Gas-Phase Heterogeneous Photocatalytic Oxidation of Ethanol

Environ. Sci. Technol. 1996, 30, 3102-3110

Gas-Phase Heterogeneous Photocatalytic Oxidation of Ethanol: Pathways and Kinetic Modeling MARK R. NIMLOS,* EDWARD J. WOLFRUM, MATTHEW L. BREWER, JOHN A. FENNELL, AND GAYLE BINTNER National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401

The kinetics of photocatalytic oxidation of ethanol has been studied, and the formation and destruction rates of products have been measured. The important intermediates were identified as acetaldehyde, acetic acid, formaldehyde, and formic acid. Minor reaction channels resulted in the formation of methyl formate, ethyl formate, and methyl acetate. Kinetic and “dark” adsorption parameters were measured for ethanol and all of the important intermediates. We have modeled the complete oxidation process using a sequential chemical reaction mechanism. This mechanism is based primarily upon known homogeneous chemistry. However, the formation of acids from aldehydes in photocatalytic oxidation is different from known homogeneous chemistry and demonstrates the ability of the solid surface to stabilize energized transient species. We have measured the adsorption isotherms for ethanol and the oxidized intermediates and have concluded that there are two adsorption sites for some of the chemical species. We think it is possible that the adsorption properties of the compounds will change when the solid is illuminated.

Introduction Heterogeneous photocatalysis is important because the photoactivated surface opens reaction channels not available in homogeneous chemistry and accelerates reactions without the need to add thermal energy to feed streams. Because of these unique attributes, this process is potentially applicable to a number of important areas, including the destruction of organic wastes. Studies of photocatalysis are also interesting because of what can be learned about the chemistry that occurs during catalysis. The reactions are often conducted at ambient temperature, and techniques for the analysis of adsorbed and gas-phase products are simplified relative to high-temperature catalysis. Effective use of this technology in waste destruction requires that the fundamental physical chemistry be * Corresponding author telephone: (303) 275-3753; fax: (303) 2752905; e-mail address: [email protected].

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understood. This will help researchers determine how to increase destruction rates of the wastes and control noxious byproduct formation. With gas-phase photocatalysis studies, much can be learned about chemical reaction pathways in all photocatalysis because the analysis of the gas-phase species can be easily accomplished. Ethanol is a useful molecule to study because it is relatively simple and because it is an important pollutant from many industries (bakeries, breweries, metal coating, etc.). There are few reports on the chemistry of the photocatalytic oxidation of ethanol, though a number of other aliphatic alcohols have been studied more thoroughly. Recently, Sauer and Ollis (1) modeled the photocatalytic oxidation of ethanol over a TiO2-coated honeycomb monolith and a nonporous glass plate. They used a sequential reaction mechanism as we did in earlier work (2). In these reports the following reaction pathway was assumed:

ethanol f acetaldehyde f

formaldehyde f (+ carbon dioxide) carbon dioxide

We had identified formic acid, but attributed it to a minor reaction pathway. Sauer and Ollis included both formic acid and acetic acid in their reaction scheme involving their monolith reactor. Photocatalytic oxidation of ethanol in aqueous (3) and in neat solutions (4-7) has been studied. Again, acetaldehyde was an important product from these studies, though the formation of ethylene was also measured (20). Acetaldehyde was formed from the dehydration of the alcohol, though the fundamental reaction mechanisms were not discussed. The gas-phase photocatalytic oxidation of other alcohols has been studied by a number of research groups, and much of the chemistry for these compounds should be relevant to ethanol. 2-Propanol has been extensively studied by a number of research groups (8-10). The products observed during this reaction were acetone, carbon dioxide, and trace amounts of propene. The gas-phase photocatalytic oxidation of butanols (11, 12) and methyl butanols (13, 14) has also been investigated. Likewise, the major byproducts were the dehydrogenation products (aldehydes or ketones) though some butene was identified from 1-butanol. In this paper, we investigate the kinetics of the gasphase conversion of ethanol to carbon dioxide over an illuminated titanium dioxide. We have studied reactions of intermediates and developed a global kinetic model for the complete conversion of ethanol to carbon dioxide. We measured the kinetics and adsorption parameters of ethanol and of the intermediates. A sequential reaction mechanism is used to model the reactions based on mechanisms developed by atmospheric chemists (15).

Experimental Section Description of System. Experiments in this study were performed in a recirculating, batch, photocatalytic reactor, shown schematically in Figure 1. The system consisted of a 22 l Pyrex reservoir, a Teflon-coated diaphragm pump (Thomas) to recirculate the gases, a gas chromatograph (GC) for analysis, and a tubular photocatalytic reactor (3/8 in. Pyrex tubes, inside diameter ) 0.7 cm) coated on the

S0013-936X(96)00229-5 CCC: $12.00

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FIGURE 1. Schematic diagram of experimental apparatus.

inside with TiO2 (Degussa P25) and illuminated externally with black lights (GE, λ ) 360 nm). This reactor was chosen because of the high linear velocity that was obtained with modest pumping speeds, and the illuminated surface area is fairly well defined, although not homogeneous. Both reactor modeling and simplified mass transfer calculations using literature data indicated that the data reported here were not mass transport limited and represented true kinetics. High linear velocities provide good mixing. The coating thickness on the tubes (1.4 mg/cm2 around the entire inside diameter of the tubes) is approximately the optical thickness for TiO2 reported elsewhere (16) but is thicker than the optical thickness reported recently (17). The volume of the reactor tubes was between 10 and 40 mL (length 26-103 cm) depending upon the number of tubes (1-4) and the total volume was 22.5 L. We have assumed that the bottom half of the tubes are shaded and the light flux on the top half of the catalyst surface is 1.7 mW/cm2. Analyses were performed using a dual-column GC (Hewlett-Packard Model 5890, DB-5 column HayeSepT) with two detectors (FID for organic compounds, TCD for CO2 and H2O). Samples were injected simultaneously onto both columns using a heated gas sampling valve (Valco). The entire sampling/analysis assembly was controlled with a personal computer using commercial software (HewlettPackard). Some gas samples were analyzed with a Fourier transform infrared (FTIR) spectrometer (Bomem). Calibrating the GC was accomplished by introducing known quantities of a compound into the recirculating system and measuring the peak areas. With acetaldehyde and ethanol, microliter quantities of these liquids were injected into the system, producing concentrations in the 10-1000 ppm range. These calibrations were tested with standard gas mixtures and were accurate over a wide range of concentrations, indicating that adsorption on the glass was insignificant. With carbon dioxide we used a gas standard. Calibrating the GC for formaldehyde was more difficult. The response of the FID to formaldehyde was low but reproducible using helium carrier gas and air and hydrogen for the flame. We found that reproducible, clean chromatographs of formaldehyde standards could be obtained by heating samples of paraformaldehyde with the system under vacuum. A similar technique has been used in spectroscopic studies of formaldehyde (18). Photocatalytic Oxidation Experiments. In described experiments, dry, zero air spiked with the organic compound of interest was recirculated from the reactor to the

FIGURE 2. Photocatalytic destruction of ethanol at various starting concentrations. The points are experimental measurements, and the lines are modeling results using a two-site adsorption model

reservoir while being sampled by the GC. Samples of a given concentration were prepared by injecting fixed amounts of the organic compound into zero air. All experiments were conducted in the absence of water vapor. This mixture was recirculated, bypassing the reactor until a steady signal with the GC was obtained. The mixture was then circulated through the reactor with the lights blocked, which allowed us to determine the amount of starting material adsorbed to the catalyst surface in the absence of light. No decomposition for any of the compounds tested was observed in the absence of light or catalyst. The lights were unblocked and the destruction of ethanol and the evolution of the byproducts were followed as a function of residence time using the GC. The effective residence time in the reactor was determined by multiplying the measured time by the ratio of the reactor volume to the system volume. All of the plots in this paper show experimentally measured gas-phase concentrations of the starting materials or products. To ensure reproducibility of the results, we standardized the preparation of the catalyst. Before each experiment, the entire system was held under modest vacuum (∼24 in. Hg) while the reactor assembly was heated to 125 °C for 30 min. This is not sufficient to drive all of the water off of the TiO2, but it removed most of the physisorbed water (19). With the use of this procedure, we were able to obtain reproducible results. Adsorption Experiments. Adsorption isotherms were measured using the same apparatus that was used for the kinetics experiment. The recirculating air was spiked with an organic compound while bypassing the reactor, and the concentration was measured with the GC. The mixture was then recirculated through the reactor, and the concentration was measured after the mixture came to equilibrium. The difference in the concentrations was used to determine the amount of organic adsorbed to the catalyst. Because this technique involved the subtraction of two large numbers, there was a fair amount of experimental error (10-20%, as determined by replicate experiments) in the data. However, the adsorption data was of sufficient quality to extract useful information for kinetic modeling.

Results and Discussion Rates of Destruction of Ethanol. In typical experiments with ethanol, we followed the destruction of ethanol for a variety of starting concentrations. Figure 2 is a plot of the log of the concentration of ethanol as a function of the

VOL. 30, NO. 10, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1

Products Identified from Photocatalytic Oxidation of Parent Compounds starting materiala ethanol

acetaldehyde

acetaldehyde formaldehyde acetic acid formic acidb carbon dioxide

formaldehyde acetic acid carbon dioxide

ethyl acetate methyl formate ethyl formate

methyl formate

acetic acid

formaldehyde

formic acid

Important Products formaldehyde carbon dioxide

formic acid carbon dioxide

carbon dioxide

Minor Products methyl formate methanol

a Important products are those in the reaction scheme in (eq 2). Minor products are those that arise from minor reaction channels as determined by their low concentrations, low adsorbtivities, and slow reaction rates. b Identified by FTIR only.

effective residence time in the illuminated reactor. The effective residence time was determined from the reactor and system volumes as discussed in the Experimental Section, but the experiments typically lasted 1-2 h. The data in these plots are typical of what one would expect from a heterogeneous process. In general terms, this type of reaction profile can be described by the LangmuirHinshelwood rate form

rate ) -

Kk[A] d[A] ) dt 1 + K[A]

(1)

where A is the reactant, K is the adsorption constant, and k is the intrinsic rate constant. (All of the data are modeled and analyzed in terms of effective residence time.) There are two distinct regions in an experiment started at high concentrations that are completely consistent with this model. At the start, the reaction appears limited by the absorption of light, while toward the end of the experiment, when the concentration is low, the reaction appears limited by adsorption of the ethanol. The rate of reaction of ethanol is also partially limited by the adsorption of intermediates on the catalyst surface, and the time profiles of ethanol do not strictly follow the rate form in eq 1. The adsorbed intermediates occupy reactive sites on the catalysts surface and can inhibit the reaction of ethanol. This effect has been demonstrated for gas-phase photocatalytic oxidation (12). We found that a simple, single-component Langmuir-Hinshelwood rate form, eq 1, was inadequate for fitting these curves in Figure 2 and that better fits could be obtained if intermediates were included. It is difficult to compare the rates of destruction from this study to those of Sauer and Ollis (1). In their recirculation experiments, a TiO2-coated quartz plate was placed perpendicular to the gas flow and the measured time was used in their kinetic analysis and a 100-W Hg lamp was used. In terms of elapsed time, their rate of destruction of ethanol was about 2.5 times faster than ours. However, their catalyst surface area was about four times as large as ours and their light intensity was greater. Products from the Destruction of Ethanol. We have identified a number of products from the photocatalytic oxidation of ethanol. The most significant products formed are acetaldehyde, formaldehyde, and carbon dioxide. We have also identified smaller amounts of acetic acid, formic acid, methyl formate, ethyl formate, and methyl acetate (Table 1). The identification of products was aided by FTIR

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FIGURE 3. Time profiles of products from the photocatalytic oxidation of ethanol. The points are the experimental data points, and the lines are modeling results. The concentrations for all compounds other than acetic acid are plotted relative to the left ordinate.

spectral analysis of the gas in the recirculating reactor system. This analysis and the injection of standards allowed us to identify the peaks in the chromatographs. We were able to conclusively identify the formation of formaldehyde and formic acid using FTIR. These products are difficult, though not impossible, to detect on a GC with an FID. A temporal plot of the concentrations of the important intermediates presented in Figure 3 can help elucidate the global chemical reaction mechanism for the photocatalytic oxidation of ethanol. We have determined that in spite of the low gas-phase concentration of acetic acid, its high adsorption constant makes it an important intermediate. This is supported by adsorption data below. The esters observed arise from minor reaction channels as is evident by their low concentration and low adsorbtivity. These presumably result from a reaction of aldehydes and acids. This well-known condensation chemistry may be occurring on dark catalyst surfaces (acid sites). Additional experiments with these esters as starting materials showed that they reacted slowly, so their low concentrations in the ethanol experiments cannot be attributed to their quick destruction. Thus, the data in Figure 3 supports the following global reaction scheme for the mineralization of ethanol:

ethanol f acetaldehyde f acetic acid f formaldehyde f formic acid + carbon dioxide f 2carbon dioxide (2) This is based upon the observed maxima of these different

FIGURE 4. Photocatalytic destruction of acetaldehyde at various starting concentrations. The points are the experimentally measured values, and the lines are the modeling results.

FIGURE 5. Photocatalytic destruction of acetic acid. The points are the experimentally measured values, and the lines are the modeling results.

compounds in the plot. The early maximum of acetic acid is the result of competition with ethanol for adsorption sites. Although formic acid was not detected with the FID in these experiments with ethanol, experiments with formaldehyde unambiguously demonstrated its formation. There is the possibility that a dehydration reaction of ethanol can lead to the formation of ethylene (20, 12). However, we were unable to conclusively identify any ethylene. A small peak for ethylene may have been present in the chromatographs. Based upon our calibrations, we can place an upper limit on this concentration of 0.2 ppm formed from a starting ethanol concentration of 200 ppm. Destruction Measurements of Intermediate Products. To investigate the chemistry of the complete oxidation of ethanol, we studied the reaction of all of the important intermediates over illuminated TiO2. Figures 4-6 present the destruction curves for acetaldehyde, acetic acid, and formaldehyde. The low sensitivity of the FID for formic acid prevented following the destruction of this substance with time, and we have plotted the formation of carbon dioxide (the only product seen) from formic acid in Figure 7. It is not straight forward to compare our kinetic results to those in the literature. The rate of destruction of acetaldehyde measured here appears to be faster than the rate reported recently (21). In that study, destruction of acetaldehyde was measured in a 1-L flask with a 1-cm2 illuminated area (light flux ) 1.8 mW/cm2). Though the light fluxes were similar, the rate from this earlier study

FIGURE 6. Photocatalytic destruction of formaldehyde at various concentrations. The points are the experimentally measured values, and the lines are the modeling results.

FIGURE 7. Photocatalytic destruction of formic acid as determined by measuring the formation of carbon dioxide. The points are the experimentally measured values, and the lines are the modeling results.

may have been more limited by mass transfer. Similar problems arise when our work is compared to studies using frits (1, 22). The effective light intensity at the catalyst surfaces is difficult to estimate for these frit reactors. There are two other studies of the gas-phase photocatalytic oxidation of formaldehdye (11, 23), but comparison with our results is not possible. One study used a formaldehyde solution containing methanol and water (11). The second study used a frit reactor (23). In this second study, the authors avoided the photolytic changes of formaldehyde. Our short path length (0.7 cm) makes this process insignificant. Products from Acetaldehyde. The products formed from acetaldehyde are consistent with the mechanism that we are proposing for the photocatalytic oxidation of ethanol. The four products that we have identified are listed in Table 1. Formaldehyde and carbon dioxide were significant products, while acetic acid and methyl formate were found to be formed at much smaller levels. Because of its broad peak and low response factor, we were unable to identify formic acid with a GC. Figure 8 shows time profiles for formaldehyde, acetic acid, and carbon dioxide. Although the gas-phase concentration of acetic acid is low, the adsorption constant is such that a significant amount is adsorbed to the catalyst. Acetic acid was also detected but not quantified in a recent study of acetaldehyde (21). Methyl formate does not adsorb strongly to TiO2, and the low concentrations indicate that it is formed from a minor reaction channel.


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FIGURE 8. Products from the photocatalytic oxidation of acetaldehyde. The points are the experimentally measured values, and the lines are the modeling results.

FIGURE 9. Products from the photocatalytic oxidation of acetic acid. The points are the experimentally measured values, and the lines are the modeling results.

Products from Acetic Acid. Products from the photocatalytic oxidation of acetic acid include formaldehyde and carbon dioxide, a small amount of methyl formate, and a small amount of an unknown compound. Profiles of the identified species are presented in Figure 9. Published studies of the photocatalytic destruction of acetic acid produced methane, ethane, and carbon dioxide (39). However, this photo-Kolbe reaction is conducted in neat acetic acid vapor. As discussed below, one would expect different products in mixtures of air. We identified no ethane or methane in our product stream. Products from Formaldehyde. The primary product from formaldehyde was carbon dioxide, though at higher concentrations we were able to identify formic acid. Figure 10 is a plot of the time profile showing the destruction of formaldehyde and the formation of carbon dioxide. The time profile for carbon dioxide suggests that formic acid is an intermediate in the oxidation of formaldehyde to carbon dioxide, that is, the formation rate of carbon dioxide is slower than the destruction rate of formaldehyde when one considers the adsorbed inventory. Other studies identified only carbon dioxide from the photocatalytic oxidation of formaldehyde (11, 23). Adsorption Isotherms. We have measured the adsorption isotherms for ethanol, acetaldehyde, formaldehyde and acetic acid. Because we could not quantify formic acid, we measured the adsorption isotherm of acetic acid instead. The amount adsorbed on the catalysts was determined by measuring the GC signal while bypassing the reactor and then exposing the catalyst to the gas mixture. From the

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FIGURE 10. Products from the photocatalytic oxidation of formaldehyde. The points are the experimentally measured values, and the lines are the modeling results.

FIGURE 11. Adsorption isotherms for ethanol and acetaldehyde. The points are experimental measurements, and the lines are from a Langmuir model.

difference in the signal, we determined the amount of the organic that was adsorbed to the catalyst surface. Figure 11 is a plot of the measured adsorption amounts of ethanol and acetaldehyde as a function of the gas-phase concentration. Measurements were also made for formaldehyde and acetic acid. We have fit these data to a Langmuir adsorption isotherm to obtain the adsorption parameters for these compounds. We have used the following functional form for the isotherm:

Θ)

µmaxKaC 1 + K aC

(3)

where Θ is the amount adsorbed per gram of catalyst, µmax is the maximum amount adsorbed, Ka is the adsorption equilibrium constant, and C is the concentration. The parameters that we obtained from a least squares fit of the data to eq 3 are presented in Table 2. With the surface area of the TiO2 (50 m2/g), the coverage in terms of molecules/nm2 can be calculated. We obtain a value of 2.8 molecules/nm2, which compares well with the values of 2.89 (24) and 3.03 (25) obtained elsewhere. The table shows that the adsorption maximum for ethanol and acetic acid are about the same and that the maximum adsorption of acetaldehyde is half of this value. We interpret this as a result of the difference in bonding of alcohols or acids and aldehydes to the TiO2 surface. Mechanisms. Because there are few data on the mechanisms (26) of the destruction of organic compounds

TABLE 2

Adsorption Parameters Determined from a Fit of Adsorption Measurements compd

µmax (mol/g of catalyst)

Ka (ppm-1)

ethanol acetaldehyde formaldehyde acetic acida

0.00023 0.00015 0.00030 0.00026

0.49 0.085 0.070 1.2

a

These values were used for formic acid.

on titanium dioxide at the gas-solid interface, we have found it instructive to speculate upon reaction pathways based upon the vast literature on mechanisms of homogeneous gas-phase reactions. (There is an extensive literature concerning thermal catalysis on metal oxide surrfaces, where similar reaction products can be found. However, we find it most useful to speculate using homogeneous chemistry, because a great deal more information is available concerning the elementary reactions.) We have used this approach in the past to explain the formation of products from the photocatalytic oxidation of chlorinated ethylenes (27). We do not mean to suggest that with photocatalytic oxidation the reactions occur in the gas phase. We are simply using the known homogeneous mechanisms as a first-order approximation to the chemistry on the catalyst surface. An obvious perturbation caused by the surface will be the stabilization of adducts from bimolecular reactions. We suggest that this may be important for reactions of carbonyl compounds. The important initial reactions on the surface of illuminated TiO2 are uncertain, and there are a number of conflicting studies in the literature. Separation of charge upon illumination may lead to the formation of strong oxidizers such as •OH radical (28, 29) or oxygen atom (30) from adsorbed water and oxygen. These species can oxidize adsorbed organic compounds, or the organic species can be directly oxidized by holes (31, 32). Recent surface studies show that activated O2 species are important (33). For the initial oxidation reaction of ethanol, any of the three mechanisms mentioned above will result in the formation of the ethanol radical from adsorbed ethanol

CH3CH2OH + (HO•, O, h+) f CH3C•HOH + (H2O, OH, H+) (4) The ethanol radical has been identified in aqueous-phase photocatalytic oxidation of ethanol (34), and the methanol radical has been identified in the photocatalytic oxidation of methanol on TiO2 surfaces (31). The ethanol radical can react with oxygen to form acetaldehyde

CH3C•HOH + O2 f CH3CHO + HOO•

(5)

The reaction of acetaldehyde on illuminated TiO2 is less certain and is apparently different from that found in homogeneous gas-phase chemistry. We measure the formation of acetic acid as the initial product formed from acetaldehyde (Figure 8), while with homogeneous chemistry, the reaction of •OH with acetaldehyde leads to C-C bond breaking. For instance, the following reaction series would be likely from the reaction of •OH with acetaldehyde in air (35, 36):

CH3CHO + •OH f CH3C•O + H2O

(6)

CH3C•O + O2 f CH3C(O)OO•

(7)

2CH3C(O)OO• f 2CH3C(O)O• + O2

(8)

CH3C(O)O• f CH3• + CO2

(9)

The abstraction reaction (eq 6) is actually thought to involve the formation of an adduct that decomposes primarily into the acetyl radical and water with the formation of acetic acid being a minor channel (36, 37). With heterogeneous photocatalysis it is likely that the adduct is stabilized by the TiO2 surface, favoring the formation of acetic acid:

CH3CHO + •OH f [CH3CHOHO•]a*

(10)

[CH3CHOHO•]a* f CH3CHOHOa•

(11)

CH3CHOHOa• + O2 f CH3CO2H + HOO•

(12)

This same reasoning could be extended to reactions involving O atom (36) or to reactions with formaldehyde (36). We have found that acetic acid reacts to form formaldehyde and carbon dioxide under our experimental conditions. Acetic acid is thought to react by the photo-Kolbe mechanism (38, 39)

CH3CO2H f CH4, C2H6, H2, CO2

(13)

though formaldehyde has been measured from chloroacetic acid (38). This reaction is thought to proceed by the transfer of a hole to the acid

CH3CO2H + h+ f CH3CO2• + H+

(14)

and decomposition of the acetate radical:

CH3CO2• f CH3• + CO2

(15)

In aqueous solutions or with neat vapors of acetic acid, methyl radicals react with each other or a hydrogen atom (formed by reduction of H+) to form ethane and methane. However, in air the methyl radicals can react with molecular oxygen to form formaldehyde through the following series of reactions (35, 36):

CH3• + O2 f CH3OO•

(16)

2CH3OO• f 2CH3O• + O2

(17)

CH3O• + O2 f CH2O + HOO•

(18)

The methyl peroxy radical can also be converted to the methoxy radical by reactions with •OOH or peroxy groups on the surface. Regardless of the exact mechanism for photocatalytic oxidation, it is likely that some of the reactions will result in the formation of radicals. This could result in an increase in the overall efficiency of the utilization of the photons by the propagation of chain reactions. For instance, the formation of the hydroperoxy radical (HOO•) in reactions 5, 12, and 18 may react with electrons and holes to produce •OH radicals. The esters that we have detected (ethyl acetate, ethyl formate, and methyl formate) could be formed by the


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reaction of alcohols with acetic acid or formic acid. Acetic acid could be formed by a reaction of acetaldehyde with the hydroperoxy radical in a similar manner to the formation of formic acid. This does not appear to be a major reaction channel. Modeling. Based upon the experimental evidence and the chemistry discussed above, we have modeled our results using a sequential reaction mechanism. We have used the adsorption isotherm data in the absence of light and kinetic parameters from the destruction profiles of the products. As we will show, there are effectively no adjustable parameters and a large set of data. This is very similar to the kinetic analysis that was conducted by Sauer and Ollis (1). In the first step of this process, we fit the formic acid results by assuming that formic acid reacts over the illuminated catalyst to give only carbon dioxide. We use the adsorption constants for acetic acid in the absence of light (Table 2) and fit the carbon dioxide evolution in Figure 8 to the following Langmuir-Hinshelwood rate form:

d[FA]tot d[CO2] )kfaθfa dt dt

(19)

where the surface coverage of formic acid (θfa) is

θfa )

Kfa[FA] 1 + Kfa[FA]

(20)

kfa is the rate constant for formic acid, Kfa is the adsorption constant for formic acid, [FA]tot is the total amount of formic acid, and [FA] is the gas-phase concentration of formic acid. For a recirculating batch reaction, the adsorbed inventory of molecules needs to be included in the data analysis (1). The differential equation for the complete reaction of formic acid is

-

d[FA]tot d fa ) - [[FA] + µmax mθfa] ) kfaθfa dt dt

(21)

where m is the mass of the catalyst. This differential equation was solved numerically in a spreadsheet (Microsoft Excel) using a multistep Adams-Moulton (A-M) method (40). The accuracy of the A-M method solutions was verified by inserting simple kinetic expressions (e.g., first-order kinetics) into the ordinary differential equations (ODEs) and comparing the numerical results with known analytical solutions. Each ODE had three parameters: a binding constant, a capacity constant, and a rate constant. We used the first two parameters from the adsorption isotherm data, and there was only one free parameter to fit. The value of this parameter was obtained by minimizing an objective function representing the sum of the differences between the model estimates and the actual experimental data. The objective function was minimized using a nonlinear optimization function available in the spreadsheet program. We fit the ethanol data by working the reaction scheme backwards from formic acid to ethanol. At each step, we used rate constants from previous steps to model the destruction data, and we determine an intrinsic rate constant, k, for that intermediate by minimizing the objective function. As we proceeded from formic acid to formaldehyde to acetic acid to acetaldehyde to ethanol, we had to change the adsorption term to include the intermediates. Our initial assumption was that all of these

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compounds adsorb to the same sites. For ethanol, the surface coverage term becomes

θE )

KE[E] 1 + Kfa[FA] + Kf[F] + KAc[Ac] + KA[A] + KE[E] (22)

where the following abbreviations are used: F, formaldehyde; Ac, acetic acid; A, acetaldehyde; and E, ethanol. The test of this model is to use the kinetic parameters determined by fitting the destruction data and the adsorption parameters determined from the isotherm data and attempting to fit all of the experimental data in Figures 2 and 3-10. When we attempted to fit the data using this procedure, we do not get a good fit to the product evolution profiles. For instance, we predict a slower evolution of carbon dioxide from ethanol than the experiment, and we cannot obtain the profile of acetic acid shown in Figure 3. Using the adsorption model in eq 3, we find that the acetic acid concentration maximizes at a much longer time than is found experimentally, and we could not obtain the sharp drop off in acetic acid concentration that is shown in Figure 3. Two-Site Model. We have modified the adsorption model to include the possibility of two adsorption sites. Published infrared spectroscopic studies have shown that alcohols and organic acids can dissociate upon adsorption to TiO2 to form R-O- and RO2- groups (41, 42). It has been suggested that this occurs at oxygen bridging sites. This type of bonding is unlikely with aldehydes. There is also the possibility that polar organic compounds can hydrogen bond to the OH groups on the TiO2 surface. In this case, the alcohols, acids, and aldehydes could all bind to these sites. Thus, there are two sites, one of which can accommodate only the alcohols and acids and one that can accommodate all of the organic compounds considered here. To test this two-site model, we conducted some simple adsorption experiments with ethanol and acetaldehyde. In the first experiment, we saturated the surface with ethanol. That is, we exposed the catalyst to a 170 ppm mixture of ethanol (see Figure 11). We then bypassed the reactor, introduced acetaldehyde into the mixture, and exposed the new mixture to the catalyst. No acetaldehyde adsorption was detected. When we conducted this experiment in reverse order (saturate with acetaldehyde and expose to ethanol), we get about half of the amount of ethanol adsorbed as we would with a bare catalyst. This suggests that roughly half of the sites on the catalyst are sites for dissociation and half are hydrogen binding sites. We then modified our model to include a two-site surface. In addition to the term in eq 3, which can describe the hydrogen bonding site, there will be a term describing the adsorption to the dissociation site

θ′E

K′E[E] 1 + K′fa[FA] + K′Ac[Ac] + K′E[E]

(23)

The kinetic equation for ethanol is

-

d[E]tot d E ) - [E] ) µmax m(θE + θ′E)/2] ) dt dt kfa(θE + θ′E) (24)

Note that we have assumed that there are an equal number of the two sites, as determined by our adsorption experi-

that these uncertainty do not greatly corrupt the model. Table 3 lists the kinetic parameters used for the model and the uncertainty in these values as determined by standard deviation of the fit data.

TABLE 3

Kinetic Parameters Determined from a Fit of Experimental Data reactant

concn range (ppm)

photocatalysis rate constant k (ppm s-1)

uncertainty (ppm s-1)

ethanol acetaldehyde acetic acid formaldehyde formic acid

57-232 52-232 116-203 114-420 176

79 44 44 61 54

12 5 NAa NAa 5

a Uncertainties could not be determined from the model because of the limited amount of data, but the experimental uncertainty was high (see text).

ments. We have also assumed that rate constants of the alcohols and acids are the same at both sites. This is reasonable because reactions of these species should be similar in the hydrogen bonded state or in the dissociated state (31). We assumed that the dissociative binding constants, K′, were the same for ethanol and the acids (K′ ) 1.0 ppm-1) and that the hydrogen bonding constants (K) were obtained by fitting the isotherms (KE, KA, KAc, KF ) 0.080, 0.085, 0.080, 0.070 ppm-1). These values are consistent with typical hydrogen bonding energies. As discussed above, we adjusted the intrinsic rate parameters (k) to fit the destruction data for each compound, and we used the kinetic parameters and adsorption parameters determined for the products to model the product profiles. In light of lack of adjustable parameters, it is impressive that the model fits the data as well as it does. In modeling the destruction of ethanol (Figure 3), there is a good qualitative and quantitative fit to all of the species with the possible exception of acetic acid. We were able to obtain a qualitative fit to the acetic acid data; an early maximum for the concentration of acetic acid from ethanol. A quantitative fit to the experimental measurements of acetic acid is problematic since this species is present at very low concentrations, making measurement uncertainties high. It appears as though the gas-phase acetic acid concentration is relatively high until the ethanol is destroyed. At that point, the dissociation sites become available, and the acetic acid adsorbs to the surface, decreasing its gas-phase concentration. The fit of the model to the rest of the experimental data was, for the most part, good. Acetic acid profiles were difficult to match precisely, due in large part to the difficulty associated with measuring this species (it is very sticky and often at very low concentrations). For many species, the fit is good at the start of the experiment, but gets worse as the concentration decreases below roughly 90% of the starting concentrations. This is illustrated in the destruction profiles in Figures 2 and 4-6 and suggests that improvements are needed in the adsorption model or measurements. In spite of these minor shortcomings, this model provides a fairly accurate prediction of the concentration profiles for starting materials and the products (especially for ethanol). It is likely that the data could be better fit using a more complicated model with adjustable parameters, but then there are concerns about the uniqueness of the fit and physical meaning of the parameters. A potential drawback to this technique for modeling the data is the propagation of experimental uncertainty at each step. However, the resulting good fit to the ethanol data suggests

Acknowledgments We would like to thank Michael L. Sauer and David F. Ollis at North Carolina State University, Daniel M. Blake and Yves Parent at the National Renewable Energy Laboratory, and Frank Wilkins at the Department of Energy. Support for this work was provided by the Office of Industrial Technology at the Department of Energy under Contract DE-AC02-83CH10093.

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Received for review March 13, 1996. Revised manuscript received May 15, 1996. Accepted May 23, 1996.X ES9602298 X

Abstract published in Advance ACS Abstracts, July 15, 1996.

Gas-Phase Heterogeneous Photocatalytic Oxidation of Ethanol

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