authors (50 wt %), the density of hydrogen peroxide at this concentration was about 1.2, while an apparent density of 1.326 corresponded to the molar concentration mentioned above. This value is clearly wrong and a correct value of the molarity would be 11.76. Thus, we assumed this value in our calculations. The best fitting parameters are reported in Table S6. With the corrected initial concentration of H2O2, a good fitting was obtained with equilibrium constants between 1.8 and 2.2 that were the most reasonable values in agreement with those of other authors. The parameters of Table S6 were arranged in the Arrhenius plot of Figure 9. As can be observed, the parameters we found were comparable to those determined by reinterpreting the runs performed by De Filippis et al.8 On the basis of these plots we were able to formulate a relation for both k1 and k2 as a function of temperature and to evaluate the corresponding activation energies for the kinetic runs made by De Filippis et al.:8

Figure 7. Arrhenius plot for both k1 and k2 obtained for the runs made by Sun et al.9 reinterpreted with our kinetic model. In the same plot the kinetic constants determined by us with the gas-volumetric procedure in the absence of mineral acids are also reported for comparison.

⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k1T = k1 ‐ 303 exp⎢⎜ − ⎣⎝ R ⎠⎝ T 303 ⎠⎦ ⎡⎛ −45000 ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ = 5.0 × 10−4⎢⎜ − ⎣⎝ 8.314 ⎠⎝ T 303 ⎠⎦

(66)

⎡⎛ −ΔE ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ k 2T = k 2 ‐ 303 exp⎢⎜ − ⎝ ⎠ ⎝ ⎣ R T 303 ⎠⎦ ⎡⎛ −78000 ⎞⎛ 1 1 ⎞⎤ ⎟⎜ ⎟⎥ = 2.5 × 10−5⎢⎜ − ⎣⎝ 8.314 ⎠⎝ T 303 ⎠⎦

(67)

An example of simulation of a kinetic run by De Filippis et al.8 is reported in Figure 10. K


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Figure 8. Simulation of run 33 performed by Sun et al.:9 T = 45 °C, k1 = 0.00045 L2/mol2 s, k2 = 0.00016 1/s, Ke = 1.5, [H+]° = 0.0230 mol/L.

and correctly. Moreover, we carried out a lot of runs at 50 °C, determining precisely the kinetic constants at that temperature. In conclusion, what is important for the ESBO plant optimization, in the presence of H3PO4 as catalyst, are the relations 41, 60, and 61, which can be employed to determine the formation and decomposition of performic acid as well as the depletion of hydrogen peroxide and formic acid. The model and related parameters were successfully tested also in the ESBO simulation kinetic runs, which will be reported in a future work in preparation.

■

CONCLUSIONS

The kinetics of performic acid decomposition was studied by employing a precise gas-volumetric technique. We demonstrated, by experimental work, that hydrogen peroxide did not decompose in the range of temperature adopted for the kinetic runs (30−60 °C). In contrast with previous studies, we showed that performic acid decomposition was not promoted by proton concentration but, on the contrary, a strong acidity appears to stabilize performic acid, as is already well-known to occur for hydrogen peroxide. A kinetic model was developed and tested on all the kinetic runs performed by us and also on the kinetic runs performed, with other techniques, by other authors that studied the reaction in the absence of mineral acids. The same model applied to all the performed runs and to the runs reported in the literature brought to a satisfactory agreement. However, although the applied kinetic model was the same, the kinetic parameters found, in any case, were somewhat different when operating in the presence of sulfuric acid, phosphoric acid, and in the absence of mineral acid, respectively. One reason for the observed differences could be the stability of performic acid in starting with a radicalic decomposition (initiation), most probably affected by the chemical environment. Another reason, finally, could be a significant deviation from the ideality

Figure 9. Arrhenius plot for both k1 and k2 obtained for the runs made by De Filippis et al.8 reinterpreted with our kinetic model. In the same plot the kinetic constants determined by us with the gas-volumetric procedure in the absence of mineral acids are also reported for comparison.

As mentioned before, the first experimental point of H2O2 concentration was 11.76 mol/L and not 13 mol/L but the other values were probably correct as results from an analysis of the samples withdrawn. By considering all the simulated runs we showed that the equilibrium constants were poorly affected by temperature. As was observed, the model proposed by us successfully reproduced all the runs, in the presence of sulfuric acid, phosphoric acid and in the absence of mineral acids. Our kinetic runs were definitely more precise in determining the performic acid decomposition rates, since they were based on a gas volumetric measurement. In fact, although the conversion in the decomposition of HCOOOH was low, the amount of gas that evolved was relatively high and could be measured easily

Figure 10. Simulation of run 41 performed by De Filippis et al.:8 T = 60 °C, k1 = 0.0025 L2/mol2 s, k2 = 0.00045 1/s, Ke = 2.2, [H+]° = 0.0235 mol/ L. L


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(13) Ebrahimi, F.; Kolehmainen, E.; Turunen, I. Production of Unstable Percarboxylic Acid in a Microstructured Reactor. Chem. Eng. J. 2011, 167, 713. (14) Ramos, V. D.; Derouet, D.; Visconte, L. L. Y. Epoxidation of 4Methyl-4-ene: Identification of Reaction Products and Kinetic Study. Polym. Test. 2003, 22, 889. (15) Benassi, R.; Taddei, F. Thermochemical Properties and Homolytic Bond Cleavage of Organic Peroxyacids and Peroxyester: An Empirical Approach Based on Ab Initio MO Calculations. J. Mol. Struct.: THEOCHEM 1994, 303, 101. (16) Shapilov, O. D.; Kostyukovskii, Y. L. Reaction Kinetics of Hydrogen Peroxide with Formic Acid in Aqueous Solutions. Kinet. Catal. 1974, 15, 1065. (17) Harned, H. S.; Embree, N. D. The Ionization Constant of Formic Acid from 0° to 60°C. J. Am. Chem. Soc. 1934, 56, 1042. (18) Kim, M. H.; Kim, C. S.; Lee, H. W.; Kim, K. Temperature dependence of dissociation constants for formic acid and 2,6dinitrophenol in aqueous solutions up to 175 °C. J. Chem. Soc., Faraday Trans. 1996, 2 (24), 4951. (19) Bates, R. G. First Dissociation Constant of Phosphoric Acid From 0° to 60°C. J. Res. Natl. Bur. Stand. 1951, 47 (3), 307. (20) Dickson, A. G.; Wesolowski, D. J.; Palmer, D. A.; Mesmer, R. E. Dissociation Constant of Bisulfate Ion in Aqueous Sodium Chloride Solutions to 250°C. J. Phys. Chem. 1990, 94, 7978. (21) Wu, Y. C.; Feng, D. The Second Dissociation Constant of Sulfuric Acid at Various Temperatures by the Conductometric Method. J. Solution Chem. 1995, 24 (2), 133. (22) Marshall, W. L.; Jones, E. V. Second Dissociation Constant of Sulfuric Acid from 25 to 350°C Evaluated from Solubilities of Calcium Sulfate in Sulfuric Acid Solutions. J. Phys. Chem. 1966, 70 (12), 4028.

of the components of the reacting solution, which changed according to the different reaction environment.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b00593. (Tables S1−S3) operative conditions of all the performed experimental runs together with the determined kinetic constants giving the best fitting for each run; (Tables S4−S6) operative conditions and the kinetic constants for runs performed by other researchers, simulated with our kinetic model; (Figures S1−S3) some examples of runs simulations (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: +39-02-83420817. E-mail: info@ eurochemengineering.com. ORCID

Elio Santacesaria: 0000-0002-3310-8734 Riccardo Tesser: 0000-0001-7002-7194 Martino Di Serio: 0000-0003-4489-7115 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge Desmet Ballestra SpA and Eurochem Engineering srl for financial support. REFERENCES

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Kinetics of Performic Acid Synthesis and Decomposition - Industrial

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