Effect of pH on Ether, Ester, and Carbonate Hydrolysis in High

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Ind. Eng. Chem. Res. 2008, 47, 577-584

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Effect of pH on Ether, Ester, and Carbonate Hydrolysis in High-Temperature Water Craig M. Comisar, Shawn E. Hunter, Ashley Walton, and Phillip E. Savage* Department of Chemical Engineering, UniVersity of Michigan, Ann Arbor, Michigan 48109-2136

We examined the hydrolysis of dibenzyl ether, benzyl t-butyl ether, methyl t-butyl ether, methylbenzoate, and diphenylcarbonate in high-temperature liquid water, both with and without added acid or base. The apparent reaction order for H+ did not exceed 0.2 for any of the compounds investigated. This result indicates that hydrolysis of these compounds in high-temperature water (HTW) does not follow the kinetics expected for specific acid catalysis (H+ reaction order ) 1.0), as does the hydrolysis at ambient temperatures. Rather, the greater thermal energy in the HTW system allows protonation by water molecules to become faster than protonation by H+ at near-neutral conditions. Because the water-catalyzed path is faster, the occurrence of these acid-catalyzed reactions in HTW with no added acid is not due to the elevated value of Kw, the ion product. This finding contradicts the conventional wisdom in this field. Introduction High-temperature water (HTW), defined here as liquid water above 200 °C, is a useful medium for chemical reactions. Relative to water at room temperature, HTW has a low dielectric constant, increased solubility for small organic compounds, and an increased ion product (Kw ) [H+][OH-]). All of these properties are temperature-dependent and can be manipulated to optimize the reaction environment. The ion product, in particular, is an interesting parameter in high-temperature water. It increases by 3-4 orders of magnitude from its value at ambient conditions (Kw ) 10-14 mol2 kg-2) to its maximum value at around 250 °C. Using the temperature dependence of the ion product,1 one can calculate the hydroxide and hydronium concentrations of pure liquid water at elevated temperatures. Simply increasing the temperature of the liquid water can profoundly alter ion concentrations. This enhanced acidity/basicity from the increased ion product has led researchers to explore HTW as a medium for acid-/basecatalyzed reactions. Hydrolysis reactions in HTW can be acid- or base-catalyzed. Such reactions are commonly implemented in industry for animal fat and vegetable oil splitting.2 Additionally, hydrolysis in HTW has been investigated for many other applications such as coal liquefaction, biorefineries, and waste polymer recycling.3-13 Many of the materials investigated contain ether, ester, or carbonate linkages, and hydrolysis of these groups controls the reactivity of the material in HTW. Therefore, the hydrolysis reactions of model ethers, esters, and carbonates can provide important insights into the behavior of these more complex materials. The hydrolysis of some ethers and esters in neutral HTW has been attributed to the elevated ion product. Taylor et al. proposed a hydronium-ion-catalyzed mechanism for the hydrolysis of methyl t-butyl ether.14 Patrick et al. proposed a mechanism for methyl benzoate hydrolysis that also uses the hydronium ion from water as the catalytic species.15 Other researchers have postulated that esters react via a pathway catalyzed by water-derived hydroxide ions.16 These are specific * To whom correspondence should be addressed. Tel.: (734) 7643386. Fax: (734) 763-0459. E-mail: [email protected].

examples that point to ions formed from water, along with elevated temperature, as the driving forces for the hydrolysis reactions observed in HTW with no added catalyst. If reactions in HTW are truly H+-/OH--catalyzed, then the pseudo-first-order reaction rate constant, k, for reactant disappearance should be directly proportional to the ion concentration in the solution. More specifically the slope of log k plotted against pH should be -1 for H+-catalyzed systems and +1 for OH--catalyzed reactions. In these types of catalyzed systems, small amounts of added acid or base could significantly accelerate the reactions in HTW and increase the yield of desired products. Recent research has investigated the use of carbonic acid, generated in situ in HTW through the dissolution of carbon dioxide, to improve reaction rates in acid-catalyzed HTW systems. The introduction of carbonic acid did not improve the yields as much as would be expected from a solely hydroniumion-catalyzed reaction pathway.17 Previously, these results led us to investigate the influence of H+ and OH- on aldol condensation,18 benzil rearrangement,19 butanediol dehydration,20 and bisphenol A cleavage.21 None of these systems displayed kinetics consistent with exclusive hydronium/hydroxide ion catalysis. In this article, we expand knowledge in this area by reporting on the influence of pH on the hydrolysis reactions of ethers, esters, and carbonates. Some of the compounds we investigate reportedly follow specific acid/ base catalysis, and we will test this assertion. This article also presents the first results for the hydrolysis of diphenyl carbonate in HTW. Experimental Section Quartz capillary tubes (5 mm o.d., 2 mm i.d.) served as the batch reactors in most experiments. The reactors were about 18 cm in length, which provided a 0.59 cm3 reactor volume. All chemicals were purchased from Aldrich in 98+ % purity and used as received. Deionized water and HPLC grade acetone were used. A carefully measured amount (∼5 mg) of the reactant of interest was added to the reactors, which had been flame sealed at one end. We then loaded 322-400 µL of water, precisely measured with a 500 µL syringe, into the reactors. The water loadings were selected such that 95% of the reactor volume would be occupied with liquid water at the reaction temperature. Water densities were taken from the steam tables.44 Given the

10.1021/ie0702882 CCC: $40.75 © 2008 American Chemical Society Published on Web 06/29/2007

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large amount of water and the small amount of reactant loaded, we expect a single homogeneous fluid phase to exist at reaction conditions. In some experiments, hydrochloric acid or sodium hydroxide solution was added to the reactor. A Beckman F 45 pH meter was calibrated at pH 4.0 and 10.0 with commercial buffer solutions and then used to measure the pH (at ambient conditions) of the standard acid and base solutions. The standard solutions were then diluted in deionized water to make solutions with the pH desired for loading the reactor. The pH values reported for reaction experiments in this article are those calculated to exist at reaction (not ambient) conditions. Some experiments were repeated two to four times to quantify runto-run variability. The averages of these trials are included in the tables along with the standard deviations. After the capillary reactor had been loaded, its open end was flame sealed. The low thermal conductivity of quartz and the short time in the flame allowed the sealing to occur without significant heating of the reaction solution. Once sealed, all reactors were stored in a -5 °C freezer until use, which was always within less than 12 h. Next, the reactors were placed in a Techne SBL-2 fluidized sand bath, preheated to within 1 °C of the reaction temperature. When the desired reaction duration had been reached, the reactors were removed from the sand bath and placed in front of a fan to cool for 30-90 s. At this point, the reactors were near room temperature and cool enough to handle. They were then stored in the freezer until they were opened and their contents recovered and analyzed. Upon being opened, each reactor was filled with acetone. The reactor contents were then stirred with a syringe tip to dissolve any solid reaction products, and the solution was removed from the reactor. This process was repeated at least five times to ensure complete recovery of all reactor material. The solutions in the methylbenzoate experiments were analyzed on a Waters high-pressure liquid chromatograph (HPLC) equipped with a Waters 996 photodiode array detector and a Waters 717 plus autosampler. A 4.6 mm × 75 mm × 3.5 µm Symmetry C18 reverse-phase column was used for analysis. We used a solvent flow rate of 0.8 mL/min and gradient elution with 0.1% phosphoric acid in acetonitrile (A) and in water (B) to separate the reaction products. The initial solvent composition of 20% A/80% B was held for 5 min. A linear ramp over the next 9 min brought the mobile phase to a 50%/50% mixture. This composition was held for 12 min, and then another linear ramp brought the mobile phase composition to 80% A/20% B in 5 min. During the subsequent 6 min, the mobile phase was returned linearly to its initial composition and held there for 3 min. The total gradient program took 40 min. The solutions of all of the reactions systems were analyzed on an Agilent model 6890 gas chromatograph (GC). A 50 m × 0.2 mm × 33 µm HP-5 capillary column with helium carrier gas was used to separate the sample constituents. We used a mass spectrometric (GC-MS) detector for product identification and a flame ionization detector (GC-FID) for quantitative analysis. An autoinjector was used with both devices. The GCFID injected 2 µL and used a split ratio of 25:1. The GC-MS detector injected 4 µL in splitless mode. The temperature program for the oven consisted of 5.2 min of heating at 70 °C, a temperature ramp of 70 °C/min to 240 °C, and then holding of the final temperature for 25 min. Analysis of standard solutions with known amounts of the compounds of interest provided calibration curves, which were used to determine the amount of each component present in the reaction samples. Molar yields were calculated as the

Figure 1. Ethers reacted in HTW.

numbers of moles of product formed per mole of reactant loaded into the reactor. The method outlined above is the routine procedure used for the quartz capillary reactors. We also performed some experiments in reactors fashioned from 1/4-in. stainless steel Swagelok tube fittings (a port connector and two caps). Like the quartz reactors, they provided 0.59 cm3 of reactor volume. Prior to their use in experiments, the metal reactors were loaded with water and conditioned for 1 h at 300 °C to remove any lubricants/oils that remained from the manufacture of the Swagelok parts. These reactors were then cleaned with acetone and dried prior to use. Unlike the quartz reactors, the reactions in these stainless steel vessels were quenched in cold water. Results This section provides the experimental results for the hydrolysis of three ethers, an ester, and a carbonate in HTW. For each compound, we report the yields of the reactant and, at times, of the products obtained at the different temperatures, times, and pH values. Because our interest in this work is in the kinetics of reactant disappearance, data for all of the products are not required. We discuss the trends in the data and, where possible, place the present results alongside previously published work to demonstrate their consistency. Ethers. Dibenzyl ether (DBE) was reacted at 250 °C. Benzyl t-butyl ether (BTBE) and methyl t-butyl ether (MTBE) were reacted in HTW at 175 °C. MTBE was reacted in both quartz and stainless steel reactors to determine whether the reactor surface had any effect on the results. Figure 1 shows the structures of the different ethers. Table 1 displays the results from the ether hydrolysis experiments. A major product from DBE and BTBE under all conditions was benzyl alcohol, the product expected from hydrolysis. The same major product was observed in previous work with DBE.22-24 No previous accounts of the reactivity of BTBE in HTW have been reported. The MTBE experiments in quartz and metal reactors showed no real difference in the results. This outcome indicates that catalytic wall effects are not likely a factor in the experimental systems used. Taylor et al.25 report pseudo-first-order rate constants (k′) for MTBE hydrolysis in neutral HTW that we can compare to the present results. Using their data and the Arrhenius equation, we calculated a rate constant of 2.3 × 10-4 s-1 at 175 °C. We next calculated a pseudo-first-order rate constant for MTBE at 175 °C of 3.8 × 10-4 s-1 using the data in Table 1 and eq 1, which applies to a constant-volume batch reactor

1 k′ ) - ln(1 - X) t

(1)

where X is the conversion of MTBE. It is clear that the agreement between the data from the two research groups is good. Esters. Table 2 lists the results from experiments with methyl benzoate. Benzoic acid and methanol are the expected hydrolysis products. We did not quantify the yield of methanol because it eluted from the gas chromatograph at the same time as the

Ind. Eng. Chem. Res., Vol. 47, No. 3, 2008 579 Table 1. Results from Ether Hydrolysis Experiments molar yields reactant

reactor material

temperature (°C)

time (h)

pH

reactant

benzyl alcohol

dibenzyl ether

stainless steel

250

1

2.4 3.9 5.6 7.3 8.8

0.12 ( 0.14 0.61 ( 0.10 0.82 ( 0.10 0.74 ( 0.16 0.90 ( 0.16

1.20 ( 0.50 0.43 ( 0.14 0.17 ( 0.11 0.13 ( 0.04 0.006 ( 0.002

benzyl t-butyl ether

stainless steel

175

0.25

3.4 4.4 5.2 5.7 6.2 7.2 8.2

0.53 ( 0.01 0.59 0.63 ( 0.16 0.42 ( 0.20 0.55 ( 0.05 0.6 0.67 ( 0.11

0.23 ( 0.01 0.25 0.27 ( 0.07 0.18 ( 0.09 0.23 ( 0.02 0.26 0.29 ( 0.5

methyl t-butyl ether

stainless steel

175

0.25

4.3 5.7 8.1 4.3 5.7 8.1 8.4 9.4

0.56 ( 0.04 0.72 ( 0.06 0.88 ( 0.02 0.58 ( 0.03 0.70 ( 0.05 0.81 ( 0.09 0.89 0.92

quartz

solvent (acetone). Table 2 shows that the conversion increased with both time and temperature, with other variables fixed. For a given time and temperature, the conversion was generally highest at the most acidic and basic conditions explored. Table 3 reports the pseudo-first-order rate constants and Arrhenius parameters for methyl benzoate disappearance in neutral HTW. The uncertainty here and in other rate constants in this section is the standard error. We will compare these rate constants with those in the literature. Satish et al., who were the first to examine the hydrolysis of methyl benzoate in HTW, found that it formed benzoic acid in 81% yield at 200 °C.26 The reaction time was 6 h plus a 30Table 2. Results from Methyl Benzoate Hydrolysis Experiments molar yields temperature (°C)

time (h)

175

1 1 1 1 1 1 5 24 5 5 5 5

200

300

pH 1.0 2.0 3.0 4.0 5.0 5.7 7.5 8.5 9.5 10.4 1.0 2.0 3.0 4.0 5.7

methyl benzoate

benzoic acid

0.85 1.04 1.09 1.12 0.97 0.94 0.95 0.73 0.99 0.95 0.80 0.76

0.14 0.01 0.01 0.01 0.01 0.01 0.09 0.19 0.01 0.01 0.01 0.07 0.42 0.31 ( 0.01 0.03 0.02 0.03 0.09 0.63 0.04 0.09 0.10 ( 0.05 0.12 0.79 ( 0.05 0.51 ( 0.06 0.42 ( 0.03 0.41 ( 0.09 0.40 ( 0.02 0.76 ( 0.23

1 1 1 1 2 5 24 5 5 5 5

7.4 8.4 9.4 10.3

0.40 0.53 ( 0.05 1.00 1.00 0.85 0.93 0.06 0.92 0.90 0.86 ( 0.12 0.72

1 1 1 1 1 1

2.3 3.9 5.6 7.3 8.9 10.9

0.17 ( 0.03 0.41 ( 0.09 0.56 ( 0.08 0.42 ( 0.06 0.48 ( 0.10 0.0 ( 0.00

t-butanol

0.06 ( 0.01 0.08 0.06 ( 0.02 0.07 ( 0.01 0.04 ( 0.01 0.05 0.06 ( 0.03

min heating time plus an overnight cooling. Given these nonisothermal conditions, one cannot estimate a meaningful pseudofirst-order rate constant. Aleman et al.27 later examined methyl benzoate hydrolysis in neutral water at 250 °C. Using their single data point for this compound, one can estimate the pseudo-firstorder rate constant at 250 °C to be about 3 × 10-4 s-1. Using results from Patrick et al., we estimate a pseudo-first-order rate constant at 250 °C of 8 × 10-5 s-1.15 Whereas the value from Aleman is 5 times larger than the value of 6 × 10-5 s-1 that we predict from the Arrhenius equation and the parameters in Table 3, the value from Patrick et al. is in good agreement with our data. Carbonates. Table 4 lists the results from the hydrothermal treatment of diphenylcarbonate in quartz reactors at 125, 150, 175, and 200 °C. The diphenylcarbonate conversion increases with both temperature and time. Using the reactant yields in Table 4, we calculated pseudo-first-order rate constants for diphenylcarbonate disappearance in neutral HTW. Table 5 reports the values of the rate constants and the associated Arrhenius parameters. These kinetics results are the first to be reported for the hydrolysis of a carbonate in HTW. The literature does provide an account of diphenyl carbonate hydrolysis in a 50/50 water/dioxane mixture, however, and it is instructive to compare the present results with those reported in this earlier study.28 This previous study reported an activation energy of 14.1 kcal/mol for the hydrolysis in neutral water and 19.1 kcal/ mol for the reaction when catalyzed by H+. Our results in Table 5 show an activation energy of 18.8 ( 4.3 kcal/mol, which is in good agreement with those in the previous report. Also appearing in Table 4 is the aromatic ring balance for each experiment. This quantity is the fraction of the total number of moles of aromatic rings initially added to the reactor that appear in the quantified products. This balance was near 100% in all experiments except the two at the most severe conditions explored (1 and 5 h at 200 °C). In these experiments, there was Table 3. Kinetics Parameters for Methyl Benzoate Disappearance in Neutral Htw T (°C) 175 200 300

k1 (s-1) 10-6

(3.6 ( 1.7) × (3.1 ( 1.7) × 10-5 1.6 × 10-4

log A (s-1)

E (kcal/mol)

1.6 ( 2.4

13.9 ( 5.3

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Table 4. Results from Diphenyl Carbonate Hydrolysis Experiments molar yields temperature (°C) 125

time (h)

pH

2 5 24

6.0

1.0 2.0 3.0 4.0 5.9

diphenyl carbonate

phenol

ring balance

0.97 0.85 0.61

0.35 0.34 0.37

1.14 1.02 0.80

0.62 0.67 0.76 0.77 0.95 0.85 0.67 0.57

0.36 0.35 0.38 0.44 0.30 0.61 0.34 0.30

0.80 0.85 0.95 0.99 1.10 1.15 0.84 0.72

150

1 1 1 1 0.5 1 4 5

175

0.5 1 5

5.7

0.81 0.69 0.60

0.13 0.25 0.27

0.88 0.82 0.74

200

0.5 1 5

5.7

0.48 0.29 0.09

0.40 0.40 0.45

0.68 0.49 0.32

10.7

a noticeable release of gas when the reactors were opened. These gaseous products and any liquid droplets that escaped with them can account for the missing material. Table 4 shows that phenol was always the major product. In fact, it was the only product formed in measurable yields. Phenol being the sole product suggests that the reaction pathways for diphenylcarbonate in HTW are as shown in Figure 2. Hydrolysis would occur at one of the C-O-C bonds to form phenol and phenylcarbonate. The latter compound would then decompose very rapidly to form phenol and CO2. Monoalkyl carbonates are known to decompose rapidly into carboxylic acids and carbon dioxide.29 Thus, monoalkyl carbonates are not observed among the reaction products. Dibenedetto et al., however, recently reported evidence for the existence of monomethyl carbonate at room temperature.29 Their finding lends credence to the hypothesis that a monoalkyl intermediate is formed in the hydrolysis of dialkyl carbonates. Effect of pH on Hydrolysis Kinetics A major objective of the present study was to determine the effect of pH on hydrolysis kinetics in HTW. We calculated the pH values for neutral HTW using the ion product correlation developed by Marshall and Franck.1 This correlation is accurate for high-temperature liquid water, which was used in this work, but it is not as reliable at lower water densities and supercritical conditions.30 The pH of neutral water was calculated to be 6.0, 5.9, 5.7, and 5.6 at 125, 150, 175 and 200, and 250 and 300 °C, respectively. The pH of the reactor contents at a given temperature was varied by adding either HCl or NaOH. We calculated the OH- and H+ concentrations for these systems at reaction conditions based on the amount of acid or base added and its complete dissociation.31,32 We report the kinetics results as pseudo-first-order rate constants (k) calculated from the reactant conversions measured experimentally. The dependence of the rate on the H+ concentration is embedded implicitly within the experimental pseudoTable 5. Rate Constants for Diphenyl Carbonate Disappearance in Neutral HTW T (°C) 125 150 175 200

k1 (s-1) 10-6

(5.9 ( 0.5) × (2.9 ( 0.3) × 10-5 (3.7 ( 1.4) × 10-5 (3.7 ( 0.4) × 10-4

log A (s-1)

E (kcal/mol)

5.1 ( 2.2

18.8 ( 4.3

Figure 2. Diphenyl carbonate hydrolysis pathways in HTW.

Figure 3. Effect of pH on dibenzyl ether hydrolysis kinetics at 250 °C. The solid curve is the fit of eq 3 to the data.

Figure 4. Effect of pH on benzyl t-butyl ether hydrolysis kinetics at 175 °C. The solid curve is the fit of eq 3 to the data.

first-order rate constants. Given the kinetics that follow from the previously proposed hydrolysis mechanisms,14-16 where the reaction is catalyzed by H+, the reaction rate should be firstorder in the H+ concentration (specific acid catalysis). In this case, a plot of log k vs pH should be linear with a slope of -1. Obtaining a slope other than -1 would indicate that the hydrolysis reaction does not follow specific acid catalysis. Therefore, the results in this section are presented as plots of log k at a given temperature vs pH. We pay special attention to the slopes of the lines through these data because the absolute value of the slope is the apparent H+ reaction order. Ethers. Figure 3 shows the effect of pH on the hydrolysis rate constant for DBE at 250 °C. There is a modest dependence of the reaction rate on the hydronium concentration. The slope of a line drawn through the data is about -0.18 ( 0.08, which means the apparent reaction order for H+ is 0.20, not 1.0 as would be expected for a reaction following specific acid catalysis. The curve in Figure 3 (and the three following figures) is from a mechanism-based model that will be discussed in the next section. Figure 4 shows the effect of pH on the kinetics of BTBE hydrolysis. Again, we see very little influence of pH on the kinetics, once more indicating that the reaction does not follow specific acid catalysis. The influence of pH on ether hydrolysis that we report in Figures 3 and 4 is much more modest than the apparent H+ reaction orders of 0.57-0.83 reported by Taylor et al. for MTBE

Ind. Eng. Chem. Res., Vol. 47, No. 3, 2008 581

Figure 5. Effect of pH on methyl t-butyl ether hydrolysis kinetics at 175 °C. The solid curve is the fit of eq 3 to the data.

Figure 7. Effect of pH on diphenyl carbonate hydrolysis kinetics at 150 °C.

Carbonates. Figure 7 shows the effect of pH on the pseudofirst-order rate constant for diphenyl carbonate hydrolysis at 150 °C. As was the case with the ethers and ester that we examined, there is at most a very modest increase in k with increasing acidity. The slope of the best-fit line through the data is -0.07 ( 0.02, which gives an apparent H+ reaction order (0.07) that is much less than unity. This result indicates that the dominant reaction does not follow specific acid catalysis. Hydrolysis Mechanisms and Rate Equations

Figure 6. Effect of pH on methyl benzoate hydrolysis kinetics. The solid curves are fits of eq 5 to the data.

hydrolysis between 200 and 450 °C.25 Therefore, we performed experiments with MTBE to discover whether the structure of the ether was playing a role. Figure 5 shows the results from the MTBE hydrolysis experiments at 175 °C. The effect of pH appears to be greater for MTBE than it was for BTBE, but the effect falls far short of specific acid catalysis. The slope of a line through the experimental data leads to an apparent H+ reaction order of 0.14 ( 0.03, which indicates a much weaker influence of pH than that reported by Taylor et al.25 The deviation of this apparent reaction order from unity points to a mechanism more complicated than classical hydronium-ion catalysis for this reaction. Taken collectively, the experimental data in Figures 3-5 suggest that classical hydronium-ion catalysis is not the dominant mechanism in near-neutral HTW for ether hydrolysis to form alcohols. We will discuss alternative mechanistic scenarios in a subsequent section. Esters. We explored the effect of pH on methyl benzoate hydrolysis in quartz reactors at 175 and 200 °C and in stainless steel reactors at 300 °C. Figure 6 displays the results from experiments at 200 and 300 °C. In both cases, the rate constant is largely insensitive to pH until very acidic or very basic conditions are encountered. This trend is the same for both runs, indicating that the presence of metal surfaces (in the run at 300 °C) does not alter the effect of pH on the kinetics. At pH values around 2-3, the rate constant increases with increasing acidity. As in the case of the ether hydrolysis reactions examined here, the kinetics of this ester hydrolysis reaction in HTW is less than first-order in H+.

The results in the previous section show that the hydrolysis reactions of three different ethers, an ester, and a carbonate in HTWdonotfollowspecificacidcatalysis.Previousreports9,14-16,33-36 in this field, however, have often pointed to catalysis by H+ or OH- as being the most important feature in these systems. In this section, we seek to resolve this apparent difference by developing reaction mechanisms and mechanism-based rate equations for the hydrolysis of the different compounds. Our approach is to retain the H+- or OH--catalyzed mechanisms proposed previously and to supplement them with contributions from a coexisting H2O-catalyzed mechanism. This approach has recently been used to explain and quantitatively model the influence of pH on tetrahydrofuran synthesis from 1,4-butanediol in HTW.20 Ether Hydrolysis. All of the ethers in this study are tertiary or benzylic ethers, which are expected to cleave by an SN1 or E1 mechanism because of the stable carbocation intermediates they form.40 It is therefore reasonable that Penninger et al.,37 Taylor et al.,14 and Gonzalez et al.24 used the same type of SN1 mechanism to interpret their data for ether hydrolysis reactions involving benzylic and tertiary ethers in HTW. The mechanism involves protonation of the ether by H+ to form a charged intermediate. The intermediate then decomposes unimolecularly in the rate-determining step to form an alcohol and a carbocation, which subsequently reacts with a water molecule to eventually form an alcohol and H+. In this mechanism, H+ is the catalyst. We propose that, in addition to H+, water molecules themselves can act as an acid catalyst. That is, catalysis by water is a second possible pathway to generate the initial protonated intermediate. Figure 8 shows the reaction mechanism with the water-catalyzed step indicated by a B subscript in the rate constant. Using the steps in Figure 8, with step 2 being irreversible and rate-determining, one can show that the rate equation for ether hydrolysis is

rate )

{k2K1A[H+] + (k1Bk2/k-1A)[H2O]}[ether] 1 + (k-1BKw/k-1A[H+])

(2)

582

Ind. Eng. Chem. Res., Vol. 47, No. 3, 2008 Table 6. Arrhenius Parameters for Constants a, b, and c in Eq 3 for MTBE Hydrolysis

Figure 8. Acid-catalyzed mechanism for ether hydrolysis in HTW. R1 ) benzyl, t-butyl and R2 ) benzyl, t-butyl, methyl.

Figure 9. Parity plot for methyl t-butyl ether hydrolysis kinetics.

Without the new step involving water catalysis, the mechanismbased rate equation is simply rate ) k2K1A[H+][ether]. As we pointed out in the previous section, a rate equation that is firstorder in H+ is not consistent with the modest influence of pH reported herein for ether hydrolysis in HTW. The question remains, though, of whether the rate equation from the modified mechanism is able to represent the pH effects seen experimentally. To test the mechanism-based model, we used nonlinear regression to fit the pH dependence of the experimental pseudofirst-order rate constants (k) to the form suggested by the rate equation

k)

a[H+] + b[H2O] 1 + (cKw/[H+])

(3)

This expression contains three parameters, a, b, and c, that can be adjusted to fit the data. Each parameter is a ratio of rate constants or equilibrium constants for steps in the mechanism. The curves in Figures 3-5 show the ability of this model to quantitatively capture the influence of pH on DBE, BTBE, and MTBE hydrolysis kinetics. To test the model further, we applied it to the data reported by Taylor et al. for MTBE hydrolysis.14 They provided 26 different pseudo-first-order rate constants measured over a wide temperature range (150-600 °C). Most of these data are from experiments in neutral water, but rate constants obtained with added acid and added base are also available for reactions at 200, 250, and 450 °C. To fit these data to the model, each of the three parameters in eq 3 was written in Arrhenius form, because each represents a collection of rate constants or equilibrium constants. Thus, the model has six adjustable parameters. We used the Solver routine in Microsoft Excel to minimize the sum of the squared differences between the experimental and calculated values of log k. We judged

parameter

log A

E (kJ/mol)

a (L mol-1 s-1) b (L mol-1 s-1) c (L mol-1)

18.9 -6.4 -9.8

163 -28.3 -152

goodness of fit by inspecting the sum of the squared errors divided by ν, the number of degrees of freedom [the number of experimental rate constants (26) minus the number of parameters]. This statistic can serve as a χν2 value. The value of this statistic for the six-parameter model (eq 3) was 0.11, which is much lower than the value of the statistic (0.44) obtained for the two-parameter model arising from catalysis by H+ alone (essentially eq 3 with b ) c ) 0). Although the model in eq 3 has more parameters than the competing model for catalysis by H+ alone, the lower value of the χν2 statistic for the proposed model indicates that its superior ability to fit the data is not due simply to the presence of additional parameters. Indeed, there are examples of models with additional parameters providing a worse fit of kinetics data than a model with fewer parameters.34 Figure 9 provides a parity plot that shows the agreement between the calculated and experimental rate constants for both models. It is clear that the points corresponding to the model in eq 3 (diamonds) are typically closer to the diagonal line than the points from the model with catalysis by H+ alone (squares). Table 6 reports the values of the six parameters that best fit the data. Note that we are not advancing the values in Table 6 as the true parameters for the mechanism-based model. Indeed, we were able to obtain fits of the data that were nearly as good using parameter values that differed greatly from those in Table 6. Much more work would be required if one wanted to be certain the global minimum had been reached. Our purpose here is not to find the global minimum, but rather to show that parameter values exist such that the MTBE hydrolysis mechanism that includes catalysis by water provides a better quantitative description of the data than a model that omits this step. Ester Hydrolysis. Patrick et al.15 used substituent effects to show that ester hydrolysis in HTW is acid-catalyzed. These investigators, along with Krammer and Vogel,38 advanced an AAC2 mechanism with H+ as the catalyst for ester hydrolysis in HTW. The first step in the AAC2 mechanism is protonation of the ester by H+. The second step, which is rate-determining, is addition of a water dimer to the protonated ester.39,40 This mechanism leads to a rate equation that is first-order in H+, however, so it is not capable of explaining the results presented in Figure 6, which show a much weaker dependence of the rate constant on pH. To explain these new results, we propose that

Figure 10. Acid-catlayzed mechanism for methyl benzoate hydrolysis in HTW.

Ind. Eng. Chem. Res., Vol. 47, No. 3, 2008 583 Table 7. Best-Fit Parameters for Eq 5 for Methyl Benzoate Hydrolysis T (°C) 175 200 300

a (L mol-1 s-1) 10-4

4.7 × 3.0 × 10-3 6.0 × 10-2

b (s-1) 10-7

4.1 × 5.7 × 10-6 2.0 × 10-4

d (mol L-1 s-1) 1.4 × 10-16 5.3 × 10-16 1.4 × 10-14

catalysis by water occurs along with catalysis by H+. Figure 10 shows this expanded acid-catalyzed reaction mechanism for ester hydrolysis in HTW. At room temperature, water alone does not hydrolyze most esters.39 The ability of water molecules to catalyze the hydrolysis in HTW would most likely be due to the higher thermal energy available in HTW. Ester hydrolysis can also proceed by base catalysis, and this process might be important for the experiments reported herein at high pH. The most likely mechanism here is a BAC2 process with OH- as the catalyst.39 The only kinetically significant step in this mechanism is simply the rate-determining initial attack of the ester by OH-. This expanded acid-catalysis mechanism in Figure 10 and the BAC2 base-catalysis mechanism lead to the expression in eq 4 for the pseudo-first-order rate constant for ester hydrolysis in HTW

k) {k2K1A[H+] + (k1Bk2/k-1A)[H2O]}[H2O]2 1 + (k-1BKw/k-1A[H+])

+ kB[OH-] (4)

We verified that the hydrolysis could be treated as irreversible under the conditions of the present experiments by placing benzoic acid and methanol (the hydrolysis products) in HTW at 200 °C. Whether in 0.1 M hydrochloric acid, 0.1 M sodium hydroxide, or neutral water, the conversion from the reverse reaction was always less than 5% after 24 h. This low reverse reaction rate combined with the moderate to low conversion of methyl benzoate in the present experiments (under 60% conversion in all but two trials) indicates that the reverse reaction rate can be safely neglected in this kinetics analysis. For experiments done at a fixed temperature, the water concentration and Kw value are fixed, so the rate constant expression in eq 4 can be parametrized and written as a function of the H+ concentration as

k)

a[H+] + b d + + c [H ] 1+ + [H ]

(5)

Note that we replaced [OH-] in eq 4 with Kw/[H+] to derive eq 5. One can then use this expression to fit the experimental data for the variation in the pseudo-first-order rate constant with pH. The best-fit values of a-d appear in Table 7. These values were determined by minimizing the sum of the squared relative differences between the calculated and experimental rate constants. Including the parameter c in the model did not improve the fit enough to justify its retention. Therefore, it was removed from the final model. That the model fit was essentially independent of c (c ) 0) implies that k-1B[OH-] , k-1A, which suggests that the deprotonation of the protonated ester occurs primarily to liberate H+ ions rather than to consume OH- ions. The curves in Figure 6 show the ability of this kinetics model and the parameters in Table 7 to describe the experimentally observed pH dependence for methyl benzoate hydrolysis. Carbonate Hydrolysis. The literature provides no information about hydrolysis mechanisms for carbonates in HTW, but

there are reports of alkyl carbonate hydrolysis in water/dioxane and water/ethanol mixtures at 100 °C. Miller and Case showed in 1935 that alkyl carbonates react with hydroxide ion in a twostep process. The initial second-order reaction of the reactant and hydroxide is followed by a much slower first-order reaction.41 This result was confirmed by Noring and Faurholt.42 Later, diphenyl carbonate hydrolysis was examined in acidic, basic, and neutral dioxane/water mixtures at 100 °C.28 Diphenylcarbonate hydrolyzed even without any added acid or base.43 This “uncatalyzed” reaction in neutral water was faster than that catalyzed by H+ for pH values greater than 1. A BAC2 mechanism was advanced for the neutral hydrolysis. This mechanism is consistent with ester hydrolysis reactions in neutral media generally following base catalysis.39 The hydrolysis not being catalyzed by OH- or H+ is also consistent with the results reported in Figure 7, which show a very modest influence of pH on the hydrolysis kinetics. The mechanism for carbonate hydrolysis in HTW is not known with enough clarity at this point to merit quantitative mechanism-based modeling of the influence of pH on the kinetics. Conclusions (1) Hydrolysis in HTW of the compounds investigated does not follow specific acid catalysis (the reactions are not firstorder in H+) and therefore is not consistent with classical H+catalyzed mechanisms. Modifying these well-established acidcatalyzed hydrolysis mechanisms to include a step with H2O as a proton donor leads to rate equations that are quantitatively consistent with the pH effects observed experimentally. (2) The enhanced level of H+ present in HTW does not explain some acid-catalyzed reactions occurring readily in HTW with no added acid. Rather, the higher temperature appears to be the key. The elevated temperature makes the rate of substrate protonation by water higher than the rate of protonation by H+. When taken collectively, the results for the five hydrolysis reactions reported herein along with our earlier results for bisphenol A cleavage, aldol condensation, benzil rearrangement, and buatendiol dehydration suggest that most acid- or basecatalyzed reactions that occur in HTW with no added catalyst do so because of the elevated temperature, and not because of the elevated H+ or OH- concentrations. (3) Diphenylcarbonate hydrolyzes readily to phenol in neutral HTW, and the rate is increased by the addition of acid. The Arrhenius parameters for the global first-order rate constant are log A ) 5.1 ( 2.2 s-1 and Ea ) 18.8 ( 4.3 kcal/mol. (4) The rate of MTBE hydrolysis was the same in both quartz and stainless steel reactors. Likewise, the pH dependence of methyl benzoate hydrolysis was the same in both stainless steel and in quartz. Thus, the material of construction did not influence the hydrolysis kinetics for these two compounds. Acknowledgment We thank Harald Eberhardt, Master Glassblower, and Liz Ranney, Brendon Webb, and Carly Enhrenberger for experimental assistance. This work was supported in part by NSF Grant CTS-0218772. Literature Cited (1) Marshall, W. L.; Franck, E. U. Ion product of water substance, 0-1000 °C, 1-10,000 bars, new international formulation and its background. J. Phys. Chem. Ref. Data 1981, 2, 295-304. (2) Allen, R. R.; Formo, M. W.; Krishnamurthy, R. G. In Bailey’s Industrial Oil and Fat Products; Swern, D., Ed.; Wiley-Interscience: New York, 1982; Vol. 2, p 108.

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ReceiVed for reView February 26, 2007 ReVised manuscript receiVed May 9, 2007 Accepted May 17, 2007 IE0702882