Kinetics of the Electrochemically Assisted Autoxidation of Toluene in

Nov 30, 2001 - The oxidation of toluene in acetic acid solution by dioxygen was studied at 100 and 109 °C in a classic gas−liquid reactor supplied ...
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Ind. Eng. Chem. Res. 2001, 40, 6055-6062

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Kinetics of the Electrochemically Assisted Autoxidation of Toluene in Acetic Acid Jean Lozar, Gilles Falgayrac, and Andre´ Savall* Laboratoire de Ge´ nie Chimique, UMR 5503 CNRS, Universite´ Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Ce´ dex 04, France

The oxidation of toluene in acetic acid solution by dioxygen was studied at 100 and 109 °C in a classic gas-liquid reactor supplied with two electrodes of graphite. The cobalt(III) acetate, the catalyst of the autoxidation process, was continuously regenerated on an anode of graphite. The average concentration of cobalt(III) acetate was higher than in absence of electric current; this led to an appreciable improvement of the kinetics of the oxidation of toluene by dioxygen. The obtained products were benzyl acetate, benzaldehyde, and benzoic acid. Benzyl acetate arises mainly from the direct electrochemical oxidation of toluene on the anode. The variations of the concentrations of toluene, benzaldehyde, and benzoic acid result from the two successive autoxidation reactions of toluene and benzaldehyde. It was verified that the kinetics of disappearance of toluene obeys the law: r1 ) k1[CoIII] [CoII]-1[C6H5CH3]. The values of the rate constant k1 were found equal to 0.36 h-1 at 100 °C and 0.51 h-1 at 109 °C. The limiting step of the mechanism of the toluene autoxidation should be the loss of the proton from the radical C6H5CH3+•. Introduction

ArCH3+• f ArCH2• + H+

(4)

Oxidation of the side chain of substituted aromatic hydrocarbons ArCH3 can be the source of alcohols, aldehydes, and acids, which often are of commercial interest.1 In particular, the autoxidation of alkylaromatics by dioxygen constitutes a direct way of preparing aldehydes ArCHO and acids ArCOOH.1,2 Dioxygen is easily available, and its cost is unimportant if air is used. Thus, autoxidation is an attractive way of oxidation. It is used at the industrial scale in the manufacture of terephthalic acid from p-xylene.3,4 The autoxidation of alkyl aromatics is practically conducted within a temperature interval from 50 to 150 °C, in the liquid phase, and under weak dioxygen pressure (0.2 atm, for example, if one uses air). The main products of autoxidation are benzaldehyde and the acid. Acetic acid is generally used as the solvent and cobalt(II) acetate as the catalyst.2 The autoxidation of an alkyl aromatic can be schematized by two consecutive steps. The first consists of the oxidation of the starting reagent into the aldehyde

ArCH2• + O2 f ArCH2O2•

(5)

ArCH2O2• + CoII f ArCH2O2CoIII

(6)

ArCH2O2CoIII f ArCHO + HOCoIII

(7)

HOCoIII + H+ f CoIII + H2O

(8)

ArCH3 + O2 f ArCHO + H2O

(1) C6H5CH2• + CoIII f C6H5CH2+ + CoII

In the second step, the aldehyde is oxidized into the acid 1

ArCHO + /2O2 f ArCOOH

(2)

The two steps are catalyzed by cobalt(III).1 The reaction propagates through radicals. Previous studies1,5-9 have allowed the following reaction scheme for the aldehyde formation to be determined

ArCH3 + CoIII f ArCH3+• + CoII

When the cobalt in solution is completely in its CoII form at the beginning of an autoxidation experiment, the initial velocity of the process is extremely slow; reaction begins only after a latency period that generally lasts several hours. This period results from the absence of the radical cation ArCH3+• (eq 3). It is known that use of an initiator such as sodium bromide that favors CoIII formation1,2 can remove the period of induction. On the other hand, in the case of toluene autoxidation, benzyl acetate is formed, with yields on the order of 1%,9 in addition to benzaldehyde and benzoic acid. The benzyl acetate results from the two following reactions

(3)

* Corresponding author. E-mail: [email protected].

(9)

C6H5CH2+ + CH3COOH f C6H5CH2OCOCH3 + H+ (10) Thus, the reaction between the C6H5CH2• radical and CoIII is competitive with the formation of the radical peroxide C6H5CH2O2• (eq 5). However, the low yield of benzyl acetate indicates that dioxygen is much more reactive than CoIII toward the radical C6H5CH2•. The mechanism of autoxidation illustrates the catalytic role of CoIII, consumed in the step 3 and regenerated in the step 6 through the radical peroxide ArCH2O2•. The redox couple CoIII/CoII acts as a catalyst in the autoxidation; consequently, it was suggested to activate

10.1021/ie0102091 CCC: $20.00 © 2001 American Chemical Society Published on Web 11/30/2001

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its effect by the in situ regeneration of CoIII by electrolysis.10-13 This technique of activation of the catalyst was applied successfully to the oxidations of p-methoxytoluene,10,12 toluene,11 and p-tert-butyltoluene.13 The technique was applied by plunging two graphite electrodes into the reactor and using galvanostatic conditions for electrolysis. The electrochemical activation of the catalyst presents the following characteristics: (1) The induction period is considerably reduced. When CoIII, prepared in advance by electrochemistry, is initially present in the reactor, oxidation starts immediately. (2) The kinetics of the reaction is improved. For example, for p-methoxytoluene, the maximal yield in p-methoxybenzaldehyde of 40% is reached in 1.5 h compared to 5.5 h without current.10 (3) The electrolysis contributes very weakly to the formation of the aldehyde and the acid (cf. Figure 2 in ref 12); dioxygen is the main oxidizing agent. (4) Finally, the selectivity in aldehyde remains comparable to that of an autoxidation reaction without electric current. This article addresses the modeling of the kinetics of electrochemically assisted toluene autoxidation. To this end, experimental variations in the concentrations of toluene, benzaldehyde, and benzoic acid, as well as cobalt for its two oxidation degrees (II and III), were analyzed to deduce a law for the rate of the autoxidation process. The origin of relatively important quantities of benzyl acetate under electrolysis conditions is also discussed. Experimental Section Chemicals, supplied by Aldrich, were used without purification. The autoxidation reactor was a cell (Metrohm) of 150-mL of capacity. This cell was maintained at constant temperature by means of a double envelope through which heat-regulated water flowed. Dioxygen was injected into the liquid phase (100 mL) by means of a Teflon tube provided with a glass frit in its end. The diffuser formed small bubbles, which produced a large gas-liquid exchange area. The oxygen, whose flow rate was 150 mL min-1, was in excess with respect to the quantity needed for the reaction. The high value of the gas flow improved the rate of gas transfer in the liquid phase through an increase in the mass transfer coefficient. It was verified that the oxygen flow does not have an influence on oxidation rate beyond 150 mL min-1. The concentration of oxygen in the liquid phase can be considered as close to its saturation value, which is about 3 mM at 100 °C.14 The reactor was topped with two coolers placed in series to condense the toluene and the acetic acid vapors. The temperature of the first cooler was maintained at 0 °C, that of the second was -30 °C. Sodium acetate was dissolved in the solution, at 1 mol L-1 concentration, to increase the specific conductivity of the solution. The autoxidation experiments were conducted in galvanostatic mode in this reactor supplied with two cylindrical electrodes of graphite. These electrodes were composed of two rods of graphite with diameters of 0.5 cm for the cathode and 1.2 cm for the anode. The area of the anode was 21 cm2, and the cathode area was 8 cm2. The surface of the anode, larger than that of the cathode, favored oxidation of CoII at the expense of the acetic acid oxidation and, in contrast, decreased the reduction of CoIII to the benefit of hydrogen evolution. Two series of six experiments were performed at 100 and 109 °C. The initial concentrations of toluene cal-

Table 1. Operating Conditions for Electrochemically Assisted Toluene Autoxidationa [CoIII]mean [Co]total exp

Ib (A)

[toluene]0c

[Co]totald

[CoIII]0c

1 2 3 4 5 6

0 0.12 0.20 0.24 0.89 0.90

0.9234 0.3624 0.470 0.9234 0.9234 0.9234

T ) 100 °C 0.1847 0.065 0.1847 0 0.094 0 0.1847 0 0.1847 0.064 0.4063 0.170

7 8 9 10 11 12

0.36 0.48 0.49 0.49 0.63 0.95

0.4574 0.4574 0.4574 0.4574 0.9147 0.4574

T ) 109 °C 0.402 0.200 0.402 0 0.402 0 0.402 0 0.402 0 0.402 0.175

[CoIII]meane

(%)

0.028 0.026 0.015 0.029 0.048 0.129

15 14 16 16 26 32

0.128 0.096 0.087 0.089 0.068 0.124

31 24 22 22 17 31

a Volume of solution at 20 °C ) 100 mL. Oxygen flow ) 150 mL min-1. Sodium acetate concentration at 20 °C ) 1 mol L-1. b I: current intensity. c [toluene] , [CoIII] ) initial concentrations 0 0 of toluene and cobalt(III) acetate, respectively (mol L-1). d [Co]total ) total cobalt(II) and cobalt(III) acetate concentration. e [CoIII]mean ) mean cobalt(III) acetate concentration.

culated at 20 °C were 0.40, 0.50, and 1 mol L-1. The concentrations of cobalt (CoII + CoIII), in acetate form, were 0.10, 0.20, and 0.44 mol L-1. Five experiments were carried out with an initial quantity of cobalt(III), generated by preliminary electrolysis of the solution using a current intensity of 0.8 A for 2 h. As this current intensity was higher than the limiting current (see Figure 4), the conversion rate of cobalt(II) into cobalt(III) was approximately the same (40%). The initial cobalt(III) concentration was controlled by spectrophotometry. The concentrations of different species were calculated by taking into account thermal dilatation, the coefficient of expansion of solutions14 being 0.94 × 10-3 K-1. For example, the molarities of toluene were 0.9234 mol L-1 at 100 °C and 0.9147 mol L-1 at 109 °C for the initial concentration of 1 mol L-1 at 20 °C. Table 1 summarizes the operating conditions for the two series of experiments. The molarity values indicated in Table 1 represent actual concentrations at 100 and 109 °C. An autoxidation experiment was conducted as follows. The reaction was started by simultaneous addition of toluene to the solution presaturated with oxygen and beginning of the electrolysis. Samples of solution were taken at short intervals and analyzed by liquid chromatography (Hewlett-Packard 1050). Products were separated on an ODS C18 column (10 cm in length, 4.6 mm in internal diameter). The eluent was a mixture of phosphate buffer (pH ) 7) and methanol of variable composition flowing at 1 mL min-1. The volume fraction of methanol in the eluent was linearly varied from 10 to 77% in 16 min. The concentration values of toluene and its oxidation products were obtained by using p-chlorobenzoic acid as the internal standard. The cobalt(III) concentrations were deduced from absorbance measurements at 610 nm, by taking into account the correction related to the ground absorbance of cobalt(II) at this wavelength. Voltammetric curves of cobalt(II) acetate were constructed using the reactor for concentrations between 0.01 and 0.20 mol L-1, with a potential sweep rate of 0.5 mV s-1 for which the measurement reproducibility was ensured. The hydrodynamic conditions were identical to those of an autoxidation experiment because of

Ind. Eng. Chem. Res., Vol. 40, No. 26, 2001 6057

Figure 2. Cobalt(III) concentration for experiments 1 (b) and 5 (O).

detected by the analysis but not identified. Finally, the decarboxylation of benzoic acid leading to CO2 formation can also contribute to this decrease of the material balance according to the equation2

CoIIIOH + C6H5COOH f CoII + C6H5• + CO2 + H2O (11)

Figure 1. Variation of concentration as function of time at T ) 100 °C. Toluene: experiments 1 (9) and 5 (0). Benzoic acid: experiments 1 (b) and 5 (O). Aldehyde: experiments 1 (2) and 5 (4). Benzylic acetate: experiments 1 ([) and 5 (]). The crosses (×) represent the mass balance for experiment 5. Experiment 1: I ) 0 A. Experiment 2: I ) 0.89 A. Other experimental conditions are in Table 1.

the bubbling of oxygen in the solution at a flow rate of 150 mL min-1. The above-described anode was used as the working electrode, while the cathode served as the counterelectrode. All electrode potentials were referred to a saturated calomel electrode (SCE), which was placed in a tube prolonged with a Luggin’s capillary containing a solution of the same composition as the studied solution. Results and Discussion During an autoxidation experiment, the decrease of the concentration of toluene was accompanied by the successive appearances of benzaldehyde and benzoic acid. Benzyl acetate appeared in increasing quantities with the applied intensity of current. No benzylic alcohol was formed, and the maximum yield of aldehyde never exceeded 3%. The majority end product of the reaction was benzoic acid. A decrease of the material balance was generally observed, which could reach 10% at the end of the experiment. The lack of mass balance at the beginning of an experiment (Figure 1) came from the vaporization of a small part of the toluene introduced; the toluene vapors were condensed in the two coolers. This loss reached a stationary state in a few minutes and can be evaluated as approximately 30% of the total loss. Moreover, there is a very low drop in the material balance corresponding to minority secondary products

Influence of the Current Intensity on the Kinetics of Reaction and on the Concentration of CoIII. In a previous work,11 we showed that, in the absence of electrolysis and without CoIII at the beginning of the experiment, the autoxidation reaction does not begin at all. Figure 1 shows the variations of the concentrations of toluene, acetate, and benzoic acid for experiments 1 and 5, which had the same initial conditions (see Table 1). Experiment 1, conducted without current, was a pure chemical autoxidation, whereas experiment 5 was performed under electrolysis with a current intensity of 0.89 A. With electrolysis, the conversion of toluene after 6 h was 72%, compared to 10% without electrolysis. The yield of benzoic acid was then about 55%. In this case, the selectivity in acid was appreciably decreased because of the formation of benzyl acetate with a yield of 9%; indeed, experiment 5 was performed with a high value of the current intensity (0.89 A). Figure 2 presents the variation of the concentrations of CoIII for experiments 1 and 5. In these two cases, the initial concentration of CoIII fell quickly and stabilized in a pseudoplateau. At the end of the reaction, there was a slow increase in the concentration of CoIII. The level of cobalt(III) in the reactor depends on (i) its chemical regeneration during the autoxidation process (steps 6-8 of the mechanism), (ii) its consumption by the chemical formation of benzyl acetate (step 9), (iii) its electrochemical regeneration at the anode (reaction 12), and (iv) its reduction at the cathode (reaction 13)

CoII f CoIII + e-

(12)

CoIII + e- f CoII

(13)

According to previous results,10-13 the concentration of cobalt(III) was higher with electrolysis than without electrolysis (Figure 2). At the same time that the CoIII level rose, the rate of toluene conversion increased appreciably. Thus, the electrochemical assistance ac-

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Figure 3. Oxidation current on graphite electrode: total oxidation current (0), residual current (b), oxidation current for cobalt(II) acetate (9). T ) 100 °C. Concentrations at 20 °C: [Co(CH3COO)2] ) 0.05 mol L-1; [CH3COONa] ) 1 mol L-1. Dioxygen flow ) 150 mL min-1.

celerates the rate of the autoxidation because of the increase of the concentration of the active catalytic species. Data presented in Table 1 show that a high concentration of CoIII was favored all along the reaction by the initial presence of some CoIII and by the electrolysis of the solution. When these two conditions were fulfilled, the CoIII ratio was between 26 and 32% (experiments 5-7 and 12) and depended little on the current intensity of electrolysis. In the absence of CoIII at the start of the experiment, the CoIII ratio was only about 15% at 100 °C and 22% at 109 °C. In experiments 7 and 12, which differed only in the applied current intensity (0.36 and 0.95 A, respectively), the average concentrations of CoIII were identical. These results show that the rate of electrochemical regeneration of the cobalt(III) should be limited by mass transport in solution. To estimate the limiting values of the current intensity corresponding to the transfer by the coupled process diffusion-convection of cobalt(II) toward the anode, voltammetric curves of different solutions of cobalt(II) were registered on the graphite anode under the same hydrodynamic conditions as exist in the autoxidation reactor. Figure 3 presents a voltammogram of cobalt(II) acetate solution at 100 °C. The ground current reveals that the acetic acid was oxidized in a significant way from the potential of 1.10 V/SCE. The current obtained by subtracting the residual current from the total current shows that the CoII oxidized from 1.10 V/SCE. Beyond 1.30 V/SCE, a plateau corresponding to the maximum transfer rate of the cobalt(II) from the bulk of the solution toward the electrode was reached. The limiting current was nearly proportional to the concentration of CoII. Figure 4 shows the variation of the total current intensity as a function of the cobalt(II) concentration for a potential value of 1.40 V/SCE and a temperature of 100 °C. The residual current is equal to 30 mA; it corresponds to the ordinate at the origin for the linear regression of data. The oxidation current intensities read on this figure represent maximum values for the operating conditions. Higher current values used under galvanostatic conditions should not allow the electrochemical regeneration of the CoIII to be increased. Some values of the current intensities used for electrolyses were higher than the

Figure 4. Total oxidation current as a function of cobalt(II) acetate concentration. T ) 100 °C. Concentration at 20 °C: [CH3COONa] ) 1 mol L-1. Dioxygen flow ) 150 mL min-1. E ) 1.40 V/SCE. The continuous line represents the linear regression of the data: I (mA) ) 30.4 + 532[CoII].

Figure 5. Benzylic acetate yield as a function of time for two values of the current intensity. Experiment 7 (2), I ) 0.36 A; experiment 12 (4), I ) 0.95 A.

limiting current. Thus, the formation of benzyl acetate under these conditions is discussed in the following section. Formation of the Benzyl Acetate under Electrolysis Conditions. The yield of benzyl acetate increased at the same time as the electrolysis current. Thus, at 100 °C, this yield varied from 0.5% without electrolysis to 9% for I ) 0.89 A (Figure 1), whereas at 109 °C, the final yield of benzyl acetate increased from 5.5 to 12.2% as the current intensity increased from 0.36 to 0.95 A. The increase of the CoIII concentration due to the electrochemical assistance accelerates the acetate formation rate by way of reaction 9; however, this path is not the main source of benzyl acetate. Figure 5 shows the variation of the acetate yields in experiments 7 and 12. Although concentrations of CoIII were essentially identical, the obtained quantity of acetate was sharply greater for I ) 0.95 A. Thus, the increased yield must be attributed to the electrochemical oxidation of toluene in benzyl acetate. Ross et al.15 observed that the anodic oxidation of toluene on graphite in acetic acid without cobalt salt under an atmosphere of nitrogen produced benzyl acetate with a selectivity of 89%. Also, Bejan et al.12 observed that the autoxidation of p-methoxytoluene under electrochemical assistance leads, at the same time, to p-methoxybenzaldehyde and to benzyl acetate;

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they showed that the latter product results mainly from the direct oxidation of the p-methoxytoluene on the anode. In the voltammogram of a solution of toluene in acetic acid, there is no visible signal of oxidation. It can be assumed that the electro-oxidation of toluene takes place at high potential simultaneously with the electrochemical oxidation of acetic acid. The mechanism of this electro-oxidation12,15 is made up of a succession of electron transfer and chemical steps, localized in the reaction layer, which is in contact with the electrode. The main intermediary is the benzyl radical ArCH2•. Because of the low solubility of molecular dioxygen in acetic acid medium,14 the dioxygen flux onto the electrode surface is low, so that the rate of formation of the peroxide radical by way of reaction 5 is not significant. The steps of this ECEC (electrochemical-chemicalelectrochemical-chemical) mechanism are as follows16,17

C6H5CH3 f [C6H5CH3+•]ads + e-

(14)

[C6H5CH3+•]ads f [C6H5CH2•]ads + H+

(15)

[C6H5CH2•]ads f [C6H5CH2+]ads + e-

(16)

[C6H5CH2+]ads + CH3COOH f C6H5CH2OCOCH3 + H+ (17) Kinetic Modeling of the Toluene Autoxidation. The above analyses allow a reaction scheme to be proposed that quantifies the variation of the concentrations of toluene, aldehyde, and acid in the reactor. It is admitted that the formation of benzaldehyde and benzoic acid results exclusively from two successive reactions of oxidation in the liquid phase, the rates of which are denoted r1 and r2, respectively

C6H5CH3 + O2 f C6H5CHO + H2O

(18)

C6H5CHO + 1/2O2 f C6H5COOH

(19)

Benzyl acetate is formed from the chemical and the electrochemical routes, whose rates are denoted r3 and r4, respectively

C6H5CH3 + 2Co3+ + CH3COOH f C6H5CH2OCOCH3 + 2Co2+ + 2H+ (20) C6H5CH3 + CH3COOH f C6H5CH2OCOCH3 + 2H+ + 2e- (21) Because the concentration of benzyl acetate increases constantly in all of the experiments, we assume that, for the anodic current density used, the acetate is stable toward its oxidation into benzaldehyde. Considering the dual origin of benzyl acetate and its low concentration, a comprehensive and exhaustive analysis of the kinetics of reactions 20 and 21 was not undertaken. However, the experimental amount of acetate found by HPLC analysis was taken into account in the model by way of polynomial smoothing (see Appendix, eq 30). Kinetic laws proposed for the autoxidation of toluene5,7-9 present the following characteristics: (1) The reaction order with respect to toluene is 1. (2) The catalytic action of the cobalt(III) is expressed by a positive reaction order, with different values according

Figure 6. Apparent rate constant K1 as a function of the [CoIII]/ [CoII] ratio. T ) 109 °C. Data are drawn from the experiments 7-12.

to different authors.5,7-9 (3) The inhibiting effect of cobalt(II) on the autoxidation of toluene was experimentally highlighted by Scott and Chester7 by the addition of cobalt(II) during the reaction run. This inhibiting effect is expressed by a reaction order equal to -1 with respect to cobalt(II) by several authors.7-9 The expression for the rate of disappearance of the toluene is thus

r1 ) k1[CoIII]R[CoII]β[C6H5CH3]

(22)

where R and β can be determined by using Scott and Chester’s method.7 These authors showed that the natural (neperian) logarithm of [C6H5CH3] decreases linearly as a function of time when the concentration of CoIII remains practically constant during the course of the reaction; hence, the order of the reaction with respect to toluene is 1, with an apparent rate constant of K1 ) k1[CoIII]R[CoII]β. For example, this is the case for experiment 1, for which the concentration of CoIII remains nearly constant during the interval 1-4 h. The values of K1 obtained in various experiments should be proportional to the product [CoIII]R[CoII]β for the correct values of R and β. Different pairs of values for R (1, 3/2, and 2) and β (1, 0, and 1) were tested. At 100 and 109 °C, the best results were obtained for R ) 1 and β ) -1. The variation of the K1 values as a function of [CoIII][CoII]-1 is a straight line that essentially passes through the origin (Figure 6). The expression obtained for r1 is finally

r1 ) k1

[CoIII] [C6H5CH3] [CoII]

(23)

In the case of benzaldehyde oxidation into benzoic acid, it was not possible to obtain an optimal form of the kinetic law because of the low concentration of benzaldehyde during the experiments. Indeed, the benzaldehyde yields did not exceed 3% (Figure 1). Thus, the oxidation rate of aldehyde into acid should be faster than the rate of toluene oxidation into aldehyde. Taking into account the former results for benzaldehyde autoxidation18,19 at 25 °C, we obtained the following expression for the kinetic law suggested in these works

r2 ) k2[CoIII]0.5[C6H5CHO]

(24)

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Figure 7. Concentrations as functions of time. The continuous lines represent the smoothing of data for experiment 4. Experimental values of toluene (9), benzoic acid (b), and benzaldehyde concentrations (2) concentrations. Table 2. k1 and k2 Rate Constant Values for Each Experiment exp k1 (h-1) k2 (h-1 mol-0.5 L-0.5)

1 0.268 5.46

2 0.262 5.71

T = 100 °C 3 4 0.409 0.351 10.4 8.64

5 0.479 9.84

6 0.392 9.95

mean 0.36 ( 0.08 8.3 ( 2.2

exp k1 (h-1) k2 (h-1 mol-0.5 L-0.5)

7 0.537 16.99

8 0.457 8.86

T ) 109 °C 9 10 0.448 0.529 7.37 7.25

11 0.406 7.07

12 0.666 15.17

mean 0.51 ( 0.09 10.5 ( 4.4

In the present work, the values of k2 were determined together with k1 values at 100 and 109 °C by a numerical method of resolution of the rate equations (see the Appendix). The principle of the calculation requires preliminary knowledge of the variation of the concentration of CoIII in the reactor. Calculations were performed using the spreadsheet Excel. The optimization function Solver of this software allows one to seek the values of k1 and of k2 that minimize the sum of the square of the difference between the experimental values of the concentrations (of toluene, benzaldehyde, and benzoic acid) and the values calculated with the model. The experimental concentrations of benzyl acetate are represented by a polynomial smoothing and are subtracted from the calculated toluene concentrations at every stage of the calculation. Figure 7 shows the results obtained for experiment 4. Table 2 shows the set of values of k1 and k2. The energy of activation calculated from the k1 values is 45 kJ mol-1. Despite experimental uncertainty, this value is in agreement with the 42.3 kJ mol-1 value previously found.8 The mean standard deviation in the values of k1 is about 20%; the fall of the material balance is decrease likely cause of this variation, because it introduces a systematic difference between the sums of the experimental and calculated concentrations. For k2, the mean standard deviation of 40% results mainly from experimental errors in measurements of the aldehyde concentrations. In the case of toluene autoxidation, Morimoto and Ogata5 proposed a reaction order of 1 with respect to

Figure 8. Concentrations as functions of time for experiment 3. Toluene concentrations (0) are on the left axis, and cobalt(III) concentrations (b) are on the right axis. The continuous line was calculated for R ) 1, and the dotted line was calculated for R ) 2.

the CoIII concentration, whereas Scott and Chester7 suggested a complex kinetic law. However, the study of Hendriks et al.,9 which concerns the oxidation of 18 alkyl aromatics including toluene, deserves particular attention. The law proposed by these authors is characterized by an order of 2 with respect to the CoIII concentration

r1 ) k1

[CoIII]2 [C6H5CH3] [CoII]

(25)

This law is associated with a complex reaction mechanism. Without electrolysis, the concentration of CoIII is practically constant,9 whereas by analysis of a unique experiment, the determination of the reaction order with respect to CoIII is possible only if its concentration varies significantly. For example, in experiment 3, the concentration of cobalt(III) varies continuously (Figure 8). Figure 8 shows that, in this case, a better fitting is obtained for R ) 1 than for R ) 2. On the basis of our experimental results, the kinetic law summarized by eq 23 can be established from the following basic hypotheses for the first two steps

ArCH3 + CoIII h ArCH3+• + CoII k

ArCH3+• 98 ArCH2• + H2

(3) (4)

If one considers that reaction 3 is almost an equilibrium, of which the constant is K, and that reaction 4, with rate constant k, is kinetically limiting, one can write

[ArCH3][CoIII]

[ArCH3+•] ) K

[CoII]

(26)

and

r1 ) k[ArCH3+•] ) kK

[ArCH3][CoIII] [CoII]

(27)

The rate constant k1 in eq 22 becomes identified in this case with the product kK. Deprotonation of the radical

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cation C6H5CH3+• should, thus, be the rate-determining step of the autoxidation of toluene. Conclusion In the autoxidation of toluene, the catalytic action of cobalt acetate can be activated by the electrochemical oxidation of CoII into CoIII. The average concentration of CoIII during autoxidation with electrolysis is larger than that during purely chemical autoxidation. The electrochemical assistance of the autoxidation of toluene removes the induction period that characterizes this reaction in the absence of a promoter. It increases the reaction rate and increases the productivity. Benzyl acetate, which is formed in higher quantities under electrolysis, mainly results from the direct electrochemical oxidation of toluene on the anode. The voltammetric data obtained for the oxidation of cobalt(II) acetate on the graphite electrode allowed for the evaluation of the intensities needed for the selective oxidation of CoII into CoIII. In practice, the use of appropriate current intensities should reduce the amount of acetate without damaging the efficiency of the process. The autoxidation rate of toluene is proportional to the ratio [CoIII]/[CoII]. This form of the kinetic law can be interpreted by assuming that the deprotonation of the radical cation C6H5CH3+• is the rate-limiting step. However, knowledge of the kinetic law is not sufficient to develop a simulation of the autoxidation reaction, because it cannot predict the variations of the concentration of CoIII, which constitutes the basis for the calculation of the concentration variations of the reactant and products. Work is in progress to elaborate a modeling technique that takes into account the generation rate of CoIII under electrolysis conditions in view of developing a better understanding of electrochemically assisted autoxidation.

integral ∫t0(r3 + r4) dt represents the quantity of benzyl acetate formed at time t. This amount of acetate is denoted w(t). The function w(t) is represented by a polynomial smoothing of experimental values. Let ∆t be a small interval of time t that divides t into n equal parts; eq 30 becomes

∫0∆tg(t) x(t) dt + ∫∆t2∆tg(t) x(t) dt + ... + t g(t) x(t) dt} - w(t) (31) ∫t-∆t

x(t) ) x0 - k1{

One sees a recurrence formula appearing, which allows the concentration of toluene to be calculated stepby-step over the course of the experiment

xi ) xi-1 - k1

d[C6H5CH3] ) -r1 - r3 - r4 ) dt [CoIII][C6H5CH3] -k1 - r3 - r4 (28) [CoII] The function f(t), which describes the concentration variation of CoIII as a function of time, is obtained by a polynomial smoothing of the experimental data. Equation 28 then becomes

f(t) dx(t) ) -k1 x(t) - r3 - r4 dt [Co]total - f(t)

(29)

Let g(t) ) f(t)/[Co]total - f(t). By integration

∫0tg(t) x(t) dt - ∫0t(r3 + r4) dt

x(t) ) x0 - k1

(30)

where x0 is the initial concentration of toluene. The

i

g(t) x(t) dt - (wi - wi-1)

i-1

(32)

with i ) 1, ..., n. If ∆t (∆t ) ti - ti-1) is small enough, the integral can be calculated by the trapezoid method

xi ) xi-1 - k1

gixi + gi-1xi-1 ∆t - (wi - wi-1) (33) 2

Rearrangement of eq 33 gives an expression for xi as a function of xi-1

(

)

gi-1∆t xi-1 1 - k1 - (wi - wi-1) 2 xi ) gi∆t 1 + k1 2

(34)

The same method allows y(t) and z(t) to be calculated from the set of differential equations

Appendix: Numerical Resolution of the Rate Equations Let [C6H5CH3] ) x(t), [CH3CHO] ) y(t), [C6H5COOH] ) z(t), [C6H5CH2OCOCH3] ) w(t), [CoIII] ) f(t), and [CoII] ) [Co]total - f(t). Toluene is oxidized into aldehyde by oxygen (autoxidation assisted by electrochemistry) and, in a parallel direction, into acetate by direct anodic oxidation

∫tt

dy(t) ) r 1 - r2 dt

(35)

dz(t) ) r2 dt

(36)

Let h(t) ) [f(t)]1/2 ) [CoIII]1/2. Integration leads to the following formulas of recurrence for yi and zi

(

)

hi-1∆t ∆t yi-1 1 - k2 + k1(gi-1xi-1 + gixi) 2 2 yi ) hi∆t 1 + k2 2 ∆t 2

zi ) zi-1 + k2(hi-1yi-1 + hiyi)

(37)

(38)

The calculation converges for a ∆t value of 0.05 h. Literature Cited (1) Sheldon, R. A.; Kochi, J. K. Metal-Catalyzed Oxidations of Aromatic Compounds; Academic Press: New York, 1981. (2) Partenheimer, W. Methodology and Scope of Metal/Bromide Autoxidation of Hydrocarbons. Catal. Today 1995, 23, 69-158. (3) Suffer, A.; Baker, R. S. Aromatic Polycarboxylic Acids. U.S. Patent 2,833,816, 1958. (4) Raghavendrachar, P.; Ramachandran, S. Liquid-Phase Catalytic Oxidation of p-Xylene. Ind. Eng. Chem. Res. 1992, 31, 453-462. (5) Morimoto, T.; Ogata, Y. Kinetics of the Autoxidation of Toluenes Catalysed by Cobaltic Acetate. Part II. Effects of Benzaldehyde, Cobalt and Substituent. J. Chem. Soc. B 1967, 13531357.

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(6) Heiba, E. I.; Dessau, R. M.; Koehl, W. J. Oxidation by Metal Salts. V. Cobaltic Acetate Oxidation of Alkylbenzenes. J. Am. Chem. Soc. 1969, 91, 6830-6837. (7) Scott, E. J.; Chester, A. W. Kinetics of the Cobalt-Catalyzed Autoxidation of Toluene in Acetic Acid. The Role of Cobalt. J. Phys. Chem. 1972, 76, 1520-1524. (8) Kamiya, Y.; Kashima, M. Autoxidation of Aromatic Hydrocarbons Catalyzed with Cobaltic Acetate in Acetic Acid Solution. II. Oxidation of Ethylbenzene and Cumene. Bull. Chem. Soc. Jpn. 1973, 46, 905-908. (9) Hendricks, C. F.; van Beek, H. C. A.; Heertjes, P. M. The Oxidation of Substituted Toluenes by Cobalt(III) Acetate in Acetic Acid Solution. Ind. Eng. Chem. Prod. Res. Dev. 1978, 17, 256260. (10) Falgayrac, G.; Savall, A. Autoxidation of Methoxytoluene in Acetic Acid: Electrochemical Assistance of the Catalytic Effect of Cobalt. Catal. Today 1995, 24, 189-194. (11) Falgayrac, G.; Savall, A. Electrochemical Activation of the Catalytic Effect of Cobalt in Autoxidation of Toluene in Acetic Acid. J. Appl. Electrochem. 1999, 29, 253-258. (12) Bejan, D.; Lozar, J.; Falgayrac, G.; Savall, A. Electrochemical Assistance of Catalytic Oxidation in Liquid Phase Using Molecular Oxygen. Oxidation of Toluenes. Catal. Today 1999, 48, 363-369. (13) Bejan, D.; Lozar, J.; Savall, A. The Kinetics of p-tertbutyltoluene Autoxidation Assisted by Electrochemistry. Re´ cents Prog. Ge´ nie Proce´ de´ s 1999, 13, 83-90. (14) Lozar, J.; Bachelot, B.; Falgayrac, G.; Savall, A. Diffusivity and Solubility Measurement of Oxygen in Water-Acetic Acid-

Sodium Acetate Solutions on a Rotating Ring Disc Electrode. Electrochim. Acta 1998, 43, 3293-3296. (15) Ross, S. D.; Finkelstein, M.; Petersen, R. C. Anodic Oxidations. VI. Products and Mechanism in the Electrochemical Oxidation of Toluene in Acetic Acid. J. Org. Chem. 1970, 35, 781785. (16) Eberson L.; Nyberg K. Studies on Electrolytic Substitution Reactions. I. Anodic Acetoxylation. J. Am. Chem. Soc. 1966, 88, 1686-1691. (17) Eberson L. Studies on Electrolytic Substitution Reactions. III. Isomer Distributions and Isotope Effects in Nuclear and Sidechain Anodic Acetoxylation of Aromatic Compounds. J. Am. Chem. Soc. 1967, 89, 4669-4677. (18) Boga, E.; Kiricsi, I.; Deer, A.; Marta F. Oxidation of Benzaldehyde Catalysed by Transition Metals Ions. I. Kinetics of Catalysis by Cobalt(II) Acetate in Acetic Acid. Acta Chim. Acad. Sci. Hung. 1973, 78, 75-88. (19) Hendricks, C. F.; van Beek, H. C. A.; Heertjes, P. M. The Kinetics of the Autoxidation of Aldehydes in the Presence of Cobalt(II) and Cobalt(III) Acetate in Acetic Acid Solution. Ind. Eng. Chem. Prod. Res. Dev. 1978, 17, 260-264.

Received for review March 6, 2001 Revised manuscript received August 30, 2001 Accepted September 30, 2001 IE0102091